The Many-Worlds FAQ

(c) Michael Clive Price, February 1995

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Contents:

Q0 Why this FAQ?

Q1 Who believes in many-worlds?

Q2 What is many-worlds?

Q3 What are the alternatives to many-worlds?

Q4 What is a "world"?

Q5 What is a measurement?

Q6 Why do worlds split?

What is decoherence?

Q7 When do worlds split?

Q8 When does Schrodinger's cat split?

Q9 What is sum-over-histories?

Q10 What is many-histories?

What is the environment basis?

Q11 How many worlds are there?

Q12 Is many-worlds a local theory?

Q13 Is many-worlds a deterministic theory?

Q14 Is many-worlds a relativistic theory?

What about quantum field theory?

What about quantum gravity?

Q15 Where are the other worlds?

Q16 Is many-worlds (just) an interpretation?

Q17 Why don't worlds fuse, as well as split?

Do splitting worlds imply irreversible physics?

Q18 What retrodictions does many-worlds make?

Q19 Do worlds differentiate or split?

Q20 What is many-minds?

Q21 Does many-worlds violate Ockham's Razor?

Q22 Does many-worlds violate conservation of energy?

Q23 How do probabilities emerge within many-worlds?

Q24 Does many-worlds allow free-will?

Q25 Why am I in this world and not another?

Why does the universe appear random?

Q26 Can wavefunctions collapse?

Q27 Is physics linear?

Could we ever communicate with the other worlds?

Why do I only ever experience one world?

Why am I not aware of the world (and myself) splitting?

Q28 Can we determine what other worlds there are?

Is the form of the Universal Wavefunction knowable?

Q29 Who was Everett?

Q30 What are the problems with quantum theory?

Q31 What is the Copenhagen interpretation?

Q32 Does the EPR experiment prohibit locality?

What about Bell's Inequality?

Q33 Is Everett's relative state formulation the same as many-worlds?

Q34 What is a relative state?

Q35 Was Everett a "splitter"?

Q36 What unique predictions does many-worlds make?

Q37 Could we detect other Everett-worlds?

Q38 Why *quantum* gravity?

Q39 Is linearity exact?

Q41 Why can't the boundary conditions be updated to reflect my

observations in this one world?

A1 References and further reading

A2 Quantum mechanics and Dirac notation

Q0 Why this FAQ?

-------------

This FAQ shows how quantum paradoxes are resolved by the "many-worlds"

interpretation or metatheory of quantum mechanics. This FAQ does not

seek to *prove* that the many-worlds interpretation is the "correct"

quantum metatheory, merely to correct some of the common errors and

misinformation on the subject floating around.

As a physics undergraduate I was struck by the misconceptions of my

tutors about many-worlds, despite that it seemed to resolve all the

paradoxes of quantum theory [A]. The objections raised to many-worlds

were either patently misguided [B] or beyond my ability to assess at the

time [C], which made me suspect (confirmed during my graduate QFT

studies) that the more sophisticated rebuttals were also invalid. I

hope this FAQ will save other investigators from being lead astray by

authoritative statements from mentors.

I have attempted, in the answers, to translate the precise mathematics

of quantum theory into woolly and ambiguous English - I would appreciate

any corrections. In one or two instances I couldn't avoid using some

mathematical (Dirac) notation, in particular in describing the Einstein-

Podolsky-Rosen (EPR) experiment and Bell's Inequality and in showing how

probabilities are derived, so I've included an appendix on the Dirac

notation.

[A] See "Does the EPR experiment prohibit locality?", "What about Bell's

Inequality?" and "When does Schrodinger's cat split?" for how many-

worlds handles the most quoted paradoxes.

[B] Sample objection: "Creation of parallel universes violates energy

conservation/Ockham's razor". (See "Does many-worlds violate

conservation of energy?" and "Does many-worlds violate Ockham's Razor?")

[C] eg "In quantum field theory the wavefunction becomes an operator".

Er, what does that mean? And is this relevant? (See "What about

quantum field theory?")

Q1 Who believes in many-worlds?

----------------------------

"Political scientist" L David Raub reports a poll of 72 of the "leading

cosmologists and other quantum field theorists" about the "Many-Worlds

Interpretation" and gives the following response breakdown [T].

1) "Yes, I think MWI is true" 58%

2) "No, I don't accept MWI" 18%

3) "Maybe it's true but I'm not yet convinced" 13%

4) "I have no opinion one way or the other" 11%

Amongst the "Yes, I think MWI is true" crowd listed are Stephen Hawking

and Nobel Laureates Murray Gell-Mann and Richard Feynman. Gell-Mann and

Hawking recorded reservations with the name "many-worlds", but not with

the theory's content. Nobel Laureate Steven Weinberg is also mentioned

as a many-worlder, although the suggestion is not when the poll was

conducted, presumably before 1988 (when Feynman died). The only "No,

I don't accept MWI" named is Penrose.

The findings of this poll are in accord with other polls, that many-

worlds is most popular amongst scientists who may rather loosely be

described as string theorists or quantum gravitists/cosmologists. It

is less popular amongst the wider scientific community who mostly remain

in ignorance of it.

More detail on Weinberg's views can be found in _Dreams of a Final

Theory_ or _Life in the Universe_ Scientific American (October 1994),

the latter where Weinberg says about quantum theory:

"The final approach is to take the Schrodinger equation seriously

[..description of the measurement process..] In this way, a

measurement causes the history of the universe for practical

purposes to diverge into different non-interfering tracks, one for

each possible value of the measured quantity. [...] I prefer this

last approach"

In the _The Quark and the Jaguar_ and _Quantum Mechanics in the Light

of Quantum Cosmology_ [10] Gell-Mann describes himself as an adherent

to the (post-)Everett interpretation, although his exact meaning is

sometimes left ambiguous.

Steven Hawking is well known as a many-worlds fan and says, in an

article on quantum gravity [H], that measurement of the gravitational

metric tells you which branch of the wavefunction you're in and

references Everett.

Feynman, apart from the evidence of the Raub poll, directly favouring

the Everett interpretation, always emphasized to his lecture students

[F] that the "collapse" process could only be modelled by the

Schrodinger wave equation (Everett's approach).

[F] Jagdish Mehra _The Beat of a Different Drum: The Life and Science

Richard Feynman_

[H] Stephen W Hawking _Black Holes and Thermodynamics_ Physical Review

D Vol 13 #2 191-197 (1976)

[T] Frank J Tipler _The Physics of Immortality_ 170-171

Q2 What is many-worlds?

--------------------

AKA as the Everett, relative-state, many-histories or many-universes

interpretation or metatheory of quantum theory. Dr Hugh Everett, III,

its originator, called it the "relative-state metatheory" or the "theory

of the universal wavefunction" [1], but it is generally called "many-

worlds" nowadays, after DeWitt [4a],[5].

Many-worlds comprises of two assumptions and some consequences. The

assumptions are quite modest:

1) The metaphysical assumption: That the wavefunction does not merely

encode the all the information about an object, but has an

observer-independent objective existence and actually *is* the

object. For a non-relativistic N-particle system the wavefunction

is a complex-valued field in a 3-N dimensional space.

2) The physical assumption: The wavefunction obeys the empirically

derived standard linear deterministic wave equations at all times.

The observer plays no special role in the theory and, consequently,

there is no collapse of the wavefunction. For non-relativistic

systems the Schrodinger wave equation is a good approximation to

reality. (See "Is many-worlds a relativistic theory?" for how the

more general case is handled with quantum field theory or third quantisation.)

The rest of the theory is just working out consequences of the above

assumptions. Measurements and observations by a subject on an object

are modelled by applying the wave equation to the joint subject-object

system. Some consequences are:

1) That each measurement causes a decomposition or decoherence of the

universal wavefunction into non-interacting and mostly non-

interfering branches, histories or worlds. (See "What is

decoherence?") The histories form a branching tree which

encompasses all the possible outcomes of each interaction. (See

"Why do worlds split?" and "When do worlds split?") Every

historical what-if compatible with the initial conditions and

physical law is realised.

2) That the conventional statistical Born interpretation of the

amplitudes in quantum theory is *derived* from within the theory

rather than having to be *assumed* as an additional axiom. (See

"How do probabilities emerge within many-worlds?")

Many-worlds is a re-formulation of quantum theory [1], published in 1957

by Dr Hugh Everett III [2], which treats the process of observation or

measurement entirely within the wave-mechanics of quantum theory, rather

than an input as additional assumption, as in the Copenhagen

interpretation. Everett considered the wavefunction a real object.

Many-worlds is a return to the classical, pre-quantum view of the

universe in which all the mathematical entities of a physical theory are

real. For example the electromagnetic fields of James Clark Maxwell or

the atoms of Dalton were considered as real objects in classical

physics. Everett treats the wavefunction in a similar fashion. Everett

also assumed that the wavefunction obeyed the same wave equation during

observation or measurement as at all other times. This is the central

assumption of many-worlds: that the wave equation is obeyed universally

and at all times.

Everett discovered that the new, simpler theory - which he named the

"relative state" formulation - predicts that interactions between two

(or more) macrosystems typically split the joint system into a

superposition of products of relative states. The states of the

macrosystems are, after the subsystems have jointly interacted,

henceforth correlated with, or dependent upon, each other. Each element

of the superposition - each a product of subsystem states - evolves

independently of the other elements in the superposition. The states

of the macrosystems are, by becoming correlated or entangled with each

other, impossible to understand in isolation from each other and must

be viewed as one composite system. It is no longer possible to speak

the state of one (sub)system in isolation from the other (sub)systems.

Instead we are forced to deal with the states of subsystems *relative*

to each other. Specifying the state of one subsystem leads to a unique

specification of the state (the "relative state") of the other

subsystems. (See "What is a relative state?")

If one of the systems is an observer and the interaction an observation

then the effect of the observation is to split the observer into a

number of copies, each copy observing just one of the possible results

of a measurement and unaware of the other results and all its observer-

copies. Interactions between systems and their environments, including

communication between different observers in the same world, transmits

the correlations that induce local splitting or decoherence into non-

interfering branches of the universal wavefunction. Thus the entire

world is split, quite rapidly, into a host of mutually unobservable but

equally real worlds.

According to many-worlds all the possible outcomes of a quantum

interaction are realised. The wavefunction, instead of collapsing at

the moment of observation, carries on evolving in a deterministic

fashion, embracing all possibilities embedded within it. All outcomes

exist simultaneously but do not interfere further with each other, each

single prior world having split into mutually unobservable but equally

real worlds.

Q3 What are the alternatives to many-worlds?

-----------------------------------------

There is no other quantum theory, besides many-worlds, that is

scientific, in the sense of providing a reductionist model of reality,

and free of internal inconsistencies, that I am aware of. Briefly here

are the defects of the most popular alternatives:

1) Copenhagen Interpretation. Postulates that the observer obeys

different physical laws than the non-observer, which is a return

to vitalism. The definition of an observer varies from one

adherent to another, if present at all. The status of the

wavefunction is also ambiguous. If the wavefunction is real the

theory is non-local (not fatal, but unpleasant). If the

wavefunction is not real then the theory supplies no model of

reality. (See "What are the problems with quantum theory?")

2) Hidden Variables [B]. Explicitly non-local. Bohm accepts that all

the branches of the universal wavefunction exist. Like Everett

Bohm held that the wavefunction is real complex-valued field which

never collapses. In addition Bohm postulated that there were

particles that move under the influence of a non-local "quantum-

potential" derived from the wavefunction (in addition to the

classical potentials which are already incorporated into the

structure of the wavefunction). The action of the quantum-

potential is such that the particles are affected by only one of

the branches of the wavefunction. (Bohm derives what is

essentially a decoherence argument to show this, see section 7,#I

[B]).

The implicit, unstated assumption made by Bohm is that only the

single branch of wavefunction associated with particles can contain

self-aware observers, whereas Everett makes no such assumption.

Most of Bohm's adherents do not seem to understand (or even be

aware of) Everett's criticism, section VI [1], that the hidden-

variable particles are not observable since the wavefunction alone

is sufficient to account for all observations and hence a model of

reality. The hidden variable particles can be discarded, along

with the guiding quantum-potential, yielding a theory isomorphic

to many-worlds, without affecting any experimental results.

[B] David J Bohm _A suggested interpretation of the quantum theory

in terms of "hidden variables" I and II_ Physical Review Vol

85 #2 166-193 (1952)

3) Quantum Logic. Undoubtedly the most extreme of all attempts to

solve the QM measurement problem. Apart from abandoning one or

other of the classical tenets of logic these theories are all

unfinished (presumably because of internal inconsistencies). Also

it is unclear how and why different types of logic apply on

different scales.

4) Extended Probability [M]. A bold theory in which the concept of

probability is "extended" to include complex values [Y]. Whilst

quite daring, I am not sure if this is logically permissable, being

in conflict with the relative frequency notion of probability, in

which case it suffers from the same criticism as quantum logic.

Also it is unclear, to me anyway, how the resultant notion of

"complex probability" differs from the quantum "probability

amplitude" and thus why we are justified in collapsing the complex-

valued probability as if it were a classical, real-valued

probability.

[M] W Muckenheim _A review of extended probabilities_ Physics

Reports Vol 133 339- (1986)

[Y] Saul Youssef _Quantum Mechanics as Complex Probability Theory_

hep-th 9307019

5) Transactional model [C]. Explicitly non-local. An imaginative

theory, based on the Feynman-Wheeler absorber-emitter model of EM,

in which advanced and retarded probability amplitudes combine into

an atemporal "transaction" to form the Born probability density.

It requires that the input and output states, as defined by an

observer, act as emitters and absorbers respectively, but not any

internal states (inside the "black box"), and, consequently,

suffers from the familiar measurement problem of the Copenhagen

interpretation.

If the internal states *did* act as emitters/absorbers then the

wavefunction would collapse, for example, around one of the double

slits (an internal state) in the double slit experiment, destroying

the observed interference fringes. In transaction terminology a

transaction would form between the first single slit and one of the

double slits and another transaction would form between the same

double slit and the point on the screen where the photon lands.

This never observed.

[C] John G Cramer _The transactional interpretation of quantum

mechanics_ Reviews of Modern Physics Vol 58 #3 647-687 (1986)

6) Many-minds. Despite its superficial similarities with many-worlds

this is actually a very unphysical, non-operational theory. (See

"What is many-minds?")

7) Non-linear theories in general. So far no non-linear theory has

any accepted experimental support, whereas many have failed

experiment. (See "Is physics linear?") Many-worlds predicts that

non-linear theories will always fail experiment. (See "Is

linearity exact?")

Q4 What is a "world"?

------------------

Loosely speaking a "world" is a complex, causally connected, partially

or completely closed set of interacting sub-systems which don't

significantly interfere with other, more remote, elements in the

superposition. Any complex system and its coupled environment, with a

large number of internal degrees of freedom, qualifies as a world. An

observer, with internal irreversible processes, counts as a complex

system. In terms of the wavefunction, a world is a decohered branch of

the universal wavefunction, which represents a single macrostate. (See

"What is decoherence?") The worlds all exist simultaneously in a non-

interacting linear superposition.

Sometimes "worlds" are called "universes", but more usually the latter

is reserved the totality of worlds implied by the universal

wavefunction. Sometimes the term "history" is used instead of "world".

(Gell-Mann/Hartle's phrase, see "What is many-histories?").

Q5 What is a measurement?

----------------------

A measurement is an interaction, usually irreversible, between

subsystems that correlates the value of a quantity in one subsystem with

the value of a quantity in the other subsystem. The interaction may

trigger an amplification process within one object or subsystem with

many internal degrees of freedom, leading to an irreversible high-level

change in the same object. If the course of the amplification is

sensitive to the initial interaction then we can designate the system

containing the amplified process as the "measuring apparatus", since the

trigger is sensitive to some (often microphysical) quantity or parameter

of the one of the other subsystems, which we designate the "object"

system. Eg the detection of a charged particle (the object) by a Geiger

counter (the measuring apparatus) leads to the generation of a "click"

(high-level change). The absence of a charged particle does not

generate a click. The interaction is with those elements of the charged

particle's wavefunction that passes *between* the charged detector

plates, triggering the amplification process (an irreversible electron

cascade or avalanche), which is ultimately converted to a click.

A measurement, by this definition, does not require the presence of an

conscious observer, only of irreversible processes.

Q6 Why do worlds split?

---------------------

What is decoherence?

--------------------

Worlds, or branches of the universal wavefunction, split when different

components of a quantum superposition "decohere" from each other [7a],

[7b], [10]. Decoherence refers to the loss of coherency or absence of

interference effects between the elements of the superposition. For two

branches or worlds to interfere with each other all the atoms, subatomic

particles, photons and other degrees of freedom in each world have to

be in the same state, which usually means they all must be in the same

place or significantly overlap in both worlds, simultaneously.

For small microscopic systems it is quite possible for all their atomic

components to overlap at some future point. In the double slit

experiment, for instance, it only requires that the divergent paths of

the diffracted particle overlap again at some space-time point for an

interference pattern to form, because only the single particle has been

split.

Such future coincidence of positions in all the components is virtually

impossible in more complex, macroscopic systems because all the

constituent particles have to overlap with their counterparts

simultaneously. Any system complex enough to be described by

thermodynamics and exhibit irreversible behaviour is a system complex

enough to exclude, for all practical purposes, any possibility of future

interference between its decoherent branches. An irreversible process

is one in, or linked to, a system with a large number of internal,

unconstrained degrees of freedom. Once the irreversible process has

started then alterations of the values of the many degrees of freedom

leaves an imprint which can't be removed. If we try to intervene to

restore the original status quo the intervention causes more disruption

elsewhere.

In QM jargon we say that the components (or vectors in the underlying

Hilbert state space) have become permanently orthogonal due to the

complexity of the systems increasing the dimensionality of the vector

space, where each unconstrained degree of freedom contributes a

dimension to the state vector space. In a high dimension space almost

all vectors are orthogonal, without any significant degree of overlap.

Thus vectors for complex systems, with a large number of degrees of

freedom, naturally decompose into mutually orthogonal components which,

because they can never significantly interfere again, are unaware of

each other. The complex system, or world, has split into different,

mutually unobservable worlds.

According to thermodynamics each activated degree of freedom acquires

kT energy. This works the other way around as well: the release of

approximately kT of energy increases the state-space dimensionality.

Even the quite small amounts of energy released by an irreversible

frictive process are quite large on this scale, increasing the size of

the associated Hilbert space.

Contact between a system and a heat sink is equivalent to increasing the

dimensionality of the state space, because the description of the system

has to be extended to include all parts of the environment in causal

contact with it. Contact with the external environment is a very

effective destroyer of coherency. (See "What is the environment

basis?")

Q7 When do worlds split?

---------------------

Worlds irrevocably "split" at the sites of measurement-like interactions

associated with thermodynamically irreversible processes. (See "What

is a measurement?") An irreversible process will always produce

decoherence which splits worlds. (See "Why do worlds split?", "What is

decoherence?" and "When does Schrodinger's cat split?" for a concrete

example.)

In the example of a Geiger counter and a charged particle after the

particle has passed the counter one world contains the clicked counter

and that portion of the particle's wavefunction which passed though the

detector. The other world contains the unclicked counter with the

particle's wavefunction with a "shadow" cast by the counter taken out

of the particle's wavefunction.

The Geiger counter splits when the amplification process became

irreversible, before the click is emitted. (See "What is a

measurement?") The splitting is local (originally in the region of the

Geiger counter in our example) and is transmitted causally to more

distant systems. (See "Is many-worlds a local theory?" and "Does the

EPR experiment prohibit locality?") The precise moment/location of the

split is not sharply defined due to the subjective nature of

irreversibility, but can be considered complete when much more than kT

of energy has been released in an uncontrolled fashion into the

environment. At this stage the event has become irreversible.

In the language of thermodynamics the amplification of the charged

particle's presence by the Geiger counter is an irreversible event.

These events have caused the decoherence of the different branches of

the wavefunction. (See "What is decoherence?" and "Why do worlds

split?") Decoherence occurs when irreversible macro-level events take

place and the macrostate description of an object admits no single

description. (A macrostate, in brief, is the description of an object

in terms of accessible external characteristics.)

The advantage of linking the definition of worlds and the splitting

process with thermodynamics is the splitting process becomes

irreversible and only permits forward-time-branching, following the

increase with entropy. (See "Why don't worlds fuse, as well as split?")

Like all irreversible processes, though, there are exceptions even at

the coarse-grained level and worlds will occasionally fuse. A

necessary, although not sufficient, precondition for fusing is for all

records, memories etc that discriminate between the pre-fused worlds or

histories be lost. This is not a common occurrence.

Q8 When does Schrodinger's cat split?

----------------------------------

Consider Schrodinger's cat. A cat is placed in a sealed box with a

device that releases a lethal does of cyanide if a certain radioactive

decay is detected. For simplicity we'll imagine that the box, whilst

closed, completely isolates the cat from its environment. After a while

an investigator opens the box to see if the cat is alive or dead.

According to the Copenhagen Interpretation the cat was neither alive nor

dead until the box was opened, whereupon the wavefunction of the cat

collapsed into one of the two alternatives (alive or dead cat). The

paradox, according to Schrodinger, is that the cat presumably knew if

it was alive *before* the box was opened. According to many-worlds the

device was split into two states (cyanide released or not) by the

radioactive decay, which is a thermodynamically irreversible process

(See "When do worlds split?" and "Why do worlds split?"). As the

cyanide/no-cyanide interacts with the cat the cat is split into two

states (dead or alive). From the surviving cat's point of view it

occupies a different world from its deceased copy. The onlooker is

split into two copies only when the box is opened and they are altered

by the states of the cat.

The cat splits when the device is triggered, irreversibly. The

investigator splits when they open the box. The alive cat has no idea

that investigator has split, any more than it is aware that there is a

dead cat in the neighbouring split-off world. The investigator can

deduce, after the event, by examining the cyanide mechanism, or the

cat's memory, that the cat split prior to opening the box.

Q9 What is sum-over-histories?

---------------------------

The sum-over-histories or path-integral formalism of quantum mechanics

was developed by Richard Feynman in the 1940s [F] as a third

interpretation of quantum mechanics, alongside Schrodinger's wave

picture and Heisenberg's matrix mechanics, for calculating transition

amplitudes. All three approaches are mathematically equivalent, but the

path-integral formalism offers some interesting additional insights into

many-worlds.

In the path-integral picture the wavefunction of a single particle at

(x',t') is built up of contributions of all possible paths from (x,t),

where each path's contribution is weighted by a (phase) factor of

exp(i*Action[path]/hbar) * wavefunction at (x,t), summed, in turn, over

all values of x. The Action[path] is the time-integral of the

lagrangian (roughly: the lagrangian equals kinetic minus the potential

energy) along the path from (x,t) to (x',t'). The final expression is

thus the sum or integral over all paths, irrespective of any classical

dynamical constraints. For N-particle systems the principle is the

same, except that the paths run through a 3-N space.

In the path-integral approach every possible path through configuration

space makes a contribution to the transition amplitude. From this point

of view the particle explores every possible intermediate configuration

between the specified start and end states. For this reason the path-

integral technique is often referred to as "sum-over-histories". Since

we do not occupy a privileged moment in history it is natural to wonder

if alternative histories are contributing equally to transition

amplitudes in the future, and that each possible history has an equal

reality. Perhaps we shouldn't be surprised that Feynman is on record

as believing in many-worlds. (See "Who believes in many-worlds?") What

is surprising is that Everett developed his many-worlds theory entirely

from the Schrodinger viewpoint without any detectable influence from

Feynman's work, despite Feynman and Everett sharing the same Princeton

thesis supervisor, John A Wheeler.

Feynman developed his path-integral formalism further during his work

on quantum electrodynamics, QED, in parallel with Schwinger and Tomonoga

who had developed a less visualisable form of QED. Dyson showed that

these approaches were all equivalent. Feynman, Schwinger and Tomonoga

were awarded the 1965 Physics Nobel Prize for this work. Feynman's

approach was to show how any process, with defined in (initial) and out

(final) states, can be represented by a series of (Feynman) diagrams,

which allow for the creation, exchange and annihilation of particles.

Each Feynman diagram represents a different contribution to the complete

transition amplitude, provided that the external lines map onto the

required boundary initial and final conditions (the defined in and out

states). QED became the prototype for all the other, later, field

theories like electro-weak and quantum chromodynamics.

[F] Richard P Feynman _Space-time approach to non-relativistic quantum

mechanics_ Reviews of Modern Physics, Vol 20: 267-287 (1948)

Q10 What is many-histories?

-----------------------

What is the environment basis?

------------------------------

There is considerable linkage between thermodynamics and many-worlds,

explored in the "decoherence" views of Zurek [7a], [7b] and Gell-Mann

and Hartle [10], Everett [1], [2] and others [4b]. (See "What is

decoherence?")

Gell-Mann and Hartle, in particular, have extended the role of

decoherence in defining the Everett worlds, or "histories" in their

nomenclature. They call their approach the "many-histories" approach,

where each "coarse-grained or classical history" is associated with a

unique time-ordered sequence of sets of irreversible events, including

measurements, records, observations and the like. (See "What is a

measurement?") Fine-grained histories effectively relax the

irreversible criterion. Mathematically the many-histories approach is

isomorphic to Everett's many-worlds.

The worlds split or "decohere" from each other when irreversible events

occur. (See "Why do worlds split?" and "When do worlds split?".)

Correspondingly many-histories defines a multiply-connected hierarchy

of classical histories where each classical history is a "child" of any

parent history which has only a subset of the child defining

irreversible events and a parent of any history which has a superset of

such events. Climbing up the tree from child to parent moves to

progressively coarser grained consistent histories until eventually the

top is reached where the history has *no* defining events (and thus

consistent with everything!). This is Everett's universal wavefunction.

The bottom of the coarse-grained tree terminates with the maximally

refined set of decohering histories. The classical histories each have

a probability assigned to them and probabilities are additive in the

sense that the sum of the probabilities associated a set classical

histories is equal to the probability associated with the unique parent

history defined by the set. (Below the maximally refined classical

histories are the fine grained or quantum histories, where probabilities

are no longer additive and different histories significantly interfere

with each other. The bottom level consists of complete microstates,

which fully specified states.)

The decoherence approach is useful in considering the effect of the

environment on a system. In many ways the environment, acting as a heat

sink, can be regarded as performing a succession of measurement-like

interactions upon any system, inducing associated system splits. All

the environment basis is is a basis chosen so as to minimise the cross-

basis interference terms. It makes any real-worlds calculation easy,

since the cross terms are so small, but it does not *uniquely* select

a basis, just eliminates a large number.

Q11 How many worlds are there?

--------------------------

The thermodynamic Planck-Boltzmann relationship, S = k*log(W), counts

the branches of the wavefunction at each splitting, at the lowest,

maximally refined level of Gell-Mann's many-histories tree. (See "What

is many-histories?") The bottom or maximally divided level consists of

microstates which can be counted by the formula W = exp (S/k), where S

= entropy, k = Boltzmann's constant (approx 10^-23 Joules/Kelvin) and

W = number of worlds or macrostates. The number of coarser grained

worlds is lower, but still increasing with entropy by the same ratio,

ie the number of worlds a single world splits into at the site of an

irreversible event, entropy dS, is exp(dS/k). Because k is very small

a great many worlds split off at each macroscopic event.

Q12 Is many-worlds a local theory?

------------------------------

The simplest way to see that the many-worlds metatheory is a local

theory is to note that it requires that the wavefunction obey some

relativistic wave equation, the exact form of which is currently

unknown, but which is presumed to be locally Lorentz invariant at all

times and everywhere. This is equivalent to imposing the requirement

that locality is enforced at all times and everywhere. Ergo many-worlds

is a local theory.

Another way of seeing this is examine how macrostates evolve.

Macrostates descriptions of objects evolve in a local fashion. Worlds

split as the macrostate description divides inside the light cone of the

triggering event. Thus the splitting is a local process, transmitted

causally at light or sub-light speeds. (See "Does the EPR experiment

prohibit locality?" and "When do worlds split?")

Q13 Is many-worlds a deterministic theory?

--------------------------------------

Yes, many-worlds is a deterministic theory, since the wavefunction obeys

a deterministic wave equation at all times. All possible outcomes of

a measurement or interaction (See "What is a measurement?") are embedded

within the universal wavefunction although each observer, split by each

observation, is only aware of single outcomes due to the linearity of

the wave equation. The world appears indeterministic, with the usual

probabilistic collapse of the wavefunction, but at the objective level,

which includes all outcomes, determinism is restored.

Some people are under the impression that the only motivation for many-

worlds is a desire to return to a deterministic theory of physics. This

is not true. As Everett pointed out, the objection with the standard

Copenhagen interpretation is not the indeterminism per se, but that

indeterminism occurs only with the intervention of an observer, when the

wavefunction collapses. (See "What is the Copenhagen interpretation?")

Q14 Is many-worlds a relativistic theory?

-------------------------------------

What about quantum field theory?

--------------------------------

What about quantum gravity?

---------------------------

It is trivial to relativise many-worlds, at least to the level of

special relativity. All relativistic theories of physics are quantum

theories with linear wave equations. There are three or more stages to

developing a fully relativised quantum field theory:

First quantisation: the wavefunction of an N particle system is a

complex field which evolves in 3N dimensions as the solution to either

the many-particle Schrodinger, Dirac or Klein-Gordon or some other wave

equation. External forces applied to the particles are represented or

modelled via a potential, which appears in the wave equation as a

classical, background field.

Second quantisation: AKA (relativistic) quantum field theory (QFT)

handles the creation and destruction of particles by quantising the

classical fields and potentials as well as the particles. Each particle

corresponds to a field, in QFT, and becomes an operator. Eg the

electromagnetic field's particle is the photon. The wavefunction of a

collection of particles/fields exists in a Fock space, where the number

of dimensions varies from component to component, corresponding to the

indeterminacy in the particle number. Many-worlds has no problems

incorporating QFT, since a theory (QFT) is not altered by a metatheory

(many-worlds), which makes statements *about* the theory.

Third quantisation: AKA quantum gravity. The gravitational metric is

quantised, along with (perhaps) the topology of the space-time manifold.

The role of time plays a less central role, as might be expected, but

the first and second quantisation models are as applicable as ever for

modelling low-energy events. The physics of this is incomplete,

including some thorny, unresolved conceptual issues, with a number of

proposals (strings, supersymmetry, supergravity...) for ways forward,

but the extension required by many-worlds is quite trivial since the

mathematics would be unchanged.

One of the original motivations of Everett's scheme was to provide a

system for quantising the gravitational field to yield a quantum

cosmology, permitting a complete, self-contained description of the

universe. Indeed many-words actually *requires* that gravity be

quantised, in contrast to other interpretations which are silent about

the role of gravity. (See "Why *quantum* gravity?")

Q15 Where are the other worlds?

---------------------------

Non-relativistic quantum mechanics and quantum field theory are quite

unambiguous: the other Everett-worlds occupy the same space and time as

we do.

The implicit question is really, why aren't we aware of these other

worlds, unless they exist "somewhere" else? To see why we aren't aware

of the other worlds, despite occupying the same space-time, see "Why do

I only ever experience one world?" Some popular accounts describe the

other worlds as splitting off into other, orthogonal, dimensions. These

dimensions are the dimensions of Hilbert space, not the more familiar

space-time dimensions.

The situation is more complicated, as we might expect, in theories of

quantum gravity (See "What about quantum gravity?"), because gravity can

be viewed as perturbations in the space-time metric. If we take a

geometric interpretation of gravity then we can regard differently

curved space-times, each with their own distinct thermodynamic history,

as non-coeval. In that sense we only share the same space-time manifold

with other worlds with a (macroscopically) similar mass distribution.

Whenever the amplification of a quantum-scale interaction effects the

mass distribution and hence space-time curvature the resultant

decoherence can be regarded as splitting the local space-time manifold

into discrete sheets.

Q16 Is many-worlds (just) an interpretation?

----------------------------------------

No, for four reasons:

First, many-worlds makes predictions that differ from the other so-

called interpretations of quantum theory. Interpretations do not make

predictions that differ. (See "What unique predictions does many-worlds

make?") In addition many-worlds retrodicts a lot of data that has no

other easy interpretation. (See "What retrodictions does many-worlds

make?")

Second, the mathematical structure of many-worlds is not isomorphic to

other formulations of quantum mechanics like the Copenhagen

interpretation or Bohm's hidden variables. The Copenhagen

interpretation does not contain those elements of the wavefunction that

correspond to the other worlds. Bohm's hidden variables contain

particles, in addition to the wavefunction. Neither theory is

isomorphic to each other or many-worlds and are not, therefore, merely

rival "interpretations".

Third, there is no scientific, reductionistic alternative to many-

worlds. All the other theories fail for logical reasons. (See "Is

there any alternative theory?")

Fourth, the interpretative side of many-worlds, like the subjective

probabilistic elements, are derived from within the theory, rather than

added to it by assumption, as in the conventional approach. (See "How

do probabilities emerge within many-worlds?")

Many-worlds should really be described as a theory or, more precisely,

a metatheory, since it makes statements that are applicable about a

range of theories. Many-worlds is the unavoidable implication of any

quantum theory which obeys some type of linear wave equation. (See "Is

physics linear?")

Q17 Why don't worlds fuse, as well as split?

---------------------------------------

Do splitting worlds imply irreversible physics?

-----------------------------------------------

This is really a question about why thermodynamics works and what is the

origin of the "arrow of time", rather than about many-worlds.

First, worlds almost never fuse, in the forward time direction, but

often divide, because of the way we have defined them. (See "What is

decoherence?", "When do worlds split?" and "When do worlds split?") The

Planck-Boltzmann formula for the number of worlds (See "How many worlds

are there?") implies that where worlds to fuse together then entropy

would decrease, violating the second law of thermodynamics.

Second, this does not imply that irreversible thermodynamics is

incompatible with reversible (or nearly so) microphysics. The laws of

physics are reversible (or CPT invariant, more precisely) and fully

compatible with the irreversibility of thermodynamics, which is solely

due to the boundary conditions (the state of universe at some chosen

moment) imposed by the Big Bang or whatever we chose to regard as the

initial conditions. (See "Why can't the boundary conditions be updated

to reflect my observations in this one world?")

Q18 What retrodictions does many-worlds make?

-----------------------------------------

A retrodiction occurs when already gathered data is accounted for by a

later theoretical advance in a more convincing fashion. The advantage

of a retrodiction over a prediction is that the already gathered data

is more likely to be free of experimenter bias. An example of a

retrodiction is the perihelion shift of Mercury which Newtonian

mechanics plus gravity was unable, totally, to account for whilst

Einstein's general relativity made short work of it.

Many-worlds retrodicts all the peculiar properties of the (apparent)

wavefunction collapse in terms of decoherence. (See "What is

decoherence?", "Can wavefunctions collapse?", "When do worlds split?"

& "Why do worlds split?") No other quantum theory has yet accounted for

this behaviour scientifically. (See "What are the alternatives to many-

worlds?")

Q19 Do worlds differentiate or split?

---------------------------------

Can we regard the separate worlds that result from a measurement-like

interaction (See "What is a measurement?") as having previous existed

distinctly and merely differentiated, rather than the interaction as

having split one world into many? This is definitely not permissable

in many-worlds or any theory of quantum theory consistent with

experiment. Worlds do not exist in a quantum superposition

independently of each other before they decohere or split. The

splitting is a physical process, grounded in the dynamical evolution of

the wave vector, not a matter of philosophical, linguistic or mental

convenience (see "Why do worlds split?" and "When do worlds split?")

If you try to treat the worlds as pre-existing and separate then the

maths and probabilistic behaviour all comes out wrong. Also the

differentiation theory isn't deterministic, in contradiction to the wave

equations which are deterministic, since many-minds says that:

AAAAAAAAAAAAAAABBBBBBBBBBBBBBB --------------> time

(Worlds differentiate)

AAAAAAAAAAAAAAACCCCCCCCCCCCCCC

occurs, rather than:

BBBBBBBBBBBBBBB

B

AAAAAAAAAAAAAA (Worlds split)

C

CCCCCCCCCCCCCCC

according to many-worlds.

This false differentiation model, at the mental level, seems favoured

by adherents of many-minds. (See "What is many-minds?")

Q20 What is many-minds?

------------------

Many-minds proposes, as an extra fundamental axiom, that an infinity of

separate minds or mental states be associated with each single brain

state. When the single physical brain state is split into a quantum

superposition by a measurement (See "What is a measurement?") the

associated infinity of minds are thought of as differentiating rather

than splitting. The motivation for this brain-mind dichotomy seems

purely to avoid talk of minds splitting and talk instead about the

differentiation of pre-existing separate mental states. There is no

physical basis for this interpretation, which is incapable of an

operational definition. Indeed the differentiation model for physical

systems is specifically not permitted in many-worlds. Many-minds seems

to be proposing that minds follow different rules than matter. (See "Do

worlds differentiate or split?")

In many-minds the role of the conscious observer is accorded special

status, with its fundamental axiom about infinities of pre-existing

minds, and as such is philosophically opposed to many-worlds, which

seeks to remove the observer from any privileged role in physics.

(Many-minds was co-invented by David Albert, who has, apparently, since

abandoned it. See Scientific American July 1992 page 80 and contrast

with Albert's April '94 Scientific American article.)

The two theories must not be confused.

Q21 Does many-worlds violate Ockham's Razor?

---------------------------------------

William of Ockham, 1285-1349(?) English philosopher and one of the

founders of logic, proposed a maxim for judging theories which says that

hypotheses should not be multiplied beyond necessity. This is known as

Ockham's razor and is interpreted, today, as meaning that to account for

any set of facts the simplest theories are to be preferred over more

complex ones. Many-worlds is viewed as unnecessarily complex, by some,

by requiring the existence of a multiplicity of worlds to explain what

we see, at any time, in just one world.

This is to mistake what is meant by "complex". Here's an example.

Analysis of starlight reveals that starlight is very similar to faint

sunlight, both with spectroscopic absorption and emission lines.

Assuming the universality of physical law we are led to conclude that

other stars and worlds are scattered, in great numbers, across the

cosmos. The theory that "the stars are distant suns" is the simplest

theory and so to be preferred by Ockham's Razor to other geocentric

theories.

Similarly many-worlds is the simplest and most economical quantum theory

because it proposes that same laws of physics apply to animate observers

as has been observed for inanimate objects. The multiplicity of worlds

predicted by the theory is not a weakness of many-worlds, any more than

the multiplicity of stars are for astronomers, since the non-interacting

worlds emerge from a simpler theory.

(As an historical aside it is worth noting that Ockham's razor was also

falsely used to argue in favour of the older heliocentric theories

*against* Galileo's notion of the vastness of the cosmos. The notion

of vast empty interstellar spaces was too uneconomical to be believable

to the Medieval mind. Again they were confusing the notion of vastness

with complexity [15].)

Q22 Does many-worlds violate conservation of energy?

------------------------------------------------

First, the law conservation of energy is based on observations within

each world. All observations within each world are consistent with

conservation of energy, therefore energy is conserved.

Second, and more precisely, conservation of energy, in QM, is formulated

in terms of weighted averages or expectation values. Conservation of

energy is expressed by saying that the time derivative of the expected

energy of a closed system vanishes. This statement can be scaled up to

include the whole universe. Each world has an approximate energy, but

the energy of the total wavefunction, or any subset of, involves summing

over each world, weighted with its probability measure. This weighted

sum is a constant. So energy is conserved within each world and also

across the totality of worlds.

One way of viewing this result - that observed conserved quantities are

conserved across the totality of worlds - is to note that new worlds are

not created by the action of the wave equation, rather existing worlds

are split into successively "thinner" and "thinner" slices, if we view

the probability densities as "thickness".

Q23 How do probabilities emerge within many-worlds?

-----------------------------------------------

Everett demonstrated [1], [2] that observations in each world obey all

the usual conventional statistical laws predicted by the probabilistic

Born interpretation, by showing that the Hilbert space's inner product

or norm has a special property which allows us to makes statements about

the worlds where quantum statistics break down. The norm of the vector

of the set of worlds where experiments contradict the Born

interpretation ("non-random" or "maverick" worlds) vanishes in the limit

as the number of probabilistic trials goes to infinity, as is required

by the frequentist definition of probability. Hilbert space vectors

with zero norm don't exist (see below), thus we, as observers, only

observe the familiar, probabilistic predictions of quantum theory.

Everett-worlds where probability breaks down are never realised.

Strictly speaking Everett did not prove that the usual statistical laws

of the Born interpretation would hold true for all observers in all

worlds. He merely showed that no other statistical laws could hold true

and asserted the vanishing of the Hilbert space "volume" or norm of the

set of "maverick" worlds. DeWitt later published a longer *derivation*

of Everett's assertion [4a], [4b], closely based on an earlier,

independent demonstration by Hartle [H]. What Everett asserted, and

DeWitt/Hartle derived, is that the collective norm of all the maverick

worlds, as the number of trials goes to infinity, vanishes. Since the

only vector in a Hilbert space with vanishing norm is the null vector

(a defining axiom of Hilbert spaces) this is equivalent to saying that

non-randomness is never realised. All the worlds obey the usual Born

predictions of quantum theory. That's why we never observe the

consistent violation of the usual quantum statistics, with, say, heat

flowing from a colder to a hotter macroscopic object. Zero-probability

events never happen.

Of course we have to assume that the wavefunction is a Hilbert space

vector in the first place but, since this assumption is also made in the

standard formulation, this is not a weakness of many-worlds since we are

not trying to justify all the axioms of the conventional formulation of

QM, merely those that relate to probabilities and collapse of the

wavefunction.

In more detail the steps are:

1) Construct the tensor product of N identical systems in state |psi> ,

according to the usual rules for Hilbert space composition

(repeated indices summed):

|PSI_N> = |psi_1> *|psi_2> *...... |psi_N> where

|psi_j> = jth system prepared in state |psi>

= |i_j> < i_j|psi> (ie the amplitude of the ith eigenstate

is independent of which system it is in)

so that

|PSI_N> = |i_1> |i_2> ...|i_N> < i_1|psi> < i_2|psi> ...< i_N|psi>

2) Quantify the deviation from the "expected" Born-mean for each

component of |PSI_N> with respect to the above |i_1> |i_2> ...|i_N>

basis by counting the number of occurrences of the ith

eigenstate/N. Call this number RF(i). Define the Born-deviation

as D = sum(i)( (RF(i) - |< i|psi> |^2)^2 ). Thus D, loosely

speaking, for each N length sequence, quantifies by how much the

particular sequence differs from the Born-expectation.

3) Sort out terms in the expansion of |PSI_N> according to whether D

is less/equal to (.LE.) or greater than (.GT.) E, where E is a

real, positive constant. Collecting terms together we get:

|PSI_N> = |N,"D.GT.E"> + |N,"D.LE.E">

worlds worlds

for which for which

D > E D < = E

4) What DeWitt showed was that:

< N,"D.GT.E"|N,"D.GT.E"> < 1/(NE) (proof in appendix of [4b])

Thus as N goes to infinity the right-hand side vanishes for all

positive values of E. (This mirrors the classical "frequentist"

position on probability which states that if event i occurs with

probability p(i) then the proportion of N trials with outcome i

approaches p(i)/N as N goes to infinity [H]. This has the

immediate benefit that sum(i) p(i) = 1.) The norm of |N,"D.LE.E"> ,

by contrast, approaches 1 as N goes to infinity.

Note: this property of D is not shared by other definitions, which

is why we haven't investigated them. If, say, we had defined, in

step 2), A = sum(i)( (RF(i) - |< i|psi> |)^2 ), so that A measures

the deviation from |psi|, rather than |psi|^2, then we find that

< A> does not have the desired property of vanishing as N goes to

infinity.

5) The norm of the collection of non-random worlds vanishes and

therefore must be identified with some complex multiple of the null

vector.

6) Since (by assumption) the state vector faithfully models reality

then the null vector cannot represent any element of reality, since

it can be added to (or subtracted from) any other state vector

without altering the other state vector.

7) Ergo the non-random worlds are not realised, without making any

additional physical assumptions, such as the imposition of a measure.

Note: no finite sequence of outcomes is excluded from happening,

since the concept of probability and randomness only becomes

precise only as N goes to infinity [H]. Thus, heat *could* be

observed to flow from a cold to hotter object, but we might have

to wait a very long time before observing it. What *is* excluded

is the possibility of this process going on forever.

The emergence of Born-style probabilities as a consequence of the

mathematical formalism of the theory, without any extra interpretative

assumptions, is another reason why the Everett metatheory should not be

regarded as just an interpretation. (See "Is many-worlds (just) an

interpretation?") The interpretative elements are forced by the

mathematical structure of the axioms of Hilbert space.

[H] JB Hartle _Quantum Mechanics of Individual Systems_ American

Journal of Physics Vol 36 #8 704-712 (1968) Hartle has

investigated the N goes to infinity limit in more detail and more

generally. He shows that the relative frequency operator, RF,

obeys RF(i) |psi_1> |psi_2> .... = |< i|psi> |^2 |psi_1> |psi_2> ....,

for a normed state. Hartle regarded his derivation as essentially

the same as Everett's, despite being derived independently.

Q24 Does many-worlds allow free-will?

---------------------------------

Many-Worlds, whilst deterministic on the objective universal level, is

indeterministic on the subjective level so the situation is certainly

no better or worse for free-will than in the Copenhagen view.

Traditional Copenhagen indeterministic quantum mechanics only slightly

weakens the case for free-will. In quantum terms each neuron is an

essentially classical object. Consequently quantum noise in the brain

is at such a low level that it probably doesn't often alter, except very

rarely, the critical mechanistic behaviour of sufficient neurons to

cause a decision to be different than we might otherwise expect. The

consensus view amongst experts is that free-will is the consequence of

the mechanistic operation of our brains, the firing of neurons,

discharging across synapses etc and fully compatible with the

determinism of classical physics. Free-will is the inability of an

intelligent, self-aware mechanism to predict its own future actions due

to the logical impossibility of any mechanism containing a complete

internal model of itself rather than any inherent indeterminism in the

mechanism's operation.

Nevertheless, some people find that with all possible decisions being

realised in different worlds that the prima facia situation for free-

will looks quite difficult. Does this multiplicity of outcomes destroy

free-will? If both sides of a choice are selected in different worlds

why bother to spend time weighing the evidence before selecting? The

answer is that whilst all decisions are realised, some are realised more

often than others - or to put to more precisely each branch of a

decision has its own weighting or measure which enforces the usual laws

of quantum statistics.

This measure is supplied by the mathematical structure of the Hilbert

spaces. Every Hilbert space has a norm, constructed from the inner

product, - which we can think of as analogous to a volume - which

weights each world or collection of worlds. A world of zero volume is

never realised. Worlds in which the conventional statistical

predictions consistently break down have zero volume and so are never

realised. (See "How do probabilities emerge within many-worlds?")

Thus our actions, as expressions of our will, correlate with the weights

associated with worlds. This, of course, matches our subjective

experience of being able to exercise our will, form moral judgements and

be held responsible for our actions.

Q25 Why am I in this world and not another?

---------------------------------------

Why does the universe appear random?

------------------------------------

These are really the same questions. Consider, for a moment, this

analogy:

Suppose Fred has his brain divided in two and transplanted into two

different cloned bodies (this is a gedanken operation! [*]). Let's

further suppose that each half-brain regenerates to full functionality

and call the resultant individuals Fred-Left and Fred-Right. Fred-Left

can ask, why did I end up as Fred-Left? Similarly Fred-Right can ask,

why did I end up as Fred-Right? The only answer possible is that there

was *no* reason. From Fred's point of view it is a subjectively

*random* choice which individual "Fred" ends up as. To the surgeon the

whole process is deterministic. To both the Freds it seems random.

Same with many-worlds. There was no reason "why" you ended up in this

world, rather than another - you end up in all the quantum worlds. It

is a subjectively random choice, an artifact of your brain and

consciousness being split, along with the rest of the world, that makes

our experiences seem random. The universe is, in effect, performing

umpteen split-brain operations on us all the time. The randomness

apparent in nature is a consequence of the continual splitting into

mutually unobservable worlds.

(See "How do probabilities emerge within many-worlds?" for how the

subjective randomness is moderated by the usual probabilistic laws of

QM.)

[*] Split brain experiments *were* performed on epileptic patients

(severing the corpus callosum, one of the pathways connecting the

cerebral hemispheres, moderated epileptic attacks). Complete

hemispherical separation was discontinued when testing of the patients

revealed the presence of two distinct consciousnesses in the same skull.

So this analogy is only partly imaginary.

Q26 Can wavefunctions collapse?

---------------------------

Many-worlds predicts/retrodicts that wavefunctions appear to collapse

(See "Does the EPR experiment prohibit locality?"), when measurement-

like interactions (See "What is a measurement?") and processes occur via

a process called decoherence (See "What is decoherence?"), but claims

that the wavefunction does not *actually* collapse but continues to

evolve according to the usual wave-equation. If a *mechanism* for

collapse could be found then there would be no need for many-worlds.

The reason why we doubt that collapse takes place is because no one has

ever been able to devise a physical mechanism that could trigger it.

The Copenhagen interpretation posits that observers collapse

wavefunctions, but is unable to define "observer". (See "What is the

Copenhagen interpretation?" and "Is there any alternative theory?")

Without a definition of observer there can be no mechanism triggered by

their presence.

Another popular view is that irreversible processes trigger collapse.

Certainly wavefunctions *appear* to collapse whenever irreversible

processes are involved. And most macroscopic, day-to-day events are

irreversible. The problem is, as with positing observers as a cause of

collapse, that any irreversible process is composed of a large number

of sub-processes that are each individually reversible. To invoke

irreversibility as a *mechanism* for collapse we would have to show that

new *fundamental* physics comes into play for complex systems, which is

quite absent at the reversible atom/molecular level. Atoms and

molecules are empirically observed to obey some type of wave equation.

We have no evidence for an extra mechanism operating on more complex

systems. As far as we can determine complex systems are described by

the quantum-operation of their simpler components interacting together.

(Note: chaos, complexity theory, etc, do not introduce new fundamental

physics. They still operate within the reductionistic paradigm -

despite what many popularisers say.)

Other people have attempted to construct non-linear theories so that

microscopic systems are approximately linear and obey the wave equation,

whilst macroscopic systems are grossly non-linear and generates

collapse. Unfortunately all these efforts have made additional

predictions which, when tested, have failed. (See "Is physics linear?")

(Another reason for doubting that any collapse actually takes place is

that the collapse would have to propagate instantaneously, or in some

space-like fashion, otherwise the same particle could be observed more

than once at different locations. Not fatal, but unpleasant and

difficult to reconcile with special relativity and some conservation

laws.)

The simplest conclusion, which is to be preferred by Ockham's razor, is

that wavefunctions just *don't* collapse and that all branches of the

wavefunction exist.

Q27 Is physics linear?

------------------

Could we ever communicate with the other worlds?

------------------------------------------------

Why do I only ever experience one world?

----------------------------------------

Why am I not aware of the world (and myself) splitting?

-------------------------------------------------------

According to our present knowledge of physics whilst it is possible to

detect the presence of other nearby worlds, through the existence of

interference effects, it is impossible travel to or communicate with

them. Mathematically this corresponds to an empirically verified

property of all quantum theories called linearity. Linearity implies

that the worlds can interfere with each other with respect to a

external, unsplit, observer or system but the interfering worlds can't

influence each other in the sense that an experimenter in one of the

worlds can arrange to communicate with their own, already split-off,

quantum copies in other worlds.

Specifically, the wave equation is linear, with respect to the

wavefunction or state vector, which means that given any two solutions

of the wavefunction, with identical boundary conditions, then any linear

combination of the solutions is another solution. Since each component

of a linear solution evolves with complete indifference as to the

presence or absence of the other terms/solutions then we can conclude

that no experiment in one world can have any effect on another

experiment in another world. Hence no communication is possible between

quantum worlds. (This type of linearity mustn't be confused with the

evident non-linearity of the equations with respect to the *fields*.)

Non communication between the splitting Everett-worlds also explains why

we are not aware of any splitting process, since such awareness needs

communication between worlds. To be aware of the world splitting you

would have to be receiving sensory information from, and thereby effect

by the reverse process, more than one world. This would enable

communication between worlds, which is forbidden by linearity. Ergo,

we are not aware of any splitting precisely because we are split into

non-interfering copies along with the rest of the world.

See also "Is linearity exact?"

Q28 Can we determine what other worlds there are?

---------------------------------------------

Is the form of the Universal Wavefunction knowable?

---------------------------------------------------

To calculate the form of the universal wavefunction requires not only

a knowledge of its dynamics (which we have a good approximation to, at

the moment) but also of the boundary conditions. To actually calculate

the form of the universal wavefunction, and hence make inferences about

*all* the embedded worlds, we would need to know the boundary conditions

as well. We are presently restricted to making inferences about those

worlds with which have shared a common history up to some point, which

have left traces (records, fossils, etc) still discernable today. This

restricts us to a subset of the extant worlds which have shared the same

boundary conditions with us. The further we probe back in time the less

we know of the boundary conditions and the less we can know of the

universal wavefunction.

This limits us to drawing conclusions about a restricted subset of the

worlds - all the worlds which are consistent with our known history up

to a some common moment, before we diverged. The flow of historical

events is, according to chaos/complexity theory/thermodynamics, very

sensitive to amplification of quantum-scale uncertainty and this

sensitivity is a future-directed one-way process. We can make very

reliable deductions about the past from the knowledge future/present but

we can't predict the future from knowledge the past/present.

Thermodynamics implies that the future is harder to predict than the

past is to retrodict. Books get written about this "arrow of time"

problem but, for the purposes of this discussion, we'll accept the

thermodynamic origin of time's arrow is as given. The fossil and

historical records say that dinosaurs and Adolf Hitler once existed but

have less to say about the future.

Consider the effects of that most quantum of activities, Brownian

motion, on the conception of individuals and the knock-on effects on the

course of history. Mutation itself, one of the sources of evolutionary

diversity, is a quantum event. For an example of the

biological/evolutionary implications see Stephen Jay Gould's book

"Wonderful Life" for an popular exploration of the thesis that the path

of evolution is driven by chance. According to Gould evolutionary

history forms an enormously diverse tree of possible histories - all

very improbable - with our path being selected by chance. According to

many-worlds all these other possibilities are realised. Thus there are

worlds in which Hitler won WW-II and other worlds in which the dinosaurs

never died out. We can be as certain of this as we are that Hitler and

the dinosaurs once existed in our own past.

Whether or not we can ever determine the totality of the universal

wavefunction is an open question. If Steven Hawking's work on the no-

boundary-condition condition is ultimately successful, or it emerges

from some theory of everything, and many think it will, then the actual

form of the *total* wavefunction could, in principle, we determined from

a complete knowledge of physical law itself.

Q29 Who was Everett?

----------------

Hugh Everett III (1930-1982) did his undergraduate study in chemical

engineering at the Catholic University of America. Studying von

Neumann's and Bohm's textbooks as part of his graduate studies, under

Wheeler, in mathematical physics at Princeton University in the 1950s

he became dissatisfied (like many others before and since) with the

collapse of the wavefunction. He developed, during discussions with

Charles Misner and Aage Peterson (Bohr' assistant, then visiting

Princeton), his "relative state" formulation. Wheeler encouraged his

work and preprints were circulated in January 1956 to a number of

physicists. A condensed version of his thesis was published as a paper

to "The Role of Gravity in Physics" conference held at the University

of North Carolina, Chapel Hill, in January 1957.

Everett was discouraged by the lack of response from others,

particularly Bohr, whom he flew to Copenhagen to meet but got the

complete brush-off from. Leaving physics after completing his Ph.D,

Everett worked as a defense analyst at the Weapons Systems Evaluation

Group, Pentagon and later became a private contractor, apparently quite

successfully for he became a multimillionaire. In 1968 Everett worked

for the Lambda Corp. His published papers during this period cover

things like optimising resource allocation and, in particular,

maximising kill rates during nuclear-weapon campaigns.

From 1968 onwards Bryce S DeWitt, one of the 1957 Chapel Hill conference

organisers, but better known as one of the founders of quantum gravity,

successfully popularised Everett's relative state formulation as the

"many-worlds interpretation" in a series of articles [4a],[4b],[5].

Sometime in 1976-9 Everett visited Austin, Texas, at Wheeler or DeWitt's

invitation, to give some lectures on QM. The strict no-smoking rule in

the auditorium was relaxed for Everett (a chain smoker); the only

exception ever. Everett, apparently, had a very intense manner,

speaking acutely and anticipating questions after a few words. Oh yes,

a bit of trivia, he drove a Cadillac with horns.

With the steady growth of interest in many-worlds in the late 1970s

Everett planned returning to physics to do more work on measurement in

quantum theory, but died of a heart attack in 1982. Survived by his

wife.

Q30 What are the problems with quantum theory?

------------------------------------------

Quantum theory is the most successful description of microscopic systems

like atoms and molecules ever, yet often it is not applied to larger,

classical systems, like observers or the entire universe. Many

scientists and philosophers are unhappy with the theory because it seems

to require a fundamental quantum-classical divide. Einstein, for

example, despite his early contributions to the subject, was never

reconciled with assigning to the act of observation a physical

significance, which most interpretations of QM require. This

contradicts the reductionist ethos that, amongst other things,

observations should emerge only as a consequence of an underlying

physical theory and not be present at the axiomatic level, as they are

in the Copenhagen interpretation. Yet the Copenhagen interpretation

remains the most popular interpretation of quantum mechanics amongst the

broad scientific community. (See "What is the Copenhagen

interpretation?")

Q31 What is the Copenhagen interpretation?

--------------------------------------

An unobserved system, according to the Copenhagen interpretation of

quantum theory, evolves in a deterministic way determined by a wave

equation. An observed system changes in a random fashion, at the moment

of observation, instantaneously, with the probability of any particular

outcome given by the Born formula. This is known as the "collapse" or

"reduction" of the wavefunction. The problems with this approach are:

(1) The collapse is an instantaneous process across an extended

region ("non-local") which is non-relativistic.

(2) The idea of an observer having an effect on microphysics is

repugnant to reductionism and smacks of a return to pre-scientific

notions of vitalism. Copenhagenism is a return to the old vitalist

notions that life is somehow different from other matter, operating

by different laws from inanimate matter. The collapse is triggered

by an observer, yet no definition of what an "observer" is

available, in terms of an atomic scale description, even in

principle.

For these reasons the view has generally been adopted that the

wavefunction associated with an object is not a real "thing", but merely

represents our *knowledge* of the object. This approach was developed

by Bohr and others, mainly at Copenhagen in the late 1920s. When we

perform an measurement or observation of an object we acquire new

information and so adjust the wavefunction as we would boundary

conditions in classical physics to reflect this new information. This

stance means that we can't answer questions about what's actually

happening, all we can answer is what will be the probability of a

particular result if we perform a measurement. This makes a lot of

people very unhappy since it provides no model for the object.

It should be added that there are other, less popular, interpretations

of quantum theory, but they all have their own drawbacks, which are

widely reckoned more severe. Generally speaking they try to find a

mechanism that describes the collapse process or add extra physical

objects to the theory, in addition to the wavefunction. In this sense

they are more complex. (See "Is there any alternative theory?")

Q32 Does the EPR experiment prohibit locality?

------------------------------------------

What about Bell's Inequality?

-----------------------------

The EPR experiment is widely regarded as the definitive gedanken

experiment for demonstrating that quantum mechanics is non-local

(requires faster-than-light communication) or incomplete. We shall see

that it implies neither.

The EPR experiment was devised, in 1935, by Einstein, Podolsky and Rosen

to demonstrate that quantum mechanics was incomplete [E]. Bell, in

1964, demonstrated that any hidden variables theory, to replicate the

predictions of QM, must be non-local [B]. QM predicts strong

correlations between separated systems, stronger than any local hidden

variables theory can offer. Bell encoded this statistical prediction

in the form of some famous inequalities that apply to any type of EPR

experiment. Eberhard, in the late 1970s, extended Bell's inequalities

to cover any local theory, with or without hidden variables. Thus the

EPR experiment plays a central role in sorting and testing variants of

QM. All the experiments attempting to test EPR/Bell's inequality to

date (including Aspect's in the 1980s [As]) are in line with the

predictions of standard QM - hidden variables are ruled out. Here is

the paradox of the EPR experiment. It seems to imply that any physical

theory must involve faster-than-light "things" going on to maintain

these "spooky" action-at-a-distance correlations and yet still be

compatible with relativity, which seems to forbid FTL.

Let's examine the EPR experiment in more detail.

So what did EPR propose? The original proposal was formulated in terms

of correlations between the positions and momenta of two once-coupled

particles. Here I shall describe it in terms of the spin (a type of

angular momentum intrinsic to the particle) of two electrons. [In this

treatment I shall ignore the fact that electrons always form

antisymmetric combinations. This does not alter the results but does

simplify the maths.] Two initially coupled electrons, with opposed

spins that sum to zero, move apart from each other across a distance of

perhaps many light years, before being separately detected, say, by me

on Earth and you on Alpha Centauri with our respective measuring

apparatuses. The EPR paradox results from noting that if we choose the

same (parallel) spin axes to measure along then we will observe the two

electrons' spins to be anti-parallel (ie when we communicate we find

that the spin on our electrons are correlated and opposed). However if

we choose measurement spin axes that are perpendicular to each other

then there is no correlation between electron spins. Last minute

alterations in a detector's alignment can create or destroy correlations

across great distances. This implies, according to some theorists, that

faster-than-light influences maintain correlations between separated

systems in some circumstances and not others.

Now let's see how many-worlds escapes from this dilemma.

The initial state of the wavefunction of you, me and the electrons and

the rest of the universe may be written:

|psi> = |me> |electrons> |you> |rest of universe>

on in on

Earth deep Alpha

space Centauri

or more compactly, ignoring the rest of the universe, as:

|psi> = |me,electrons,you>

And

|me> represents me on Earth with my detection apparatus.

|electrons> = (|+,-> - |-,+> )/sqrt(2)

represents a pair electrons, with the first electron travelling

towards Earth and the second electron travelling towards Alpha

Centauri.

|+> represents an electron with spin in the +z direction

|-> represents an electron with spin in the -z direction

It is an empirically established fact, which we just have to accept,

that we can relate spin states in one direction to spin states in other

directions like so (where "i" is the sqrt(-1)):

|left> = (|+> - |-> )/sqrt(2) (electron with spin in -x direction)

|right> = (|+> + |-> )/sqrt(2) (electron with spin in +x direction)

|up> = (|+> + |-> i)/sqrt(2) (electron with spin in +y direction)

|down> = (|+> - |-> i)/sqrt(2) (electron with spin in -y direction)

and inverting:

|+> = (|right> + |left> )/sqrt(2) = (|up> + |down> )/sqrt(2)

|-> = (|right> - |left> )/sqrt(2) = (|down> - |up> )i/sqrt(2)

(In fancy jargon we say that the spin operators in different directions

form non-commuting observables. I shall eschew such obfuscations.)

Working through the algebra we find that for pairs of electrons:

|+,-> - |-,+> = |left,right> - |right,left>

= |up,down> i - |down,up> i

I shall assume that we are capable of either measuring spin in the x or

y direction, which are both perpendicular the line of flight of the

electrons. After having measured the state of the electron my state is

described as one of either:

|me[l]> represents me + apparatus + records having measured

and recorded the x-axis spin as "left"

|me[r]> ditto with the x-axis spin as "right"

|me[u]> ditto with the y-axis spin as "up"

|me[d]> ditto with the y-axis spin as "down"

Similarly for |you> on Alpha Centauri. Notice that it is irrelevant

*how* we have measured the electron's spin. The details of the

measurement process are irrelevant. (See "What is a measurement?" if

you're not convinced.) To model the process it is sufficient to assume

that there is a way, which we have further assumed does not disturb the

electron. (The latter assumption may be relaxed without altering the

results.)

To establish familiarity with the notation let's take the state of the

initial wavefunction as:

|psi> _1 = |me,left,up,you>

/ \

/ \

first electron in left second electron in up state

state heading towards heading towards you on

me on Earth Alpha Centauri

After the electrons arrive at their detectors, I measure the spin

along the x-axis and you along the y-axis. The wavefunction evolves

into |psi> _2:

local

|psi> _1 ============> |psi> _2 = |me[l],left,up,you[u]>

observation

which represents me having recorded my electron on Earth with spin left

and you having recorded your electron on Alpha Centauri with spin up.

The index in []s indicates the value of the record. This may be held

in the observer's memory, notebooks or elsewhere in the local

environment (not necessarily in a readable form). If we communicate our

readings to each other the wavefunctions evolves into |psi> _3:

remote

|psi> _2 ============> |psi> _3 = |me[l,u],left,up,you[u,l]>

communication

where the second index in []s represents the remote reading communicated

to the other observer and being recorded locally. Notice that the

results both agree with each other, in the sense that my record of your

result agrees with your record of your result. And vice versa. Our

records are consistent.

That's the notation established. Now let's see what happens in the more

general case where, again,:

|electrons> = (|+,-> - |-,+> )/sqrt(2).

First we'll consider the case where you and I have previously arranged

to measure the our respective electron spins along the same x-axis.

Initially the wavefunction of the system of electrons and two

experimenters is:

|psi> _1

= |me,electrons,you>

= |me> (|left,right> - |right,left> )|you> /sqrt(2)

= |me,left,right,you> /sqrt(2)

- |me,right,left,you> /sqrt(2)

Neither you or I are yet unambiguously split.

Suppose I perform my measurement first (in some time frame). We get

|psi> _2

= (|me[l],left,right> - |me[r],right,left> )|you> /sqrt(2)

= |me[l],left,right,you> /sqrt(2)

- |me[r],right,left,you> /sqrt(2)

My measurement has split me, although you, having made no measurement,

remain unsplit. In the full expansion the terms that correspond to you

are identical.

After the we each have performed our measurements we get:

|psi> _3

= |me[l],left,right,you[r]> /sqrt(2)

- |me[r],right,left,you[l]> /sqrt(2)

The observers (you and me) have been split (on Earth and Alpha Centauri)

into relative states (or local worlds) which correlate with the state

of the electron. If we now communicate over interstellar modem (this

will take a few years since you and I are separated by light years, but

no matter). We get:

|psi> _4

= |me[l,r],left,right,you[r,l]> /sqrt(2)

- |me[r,l],right,left,you[l,r]> /sqrt(2)

The world corresponding to the 2nd term in the above expansion, for

example, contains me having seen my electron with spin right and knowing

that you have seen your electron with spin left. So we jointly agree,

in both worlds, that spin has been conserved.

Now suppose that we had prearranged to measure the spins along different

axes. Suppose I measure the x-direction spin and you the y-direction

spin. Things get a bit more complex. To analyse what happens we need

to decompose the two electrons along their respective spin axes.

|psi> _1 =

|me,electrons,you>

= |me> (|+,-> - |-,+> )|you> /sqrt(2)

= |me> (

(|right> +|left> )i(|down> -|up> )

- (|right> -|left> )(|down> +|up> )

) |you> /2*sqrt(2)

= |me> (

|right> (|down> -|up> )i

+ |left> (|down> -|up> )i

- |right> (|down> +|up> )

+ |left> (|down> +|up> )

) |you> /2*sqrt(2)

= |me> (

|right,down> (i-1) - |right,up> (1+i)

+ |left,up> (1-i) + |left,down> (1+i)

) |you> /2*sqrt(2)

= (

+ |me,right,down,you> (i-1)

- |me,right,up,you> (i+1)

+ |me,left,up,you> (1-i)

+ |me,left,down,you> (1+i)

) /2*sqrt(2)

So after you and I make our local observations we get:

|psi> _2 =

(

+ |me[r],right,down,you[d]> (i-1)

- |me[r],right,up,you[u]> (i+1)

+ |me[l],left,up,you[u]> (1-i)

+ |me[l],left,down,you[d]> (1+i)

) /2*sqrt(2)

Each term realises a possible outcome of the joint measurements. The

interesting thing is that whilst we can decompose it into four terms

there are only two states for each observer. Looking at myself, for

instance, we can rewrite this in terms of states relative to *my*

records/memories.

|psi> _2 =

(

|me[r],right> ( |down,you[d]> (i-1) - |up,you[u]> (i+1) )

+ |me[l],left> ( |up,you[u]> (1-i) + |down,you[d]> (1+i) )

) /2*sqrt(2)

And we see that there are only two copies of *me*. Equally we can

rewrite the expression in terms of states relative to *your*

records/memory.

|psi> _2 =

(

( |me[l],left> (1-i) - |me[r],right> (i+1) ) |up,you[u]>

+ ( |me[r],right> (i-1) + |me[l],left> (1+i) ) |down,you[d]>

) /2*sqrt(2)

And see that there are only two copies of *you*. We have each been

split into two copies, each perceiving a different outcome for our

electron's spin, but we have not been split by the measurement of the

remote electron's spin.

*After* you and I communicate our readings to each other, more than four

years later, we get:

|psi> _3 =

(

+ |me[r,d],right,down,you[d,r]> (i-1)

- |me[r,u],right,up,you[u,r]> (i+1)

+ |me[l,u],left,up,you[u,l]> (1-i)

+ |me[l,d],left,down,you[d,l]> (1+i)

) /2*sqrt(2)

The decomposition into four worlds is forced and unambiguous after

communication with the remote system. Until the two observers

communicated their results to each other they were each unsplit by each

others' measurements, although their own local measurements had split

themselves. The splitting is a local process that is causally

transmitted from system to system at light or sub-light speeds. (This

is a point that Everett stressed about Einstein's remark about the

observations of a mouse, in the Copenhagen interpretation, collapsing

the wavefunction of the universe. Everett observed that it is the mouse

that's split by its observation of the rest of the universe. The rest

of the universe is unaffected and unsplit.)

When all communication is complete the worlds have finally decomposed

or decohered from each other. Each world contains a consistent set of

observers, records and electrons, in perfect agreement with the

predictions of standard QM. Further observations of the electrons will

agree with the earlier ones and so each observer, in each world, can

henceforth regard the electron's wavefunction as having collapsed to

match the historically recorded, locally observed values. This

justifies our operational adoption of the collapse of the wavefunction

upon measurement, without having to strain our credibility by believing

that it actually happens.

To recap. Many-worlds is local and deterministic. Local measurements

split local systems (including observers) in a subjectively random

fashion; distant systems are only split when the causally transmitted

effects of the local interactions reach them. We have not assumed any

non-local FTL effects, yet we have reproduced the standard predictions

of QM.

So where did Bell and Eberhard go wrong? They thought that all theories

that reproduced the standard predictions must be non-local. It has been

pointed out by both Albert [A] and Cramer [C] (who both support

different interpretations of QM) that Bell and Eberhard had implicity

assumed that every possible measurement - even if not performed - would

have yielded a *single* definite result. This assumption is called

contra-factual definiteness or CFD [S]. What Bell and Eberhard really

proved was that every quantum theory must either violate locality *or*

CFD. Many-worlds with its multiplicity of results in different worlds

violates CFD, of course, and thus can be local.

Thus many-worlds is the only local quantum theory in accord with the

standard predictions of QM and, so far, with experiment.

[A] David Z Albert, _Bohm's Alternative to Quantum Mechanics_

Scientific American (May 1994)

[As] Alain Aspect, J Dalibard, G Roger _Experimental test of Bell's

inequalities using time-varying analyzers_ Physical Review Letters

Vol 49 #25 1804 (1982).

[C] John G Cramer _The transactional interpretation of quantum

mechanics_ Reviews of Modern Physics Vol 58 #3 647-687 (1986)

[B] John S Bell: _On the Einstein Podolsky Rosen paradox_ Physics 1

#3 195-200 (1964).

[E] Albert Einstein, Boris Podolsky, Nathan Rosen: _Can

quantum-mechanical description of physical reality be considered

complete?_ Physical Review Vol 41 777-780 (15 May 1935).

[S] Henry P Stapp _S-matrix interpretation of quantum-theory_ Physical

Review D Vol 3 #6 1303 (1971)

Q33 Is Everett's relative state formulation the same as many-worlds?

----------------------------------------------------------------

Yes, Everett's formulation of the relative state metatheory is the same

as many-worlds, but the language has evolved a lot from Everett's

original article [2] and some of his work has been extended, especially

in the area of decoherence. (See "What is decoherence?") This has

confused some people into thinking that Everett's "relative state

metatheory" and DeWitt's "many-worlds interpretation" are different

theories.

Everett [2] talked about the observer's memory sequences splitting to

form a "branching tree" structure or the state of the observer being

split by a measurement. (See "What is a measurement?") DeWitt

introduced the term "world" for describing the split states of an

observer, so that we now speak of the observer's world splitting during

the measuring process. The maths is the same, but the terminology is

different. (See "What is a world?")

Everett tended to speak in terms of the measuring apparatus being split

by the measurement, into non-interfering states, without presenting a

detailed analysis of *why* a measuring apparatus was so effective at

destroying interference effects after a measurement, although the topics

of orthogonality, amplification and irreversibility were covered. (See

"What is a measurement?", "Why do worlds split?" and "When do worlds

split?") DeWitt [4b], Gell-Mann and Hartle [10], Zurek [7a] and others

have introduced the terminology of "decoherence" (See "What is

decoherence?") to describe the role of amplification and irreversibility

within the framework of thermodynamics.

Q34 What is a relative state?

-------------------------

The relative state of something is the state that something is in,

*conditional* upon, or relative to, the state of something else. What

the heck does that mean? It means, amongst other things, that states

in the same Everett-world are all states relative to each other. (See

"Quantum mechanics and Dirac notation" for more precise details.)

Let's take the example of Schrodinger's cat and ask what is the relative

state of the observer, after looking inside the box? The relative state

of the observer (either "saw cat dead" or "saw cat alive") is

conditional upon the state of the cat (either "dead" or "alive").

Another example: the relative state of the last name of the President

of the Unites States, in 1995, is "Clinton". Relative to what?

Relative to you and me, in this world. In some other worlds it will be

"Bush", "Smith", etc ....... Each possibility is realised in some world

and it is the relative state of the President's name, relative to the

occupants of that world.

According to Everett almost all states are relative states. Only the

state of the universal wavefunction is not relative but absolute.

Q35 Was Everett a "splitter"?

-------------------------

Some people believe that Everett eschewed all talk all splitting or

branching observers in his original relative state formulation [2].

This is contradicted by the following quote from [2]:

[...] Thus with each succeeding observation (or interaction),

the observer state "branches" into a number of different

states. Each branch represents a different outcome of the

measurement and the *corresponding* eigenstate for the object-

system state. All branches exist simultaneously in the

superposition after any given sequence of observations.[#]

The "trajectory" of the memory configuration of an observer

performing a sequence of measurements is thus not a linear

sequence of memory configurations, but a branching tree, with

all possible outcomes existing simultaneously in a final

superposition with various coefficients in the mathematical

model. [...]

[#] Note added in proof-- In reply to a preprint of this

article some correspondents have raised the question of the

"transition from possible to actual," arguing that in

"reality" there is-as our experience testifies-no such

splitting of observers states, so that only one branch can

ever actually exist. Since this point may occur to other

readers the following is offered in explanation.

The whole issue of the transition from "possible" to

"actual" is taken care of in the theory in a very simple way-

there is no such transition, nor is such a transition

necessary for the theory to be in accord with our experience.

From the viewpoint of the theory *all* elements of a

superposition (all "branches") are "actual," none are any more

"real" than the rest. It is unnecessary to suppose that all

but one are somehow destroyed, since all separate elements of

a superposition individually obey the wave equation with

complete indifference to the presence or absence ("actuality"

or not) of any other elements. This total lack of effect of

one branch on another also implies that no observer will ever

be aware of any "splitting" process.

Arguments that the world picture presented by this theory

is contradicted by experience, because we are unaware of any

branching process, are like the criticism of the Copernican

theory that the mobility of the earth as a real physical fact

is incompatible with the common sense interpretation of nature

because we feel no such motion. In both case the arguments

fails when it is shown that the theory itself predicts that

our experience will be what it in fact is. (In the Copernican

case the addition of Newtonian physics was required to be able

to show that the earth's inhabitants would be unaware of any

motion of the earth.)

Q36 What unique predictions does many-worlds make?

----------------------------------------------

A prediction occurs when a theory suggests new phenomena. Many-worlds

makes at least three predictions, two of them unique: about linearity,

(See "Is linearity exact?"), quantum gravity (See "Why *quantum*

gravity?") and reversible quantum computers (See "Could we detect other

Everett-worlds?").

Q37 Could we detect other Everett-worlds?

-------------------------------------

Many-Worlds predicts that the Everett-worlds do not interact with each

other because of the presumed linearity of the wave equation. However

worlds *do* interfere with each other, and this enables the theory to

be tested. (Interfere and interact mean different things in quantum

mechanics. Pictorially: Interactions occur at the vertices within

Feynman diagrams. Interference occurs when you add together different

Feynman diagrams with the same external lines.)

According to many-worlds model worlds split with the operation of every

thermodynamically irreversible process. The operation of our minds are

irreversible, carried along for the ride, so to speak, and divide with

the division of worlds. Normally this splitting is undetectable to us.

To detect the splitting we need to set an up experiment where a mind is

split but the world *isn't*. We need a reversible mind.

The general consensus in the literature [11], [16] is that the

experiment to detect other worlds, with reversible minds, will be doable

by, perhaps, about mid-21st century. That date is predicted from two

trendlines, both of which are widely accepted in their own respective

fields. To detect the other worlds you need a reversible machine

intelligence. This requires two things: reversible nanotechnology and

AI.

1) Reversible nanoelectronics. This is an straight-line extrapolation

based upon the log(energy) / logic operation figures, which are

projected to drop below kT in about 2020. This trend has held good for

50 years. An operation that thermally dissipates much less than kT of

energy is reversible. (This implies that frictive or dissipative forces

are insignificant by comparison with other processes.) If more than kT

of energy is released then, ultimately, new degrees of freedom are

activated in the environment and the change becomes irreversible.

2) AI. Complexity of human brain = approx 10^17 bits/sec, based on the

number of neurons (approx 10^10) per human brain, average number of

synapses per neuron (approx 10^4) and the average firing rate (approx

10^3 Hz). Straight line projection of log(cost) / logic operation says

that human level, self-aware machine intelligences will be commercially

available by about 2030-2040. Uncertainty due to present human-level

complexity, but the trend has held good for 40 years.

Assuming that we have a reversible machine intelligence to hand then the

experiment consists of the machine making three reversible measurements

of the spin of an electron (or polarisation of a photon). (1) First it

measures the spin along the z-axis. It records either spin "up" or spin

"down" and notes this in its memory. This measurement acts just to

prepare the electron in a definite state. (2) Second it measures the

spin along the x-axis and records either spin "left" or spin "right" and

notes *this* in its memory. The machine now reverses the entire x-axis

measurement - which must be possible, since physics is effectively

reversible, if we can describe the measuring process physically -

including reversibly erasing its memory of the second measurement. (3)

Third the machine takes a spin measurement along the z-axis. Again the

machine makes a note of the result.

According to the Copenhagen interpretation the original (1) and final

(3) z-axis spin measurements have only a 50% chance of agreeing because

the intervention of the x-axis measurement by the conscious observer

(the machine) caused the collapse of the electron's wavefunction.

According to many-worlds the first and third measurements will *always*

agree, because there was no intermediate wavefunction collapse. The

machine was split into two states or different worlds, by the second

measurement; one where it observed the electron with spin "left"; one

where it observed the electron with spin "right". Hence when the

machine reversed the second measurement these two worlds merged back

together, restoring the original state of the electron 100% of the time.

Only by accepting the existence of the other Everett-worlds is this 100%

restoration explicable.

Q38 Why *quantum* gravity?

----------------------

Many-worlds makes a very definite prediction - gravity must be

quantised, rather than exist as the purely classical background field

of general relativity. Indeed, no one has conclusively directly

detected (classical) gravity waves (as of 1994), although their

existence has been indirectly observed in the slowing of the rotation

of pulsars and binary systems. Some claims have been made for the

detection of gravity waves from supernova explosions in our galaxy, but

these are not generally accepted. Neither has anyone has directly

observed gravitons, which are predicted by quantum gravity, presumably

because of the weakness of the gravitational interaction. Their

existence has been, and is, the subject of much speculation. Should,

in the absence of any empirical evidence, gravity be quantised at all?

Why not treat gravity as a classical force, so that quantum physics in

the vicinity of a mass becomes quantum physics on a curved Riemannian

background? According to many-worlds there *is* empirical evidence for

quantum gravity.

To see why many-worlds predicts that gravity must be quantised, let's

suppose that gravity is not quantised, but remains a classical force.

If all the other worlds that many-worlds predicts exist then their

gravitational presence should be detectable -- we would all share the

same background gravitational metric with our co-existing quantum

worlds. Some of these effects might be undetectable. For instance if

all the parallel Earths shared the same gravitational field small

perturbations in one Earth's orbit from the averaged background orbit

across all the Everett-worlds would damp down, eventually, and remain

undetectable.

However theories of galactic evolution would need considerable

revisiting if many-worlds was true and gravity was not quantised, since,

according to the latest cosmological models, the original density

fluctuations derive from quantum fluctuations in the early universe,

during the inflationary era. These quantum fluctuations lead to the

formation of clusters and super-clusters of galaxies, along with

variations in the cosmic microwave background (detected by Smoots et al)

which vary in location from Everett-cosmos to cosmos. Such fluctuations

could not grow to match the observed pattern if all the density

perturbations across all the parallel Everett-cosmoses were

gravitationally interacting. Stars would bind not only to the observed

galaxies, but also to the host of unobserved galaxies.

A theory of classical gravity also breaks down at the scale of objects

that are not bound together gravitationally. Henry Cavendish, in 1798,

measured the torque produced by the gravitational force on two separated

lead spheres suspended from a torsion fibre in his laboratory to

determine the value of Newton's gravitational constant. Cavendish

varied the positions of other, more massive lead spheres and noted how

the torsion in the suspending fibre varied. Had the suspended lead

spheres been gravitationally influenced by their neighbours, placed in

different positions by parallel Henry Cavendishs in the parallel

Everett-worlds, then the torsion would have been the averaged sum of all

these contributions, which was not observed. In retrospect Cavendish

established that the Everett-worlds are not detectable gravitationally.

More recent experiments where the location of attracting masses were

varied by a quantum random (radioactive) source have confirmed these

findings. [W]

A shared gravitational field would also screw up geo-gravimetric

surveys, which have successfully detected the presence of mountains,

ores and other density fluctuations at the Earth's surface. Such

surveys are not sensitive to the presence of the parallel Everett-Earths

with different geological structures. Ergo the other worlds are not

detectable gravitationally. That gravity must be quantised emerges as

a unique prediction of many-worlds.

[W] Louis Witten _Gravitation: an introduction to current research_

New York, Wiley (1962).

_Essays in honor of Louis Witten on his retirement. Topics on

quantum gravity and beyond_: University of Cincinnati, USA, 3-4

April 1992 / editors, Freydoon Mansouri & Joseph J. Scanio.

Singapore ; River Edge, NJ : World Scientific, c1993 ISBN 981021290

Q39 Is linearity exact?

-------------------

Linearity (of the wavefunction) has been verified to hold true to better

than 1 part in 10^27 [W]. If slight non-linear effects were ever

discovered then the possibility of communication with, or travel to, the

other worlds would be opened up. The existence of parallel Everett-

worlds can be used to argue that physics must be *exactly* linear, that

non-linear effects will never be detected. (See "Is physics linear" for

more about linearity.)

The argument for exactness uses a version of the weak anthropic

principle and proceeds thus: the exploitation of slight non-linear

quantum effects could permit communication with and travel to the other

Everett-worlds. A sufficiently advanced "early" civilisation [F] might

colonise uninhabited other worlds, presumably in an exponentially

spreading fashion. Since the course of evolution is dictated by random

quantum events (mutations, genetic recombination) and environmental

effects (asteroidal induced mass extinctions, etc) it seems inevitable

that in a minority, although still a great many, of these parallel

worlds life on Earth has already evolved sapient-level intelligence and

developed an advanced technology millions or even billions of years ago.

Such early arrivals, under the usual Darwinian pressure to expand, would

spread across the parallel time tracks, if they had the ability,

displacing their less-evolved quantum neighbours.

The fossil record indicates that evolution, in our ancestral lineage,

has proceeded at varying rates at different times. Periods of rapid

development in complexity (eg the Cambrian explosion of 530 millions

years ago or the quadrupling of brain size during the recent Ice Ages)

are interspersed with long periods of much slower development. This

indicates that we are not in the fast lane of evolution, where all the

lucky breaks turned out just right for the early development of

intelligence and technology. Ergo none of the more advanced

civilisations that exist in other worlds have ever been able to cross

from one quantum world to another and interrupt our long, slow

biological evolution.

The simplest explanation is that physics is sufficiently linear to

prevent travel between Everett worlds. If technology is only bounded

by physical law (the Feinberg principle [F]) then linearity would have

to be exact.

[F] Gerald Feinberg. _Physics and Life Prolongation_ Physics Today Vol

19 #11 45 (1966). "A good approximation for such [technological]

predictions is to assume that everything will be accomplished that

does not violate known fundamental laws of science as well as many

things that do violate these laws."

[W] Steven Weinberg _Testing Quantum Mechanics_ Annals of Physics Vol

194 #2 336-386 (1989) and _Dreams of a Final Theory_ (1992)

Q40 Why can't the boundary conditions be updated to reflect my

----------------------------------------------------------

observations in this one world?

-------------------------------

What is lost by this approach is a unique past assigned to each future.

If you time-evolve the world-we-now-see backwards in time you get a

superposition of earlier starting worlds. Similarly if you time evolve

a single (initial) world forward you get a superposition of later

(final) worlds.

For example consider a photon that hits a half-silvered mirror and turns

into a superposition of a transmitted and a reflected photon. If we

time-evolve one of these later states backwards we get not the original

photon, but the original photon plus a "mirror image" of the original

photon. (Try the calculation and see.) Only if we retain both the

reflected and transmitted photons, with the correct relative phase, do

we recover the single incoming photon when we time-reverse everything.

(The mirror image contributions from both the final states have opposite

signs and cancel out, when they are evolved backwards in time to before

the reflection event.)

All the starting states have to have their relative phases coordinated

or correlated just right (ie coherently) or else it doesn't work out.

Needless to say the chances that the initial states should be arranged

coherently just so that they yield the one final observed state are

infinitesimal and in violation of observed thermodynamics, which states,

in one form, that correlations only increase with time.

A1 References and further reading

------------------------------

[1] Hugh Everett III _The Theory of the Universal Wavefunction,

Princeton thesis_ (1956?)

The original and most comprehensive paper on many-worlds.

Investigates and recasts the foundations of quantum theory in

information theoretic terms, before moving on to consider the

nature of interactions, observation, entropy, irreversible

processes, classical objects etc. 138 pages. Only published in

[5].

[2] Hugh Everett III _"Relative State" Formulation of Quantum

Mechanics_ Reviews of Modern Physics Vol 29 #3 454-462, (July

1957) A condensation of [1] focusing on observation.

[3] John A Wheeler _Assessment of Everett's "Relative State"

Formulation of Quantum Theory_, Reviews of Modern Physics Vol

29 #3 463-465 (July 1957) Wheeler was Everett's PhD

supervisor.

[4a] Bryce S DeWitt _Quantum Mechanics and Reality_ Physics Today,

Vol 23 #9 30-40 (September 1970) An early and accurate

popularisations of Everett's work. The April 1971 issue has

reader feedback and DeWitt's responses.

[4b] Bryce S DeWitt _The Many-Universes Interpretation of Quantum

Mechanics_ in _Proceedings of the International School of Physics

"Enrico Fermi" Course IL: Foundations of Quantum Mechanics_

Academic Press (1972)

[5] Bryce S DeWitt, R Neill Graham eds _The many-worlds

Interpretation of Quantum Mechanics_, Contains

[1],[2],[3],[4a],[4b] plus other material. Princeton Series

in Physics, Princeton University Press (1973) ISBN 0-691-

08126-3 (hard cover), 0-691-88131-X (paper back) The

definitive guide to many-worlds, if you can get hold of a

copy, but now (1994) only available xeroxed from microfilm

(ISBN 0-7837-1942-6) from Books On Demand, 300 N Zeeb Road,

Ann Arbor, MI 48106-1346, USA. Tel: +01-313 761 4700 or 800

521 0600.

[15] Frank J Tipler _The many-worlds interpretation of quantum mechanics

in quantum cosmology_ in _Quantum Concepts of Space and Time_ eds

Roger Penrose and Chris Isham, Oxford University Press (1986). Has

a discussion of Ockham's razor.

On quantum theory, measurement and decoherence generally:

[6] John A Wheeler, Wojciech H Zurek eds _Quantum Theory and

Measurement_ Princeton Series in Physics, Princeton University

Press (1983) ISBN 0-691-08316-9. Contains 49 classic

articles, including [2], covering the history and development

of interpretations of quantum theory.

[7a] Wojciech H Zurek _Decoherence and the Transition from the

Quantum to the Classical_, Physics Today, 36-44 (October

1991). The role of thermodynamics and the properties of large

ergodic systems (like the environment) are related to the

decoherence or loss of interference effects between superposed

macrostates.

[7b] Wojciech H Zurek _Preferred States, Predictability, Classicality,

and the Environment-Induced Decoherence_ Progress of Theoretical

Physics, Vol 89 #2 281-312 (1993) A fuller expansion of [7a]

[8] Max Jammer _The Philosophy of Quantum Mechanics_ Wiley, New

York (1974) Almost every interpretation of quantum mechanics

is covered and contrasted. Section 11.6 contains a lucid

review of many-worlds theories.

[9] Bethold-Georg Englert, Marlan O Scully, Herbert Walther _Quantum

optical tests of complementarity_ Nature, Vol 351, 111-116 (9 May

1991). Demonstrates that quantum interference effects are destroyed

by irreversible object-apparatus correlations ("measurement"), not

by Heisenberg's uncertainty principle itself. See also _The

Duality in Matter and Light_ Scientific American, (December 1994)

[10] Murray Gell-Mann, James B Hartle _Quantum Mechanics in the Light

of Quantum Cosmology_ Proceedings of the 3rd International

Symposium on the Foundations of Quantum Mechanics (1989) 321-343.

They accept the Everett's decoherence analysis, and have extended

it further.

Tests of the Everett metatheory:

[11] David Deutsch _Quantum theory as a universal physical theory_

International Journal of Theoretical Physics, Vol 24 #1

(1985). Describes an experiment which tests for the existence

of superpositions of *consciousness (in an AI).

[16] David Deutsch _Three connections between Everett's interpretation

and experiment_ Quantum Concepts of Space and Time, eds Roger

Penrose and Chris Isham, Oxford University Press (1986). Discusses

a testable split observer experiment and quantum computing.

On quantum computers:

[12] David Deutsch _Quantum theory, the Church-Turing principle and the

universal quantum computer_ Proceedings of the Royal Society of

London, Vol. A400, 96-117 (1985).

[13] David Deutsch _Quantum computational networks_ Proceedings of

the Royal Society of London, Vol. A425, 73-90 (1989).

[14] David Deutsch and R. Jozsa _Rapid solution of problems by

quantum computation_ Proceedings of the Royal Society of

London, Vol. A439, 553-558 (1992).

[17] Julian Brown _A Quantum Revolution for Computing_ New Scientist,

pages 21-24, 24-September-1994

A2 Quantum mechanics and Dirac notation

------------------------------------

Note: this is a very inadequate guide. Read a more comprehensive text

ASAP. For a more technical exposition of QM the reader is referred to

the standard textbooks. Here are 3 I recommend:

Richard P Feynman _QED: the strange story of light and matter_ ISBN 0-

14-012505-1. (Requires almost no maths and is universally regarded as

outstanding, despite being about quantum electrodynamics.)

Richard P Feynman _The Feynman Lectures in Physics_ Volume III Addison-

Wesley (1965) ISBN 0-201-02118-8-P. The other volumes are worth reading

too!

Daniel T Gillespie _A Quantum Mechanics Primer: An Elementary

Introduction to the Formal Theory of Non-relativistic Quantum Mechanics_

(Takes an axiomatic, geometric approach and teaches all the Hilbert

space stuff entirely by analogy with Euclidean vector spaces. Not sure

if it is still in print.)

Quantum theory is the most successful theory of physics and chemistry

ever. It accounts for a wide range of phenomena from black body

radiation, atomic structure and chemistry, which were very puzzling

before quantum mechanics was first developed (c1926) in its modern form.

All theories of physics are quantum physics, with whole new fields, like

the semiconductor and microchip technology, based upon the quantum

effects. This FAQ assumes familiarity with the basics of quantum theory

and with the associated "paradoxes" of wave-particle duality. It will

not explain the uncertainty principle or delve into the significance of

non-commuting matrix operators. Only those elements of quantum theory

necessary for an understanding of many-worlds are covered here.

Quantum theory contains, as a central object, an abstract mathematical

entity called the "wavefunction" or "state vector". Determining the

equations that describe its form and evolution with time is an

unfinished part of fundamental theoretical physics. Presently we only

have approximations to some "correct" set of equations, often referred

to whimsically as the Theory of Everything.

The wavefunction, in bracket or Dirac notation, is written as |symbol> ,

where "symbol" labels the object. A dog, for example, might be

represented as |dog> .

A general object, labelled "psi" by convention, is represented as |psi>

and called a "ket". Objects called "bra"s, written < psi|, may be formed

from kets. An arbitrary bra < psi'| and ket |psi> may be combined

together to form the bracket, < psi'|psi> , or inner product, which is

just a fancy way of constructing a complex number. Amongst the

properties of the inner product is:

< psi'|(|psi1> *a_1 + |psi2> *a_2) = < psi'|psi1> *a_1 + < psi'|psi2> *a_2

where the a_i are arbitrary complex numbers. This is what is meant by

saying that the inner product is linear on the right or ket side. It

is made linear on the left-hand or bra side by defining

< psi|psi'> = complex conjugate of < psi'|psi>

Any ket may be expanded as:

|psi> = sum |i> *< i|psi>

i

= |1> *< 1|psi> + |2> *< 2|psi> + ...

where the states |i> form an orthonormal basis, with < i|j> = 1 for i =

j and = 0 otherwise, and where i labels some parameter of the object

(like position or momentum).

The probability amplitudes, < i|psi> , are complex numbers. It is

empirically observed, first noted by Max Born and afterwards called the

Born interpretation, that their magnitudes squared represent the

probability that, upon observation, that the value of the parameter,

labelled by i, will be observed if the system is the state represented

by |psi> . It is also empirically observed that after observing the

system in state |i> that we can henceforth replace the old value of the

wavefunction, |psi> , with the observed value, |i> . This replacement is

known as the collapse of the wavefunction and is the source of much

philosophical controversy. Somehow the act of measurement has selected

out one of the components. This is known as the measurement problem and

it was this phenomenon that Everett addressed.

When a bra, < psi|, is formed from a ket, |psi> , and both are inner

productted together the result, < psi|psi> , is a non-negative real

number, called the norm of the vector. The norm of a vector provides

a basis-independent way of measuring the "volume" of the vector.

The wavefunction for a joint system is built out of products of the

components from the individual subsystems.

For example if the two systems composing the joint system are a cat and

a dog, each of which may be in two states, alive or dead, and the state

of the cat and the dog were *independent* of each other then we could

write the total wavefunction as a product of terms. If

|cat> = |cat alive> * c_a + |cat dead> * c_d

and

|dog> = |dog alive> * d_a + |dog dead> * d_d

then

|dog+cat> = |cat> x|dog> where x = tensor product

= (|cat alive> * c_a + |cat dead> * c_d)

x (|dog alive> * d_a + |dog dead> * d_d)

= |cat alive> x |dog alive> * c_a * d_a

+ |cat alive> x |dog dead> * c_a * d_d

+ |cat dead> x |dog alive> * c_d * d_a

+ |cat dead> x |dog dead> * c_d * d_d

= |cat alive, dog alive> * c_a * d_a

+ |cat alive, dog dead> * c_a * d_d

+ |cat dead, dog alive> * c_d * d_a

+ |cat dead, dog dead> * c_d * d_d

More generally, though, we states of subsystems are not independent of

each other we have to use a more general formula:

|dog+cat> = |cat alive, dog alive> * a_1

(C) Michael Clive Price, February 1995

Permission to copy in its entirety granted for non-commercial purposes.

Contents:

Q0 Why this FAQ?

Q1 Who believes in many-worlds?

Q2 What is many-worlds?

Q3 What are the alternatives to many-worlds?

Q4 What is a "world"?

Q5 What is a measurement?

Q6 Why do worlds split?

What is decoherence?

Q7 When do worlds split?

Q8 When does Schrodinger's cat split?

Q9 What is sum-over-histories?

Q10 What is many-histories?

What is the environment basis?

Q11 How many worlds are there?

Q12 Is many-worlds a local theory?

Q13 Is many-worlds a deterministic theory?

Q14 Is many-worlds a relativistic theory?

What about quantum field theory?

What about quantum gravity?

Q15 Where are the other worlds?

Q16 Is many-worlds (just) an interpretation?

Q17 Why don't worlds fuse, as well as split?

Do splitting worlds imply irreversible physics?

Q18 What retrodictions does many-worlds make?

Q19 Do worlds differentiate or split?

Q20 What is many-minds?

Q21 Does many-worlds violate Ockham's Razor?

Q22 Does many-worlds violate conservation of energy?

Q23 How do probabilities emerge within many-worlds?

Q24 Does many-worlds allow free-will?

Q25 Why am I in this world and not another?

Why does the universe appear random?

Q26 Can wavefunctions collapse?

Q27 Is physics linear?

Could we ever communicate with the other worlds?

Why do I only ever experience one world?

Why am I not aware of the world (and myself) splitting?

Q28 Can we determine what other worlds there are?

Is the form of the Universal Wavefunction knowable?

Q29 Who was Everett?

Q30 What are the problems with quantum theory?

Q31 What is the Copenhagen interpretation?

Q32 Does the EPR experiment prohibit locality?

What about Bell's Inequality?

Q33 Is Everett's relative state formulation the same as many-worlds?

Q34 What is a relative state?

Q35 Was Everett a "splitter"?

Q36 What unique predictions does many-worlds make?

Q37 Could we detect other Everett-worlds?

Q38 Why *quantum* gravity?

Q39 Is linearity exact?

Q41 Why can't the boundary conditions be updated to reflect my

observations in this one world?

A1 References and further reading

A2 Quantum mechanics and Dirac notation

Q0 Why this FAQ?

-------------

This FAQ shows how quantum paradoxes are resolved by the "many-worlds"

interpretation or metatheory of quantum mechanics. This FAQ does not

seek to *prove* that the many-worlds interpretation is the "correct"

quantum metatheory, merely to correct some of the common errors and

misinformation on the subject floating around.

As a physics undergraduate I was struck by the misconceptions of my

tutors about many-worlds, despite that it seemed to resolve all the

paradoxes of quantum theory [A]. The objections raised to many-worlds

were either patently misguided [B] or beyond my ability to assess at the

time [C], which made me suspect (confirmed during my graduate QFT

studies) that the more sophisticated rebuttals were also invalid. I

hope this FAQ will save other investigators from being lead astray by

authoritative statements from mentors.

I have attempted, in the answers, to translate the precise mathematics

of quantum theory into woolly and ambiguous English - I would appreciate

any corrections. In one or two instances I couldn't avoid using some

mathematical (Dirac) notation, in particular in describing the Einstein-

Podolsky-Rosen (EPR) experiment and Bell's Inequality and in showing how

probabilities are derived, so I've included an appendix on the Dirac

notation.

[A] See "Does the EPR experiment prohibit locality?", "What about Bell's

Inequality?" and "When does Schrodinger's cat split?" for how many-

worlds handles the most quoted paradoxes.

[B] Sample objection: "Creation of parallel universes violates energy

conservation/Ockham's razor". (See "Does many-worlds violate

conservation of energy?" and "Does many-worlds violate Ockham's Razor?")

[C] eg "In quantum field theory the wavefunction becomes an operator".

Er, what does that mean? And is this relevant? (See "What about

quantum field theory?")

Q1 Who believes in many-worlds?

----------------------------

"Political scientist" L David Raub reports a poll of 72 of the "leading

cosmologists and other quantum field theorists" about the "Many-Worlds

Interpretation" and gives the following response breakdown [T].

1) "Yes, I think MWI is true" 58%

2) "No, I don't accept MWI" 18%

3) "Maybe it's true but I'm not yet convinced" 13%

4) "I have no opinion one way or the other" 11%

Amongst the "Yes, I think MWI is true" crowd listed are Stephen Hawking

and Nobel Laureates Murray Gell-Mann and Richard Feynman. Gell-Mann and

Hawking recorded reservations with the name "many-worlds", but not with

the theory's content. Nobel Laureate Steven Weinberg is also mentioned

as a many-worlder, although the suggestion is not when the poll was

conducted, presumably before 1988 (when Feynman died). The only "No,

I don't accept MWI" named is Penrose.

The findings of this poll are in accord with other polls, that many-

worlds is most popular amongst scientists who may rather loosely be

described as string theorists or quantum gravitists/cosmologists. It

is less popular amongst the wider scientific community who mostly remain

in ignorance of it.

More detail on Weinberg's views can be found in _Dreams of a Final

Theory_ or _Life in the Universe_ Scientific American (October 1994),

the latter where Weinberg says about quantum theory:

"The final approach is to take the Schrodinger equation seriously

[..description of the measurement process..] In this way, a

measurement causes the history of the universe for practical

purposes to diverge into different non-interfering tracks, one for

each possible value of the measured quantity. [...] I prefer this

last approach"

In the _The Quark and the Jaguar_ and _Quantum Mechanics in the Light

of Quantum Cosmology_ [10] Gell-Mann describes himself as an adherent

to the (post-)Everett interpretation, although his exact meaning is

sometimes left ambiguous.

Steven Hawking is well known as a many-worlds fan and says, in an

article on quantum gravity [H], that measurement of the gravitational

metric tells you which branch of the wavefunction you're in and

references Everett.

Feynman, apart from the evidence of the Raub poll, directly favouring

the Everett interpretation, always emphasized to his lecture students

[F] that the "collapse" process could only be modelled by the

Schrodinger wave equation (Everett's approach).

[F] Jagdish Mehra _The Beat of a Different Drum: The Life and Science

Richard Feynman_

[H] Stephen W Hawking _Black Holes and Thermodynamics_ Physical Review

D Vol 13 #2 191-197 (1976)

[T] Frank J Tipler _The Physics of Immortality_ 170-171

Q2 What is many-worlds?

--------------------

AKA as the Everett, relative-state, many-histories or many-universes

interpretation or metatheory of quantum theory. Dr Hugh Everett, III,

its originator, called it the "relative-state metatheory" or the "theory

of the universal wavefunction" [1], but it is generally called "many-

worlds" nowadays, after DeWitt [4a],[5].

Many-worlds comprises of two assumptions and some consequences. The

assumptions are quite modest:

1) The metaphysical assumption: That the wavefunction does not merely

encode the all the information about an object, but has an

observer-independent objective existence and actually *is* the

object. For a non-relativistic N-particle system the wavefunction

is a complex-valued field in a 3-N dimensional space.

2) The physical assumption: The wavefunction obeys the empirically

derived standard linear deterministic wave equations at all times.

The observer plays no special role in the theory and, consequently,

there is no collapse of the wavefunction. For non-relativistic

systems the Schrodinger wave equation is a good approximation to

reality. (See "Is many-worlds a relativistic theory?" for how the

more general case is handled with quantum field theory or third quantisation.)

The rest of the theory is just working out consequences of the above

assumptions. Measurements and observations by a subject on an object

are modelled by applying the wave equation to the joint subject-object

system. Some consequences are:

1) That each measurement causes a decomposition or decoherence of the

universal wavefunction into non-interacting and mostly non-

interfering branches, histories or worlds. (See "What is

decoherence?") The histories form a branching tree which

encompasses all the possible outcomes of each interaction. (See

"Why do worlds split?" and "When do worlds split?") Every

historical what-if compatible with the initial conditions and

physical law is realised.

2) That the conventional statistical Born interpretation of the

amplitudes in quantum theory is *derived* from within the theory

rather than having to be *assumed* as an additional axiom. (See

"How do probabilities emerge within many-worlds?")

Many-worlds is a re-formulation of quantum theory [1], published in 1957

by Dr Hugh Everett III [2], which treats the process of observation or

measurement entirely within the wave-mechanics of quantum theory, rather

than an input as additional assumption, as in the Copenhagen

interpretation. Everett considered the wavefunction a real object.

Many-worlds is a return to the classical, pre-quantum view of the

universe in which all the mathematical entities of a physical theory are

real. For example the electromagnetic fields of James Clark Maxwell or

the atoms of Dalton were considered as real objects in classical

physics. Everett treats the wavefunction in a similar fashion. Everett

also assumed that the wavefunction obeyed the same wave equation during

observation or measurement as at all other times. This is the central

assumption of many-worlds: that the wave equation is obeyed universally

and at all times.

Everett discovered that the new, simpler theory - which he named the

"relative state" formulation - predicts that interactions between two

(or more) macrosystems typically split the joint system into a

superposition of products of relative states. The states of the

macrosystems are, after the subsystems have jointly interacted,

henceforth correlated with, or dependent upon, each other. Each element

of the superposition - each a product of subsystem states - evolves

independently of the other elements in the superposition. The states

of the macrosystems are, by becoming correlated or entangled with each

other, impossible to understand in isolation from each other and must

be viewed as one composite system. It is no longer possible to speak

the state of one (sub)system in isolation from the other (sub)systems.

Instead we are forced to deal with the states of subsystems *relative*

to each other. Specifying the state of one subsystem leads to a unique

specification of the state (the "relative state") of the other

subsystems. (See "What is a relative state?")

If one of the systems is an observer and the interaction an observation

then the effect of the observation is to split the observer into a

number of copies, each copy observing just one of the possible results

of a measurement and unaware of the other results and all its observer-

copies. Interactions between systems and their environments, including

communication between different observers in the same world, transmits

the correlations that induce local splitting or decoherence into non-

interfering branches of the universal wavefunction. Thus the entire

world is split, quite rapidly, into a host of mutually unobservable but

equally real worlds.

According to many-worlds all the possible outcomes of a quantum

interaction are realised. The wavefunction, instead of collapsing at

the moment of observation, carries on evolving in a deterministic

fashion, embracing all possibilities embedded within it. All outcomes

exist simultaneously but do not interfere further with each other, each

single prior world having split into mutually unobservable but equally

real worlds.

Q3 What are the alternatives to many-worlds?

-----------------------------------------

There is no other quantum theory, besides many-worlds, that is

scientific, in the sense of providing a reductionist model of reality,

and free of internal inconsistencies, that I am aware of. Briefly here

are the defects of the most popular alternatives:

1) Copenhagen Interpretation. Postulates that the observer obeys

different physical laws than the non-observer, which is a return

to vitalism. The definition of an observer varies from one

adherent to another, if present at all. The status of the

wavefunction is also ambiguous. If the wavefunction is real the

theory is non-local (not fatal, but unpleasant). If the

wavefunction is not real then the theory supplies no model of

reality. (See "What are the problems with quantum theory?")

2) Hidden Variables [B]. Explicitly non-local. Bohm accepts that all

the branches of the universal wavefunction exist. Like Everett

Bohm held that the wavefunction is real complex-valued field which

never collapses. In addition Bohm postulated that there were

particles that move under the influence of a non-local "quantum-

potential" derived from the wavefunction (in addition to the

classical potentials which are already incorporated into the

structure of the wavefunction). The action of the quantum-

potential is such that the particles are affected by only one of

the branches of the wavefunction. (Bohm derives what is

essentially a decoherence argument to show this, see section 7,#I

[B]).

The implicit, unstated assumption made by Bohm is that only the

single branch of wavefunction associated with particles can contain

self-aware observers, whereas Everett makes no such assumption.

Most of Bohm's adherents do not seem to understand (or even be

aware of) Everett's criticism, section VI [1], that the hidden-

variable particles are not observable since the wavefunction alone

is sufficient to account for all observations and hence a model of

reality. The hidden variable particles can be discarded, along

with the guiding quantum-potential, yielding a theory isomorphic

to many-worlds, without affecting any experimental results.

[B] David J Bohm _A suggested interpretation of the quantum theory

in terms of "hidden variables" I and II_ Physical Review Vol

85 #2 166-193 (1952)

3) Quantum Logic. Undoubtedly the most extreme of all attempts to

solve the QM measurement problem. Apart from abandoning one or

other of the classical tenets of logic these theories are all

unfinished (presumably because of internal inconsistencies). Also

it is unclear how and why different types of logic apply on

different scales.

4) Extended Probability [M]. A bold theory in which the concept of

probability is "extended" to include complex values [Y]. Whilst

quite daring, I am not sure if this is logically permissable, being

in conflict with the relative frequency notion of probability, in

which case it suffers from the same criticism as quantum logic.

Also it is unclear, to me anyway, how the resultant notion of

"complex probability" differs from the quantum "probability

amplitude" and thus why we are justified in collapsing the complex-

valued probability as if it were a classical, real-valued

probability.

[M] W Muckenheim _A review of extended probabilities_ Physics

Reports Vol 133 339- (1986)

[Y] Saul Youssef _Quantum Mechanics as Complex Probability Theory_

hep-th 9307019

5) Transactional model [C]. Explicitly non-local. An imaginative

theory, based on the Feynman-Wheeler absorber-emitter model of EM,

in which advanced and retarded probability amplitudes combine into

an atemporal "transaction" to form the Born probability density.

It requires that the input and output states, as defined by an

observer, act as emitters and absorbers respectively, but not any

internal states (inside the "black box"), and, consequently,

suffers from the familiar measurement problem of the Copenhagen

interpretation.

If the internal states *did* act as emitters/absorbers then the

wavefunction would collapse, for example, around one of the double

slits (an internal state) in the double slit experiment, destroying

the observed interference fringes. In transaction terminology a

transaction would form between the first single slit and one of the

double slits and another transaction would form between the same

double slit and the point on the screen where the photon lands.

This never observed.

[C] John G Cramer _The transactional interpretation of quantum

mechanics_ Reviews of Modern Physics Vol 58 #3 647-687 (1986)

6) Many-minds. Despite its superficial similarities with many-worlds

this is actually a very unphysical, non-operational theory. (See

"What is many-minds?")

7) Non-linear theories in general. So far no non-linear theory has

any accepted experimental support, whereas many have failed

experiment. (See "Is physics linear?") Many-worlds predicts that

non-linear theories will always fail experiment. (See "Is

linearity exact?")

Q4 What is a "world"?

------------------

Loosely speaking a "world" is a complex, causally connected, partially

or completely closed set of interacting sub-systems which don't

significantly interfere with other, more remote, elements in the

superposition. Any complex system and its coupled environment, with a

large number of internal degrees of freedom, qualifies as a world. An

observer, with internal irreversible processes, counts as a complex

system. In terms of the wavefunction, a world is a decohered branch of

the universal wavefunction, which represents a single macrostate. (See

"What is decoherence?") The worlds all exist simultaneously in a non-

interacting linear superposition.

Sometimes "worlds" are called "universes", but more usually the latter

is reserved the totality of worlds implied by the universal

wavefunction. Sometimes the term "history" is used instead of "world".

(Gell-Mann/Hartle's phrase, see "What is many-histories?").

Q5 What is a measurement?

----------------------

A measurement is an interaction, usually irreversible, between

subsystems that correlates the value of a quantity in one subsystem with

the value of a quantity in the other subsystem. The interaction may

trigger an amplification process within one object or subsystem with

many internal degrees of freedom, leading to an irreversible high-level

change in the same object. If the course of the amplification is

sensitive to the initial interaction then we can designate the system

containing the amplified process as the "measuring apparatus", since the

trigger is sensitive to some (often microphysical) quantity or parameter

of the one of the other subsystems, which we designate the "object"

system. Eg the detection of a charged particle (the object) by a Geiger

counter (the measuring apparatus) leads to the generation of a "click"

(high-level change). The absence of a charged particle does not

generate a click. The interaction is with those elements of the charged

particle's wavefunction that passes *between* the charged detector

plates, triggering the amplification process (an irreversible electron

cascade or avalanche), which is ultimately converted to a click.

A measurement, by this definition, does not require the presence of an

conscious observer, only of irreversible processes.

Q6 Why do worlds split?

---------------------

What is decoherence?

--------------------

Worlds, or branches of the universal wavefunction, split when different

components of a quantum superposition "decohere" from each other [7a],

[7b], [10]. Decoherence refers to the loss of coherency or absence of

interference effects between the elements of the superposition. For two

branches or worlds to interfere with each other all the atoms, subatomic

particles, photons and other degrees of freedom in each world have to

be in the same state, which usually means they all must be in the same

place or significantly overlap in both worlds, simultaneously.

For small microscopic systems it is quite possible for all their atomic

components to overlap at some future point. In the double slit

experiment, for instance, it only requires that the divergent paths of

the diffracted particle overlap again at some space-time point for an

interference pattern to form, because only the single particle has been

split.

Such future coincidence of positions in all the components is virtually

impossible in more complex, macroscopic systems because all the

constituent particles have to overlap with their counterparts

simultaneously. Any system complex enough to be described by

thermodynamics and exhibit irreversible behaviour is a system complex

enough to exclude, for all practical purposes, any possibility of future

interference between its decoherent branches. An irreversible process

is one in, or linked to, a system with a large number of internal,

unconstrained degrees of freedom. Once the irreversible process has

started then alterations of the values of the many degrees of freedom

leaves an imprint which can't be removed. If we try to intervene to

restore the original status quo the intervention causes more disruption

elsewhere.

In QM jargon we say that the components (or vectors in the underlying

Hilbert state space) have become permanently orthogonal due to the

complexity of the systems increasing the dimensionality of the vector

space, where each unconstrained degree of freedom contributes a

dimension to the state vector space. In a high dimension space almost

all vectors are orthogonal, without any significant degree of overlap.

Thus vectors for complex systems, with a large number of degrees of

freedom, naturally decompose into mutually orthogonal components which,

because they can never significantly interfere again, are unaware of

each other. The complex system, or world, has split into different,

mutually unobservable worlds.

According to thermodynamics each activated degree of freedom acquires

kT energy. This works the other way around as well: the release of

approximately kT of energy increases the state-space dimensionality.

Even the quite small amounts of energy released by an irreversible

frictive process are quite large on this scale, increasing the size of

the associated Hilbert space.

Contact between a system and a heat sink is equivalent to increasing the

dimensionality of the state space, because the description of the system

has to be extended to include all parts of the environment in causal

contact with it. Contact with the external environment is a very

effective destroyer of coherency. (See "What is the environment

basis?")

Q7 When do worlds split?

---------------------

Worlds irrevocably "split" at the sites of measurement-like interactions

associated with thermodynamically irreversible processes. (See "What

is a measurement?") An irreversible process will always produce

decoherence which splits worlds. (See "Why do worlds split?", "What is

decoherence?" and "When does Schrodinger's cat split?" for a concrete

example.)

In the example of a Geiger counter and a charged particle after the

particle has passed the counter one world contains the clicked counter

and that portion of the particle's wavefunction which passed though the

detector. The other world contains the unclicked counter with the

particle's wavefunction with a "shadow" cast by the counter taken out

of the particle's wavefunction.

The Geiger counter splits when the amplification process became

irreversible, before the click is emitted. (See "What is a

measurement?") The splitting is local (originally in the region of the

Geiger counter in our example) and is transmitted causally to more

distant systems. (See "Is many-worlds a local theory?" and "Does the

EPR experiment prohibit locality?") The precise moment/location of the

split is not sharply defined due to the subjective nature of

irreversibility, but can be considered complete when much more than kT

of energy has been released in an uncontrolled fashion into the

environment. At this stage the event has become irreversible.

In the language of thermodynamics the amplification of the charged

particle's presence by the Geiger counter is an irreversible event.

These events have caused the decoherence of the different branches of

the wavefunction. (See "What is decoherence?" and "Why do worlds

split?") Decoherence occurs when irreversible macro-level events take

place and the macrostate description of an object admits no single

description. (A macrostate, in brief, is the description of an object

in terms of accessible external characteristics.)

The advantage of linking the definition of worlds and the splitting

process with thermodynamics is the splitting process becomes

irreversible and only permits forward-time-branching, following the

increase with entropy. (See "Why don't worlds fuse, as well as split?")

Like all irreversible processes, though, there are exceptions even at

the coarse-grained level and worlds will occasionally fuse. A

necessary, although not sufficient, precondition for fusing is for all

records, memories etc that discriminate between the pre-fused worlds or

histories be lost. This is not a common occurrence.

Q8 When does Schrodinger's cat split?

----------------------------------

Consider Schrodinger's cat. A cat is placed in a sealed box with a

device that releases a lethal does of cyanide if a certain radioactive

decay is detected. For simplicity we'll imagine that the box, whilst

closed, completely isolates the cat from its environment. After a while

an investigator opens the box to see if the cat is alive or dead.

According to the Copenhagen Interpretation the cat was neither alive nor

dead until the box was opened, whereupon the wavefunction of the cat

collapsed into one of the two alternatives (alive or dead cat). The

paradox, according to Schrodinger, is that the cat presumably knew if

it was alive *before* the box was opened. According to many-worlds the

device was split into two states (cyanide released or not) by the

radioactive decay, which is a thermodynamically irreversible process

(See "When do worlds split?" and "Why do worlds split?"). As the

cyanide/no-cyanide interacts with the cat the cat is split into two

states (dead or alive). From the surviving cat's point of view it

occupies a different world from its deceased copy. The onlooker is

split into two copies only when the box is opened and they are altered

by the states of the cat.

The cat splits when the device is triggered, irreversibly. The

investigator splits when they open the box. The alive cat has no idea

that investigator has split, any more than it is aware that there is a

dead cat in the neighbouring split-off world. The investigator can

deduce, after the event, by examining the cyanide mechanism, or the

cat's memory, that the cat split prior to opening the box.

Q9 What is sum-over-histories?

---------------------------

The sum-over-histories or path-integral formalism of quantum mechanics

was developed by Richard Feynman in the 1940s [F] as a third

interpretation of quantum mechanics, alongside Schrodinger's wave

picture and Heisenberg's matrix mechanics, for calculating transition

amplitudes. All three approaches are mathematically equivalent, but the

path-integral formalism offers some interesting additional insights into

many-worlds.

In the path-integral picture the wavefunction of a single particle at

(x',t') is built up of contributions of all possible paths from (x,t),

where each path's contribution is weighted by a (phase) factor of

exp(i*Action[path]/hbar) * wavefunction at (x,t), summed, in turn, over

all values of x. The Action[path] is the time-integral of the

lagrangian (roughly: the lagrangian equals kinetic minus the potential

energy) along the path from (x,t) to (x',t'). The final expression is

thus the sum or integral over all paths, irrespective of any classical

dynamical constraints. For N-particle systems the principle is the

same, except that the paths run through a 3-N space.

In the path-integral approach every possible path through configuration

space makes a contribution to the transition amplitude. From this point

of view the particle explores every possible intermediate configuration

between the specified start and end states. For this reason the path-

integral technique is often referred to as "sum-over-histories". Since

we do not occupy a privileged moment in history it is natural to wonder

if alternative histories are contributing equally to transition

amplitudes in the future, and that each possible history has an equal

reality. Perhaps we shouldn't be surprised that Feynman is on record

as believing in many-worlds. (See "Who believes in many-worlds?") What

is surprising is that Everett developed his many-worlds theory entirely

from the Schrodinger viewpoint without any detectable influence from

Feynman's work, despite Feynman and Everett sharing the same Princeton

thesis supervisor, John A Wheeler.

Feynman developed his path-integral formalism further during his work

on quantum electrodynamics, QED, in parallel with Schwinger and Tomonoga

who had developed a less visualisable form of QED. Dyson showed that

these approaches were all equivalent. Feynman, Schwinger and Tomonoga

were awarded the 1965 Physics Nobel Prize for this work. Feynman's

approach was to show how any process, with defined in (initial) and out

(final) states, can be represented by a series of (Feynman) diagrams,

which allow for the creation, exchange and annihilation of particles.

Each Feynman diagram represents a different contribution to the complete

transition amplitude, provided that the external lines map onto the

required boundary initial and final conditions (the defined in and out

states). QED became the prototype for all the other, later, field

theories like electro-weak and quantum chromodynamics.

[F] Richard P Feynman _Space-time approach to non-relativistic quantum

mechanics_ Reviews of Modern Physics, Vol 20: 267-287 (1948)

Q10 What is many-histories?

-----------------------

What is the environment basis?

------------------------------

There is considerable linkage between thermodynamics and many-worlds,

explored in the "decoherence" views of Zurek [7a], [7b] and Gell-Mann

and Hartle [10], Everett [1], [2] and others [4b]. (See "What is

decoherence?")

Gell-Mann and Hartle, in particular, have extended the role of

decoherence in defining the Everett worlds, or "histories" in their

nomenclature. They call their approach the "many-histories" approach,

where each "coarse-grained or classical history" is associated with a

unique time-ordered sequence of sets of irreversible events, including

measurements, records, observations and the like. (See "What is a

measurement?") Fine-grained histories effectively relax the

irreversible criterion. Mathematically the many-histories approach is

isomorphic to Everett's many-worlds.

The worlds split or "decohere" from each other when irreversible events

occur. (See "Why do worlds split?" and "When do worlds split?".)

Correspondingly many-histories defines a multiply-connected hierarchy

of classical histories where each classical history is a "child" of any

parent history which has only a subset of the child defining

irreversible events and a parent of any history which has a superset of

such events. Climbing up the tree from child to parent moves to

progressively coarser grained consistent histories until eventually the

top is reached where the history has *no* defining events (and thus

consistent with everything!). This is Everett's universal wavefunction.

The bottom of the coarse-grained tree terminates with the maximally

refined set of decohering histories. The classical histories each have

a probability assigned to them and probabilities are additive in the

sense that the sum of the probabilities associated a set classical

histories is equal to the probability associated with the unique parent

history defined by the set. (Below the maximally refined classical

histories are the fine grained or quantum histories, where probabilities

are no longer additive and different histories significantly interfere

with each other. The bottom level consists of complete microstates,

which fully specified states.)

The decoherence approach is useful in considering the effect of the

environment on a system. In many ways the environment, acting as a heat

sink, can be regarded as performing a succession of measurement-like

interactions upon any system, inducing associated system splits. All

the environment basis is is a basis chosen so as to minimise the cross-

basis interference terms. It makes any real-worlds calculation easy,

since the cross terms are so small, but it does not *uniquely* select

a basis, just eliminates a large number.

Q11 How many worlds are there?

--------------------------

The thermodynamic Planck-Boltzmann relationship, S = k*log(W), counts

the branches of the wavefunction at each splitting, at the lowest,

maximally refined level of Gell-Mann's many-histories tree. (See "What

is many-histories?") The bottom or maximally divided level consists of

microstates which can be counted by the formula W = exp (S/k), where S

= entropy, k = Boltzmann's constant (approx 10^-23 Joules/Kelvin) and

W = number of worlds or macrostates. The number of coarser grained

worlds is lower, but still increasing with entropy by the same ratio,

ie the number of worlds a single world splits into at the site of an

irreversible event, entropy dS, is exp(dS/k). Because k is very small

a great many worlds split off at each macroscopic event.

Q12 Is many-worlds a local theory?

------------------------------

The simplest way to see that the many-worlds metatheory is a local

theory is to note that it requires that the wavefunction obey some

relativistic wave equation, the exact form of which is currently

unknown, but which is presumed to be locally Lorentz invariant at all

times and everywhere. This is equivalent to imposing the requirement

that locality is enforced at all times and everywhere. Ergo many-worlds

is a local theory.

Another way of seeing this is examine how macrostates evolve.

Macrostates descriptions of objects evolve in a local fashion. Worlds

split as the macrostate description divides inside the light cone of the

triggering event. Thus the splitting is a local process, transmitted

causally at light or sub-light speeds. (See "Does the EPR experiment

prohibit locality?" and "When do worlds split?")

Q13 Is many-worlds a deterministic theory?

--------------------------------------

Yes, many-worlds is a deterministic theory, since the wavefunction obeys

a deterministic wave equation at all times. All possible outcomes of

a measurement or interaction (See "What is a measurement?") are embedded

within the universal wavefunction although each observer, split by each

observation, is only aware of single outcomes due to the linearity of

the wave equation. The world appears indeterministic, with the usual

probabilistic collapse of the wavefunction, but at the objective level,

which includes all outcomes, determinism is restored.

Some people are under the impression that the only motivation for many-

worlds is a desire to return to a deterministic theory of physics. This

is not true. As Everett pointed out, the objection with the standard

Copenhagen interpretation is not the indeterminism per se, but that

indeterminism occurs only with the intervention of an observer, when the

wavefunction collapses. (See "What is the Copenhagen interpretation?")

Q14 Is many-worlds a relativistic theory?

-------------------------------------

What about quantum field theory?

--------------------------------

What about quantum gravity?

---------------------------

It is trivial to relativise many-worlds, at least to the level of

special relativity. All relativistic theories of physics are quantum

theories with linear wave equations. There are three or more stages to

developing a fully relativised quantum field theory:

First quantisation: the wavefunction of an N particle system is a

complex field which evolves in 3N dimensions as the solution to either

the many-particle Schrodinger, Dirac or Klein-Gordon or some other wave

equation. External forces applied to the particles are represented or

modelled via a potential, which appears in the wave equation as a

classical, background field.

Second quantisation: AKA (relativistic) quantum field theory (QFT)

handles the creation and destruction of particles by quantising the

classical fields and potentials as well as the particles. Each particle

corresponds to a field, in QFT, and becomes an operator. Eg the

electromagnetic field's particle is the photon. The wavefunction of a

collection of particles/fields exists in a Fock space, where the number

of dimensions varies from component to component, corresponding to the

indeterminacy in the particle number. Many-worlds has no problems

incorporating QFT, since a theory (QFT) is not altered by a metatheory

(many-worlds), which makes statements *about* the theory.

Third quantisation: AKA quantum gravity. The gravitational metric is

quantised, along with (perhaps) the topology of the space-time manifold.

The role of time plays a less central role, as might be expected, but

the first and second quantisation models are as applicable as ever for

modelling low-energy events. The physics of this is incomplete,

including some thorny, unresolved conceptual issues, with a number of

proposals (strings, supersymmetry, supergravity...) for ways forward,

but the extension required by many-worlds is quite trivial since the

mathematics would be unchanged.

One of the original motivations of Everett's scheme was to provide a

system for quantising the gravitational field to yield a quantum

cosmology, permitting a complete, self-contained description of the

universe. Indeed many-words actually *requires* that gravity be

quantised, in contrast to other interpretations which are silent about

the role of gravity. (See "Why *quantum* gravity?")

Q15 Where are the other worlds?

---------------------------

Non-relativistic quantum mechanics and quantum field theory are quite

unambiguous: the other Everett-worlds occupy the same space and time as

we do.

The implicit question is really, why aren't we aware of these other

worlds, unless they exist "somewhere" else? To see why we aren't aware

of the other worlds, despite occupying the same space-time, see "Why do

I only ever experience one world?" Some popular accounts describe the

other worlds as splitting off into other, orthogonal, dimensions. These

dimensions are the dimensions of Hilbert space, not the more familiar

space-time dimensions.

The situation is more complicated, as we might expect, in theories of

quantum gravity (See "What about quantum gravity?"), because gravity can

be viewed as perturbations in the space-time metric. If we take a

geometric interpretation of gravity then we can regard differently

curved space-times, each with their own distinct thermodynamic history,

as non-coeval. In that sense we only share the same space-time manifold

with other worlds with a (macroscopically) similar mass distribution.

Whenever the amplification of a quantum-scale interaction effects the

mass distribution and hence space-time curvature the resultant

decoherence can be regarded as splitting the local space-time manifold

into discrete sheets.

Q16 Is many-worlds (just) an interpretation?

----------------------------------------

No, for four reasons:

First, many-worlds makes predictions that differ from the other so-

called interpretations of quantum theory. Interpretations do not make

predictions that differ. (See "What unique predictions does many-worlds

make?") In addition many-worlds retrodicts a lot of data that has no

other easy interpretation. (See "What retrodictions does many-worlds

make?")

Second, the mathematical structure of many-worlds is not isomorphic to

other formulations of quantum mechanics like the Copenhagen

interpretation or Bohm's hidden variables. The Copenhagen

interpretation does not contain those elements of the wavefunction that

correspond to the other worlds. Bohm's hidden variables contain

particles, in addition to the wavefunction. Neither theory is

isomorphic to each other or many-worlds and are not, therefore, merely

rival "interpretations".

Third, there is no scientific, reductionistic alternative to many-

worlds. All the other theories fail for logical reasons. (See "Is

there any alternative theory?")

Fourth, the interpretative side of many-worlds, like the subjective

probabilistic elements, are derived from within the theory, rather than

added to it by assumption, as in the conventional approach. (See "How

do probabilities emerge within many-worlds?")

Many-worlds should really be described as a theory or, more precisely,

a metatheory, since it makes statements that are applicable about a

range of theories. Many-worlds is the unavoidable implication of any

quantum theory which obeys some type of linear wave equation. (See "Is

physics linear?")

Q17 Why don't worlds fuse, as well as split?

---------------------------------------

Do splitting worlds imply irreversible physics?

-----------------------------------------------

This is really a question about why thermodynamics works and what is the

origin of the "arrow of time", rather than about many-worlds.

First, worlds almost never fuse, in the forward time direction, but

often divide, because of the way we have defined them. (See "What is

decoherence?", "When do worlds split?" and "When do worlds split?") The

Planck-Boltzmann formula for the number of worlds (See "How many worlds

are there?") implies that where worlds to fuse together then entropy

would decrease, violating the second law of thermodynamics.

Second, this does not imply that irreversible thermodynamics is

incompatible with reversible (or nearly so) microphysics. The laws of

physics are reversible (or CPT invariant, more precisely) and fully

compatible with the irreversibility of thermodynamics, which is solely

due to the boundary conditions (the state of universe at some chosen

moment) imposed by the Big Bang or whatever we chose to regard as the

initial conditions. (See "Why can't the boundary conditions be updated

to reflect my observations in this one world?")

Q18 What retrodictions does many-worlds make?

-----------------------------------------

A retrodiction occurs when already gathered data is accounted for by a

later theoretical advance in a more convincing fashion. The advantage

of a retrodiction over a prediction is that the already gathered data

is more likely to be free of experimenter bias. An example of a

retrodiction is the perihelion shift of Mercury which Newtonian

mechanics plus gravity was unable, totally, to account for whilst

Einstein's general relativity made short work of it.

Many-worlds retrodicts all the peculiar properties of the (apparent)

wavefunction collapse in terms of decoherence. (See "What is

decoherence?", "Can wavefunctions collapse?", "When do worlds split?"

& "Why do worlds split?") No other quantum theory has yet accounted for

this behaviour scientifically. (See "What are the alternatives to many-

worlds?")

Q19 Do worlds differentiate or split?

---------------------------------

Can we regard the separate worlds that result from a measurement-like

interaction (See "What is a measurement?") as having previous existed

distinctly and merely differentiated, rather than the interaction as

having split one world into many? This is definitely not permissable

in many-worlds or any theory of quantum theory consistent with

experiment. Worlds do not exist in a quantum superposition

independently of each other before they decohere or split. The

splitting is a physical process, grounded in the dynamical evolution of

the wave vector, not a matter of philosophical, linguistic or mental

convenience (see "Why do worlds split?" and "When do worlds split?")

If you try to treat the worlds as pre-existing and separate then the

maths and probabilistic behaviour all comes out wrong. Also the

differentiation theory isn't deterministic, in contradiction to the wave

equations which are deterministic, since many-minds says that:

AAAAAAAAAAAAAAABBBBBBBBBBBBBBB --------------> time

(Worlds differentiate)

AAAAAAAAAAAAAAACCCCCCCCCCCCCCC

occurs, rather than:

BBBBBBBBBBBBBBB

B

AAAAAAAAAAAAAA (Worlds split)

C

CCCCCCCCCCCCCCC

according to many-worlds.

This false differentiation model, at the mental level, seems favoured

by adherents of many-minds. (See "What is many-minds?")

Q20 What is many-minds?

------------------

Many-minds proposes, as an extra fundamental axiom, that an infinity of

separate minds or mental states be associated with each single brain

state. When the single physical brain state is split into a quantum

superposition by a measurement (See "What is a measurement?") the

associated infinity of minds are thought of as differentiating rather

than splitting. The motivation for this brain-mind dichotomy seems

purely to avoid talk of minds splitting and talk instead about the

differentiation of pre-existing separate mental states. There is no

physical basis for this interpretation, which is incapable of an

operational definition. Indeed the differentiation model for physical

systems is specifically not permitted in many-worlds. Many-minds seems

to be proposing that minds follow different rules than matter. (See "Do

worlds differentiate or split?")

In many-minds the role of the conscious observer is accorded special

status, with its fundamental axiom about infinities of pre-existing

minds, and as such is philosophically opposed to many-worlds, which

seeks to remove the observer from any privileged role in physics.

(Many-minds was co-invented by David Albert, who has, apparently, since

abandoned it. See Scientific American July 1992 page 80 and contrast

with Albert's April '94 Scientific American article.)

The two theories must not be confused.

Q21 Does many-worlds violate Ockham's Razor?

---------------------------------------

William of Ockham, 1285-1349(?) English philosopher and one of the

founders of logic, proposed a maxim for judging theories which says that

hypotheses should not be multiplied beyond necessity. This is known as

Ockham's razor and is interpreted, today, as meaning that to account for

any set of facts the simplest theories are to be preferred over more

complex ones. Many-worlds is viewed as unnecessarily complex, by some,

by requiring the existence of a multiplicity of worlds to explain what

we see, at any time, in just one world.

This is to mistake what is meant by "complex". Here's an example.

Analysis of starlight reveals that starlight is very similar to faint

sunlight, both with spectroscopic absorption and emission lines.

Assuming the universality of physical law we are led to conclude that

other stars and worlds are scattered, in great numbers, across the

cosmos. The theory that "the stars are distant suns" is the simplest

theory and so to be preferred by Ockham's Razor to other geocentric

theories.

Similarly many-worlds is the simplest and most economical quantum theory

because it proposes that same laws of physics apply to animate observers

as has been observed for inanimate objects. The multiplicity of worlds

predicted by the theory is not a weakness of many-worlds, any more than

the multiplicity of stars are for astronomers, since the non-interacting

worlds emerge from a simpler theory.

(As an historical aside it is worth noting that Ockham's razor was also

falsely used to argue in favour of the older heliocentric theories

*against* Galileo's notion of the vastness of the cosmos. The notion

of vast empty interstellar spaces was too uneconomical to be believable

to the Medieval mind. Again they were confusing the notion of vastness

with complexity [15].)

Q22 Does many-worlds violate conservation of energy?

------------------------------------------------

First, the law conservation of energy is based on observations within

each world. All observations within each world are consistent with

conservation of energy, therefore energy is conserved.

Second, and more precisely, conservation of energy, in QM, is formulated

in terms of weighted averages or expectation values. Conservation of

energy is expressed by saying that the time derivative of the expected

energy of a closed system vanishes. This statement can be scaled up to

include the whole universe. Each world has an approximate energy, but

the energy of the total wavefunction, or any subset of, involves summing

over each world, weighted with its probability measure. This weighted

sum is a constant. So energy is conserved within each world and also

across the totality of worlds.

One way of viewing this result - that observed conserved quantities are

conserved across the totality of worlds - is to note that new worlds are

not created by the action of the wave equation, rather existing worlds

are split into successively "thinner" and "thinner" slices, if we view

the probability densities as "thickness".

Q23 How do probabilities emerge within many-worlds?

-----------------------------------------------

Everett demonstrated [1], [2] that observations in each world obey all

the usual conventional statistical laws predicted by the probabilistic

Born interpretation, by showing that the Hilbert space's inner product

or norm has a special property which allows us to makes statements about

the worlds where quantum statistics break down. The norm of the vector

of the set of worlds where experiments contradict the Born

interpretation ("non-random" or "maverick" worlds) vanishes in the limit

as the number of probabilistic trials goes to infinity, as is required

by the frequentist definition of probability. Hilbert space vectors

with zero norm don't exist (see below), thus we, as observers, only

observe the familiar, probabilistic predictions of quantum theory.

Everett-worlds where probability breaks down are never realised.

Strictly speaking Everett did not prove that the usual statistical laws

of the Born interpretation would hold true for all observers in all

worlds. He merely showed that no other statistical laws could hold true

and asserted the vanishing of the Hilbert space "volume" or norm of the

set of "maverick" worlds. DeWitt later published a longer *derivation*

of Everett's assertion [4a], [4b], closely based on an earlier,

independent demonstration by Hartle [H]. What Everett asserted, and

DeWitt/Hartle derived, is that the collective norm of all the maverick

worlds, as the number of trials goes to infinity, vanishes. Since the

only vector in a Hilbert space with vanishing norm is the null vector

(a defining axiom of Hilbert spaces) this is equivalent to saying that

non-randomness is never realised. All the worlds obey the usual Born

predictions of quantum theory. That's why we never observe the

consistent violation of the usual quantum statistics, with, say, heat

flowing from a colder to a hotter macroscopic object. Zero-probability

events never happen.

Of course we have to assume that the wavefunction is a Hilbert space

vector in the first place but, since this assumption is also made in the

standard formulation, this is not a weakness of many-worlds since we are

not trying to justify all the axioms of the conventional formulation of

QM, merely those that relate to probabilities and collapse of the

wavefunction.

In more detail the steps are:

1) Construct the tensor product of N identical systems in state |psi> ,

according to the usual rules for Hilbert space composition

(repeated indices summed):

|PSI_N> = |psi_1> *|psi_2> *...... |psi_N> where

|psi_j> = jth system prepared in state |psi>

= |i_j> < i_j|psi> (ie the amplitude of the ith eigenstate

is independent of which system it is in)

so that

|PSI_N> = |i_1> |i_2> ...|i_N> < i_1|psi> < i_2|psi> ...< i_N|psi>

2) Quantify the deviation from the "expected" Born-mean for each

component of |PSI_N> with respect to the above |i_1> |i_2> ...|i_N>

basis by counting the number of occurrences of the ith

eigenstate/N. Call this number RF(i). Define the Born-deviation

as D = sum(i)( (RF(i) - |< i|psi> |^2)^2 ). Thus D, loosely

speaking, for each N length sequence, quantifies by how much the

particular sequence differs from the Born-expectation.

3) Sort out terms in the expansion of |PSI_N> according to whether D

is less/equal to (.LE.) or greater than (.GT.) E, where E is a

real, positive constant. Collecting terms together we get:

|PSI_N> = |N,"D.GT.E"> + |N,"D.LE.E">

worlds worlds

for which for which

D > E D < = E

4) What DeWitt showed was that:

< N,"D.GT.E"|N,"D.GT.E"> < 1/(NE) (proof in appendix of [4b])

Thus as N goes to infinity the right-hand side vanishes for all

positive values of E. (This mirrors the classical "frequentist"

position on probability which states that if event i occurs with

probability p(i) then the proportion of N trials with outcome i

approaches p(i)/N as N goes to infinity [H]. This has the

immediate benefit that sum(i) p(i) = 1.) The norm of |N,"D.LE.E"> ,

by contrast, approaches 1 as N goes to infinity.

Note: this property of D is not shared by other definitions, which

is why we haven't investigated them. If, say, we had defined, in

step 2), A = sum(i)( (RF(i) - |< i|psi> |)^2 ), so that A measures

the deviation from |psi|, rather than |psi|^2, then we find that

< A> does not have the desired property of vanishing as N goes to

infinity.

5) The norm of the collection of non-random worlds vanishes and

therefore must be identified with some complex multiple of the null

vector.

6) Since (by assumption) the state vector faithfully models reality

then the null vector cannot represent any element of reality, since

it can be added to (or subtracted from) any other state vector

without altering the other state vector.

7) Ergo the non-random worlds are not realised, without making any

additional physical assumptions, such as the imposition of a measure.

Note: no finite sequence of outcomes is excluded from happening,

since the concept of probability and randomness only becomes

precise only as N goes to infinity [H]. Thus, heat *could* be

observed to flow from a cold to hotter object, but we might have

to wait a very long time before observing it. What *is* excluded

is the possibility of this process going on forever.

The emergence of Born-style probabilities as a consequence of the

mathematical formalism of the theory, without any extra interpretative

assumptions, is another reason why the Everett metatheory should not be

regarded as just an interpretation. (See "Is many-worlds (just) an

interpretation?") The interpretative elements are forced by the

mathematical structure of the axioms of Hilbert space.

[H] JB Hartle _Quantum Mechanics of Individual Systems_ American

Journal of Physics Vol 36 #8 704-712 (1968) Hartle has

investigated the N goes to infinity limit in more detail and more

generally. He shows that the relative frequency operator, RF,

obeys RF(i) |psi_1> |psi_2> .... = |< i|psi> |^2 |psi_1> |psi_2> ....,

for a normed state. Hartle regarded his derivation as essentially

the same as Everett's, despite being derived independently.

Q24 Does many-worlds allow free-will?

---------------------------------

Many-Worlds, whilst deterministic on the objective universal level, is

indeterministic on the subjective level so the situation is certainly

no better or worse for free-will than in the Copenhagen view.

Traditional Copenhagen indeterministic quantum mechanics only slightly

weakens the case for free-will. In quantum terms each neuron is an

essentially classical object. Consequently quantum noise in the brain

is at such a low level that it probably doesn't often alter, except very

rarely, the critical mechanistic behaviour of sufficient neurons to

cause a decision to be different than we might otherwise expect. The

consensus view amongst experts is that free-will is the consequence of

the mechanistic operation of our brains, the firing of neurons,

discharging across synapses etc and fully compatible with the

determinism of classical physics. Free-will is the inability of an

intelligent, self-aware mechanism to predict its own future actions due

to the logical impossibility of any mechanism containing a complete

internal model of itself rather than any inherent indeterminism in the

mechanism's operation.

Nevertheless, some people find that with all possible decisions being

realised in different worlds that the prima facia situation for free-

will looks quite difficult. Does this multiplicity of outcomes destroy

free-will? If both sides of a choice are selected in different worlds

why bother to spend time weighing the evidence before selecting? The

answer is that whilst all decisions are realised, some are realised more

often than others - or to put to more precisely each branch of a

decision has its own weighting or measure which enforces the usual laws

of quantum statistics.

This measure is supplied by the mathematical structure of the Hilbert

spaces. Every Hilbert space has a norm, constructed from the inner

product, - which we can think of as analogous to a volume - which

weights each world or collection of worlds. A world of zero volume is

never realised. Worlds in which the conventional statistical

predictions consistently break down have zero volume and so are never

realised. (See "How do probabilities emerge within many-worlds?")

Thus our actions, as expressions of our will, correlate with the weights

associated with worlds. This, of course, matches our subjective

experience of being able to exercise our will, form moral judgements and

be held responsible for our actions.

Q25 Why am I in this world and not another?

---------------------------------------

Why does the universe appear random?

------------------------------------

These are really the same questions. Consider, for a moment, this

analogy:

Suppose Fred has his brain divided in two and transplanted into two

different cloned bodies (this is a gedanken operation! [*]). Let's

further suppose that each half-brain regenerates to full functionality

and call the resultant individuals Fred-Left and Fred-Right. Fred-Left

can ask, why did I end up as Fred-Left? Similarly Fred-Right can ask,

why did I end up as Fred-Right? The only answer possible is that there

was *no* reason. From Fred's point of view it is a subjectively

*random* choice which individual "Fred" ends up as. To the surgeon the

whole process is deterministic. To both the Freds it seems random.

Same with many-worlds. There was no reason "why" you ended up in this

world, rather than another - you end up in all the quantum worlds. It

is a subjectively random choice, an artifact of your brain and

consciousness being split, along with the rest of the world, that makes

our experiences seem random. The universe is, in effect, performing

umpteen split-brain operations on us all the time. The randomness

apparent in nature is a consequence of the continual splitting into

mutually unobservable worlds.

(See "How do probabilities emerge within many-worlds?" for how the

subjective randomness is moderated by the usual probabilistic laws of

QM.)

[*] Split brain experiments *were* performed on epileptic patients

(severing the corpus callosum, one of the pathways connecting the

cerebral hemispheres, moderated epileptic attacks). Complete

hemispherical separation was discontinued when testing of the patients

revealed the presence of two distinct consciousnesses in the same skull.

So this analogy is only partly imaginary.

Q26 Can wavefunctions collapse?

---------------------------

Many-worlds predicts/retrodicts that wavefunctions appear to collapse

(See "Does the EPR experiment prohibit locality?"), when measurement-

like interactions (See "What is a measurement?") and processes occur via

a process called decoherence (See "What is decoherence?"), but claims

that the wavefunction does not *actually* collapse but continues to

evolve according to the usual wave-equation. If a *mechanism* for

collapse could be found then there would be no need for many-worlds.

The reason why we doubt that collapse takes place is because no one has

ever been able to devise a physical mechanism that could trigger it.

The Copenhagen interpretation posits that observers collapse

wavefunctions, but is unable to define "observer". (See "What is the

Copenhagen interpretation?" and "Is there any alternative theory?")

Without a definition of observer there can be no mechanism triggered by

their presence.

Another popular view is that irreversible processes trigger collapse.

Certainly wavefunctions *appear* to collapse whenever irreversible

processes are involved. And most macroscopic, day-to-day events are

irreversible. The problem is, as with positing observers as a cause of

collapse, that any irreversible process is composed of a large number

of sub-processes that are each individually reversible. To invoke

irreversibility as a *mechanism* for collapse we would have to show that

new *fundamental* physics comes into play for complex systems, which is

quite absent at the reversible atom/molecular level. Atoms and

molecules are empirically observed to obey some type of wave equation.

We have no evidence for an extra mechanism operating on more complex

systems. As far as we can determine complex systems are described by

the quantum-operation of their simpler components interacting together.

(Note: chaos, complexity theory, etc, do not introduce new fundamental

physics. They still operate within the reductionistic paradigm -

despite what many popularisers say.)

Other people have attempted to construct non-linear theories so that

microscopic systems are approximately linear and obey the wave equation,

whilst macroscopic systems are grossly non-linear and generates

collapse. Unfortunately all these efforts have made additional

predictions which, when tested, have failed. (See "Is physics linear?")

(Another reason for doubting that any collapse actually takes place is

that the collapse would have to propagate instantaneously, or in some

space-like fashion, otherwise the same particle could be observed more

than once at different locations. Not fatal, but unpleasant and

difficult to reconcile with special relativity and some conservation

laws.)

The simplest conclusion, which is to be preferred by Ockham's razor, is

that wavefunctions just *don't* collapse and that all branches of the

wavefunction exist.

Q27 Is physics linear?

------------------

Could we ever communicate with the other worlds?

------------------------------------------------

Why do I only ever experience one world?

----------------------------------------

Why am I not aware of the world (and myself) splitting?

-------------------------------------------------------

According to our present knowledge of physics whilst it is possible to

detect the presence of other nearby worlds, through the existence of

interference effects, it is impossible travel to or communicate with

them. Mathematically this corresponds to an empirically verified

property of all quantum theories called linearity. Linearity implies

that the worlds can interfere with each other with respect to a

external, unsplit, observer or system but the interfering worlds can't

influence each other in the sense that an experimenter in one of the

worlds can arrange to communicate with their own, already split-off,

quantum copies in other worlds.

Specifically, the wave equation is linear, with respect to the

wavefunction or state vector, which means that given any two solutions

of the wavefunction, with identical boundary conditions, then any linear

combination of the solutions is another solution. Since each component

of a linear solution evolves with complete indifference as to the

presence or absence of the other terms/solutions then we can conclude

that no experiment in one world can have any effect on another

experiment in another world. Hence no communication is possible between

quantum worlds. (This type of linearity mustn't be confused with the

evident non-linearity of the equations with respect to the *fields*.)

Non communication between the splitting Everett-worlds also explains why

we are not aware of any splitting process, since such awareness needs

communication between worlds. To be aware of the world splitting you

would have to be receiving sensory information from, and thereby effect

by the reverse process, more than one world. This would enable

communication between worlds, which is forbidden by linearity. Ergo,

we are not aware of any splitting precisely because we are split into

non-interfering copies along with the rest of the world.

See also "Is linearity exact?"

Q28 Can we determine what other worlds there are?

---------------------------------------------

Is the form of the Universal Wavefunction knowable?

---------------------------------------------------

To calculate the form of the universal wavefunction requires not only

a knowledge of its dynamics (which we have a good approximation to, at

the moment) but also of the boundary conditions. To actually calculate

the form of the universal wavefunction, and hence make inferences about

*all* the embedded worlds, we would need to know the boundary conditions

as well. We are presently restricted to making inferences about those

worlds with which have shared a common history up to some point, which

have left traces (records, fossils, etc) still discernable today. This

restricts us to a subset of the extant worlds which have shared the same

boundary conditions with us. The further we probe back in time the less

we know of the boundary conditions and the less we can know of the

universal wavefunction.

This limits us to drawing conclusions about a restricted subset of the

worlds - all the worlds which are consistent with our known history up

to a some common moment, before we diverged. The flow of historical

events is, according to chaos/complexity theory/thermodynamics, very

sensitive to amplification of quantum-scale uncertainty and this

sensitivity is a future-directed one-way process. We can make very

reliable deductions about the past from the knowledge future/present but

we can't predict the future from knowledge the past/present.

Thermodynamics implies that the future is harder to predict than the

past is to retrodict. Books get written about this "arrow of time"

problem but, for the purposes of this discussion, we'll accept the

thermodynamic origin of time's arrow is as given. The fossil and

historical records say that dinosaurs and Adolf Hitler once existed but

have less to say about the future.

Consider the effects of that most quantum of activities, Brownian

motion, on the conception of individuals and the knock-on effects on the

course of history. Mutation itself, one of the sources of evolutionary

diversity, is a quantum event. For an example of the

biological/evolutionary implications see Stephen Jay Gould's book

"Wonderful Life" for an popular exploration of the thesis that the path

of evolution is driven by chance. According to Gould evolutionary

history forms an enormously diverse tree of possible histories - all

very improbable - with our path being selected by chance. According to

many-worlds all these other possibilities are realised. Thus there are

worlds in which Hitler won WW-II and other worlds in which the dinosaurs

never died out. We can be as certain of this as we are that Hitler and

the dinosaurs once existed in our own past.

Whether or not we can ever determine the totality of the universal

wavefunction is an open question. If Steven Hawking's work on the no-

boundary-condition condition is ultimately successful, or it emerges

from some theory of everything, and many think it will, then the actual

form of the *total* wavefunction could, in principle, we determined from

a complete knowledge of physical law itself.

Q29 Who was Everett?

----------------

Hugh Everett III (1930-1982) did his undergraduate study in chemical

engineering at the Catholic University of America. Studying von

Neumann's and Bohm's textbooks as part of his graduate studies, under

Wheeler, in mathematical physics at Princeton University in the 1950s

he became dissatisfied (like many others before and since) with the

collapse of the wavefunction. He developed, during discussions with

Charles Misner and Aage Peterson (Bohr' assistant, then visiting

Princeton), his "relative state" formulation. Wheeler encouraged his

work and preprints were circulated in January 1956 to a number of

physicists. A condensed version of his thesis was published as a paper

to "The Role of Gravity in Physics" conference held at the University

of North Carolina, Chapel Hill, in January 1957.

Everett was discouraged by the lack of response from others,

particularly Bohr, whom he flew to Copenhagen to meet but got the

complete brush-off from. Leaving physics after completing his Ph.D,

Everett worked as a defense analyst at the Weapons Systems Evaluation

Group, Pentagon and later became a private contractor, apparently quite

successfully for he became a multimillionaire. In 1968 Everett worked

for the Lambda Corp. His published papers during this period cover

things like optimising resource allocation and, in particular,

maximising kill rates during nuclear-weapon campaigns.

From 1968 onwards Bryce S DeWitt, one of the 1957 Chapel Hill conference

organisers, but better known as one of the founders of quantum gravity,

successfully popularised Everett's relative state formulation as the

"many-worlds interpretation" in a series of articles [4a],[4b],[5].

Sometime in 1976-9 Everett visited Austin, Texas, at Wheeler or DeWitt's

invitation, to give some lectures on QM. The strict no-smoking rule in

the auditorium was relaxed for Everett (a chain smoker); the only

exception ever. Everett, apparently, had a very intense manner,

speaking acutely and anticipating questions after a few words. Oh yes,

a bit of trivia, he drove a Cadillac with horns.

With the steady growth of interest in many-worlds in the late 1970s

Everett planned returning to physics to do more work on measurement in

quantum theory, but died of a heart attack in 1982. Survived by his

wife.

Q30 What are the problems with quantum theory?

------------------------------------------

Quantum theory is the most successful description of microscopic systems

like atoms and molecules ever, yet often it is not applied to larger,

classical systems, like observers or the entire universe. Many

scientists and philosophers are unhappy with the theory because it seems

to require a fundamental quantum-classical divide. Einstein, for

example, despite his early contributions to the subject, was never

reconciled with assigning to the act of observation a physical

significance, which most interpretations of QM require. This

contradicts the reductionist ethos that, amongst other things,

observations should emerge only as a consequence of an underlying

physical theory and not be present at the axiomatic level, as they are

in the Copenhagen interpretation. Yet the Copenhagen interpretation

remains the most popular interpretation of quantum mechanics amongst the

broad scientific community. (See "What is the Copenhagen

interpretation?")

Q31 What is the Copenhagen interpretation?

--------------------------------------

An unobserved system, according to the Copenhagen interpretation of

quantum theory, evolves in a deterministic way determined by a wave

equation. An observed system changes in a random fashion, at the moment

of observation, instantaneously, with the probability of any particular

outcome given by the Born formula. This is known as the "collapse" or

"reduction" of the wavefunction. The problems with this approach are:

(1) The collapse is an instantaneous process across an extended

region ("non-local") which is non-relativistic.

(2) The idea of an observer having an effect on microphysics is

repugnant to reductionism and smacks of a return to pre-scientific

notions of vitalism. Copenhagenism is a return to the old vitalist

notions that life is somehow different from other matter, operating

by different laws from inanimate matter. The collapse is triggered

by an observer, yet no definition of what an "observer" is

available, in terms of an atomic scale description, even in

principle.

For these reasons the view has generally been adopted that the

wavefunction associated with an object is not a real "thing", but merely

represents our *knowledge* of the object. This approach was developed

by Bohr and others, mainly at Copenhagen in the late 1920s. When we

perform an measurement or observation of an object we acquire new

information and so adjust the wavefunction as we would boundary

conditions in classical physics to reflect this new information. This

stance means that we can't answer questions about what's actually

happening, all we can answer is what will be the probability of a

particular result if we perform a measurement. This makes a lot of

people very unhappy since it provides no model for the object.

It should be added that there are other, less popular, interpretations

of quantum theory, but they all have their own drawbacks, which are

widely reckoned more severe. Generally speaking they try to find a

mechanism that describes the collapse process or add extra physical

objects to the theory, in addition to the wavefunction. In this sense

they are more complex. (See "Is there any alternative theory?")

Q32 Does the EPR experiment prohibit locality?

------------------------------------------

What about Bell's Inequality?

-----------------------------

The EPR experiment is widely regarded as the definitive gedanken

experiment for demonstrating that quantum mechanics is non-local

(requires faster-than-light communication) or incomplete. We shall see

that it implies neither.

The EPR experiment was devised, in 1935, by Einstein, Podolsky and Rosen

to demonstrate that quantum mechanics was incomplete [E]. Bell, in

1964, demonstrated that any hidden variables theory, to replicate the

predictions of QM, must be non-local [B]. QM predicts strong

correlations between separated systems, stronger than any local hidden

variables theory can offer. Bell encoded this statistical prediction

in the form of some famous inequalities that apply to any type of EPR

experiment. Eberhard, in the late 1970s, extended Bell's inequalities

to cover any local theory, with or without hidden variables. Thus the

EPR experiment plays a central role in sorting and testing variants of

QM. All the experiments attempting to test EPR/Bell's inequality to

date (including Aspect's in the 1980s [As]) are in line with the

predictions of standard QM - hidden variables are ruled out. Here is

the paradox of the EPR experiment. It seems to imply that any physical

theory must involve faster-than-light "things" going on to maintain

these "spooky" action-at-a-distance correlations and yet still be

compatible with relativity, which seems to forbid FTL.

Let's examine the EPR experiment in more detail.

So what did EPR propose? The original proposal was formulated in terms

of correlations between the positions and momenta of two once-coupled

particles. Here I shall describe it in terms of the spin (a type of

angular momentum intrinsic to the particle) of two electrons. [In this

treatment I shall ignore the fact that electrons always form

antisymmetric combinations. This does not alter the results but does

simplify the maths.] Two initially coupled electrons, with opposed

spins that sum to zero, move apart from each other across a distance of

perhaps many light years, before being separately detected, say, by me

on Earth and you on Alpha Centauri with our respective measuring

apparatuses. The EPR paradox results from noting that if we choose the

same (parallel) spin axes to measure along then we will observe the two

electrons' spins to be anti-parallel (ie when we communicate we find

that the spin on our electrons are correlated and opposed). However if

we choose measurement spin axes that are perpendicular to each other

then there is no correlation between electron spins. Last minute

alterations in a detector's alignment can create or destroy correlations

across great distances. This implies, according to some theorists, that

faster-than-light influences maintain correlations between separated

systems in some circumstances and not others.

Now let's see how many-worlds escapes from this dilemma.

The initial state of the wavefunction of you, me and the electrons and

the rest of the universe may be written:

|psi> = |me> |electrons> |you> |rest of universe>

on in on

Earth deep Alpha

space Centauri

or more compactly, ignoring the rest of the universe, as:

|psi> = |me,electrons,you>

And

|me> represents me on Earth with my detection apparatus.

|electrons> = (|+,-> - |-,+> )/sqrt(2)

represents a pair electrons, with the first electron travelling

towards Earth and the second electron travelling towards Alpha

Centauri.

|+> represents an electron with spin in the +z direction

|-> represents an electron with spin in the -z direction

It is an empirically established fact, which we just have to accept,

that we can relate spin states in one direction to spin states in other

directions like so (where "i" is the sqrt(-1)):

|left> = (|+> - |-> )/sqrt(2) (electron with spin in -x direction)

|right> = (|+> + |-> )/sqrt(2) (electron with spin in +x direction)

|up> = (|+> + |-> i)/sqrt(2) (electron with spin in +y direction)

|down> = (|+> - |-> i)/sqrt(2) (electron with spin in -y direction)

and inverting:

|+> = (|right> + |left> )/sqrt(2) = (|up> + |down> )/sqrt(2)

|-> = (|right> - |left> )/sqrt(2) = (|down> - |up> )i/sqrt(2)

(In fancy jargon we say that the spin operators in different directions

form non-commuting observables. I shall eschew such obfuscations.)

Working through the algebra we find that for pairs of electrons:

|+,-> - |-,+> = |left,right> - |right,left>

= |up,down> i - |down,up> i

I shall assume that we are capable of either measuring spin in the x or

y direction, which are both perpendicular the line of flight of the

electrons. After having measured the state of the electron my state is

described as one of either:

|me[l]> represents me + apparatus + records having measured

and recorded the x-axis spin as "left"

|me[r]> ditto with the x-axis spin as "right"

|me[u]> ditto with the y-axis spin as "up"

|me[d]> ditto with the y-axis spin as "down"

Similarly for |you> on Alpha Centauri. Notice that it is irrelevant

*how* we have measured the electron's spin. The details of the

measurement process are irrelevant. (See "What is a measurement?" if

you're not convinced.) To model the process it is sufficient to assume

that there is a way, which we have further assumed does not disturb the

electron. (The latter assumption may be relaxed without altering the

results.)

To establish familiarity with the notation let's take the state of the

initial wavefunction as:

|psi> _1 = |me,left,up,you>

/ \

/ \

first electron in left second electron in up state

state heading towards heading towards you on

me on Earth Alpha Centauri

After the electrons arrive at their detectors, I measure the spin

along the x-axis and you along the y-axis. The wavefunction evolves

into |psi> _2:

local

|psi> _1 ============> |psi> _2 = |me[l],left,up,you[u]>

observation

which represents me having recorded my electron on Earth with spin left

and you having recorded your electron on Alpha Centauri with spin up.

The index in []s indicates the value of the record. This may be held

in the observer's memory, notebooks or elsewhere in the local

environment (not necessarily in a readable form). If we communicate our

readings to each other the wavefunctions evolves into |psi> _3:

remote

|psi> _2 ============> |psi> _3 = |me[l,u],left,up,you[u,l]>

communication

where the second index in []s represents the remote reading communicated

to the other observer and being recorded locally. Notice that the

results both agree with each other, in the sense that my record of your

result agrees with your record of your result. And vice versa. Our

records are consistent.

That's the notation established. Now let's see what happens in the more

general case where, again,:

|electrons> = (|+,-> - |-,+> )/sqrt(2).

First we'll consider the case where you and I have previously arranged

to measure the our respective electron spins along the same x-axis.

Initially the wavefunction of the system of electrons and two

experimenters is:

|psi> _1

= |me,electrons,you>

= |me> (|left,right> - |right,left> )|you> /sqrt(2)

= |me,left,right,you> /sqrt(2)

- |me,right,left,you> /sqrt(2)

Neither you or I are yet unambiguously split.

Suppose I perform my measurement first (in some time frame). We get

|psi> _2

= (|me[l],left,right> - |me[r],right,left> )|you> /sqrt(2)

= |me[l],left,right,you> /sqrt(2)

- |me[r],right,left,you> /sqrt(2)

My measurement has split me, although you, having made no measurement,

remain unsplit. In the full expansion the terms that correspond to you

are identical.

After the we each have performed our measurements we get:

|psi> _3

= |me[l],left,right,you[r]> /sqrt(2)

- |me[r],right,left,you[l]> /sqrt(2)

The observers (you and me) have been split (on Earth and Alpha Centauri)

into relative states (or local worlds) which correlate with the state

of the electron. If we now communicate over interstellar modem (this

will take a few years since you and I are separated by light years, but

no matter). We get:

|psi> _4

= |me[l,r],left,right,you[r,l]> /sqrt(2)

- |me[r,l],right,left,you[l,r]> /sqrt(2)

The world corresponding to the 2nd term in the above expansion, for

example, contains me having seen my electron with spin right and knowing

that you have seen your electron with spin left. So we jointly agree,

in both worlds, that spin has been conserved.

Now suppose that we had prearranged to measure the spins along different

axes. Suppose I measure the x-direction spin and you the y-direction

spin. Things get a bit more complex. To analyse what happens we need

to decompose the two electrons along their respective spin axes.

|psi> _1 =

|me,electrons,you>

= |me> (|+,-> - |-,+> )|you> /sqrt(2)

= |me> (

(|right> +|left> )i(|down> -|up> )

- (|right> -|left> )(|down> +|up> )

) |you> /2*sqrt(2)

= |me> (

|right> (|down> -|up> )i

+ |left> (|down> -|up> )i

- |right> (|down> +|up> )

+ |left> (|down> +|up> )

) |you> /2*sqrt(2)

= |me> (

|right,down> (i-1) - |right,up> (1+i)

+ |left,up> (1-i) + |left,down> (1+i)

) |you> /2*sqrt(2)

= (

+ |me,right,down,you> (i-1)

- |me,right,up,you> (i+1)

+ |me,left,up,you> (1-i)

+ |me,left,down,you> (1+i)

) /2*sqrt(2)

So after you and I make our local observations we get:

|psi> _2 =

(

+ |me[r],right,down,you[d]> (i-1)

- |me[r],right,up,you[u]> (i+1)

+ |me[l],left,up,you[u]> (1-i)

+ |me[l],left,down,you[d]> (1+i)

) /2*sqrt(2)

Each term realises a possible outcome of the joint measurements. The

interesting thing is that whilst we can decompose it into four terms

there are only two states for each observer. Looking at myself, for

instance, we can rewrite this in terms of states relative to *my*

records/memories.

|psi> _2 =

(

|me[r],right> ( |down,you[d]> (i-1) - |up,you[u]> (i+1) )

+ |me[l],left> ( |up,you[u]> (1-i) + |down,you[d]> (1+i) )

) /2*sqrt(2)

And we see that there are only two copies of *me*. Equally we can

rewrite the expression in terms of states relative to *your*

records/memory.

|psi> _2 =

(

( |me[l],left> (1-i) - |me[r],right> (i+1) ) |up,you[u]>

+ ( |me[r],right> (i-1) + |me[l],left> (1+i) ) |down,you[d]>

) /2*sqrt(2)

And see that there are only two copies of *you*. We have each been

split into two copies, each perceiving a different outcome for our

electron's spin, but we have not been split by the measurement of the

remote electron's spin.

*After* you and I communicate our readings to each other, more than four

years later, we get:

|psi> _3 =

(

+ |me[r,d],right,down,you[d,r]> (i-1)

- |me[r,u],right,up,you[u,r]> (i+1)

+ |me[l,u],left,up,you[u,l]> (1-i)

+ |me[l,d],left,down,you[d,l]> (1+i)

) /2*sqrt(2)

The decomposition into four worlds is forced and unambiguous after

communication with the remote system. Until the two observers

communicated their results to each other they were each unsplit by each

others' measurements, although their own local measurements had split

themselves. The splitting is a local process that is causally

transmitted from system to system at light or sub-light speeds. (This

is a point that Everett stressed about Einstein's remark about the

observations of a mouse, in the Copenhagen interpretation, collapsing

the wavefunction of the universe. Everett observed that it is the mouse

that's split by its observation of the rest of the universe. The rest

of the universe is unaffected and unsplit.)

When all communication is complete the worlds have finally decomposed

or decohered from each other. Each world contains a consistent set of

observers, records and electrons, in perfect agreement with the

predictions of standard QM. Further observations of the electrons will

agree with the earlier ones and so each observer, in each world, can

henceforth regard the electron's wavefunction as having collapsed to

match the historically recorded, locally observed values. This

justifies our operational adoption of the collapse of the wavefunction

upon measurement, without having to strain our credibility by believing

that it actually happens.

To recap. Many-worlds is local and deterministic. Local measurements

split local systems (including observers) in a subjectively random

fashion; distant systems are only split when the causally transmitted

effects of the local interactions reach them. We have not assumed any

non-local FTL effects, yet we have reproduced the standard predictions

of QM.

So where did Bell and Eberhard go wrong? They thought that all theories

that reproduced the standard predictions must be non-local. It has been

pointed out by both Albert [A] and Cramer [C] (who both support

different interpretations of QM) that Bell and Eberhard had implicity

assumed that every possible measurement - even if not performed - would

have yielded a *single* definite result. This assumption is called

contra-factual definiteness or CFD [S]. What Bell and Eberhard really

proved was that every quantum theory must either violate locality *or*

CFD. Many-worlds with its multiplicity of results in different worlds

violates CFD, of course, and thus can be local.

Thus many-worlds is the only local quantum theory in accord with the

standard predictions of QM and, so far, with experiment.

[A] David Z Albert, _Bohm's Alternative to Quantum Mechanics_

Scientific American (May 1994)

[As] Alain Aspect, J Dalibard, G Roger _Experimental test of Bell's

inequalities using time-varying analyzers_ Physical Review Letters

Vol 49 #25 1804 (1982).

[C] John G Cramer _The transactional interpretation of quantum

mechanics_ Reviews of Modern Physics Vol 58 #3 647-687 (1986)

[B] John S Bell: _On the Einstein Podolsky Rosen paradox_ Physics 1

#3 195-200 (1964).

[E] Albert Einstein, Boris Podolsky, Nathan Rosen: _Can

quantum-mechanical description of physical reality be considered

complete?_ Physical Review Vol 41 777-780 (15 May 1935).

[S] Henry P Stapp _S-matrix interpretation of quantum-theory_ Physical

Review D Vol 3 #6 1303 (1971)

Q33 Is Everett's relative state formulation the same as many-worlds?

----------------------------------------------------------------

Yes, Everett's formulation of the relative state metatheory is the same

as many-worlds, but the language has evolved a lot from Everett's

original article [2] and some of his work has been extended, especially

in the area of decoherence. (See "What is decoherence?") This has

confused some people into thinking that Everett's "relative state

metatheory" and DeWitt's "many-worlds interpretation" are different

theories.

Everett [2] talked about the observer's memory sequences splitting to

form a "branching tree" structure or the state of the observer being

split by a measurement. (See "What is a measurement?") DeWitt

introduced the term "world" for describing the split states of an

observer, so that we now speak of the observer's world splitting during

the measuring process. The maths is the same, but the terminology is

different. (See "What is a world?")

Everett tended to speak in terms of the measuring apparatus being split

by the measurement, into non-interfering states, without presenting a

detailed analysis of *why* a measuring apparatus was so effective at

destroying interference effects after a measurement, although the topics

of orthogonality, amplification and irreversibility were covered. (See

"What is a measurement?", "Why do worlds split?" and "When do worlds

split?") DeWitt [4b], Gell-Mann and Hartle [10], Zurek [7a] and others

have introduced the terminology of "decoherence" (See "What is

decoherence?") to describe the role of amplification and irreversibility

within the framework of thermodynamics.

Q34 What is a relative state?

-------------------------

The relative state of something is the state that something is in,

*conditional* upon, or relative to, the state of something else. What

the heck does that mean? It means, amongst other things, that states

in the same Everett-world are all states relative to each other. (See

"Quantum mechanics and Dirac notation" for more precise details.)

Let's take the example of Schrodinger's cat and ask what is the relative

state of the observer, after looking inside the box? The relative state

of the observer (either "saw cat dead" or "saw cat alive") is

conditional upon the state of the cat (either "dead" or "alive").

Another example: the relative state of the last name of the President

of the Unites States, in 1995, is "Clinton". Relative to what?

Relative to you and me, in this world. In some other worlds it will be

"Bush", "Smith", etc ....... Each possibility is realised in some world

and it is the relative state of the President's name, relative to the

occupants of that world.

According to Everett almost all states are relative states. Only the

state of the universal wavefunction is not relative but absolute.

Q35 Was Everett a "splitter"?

-------------------------

Some people believe that Everett eschewed all talk all splitting or

branching observers in his original relative state formulation [2].

This is contradicted by the following quote from [2]:

[...] Thus with each succeeding observation (or interaction),

the observer state "branches" into a number of different

states. Each branch represents a different outcome of the

measurement and the *corresponding* eigenstate for the object-

system state. All branches exist simultaneously in the

superposition after any given sequence of observations.[#]

The "trajectory" of the memory configuration of an observer

performing a sequence of measurements is thus not a linear

sequence of memory configurations, but a branching tree, with

all possible outcomes existing simultaneously in a final

superposition with various coefficients in the mathematical

model. [...]

[#] Note added in proof-- In reply to a preprint of this

article some correspondents have raised the question of the

"transition from possible to actual," arguing that in

"reality" there is-as our experience testifies-no such

splitting of observers states, so that only one branch can

ever actually exist. Since this point may occur to other

readers the following is offered in explanation.

The whole issue of the transition from "possible" to

"actual" is taken care of in the theory in a very simple way-

there is no such transition, nor is such a transition

necessary for the theory to be in accord with our experience.

From the viewpoint of the theory *all* elements of a

superposition (all "branches") are "actual," none are any more

"real" than the rest. It is unnecessary to suppose that all

but one are somehow destroyed, since all separate elements of

a superposition individually obey the wave equation with

complete indifference to the presence or absence ("actuality"

or not) of any other elements. This total lack of effect of

one branch on another also implies that no observer will ever

be aware of any "splitting" process.

Arguments that the world picture presented by this theory

is contradicted by experience, because we are unaware of any

branching process, are like the criticism of the Copernican

theory that the mobility of the earth as a real physical fact

is incompatible with the common sense interpretation of nature

because we feel no such motion. In both case the arguments

fails when it is shown that the theory itself predicts that

our experience will be what it in fact is. (In the Copernican

case the addition of Newtonian physics was required to be able

to show that the earth's inhabitants would be unaware of any

motion of the earth.)

Q36 What unique predictions does many-worlds make?

----------------------------------------------

A prediction occurs when a theory suggests new phenomena. Many-worlds

makes at least three predictions, two of them unique: about linearity,

(See "Is linearity exact?"), quantum gravity (See "Why *quantum*

gravity?") and reversible quantum computers (See "Could we detect other

Everett-worlds?").

Q37 Could we detect other Everett-worlds?

-------------------------------------

Many-Worlds predicts that the Everett-worlds do not interact with each

other because of the presumed linearity of the wave equation. However

worlds *do* interfere with each other, and this enables the theory to

be tested. (Interfere and interact mean different things in quantum

mechanics. Pictorially: Interactions occur at the vertices within

Feynman diagrams. Interference occurs when you add together different

Feynman diagrams with the same external lines.)

According to many-worlds model worlds split with the operation of every

thermodynamically irreversible process. The operation of our minds are

irreversible, carried along for the ride, so to speak, and divide with

the division of worlds. Normally this splitting is undetectable to us.

To detect the splitting we need to set an up experiment where a mind is

split but the world *isn't*. We need a reversible mind.

The general consensus in the literature [11], [16] is that the

experiment to detect other worlds, with reversible minds, will be doable

by, perhaps, about mid-21st century. That date is predicted from two

trendlines, both of which are widely accepted in their own respective

fields. To detect the other worlds you need a reversible machine

intelligence. This requires two things: reversible nanotechnology and

AI.

1) Reversible nanoelectronics. This is an straight-line extrapolation

based upon the log(energy) / logic operation figures, which are

projected to drop below kT in about 2020. This trend has held good for

50 years. An operation that thermally dissipates much less than kT of

energy is reversible. (This implies that frictive or dissipative forces

are insignificant by comparison with other processes.) If more than kT

of energy is released then, ultimately, new degrees of freedom are

activated in the environment and the change becomes irreversible.

2) AI. Complexity of human brain = approx 10^17 bits/sec, based on the

number of neurons (approx 10^10) per human brain, average number of

synapses per neuron (approx 10^4) and the average firing rate (approx

10^3 Hz). Straight line projection of log(cost) / logic operation says

that human level, self-aware machine intelligences will be commercially

available by about 2030-2040. Uncertainty due to present human-level

complexity, but the trend has held good for 40 years.

Assuming that we have a reversible machine intelligence to hand then the

experiment consists of the machine making three reversible measurements

of the spin of an electron (or polarisation of a photon). (1) First it

measures the spin along the z-axis. It records either spin "up" or spin

"down" and notes this in its memory. This measurement acts just to

prepare the electron in a definite state. (2) Second it measures the

spin along the x-axis and records either spin "left" or spin "right" and

notes *this* in its memory. The machine now reverses the entire x-axis

measurement - which must be possible, since physics is effectively

reversible, if we can describe the measuring process physically -

including reversibly erasing its memory of the second measurement. (3)

Third the machine takes a spin measurement along the z-axis. Again the

machine makes a note of the result.

According to the Copenhagen interpretation the original (1) and final

(3) z-axis spin measurements have only a 50% chance of agreeing because

the intervention of the x-axis measurement by the conscious observer

(the machine) caused the collapse of the electron's wavefunction.

According to many-worlds the first and third measurements will *always*

agree, because there was no intermediate wavefunction collapse. The

machine was split into two states or different worlds, by the second

measurement; one where it observed the electron with spin "left"; one

where it observed the electron with spin "right". Hence when the

machine reversed the second measurement these two worlds merged back

together, restoring the original state of the electron 100% of the time.

Only by accepting the existence of the other Everett-worlds is this 100%

restoration explicable.

Q38 Why *quantum* gravity?

----------------------

Many-worlds makes a very definite prediction - gravity must be

quantised, rather than exist as the purely classical background field

of general relativity. Indeed, no one has conclusively directly

detected (classical) gravity waves (as of 1994), although their

existence has been indirectly observed in the slowing of the rotation

of pulsars and binary systems. Some claims have been made for the

detection of gravity waves from supernova explosions in our galaxy, but

these are not generally accepted. Neither has anyone has directly

observed gravitons, which are predicted by quantum gravity, presumably

because of the weakness of the gravitational interaction. Their

existence has been, and is, the subject of much speculation. Should,

in the absence of any empirical evidence, gravity be quantised at all?

Why not treat gravity as a classical force, so that quantum physics in

the vicinity of a mass becomes quantum physics on a curved Riemannian

background? According to many-worlds there *is* empirical evidence for

quantum gravity.

To see why many-worlds predicts that gravity must be quantised, let's

suppose that gravity is not quantised, but remains a classical force.

If all the other worlds that many-worlds predicts exist then their

gravitational presence should be detectable -- we would all share the

same background gravitational metric with our co-existing quantum

worlds. Some of these effects might be undetectable. For instance if

all the parallel Earths shared the same gravitational field small

perturbations in one Earth's orbit from the averaged background orbit

across all the Everett-worlds would damp down, eventually, and remain

undetectable.

However theories of galactic evolution would need considerable

revisiting if many-worlds was true and gravity was not quantised, since,

according to the latest cosmological models, the original density

fluctuations derive from quantum fluctuations in the early universe,

during the inflationary era. These quantum fluctuations lead to the

formation of clusters and super-clusters of galaxies, along with

variations in the cosmic microwave background (detected by Smoots et al)

which vary in location from Everett-cosmos to cosmos. Such fluctuations

could not grow to match the observed pattern if all the density

perturbations across all the parallel Everett-cosmoses were

gravitationally interacting. Stars would bind not only to the observed

galaxies, but also to the host of unobserved galaxies.

A theory of classical gravity also breaks down at the scale of objects

that are not bound together gravitationally. Henry Cavendish, in 1798,

measured the torque produced by the gravitational force on two separated

lead spheres suspended from a torsion fibre in his laboratory to

determine the value of Newton's gravitational constant. Cavendish

varied the positions of other, more massive lead spheres and noted how

the torsion in the suspending fibre varied. Had the suspended lead

spheres been gravitationally influenced by their neighbours, placed in

different positions by parallel Henry Cavendishs in the parallel

Everett-worlds, then the torsion would have been the averaged sum of all

these contributions, which was not observed. In retrospect Cavendish

established that the Everett-worlds are not detectable gravitationally.

More recent experiments where the location of attracting masses were

varied by a quantum random (radioactive) source have confirmed these

findings. [W]

A shared gravitational field would also screw up geo-gravimetric

surveys, which have successfully detected the presence of mountains,

ores and other density fluctuations at the Earth's surface. Such

surveys are not sensitive to the presence of the parallel Everett-Earths

with different geological structures. Ergo the other worlds are not

detectable gravitationally. That gravity must be quantised emerges as

a unique prediction of many-worlds.

[W] Louis Witten _Gravitation: an introduction to current research_

New York, Wiley (1962).

_Essays in honor of Louis Witten on his retirement. Topics on

quantum gravity and beyond_: University of Cincinnati, USA, 3-4

April 1992 / editors, Freydoon Mansouri & Joseph J. Scanio.

Singapore ; River Edge, NJ : World Scientific, c1993 ISBN 981021290

Q39 Is linearity exact?

-------------------

Linearity (of the wavefunction) has been verified to hold true to better

than 1 part in 10^27 [W]. If slight non-linear effects were ever

discovered then the possibility of communication with, or travel to, the

other worlds would be opened up. The existence of parallel Everett-

worlds can be used to argue that physics must be *exactly* linear, that

non-linear effects will never be detected. (See "Is physics linear" for

more about linearity.)

The argument for exactness uses a version of the weak anthropic

principle and proceeds thus: the exploitation of slight non-linear

quantum effects could permit communication with and travel to the other

Everett-worlds. A sufficiently advanced "early" civilisation [F] might

colonise uninhabited other worlds, presumably in an exponentially

spreading fashion. Since the course of evolution is dictated by random

quantum events (mutations, genetic recombination) and environmental

effects (asteroidal induced mass extinctions, etc) it seems inevitable

that in a minority, although still a great many, of these parallel

worlds life on Earth has already evolved sapient-level intelligence and

developed an advanced technology millions or even billions of years ago.

Such early arrivals, under the usual Darwinian pressure to expand, would

spread across the parallel time tracks, if they had the ability,

displacing their less-evolved quantum neighbours.

The fossil record indicates that evolution, in our ancestral lineage,

has proceeded at varying rates at different times. Periods of rapid

development in complexity (eg the Cambrian explosion of 530 millions

years ago or the quadrupling of brain size during the recent Ice Ages)

are interspersed with long periods of much slower development. This

indicates that we are not in the fast lane of evolution, where all the

lucky breaks turned out just right for the early development of

intelligence and technology. Ergo none of the more advanced

civilisations that exist in other worlds have ever been able to cross

from one quantum world to another and interrupt our long, slow

biological evolution.

The simplest explanation is that physics is sufficiently linear to

prevent travel between Everett worlds. If technology is only bounded

by physical law (the Feinberg principle [F]) then linearity would have

to be exact.

[F] Gerald Feinberg. _Physics and Life Prolongation_ Physics Today Vol

19 #11 45 (1966). "A good approximation for such [technological]

predictions is to assume that everything will be accomplished that

does not violate known fundamental laws of science as well as many

things that do violate these laws."

[W] Steven Weinberg _Testing Quantum Mechanics_ Annals of Physics Vol

194 #2 336-386 (1989) and _Dreams of a Final Theory_ (1992)

Q40 Why can't the boundary conditions be updated to reflect my

----------------------------------------------------------

observations in this one world?

-------------------------------

What is lost by this approach is a unique past assigned to each future.

If you time-evolve the world-we-now-see backwards in time you get a

superposition of earlier starting worlds. Similarly if you time evolve

a single (initial) world forward you get a superposition of later

(final) worlds.

For example consider a photon that hits a half-silvered mirror and turns

into a superposition of a transmitted and a reflected photon. If we

time-evolve one of these later states backwards we get not the original

photon, but the original photon plus a "mirror image" of the original

photon. (Try the calculation and see.) Only if we retain both the

reflected and transmitted photons, with the correct relative phase, do

we recover the single incoming photon when we time-reverse everything.

(The mirror image contributions from both the final states have opposite

signs and cancel out, when they are evolved backwards in time to before

the reflection event.)

All the starting states have to have their relative phases coordinated

or correlated just right (ie coherently) or else it doesn't work out.

Needless to say the chances that the initial states should be arranged

coherently just so that they yield the one final observed state are

infinitesimal and in violation of observed thermodynamics, which states,

in one form, that correlations only increase with time.

Back to anthropic-principle.com

Appendicies:

A1 References and further reading

------------------------------

[1] Hugh Everett III _The Theory of the Universal Wavefunction,

Princeton thesis_ (1956?)

The original and most comprehensive paper on many-worlds.

Investigates and recasts the foundations of quantum theory in

information theoretic terms, before moving on to consider the

nature of interactions, observation, entropy, irreversible

processes, classical objects etc. 138 pages. Only published in

[5].

[2] Hugh Everett III _"Relative State" Formulation of Quantum

Mechanics_ Reviews of Modern Physics Vol 29 #3 454-462, (July

1957) A condensation of [1] focusing on observation.

[3] John A Wheeler _Assessment of Everett's "Relative State"

Formulation of Quantum Theory_, Reviews of Modern Physics Vol

29 #3 463-465 (July 1957) Wheeler was Everett's PhD

supervisor.

[4a] Bryce S DeWitt _Quantum Mechanics and Reality_ Physics Today,

Vol 23 #9 30-40 (September 1970) An early and accurate

popularisations of Everett's work. The April 1971 issue has

reader feedback and DeWitt's responses.

[4b] Bryce S DeWitt _The Many-Universes Interpretation of Quantum

Mechanics_ in _Proceedings of the International School of Physics

"Enrico Fermi" Course IL: Foundations of Quantum Mechanics_

Academic Press (1972)

[5] Bryce S DeWitt, R Neill Graham eds _The many-worlds

Interpretation of Quantum Mechanics_, Contains

[1],[2],[3],[4a],[4b] plus other material. Princeton Series

in Physics, Princeton University Press (1973) ISBN 0-691-

08126-3 (hard cover), 0-691-88131-X (paper back) The

definitive guide to many-worlds, if you can get hold of a

copy, but now (1994) only available xeroxed from microfilm

(ISBN 0-7837-1942-6) from Books On Demand, 300 N Zeeb Road,

Ann Arbor, MI 48106-1346, USA. Tel: +01-313 761 4700 or 800

521 0600.

[15] Frank J Tipler _The many-worlds interpretation of quantum mechanics

in quantum cosmology_ in _Quantum Concepts of Space and Time_ eds

Roger Penrose and Chris Isham, Oxford University Press (1986). Has

a discussion of Ockham's razor.

On quantum theory, measurement and decoherence generally:

[6] John A Wheeler, Wojciech H Zurek eds _Quantum Theory and

Measurement_ Princeton Series in Physics, Princeton University

Press (1983) ISBN 0-691-08316-9. Contains 49 classic

articles, including [2], covering the history and development

of interpretations of quantum theory.

[7a] Wojciech H Zurek _Decoherence and the Transition from the

Quantum to the Classical_, Physics Today, 36-44 (October

1991). The role of thermodynamics and the properties of large

ergodic systems (like the environment) are related to the

decoherence or loss of interference effects between superposed

macrostates.

[7b] Wojciech H Zurek _Preferred States, Predictability, Classicality,

and the Environment-Induced Decoherence_ Progress of Theoretical

Physics, Vol 89 #2 281-312 (1993) A fuller expansion of [7a]

[8] Max Jammer _The Philosophy of Quantum Mechanics_ Wiley, New

York (1974) Almost every interpretation of quantum mechanics

is covered and contrasted. Section 11.6 contains a lucid

review of many-worlds theories.

[9] Bethold-Georg Englert, Marlan O Scully, Herbert Walther _Quantum

optical tests of complementarity_ Nature, Vol 351, 111-116 (9 May

1991). Demonstrates that quantum interference effects are destroyed

by irreversible object-apparatus correlations ("measurement"), not

by Heisenberg's uncertainty principle itself. See also _The

Duality in Matter and Light_ Scientific American, (December 1994)

[10] Murray Gell-Mann, James B Hartle _Quantum Mechanics in the Light

of Quantum Cosmology_ Proceedings of the 3rd International

Symposium on the Foundations of Quantum Mechanics (1989) 321-343.

They accept the Everett's decoherence analysis, and have extended

it further.

Tests of the Everett metatheory:

[11] David Deutsch _Quantum theory as a universal physical theory_

International Journal of Theoretical Physics, Vol 24 #1

(1985). Describes an experiment which tests for the existence

of superpositions of *consciousness (in an AI).

[16] David Deutsch _Three connections between Everett's interpretation

and experiment_ Quantum Concepts of Space and Time, eds Roger

Penrose and Chris Isham, Oxford University Press (1986). Discusses

a testable split observer experiment and quantum computing.

On quantum computers:

[12] David Deutsch _Quantum theory, the Church-Turing principle and the

universal quantum computer_ Proceedings of the Royal Society of

London, Vol. A400, 96-117 (1985).

[13] David Deutsch _Quantum computational networks_ Proceedings of

the Royal Society of London, Vol. A425, 73-90 (1989).

[14] David Deutsch and R. Jozsa _Rapid solution of problems by

quantum computation_ Proceedings of the Royal Society of

London, Vol. A439, 553-558 (1992).

[17] Julian Brown _A Quantum Revolution for Computing_ New Scientist,

pages 21-24, 24-September-1994

A2 Quantum mechanics and Dirac notation

------------------------------------

Note: this is a very inadequate guide. Read a more comprehensive text

ASAP. For a more technical exposition of QM the reader is referred to

the standard textbooks. Here are 3 I recommend:

Richard P Feynman _QED: the strange story of light and matter_ ISBN 0-

14-012505-1. (Requires almost no maths and is universally regarded as

outstanding, despite being about quantum electrodynamics.)

Richard P Feynman _The Feynman Lectures in Physics_ Volume III Addison-

Wesley (1965) ISBN 0-201-02118-8-P. The other volumes are worth reading

too!

Daniel T Gillespie _A Quantum Mechanics Primer: An Elementary

Introduction to the Formal Theory of Non-relativistic Quantum Mechanics_

(Takes an axiomatic, geometric approach and teaches all the Hilbert

space stuff entirely by analogy with Euclidean vector spaces. Not sure

if it is still in print.)

Quantum theory is the most successful theory of physics and chemistry

ever. It accounts for a wide range of phenomena from black body

radiation, atomic structure and chemistry, which were very puzzling

before quantum mechanics was first developed (c1926) in its modern form.

All theories of physics are quantum physics, with whole new fields, like

the semiconductor and microchip technology, based upon the quantum

effects. This FAQ assumes familiarity with the basics of quantum theory

and with the associated "paradoxes" of wave-particle duality. It will

not explain the uncertainty principle or delve into the significance of

non-commuting matrix operators. Only those elements of quantum theory

necessary for an understanding of many-worlds are covered here.

Quantum theory contains, as a central object, an abstract mathematical

entity called the "wavefunction" or "state vector". Determining the

equations that describe its form and evolution with time is an

unfinished part of fundamental theoretical physics. Presently we only

have approximations to some "correct" set of equations, often referred

to whimsically as the Theory of Everything.

The wavefunction, in bracket or Dirac notation, is written as |symbol> ,

where "symbol" labels the object. A dog, for example, might be

represented as |dog> .

A general object, labelled "psi" by convention, is represented as |psi>

and called a "ket". Objects called "bra"s, written < psi|, may be formed

from kets. An arbitrary bra < psi'| and ket |psi> may be combined

together to form the bracket, < psi'|psi> , or inner product, which is

just a fancy way of constructing a complex number. Amongst the

properties of the inner product is:

< psi'|(|psi1> *a_1 + |psi2> *a_2) = < psi'|psi1> *a_1 + < psi'|psi2> *a_2

where the a_i are arbitrary complex numbers. This is what is meant by

saying that the inner product is linear on the right or ket side. It

is made linear on the left-hand or bra side by defining

< psi|psi'> = complex conjugate of < psi'|psi>

Any ket may be expanded as:

|psi> = sum |i> *< i|psi>

i

= |1> *< 1|psi> + |2> *< 2|psi> + ...

where the states |i> form an orthonormal basis, with < i|j> = 1 for i =

j and = 0 otherwise, and where i labels some parameter of the object

(like position or momentum).

The probability amplitudes, < i|psi> , are complex numbers. It is

empirically observed, first noted by Max Born and afterwards called the

Born interpretation, that their magnitudes squared represent the

probability that, upon observation, that the value of the parameter,

labelled by i, will be observed if the system is the state represented

by |psi> . It is also empirically observed that after observing the

system in state |i> that we can henceforth replace the old value of the

wavefunction, |psi> , with the observed value, |i> . This replacement is

known as the collapse of the wavefunction and is the source of much

philosophical controversy. Somehow the act of measurement has selected

out one of the components. This is known as the measurement problem and

it was this phenomenon that Everett addressed.

When a bra, < psi|, is formed from a ket, |psi> , and both are inner

productted together the result, < psi|psi> , is a non-negative real

number, called the norm of the vector. The norm of a vector provides

a basis-independent way of measuring the "volume" of the vector.

The wavefunction for a joint system is built out of products of the

components from the individual subsystems.

For example if the two systems composing the joint system are a cat and

a dog, each of which may be in two states, alive or dead, and the state

of the cat and the dog were *independent* of each other then we could

write the total wavefunction as a product of terms. If

|cat> = |cat alive> * c_a + |cat dead> * c_d

and

|dog> = |dog alive> * d_a + |dog dead> * d_d

then

|dog+cat> = |cat> x|dog> where x = tensor product

= (|cat alive> * c_a + |cat dead> * c_d)

x (|dog alive> * d_a + |dog dead> * d_d)

= |cat alive> x |dog alive> * c_a * d_a

+ |cat alive> x |dog dead> * c_a * d_d

+ |cat dead> x |dog alive> * c_d * d_a

+ |cat dead> x |dog dead> * c_d * d_d

= |cat alive, dog alive> * c_a * d_a

+ |cat alive, dog dead> * c_a * d_d

+ |cat dead, dog alive> * c_d * d_a

+ |cat dead, dog dead> * c_d * d_d

More generally, though, we states of subsystems are not independent of

each other we have to use a more general formula:

|dog+cat> = |cat alive, dog alive> * a_1

+ |cat alive, dog dead> * a_2

+ |cat dead, dog alive> * a_3

+ |cat dead, dog dead> * a_4

This is sometimes described by saying that the states of the cat and dog

have become entangled. It is fairly trivial to define the state of the

cat and the dog with respect to each other. For instance we could re-

express the above expansion with respect to the cat's two states as:

|dog+cat> =

|cat alive> x(|dog alive> * a_1 + |dog dead> * a_2)

+ |cat dead> x(|dog alive> * a_3 + |dog dead> * a_4)

We term the state of the dog the *relative state* (Everett invented this

terminology) with respect to the cat, specifying which cat state (alive

or dead) we are interested in. This thus the dog's relative state with

respect to the cat alive state is:

(|dog alive> * a_1 + |dog dead> * a_2)/sqrt(|a_1|^2 + |a_2|^2)

where the sqrt term has been added to normalise the relative state.

+ |cat alive, dog dead> * a_2

+ |cat dead, dog alive> * a_3

+ |cat dead, dog dead> * a_4

This is sometimes described by saying that the states of the cat and dog

have become entangled. It is fairly trivial to define the state of the

cat and the dog with respect to each other. For instance we could re-

express the above expansion with respect to the cat's two states as:

|dog+cat> =

|cat alive> x(|dog alive> * a_1 + |dog dead> * a_2)

+ |cat dead> x(|dog alive> * a_3 + |dog dead> * a_4)

We term the state of the dog the *relative state* (Everett invented this

terminology) with respect to the cat, specifying which cat state (alive

or dead) we are interested in. This thus the dog's relative state with

respect to the cat alive state is:

(|dog alive> * a_1 + |dog dead> * a_2)/sqrt(|a_1|^2 + |a_2|^2)

where the sqrt term has been added to normalise the relative state.

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