## THE EVERETT FAQ

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 Whyquantumgravity? 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 toprovethat the many-worlds interpretation is the "correct" quantum metatheory, merely to correct some of the common errors and misinformation on the subject floating around.

[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%

## 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].

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

derivedfrom within the theory rather than having to beassumedas 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

relativeto 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 IIPhysical 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 probabilitiesPhysics Reports Vol 133 339- (1986) [Y] Saul YoussefQuantum Mechanics as Complex Probability Theoryhep-th 93070195)

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

didact 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 passesbetweenthe charged detector plates, triggering the amplification process (an irreversible electron cascade or avalanche), which is ultimately converted to a click.

## Q6

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.

Why do worlds split?

What is decoherence?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 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 mechanicsReviews 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

nodefining 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 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

uniquelyselect 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, i.e. 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

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:

Is many-worlds a relativistic theory?

What about quantum field theory?

What about quantum gravity?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

requiresthat gravity be quantised, in contrast to other interpretations which are silent about the role of gravity. (See "Whyquantumgravity?")

## 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 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

This is really a question about why thermodynamics works and what is the origin of the "arrow of time", rather than about many-worlds.

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

Do splitting worlds imply irreversible physics?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?", "Why 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?"and "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 permissible 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.

## 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.

## 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.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.

|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>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 does not have the desired property of vanishing as N goes to infinity.

[H] JB Hartle

Quantum Mechanics of Individual SystemsAmerican 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.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

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

Why am I in this world and not another?

Why does the universe appear random?(See "How do probabilities emerge within many-worlds?" for how the subjective randomness is moderated by the usual probabilistic laws of QM.)

[*]Split brain experimentswereperformed 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 notactuallycollapse but continues to evolve according to the usual wave-equation. If amechanismfor 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

appearto 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 amechanismfor collapse we would have to show that newfundamentalphysics 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'tcollapse and that all branches of the wavefunction exist.

## Q27

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.

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?See also "Is linearity exact?"

## Q28

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

Can we determine what other worlds there are?

Is the form of the Universal Wavefunction knowable?allthe 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 discernible 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.

## 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 toThe Role of Gravity in Physicsconference held at the University of North Carolina, Chapel Hill, in January 1957.

## 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.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

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.

Does the EPR experiment prohibit locality?

What about Bell's Inequality?Let's examine the EPR experiment in more detail.

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

|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 directionIt 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)Working through the algebra we find that for pairs of electrons:

|+,-> - |-,+> = |left,right> - |right,left> = |up,down>i - |down,up>|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 irrelevanthowwe 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 CentauriAfter 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]> observationwhich 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]> communicationwhere 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 toyourrecords/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 ofyou. 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.

Afteryou 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

singledefinite 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 localityorCFD. 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 MechanicsScientific American (May 1994)

[As] Alain Aspect, J Dalibard, G RogerExperimental test of Bell's inequalities using time-varying analyzersPhysical Review Letters Vol 49 #25 1804 (1982).

[C] John G CramerThe transactional interpretation of quantum mechanicsReviews of Modern Physics Vol 58 #3 647-687 (1986)

[B] John S Bell:On the Einstein Podolsky Rosen paradoxPhysics 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 StappS-matrix interpretation of quantum-theoryPhysical 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,conditionalupon, 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 thecorrespondingeigenstate 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. [...]

## 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 "Whyquantumgravity?") 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 worldsdointerfere 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.)Only by accepting the existence of the other Everett-worlds is this 100% restoration explicable.

## Q38 Why

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 therequantumgravity?isempirical evidence for quantum gravity.

## 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 beexactlylinear, 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 (e.g. 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 ProlongationPhysics 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 MechanicsAnnals of Physics Vol 194 #2 336-386 (1989) andDreams 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.

## A1 References and further reading

[1] Hugh Everett IIIThe 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 MechanicsReviews of Modern Physics Vol 29 #3 454-462, (July 1957) A condensation of [1] focusing on observation. [3] John A WheelerAssessment 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 DeWittQuantum Mechanics and RealityPhysics 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 DeWittThe Many-Universes Interpretation of Quantum MechanicsinProceedings of the International School of Physics "Enrico Fermi" Course IL: Foundations of Quantum MechanicsAcademic Press (1972) [5] Bryce S DeWitt, R Neill Graham edsThe 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 TiplerThe many-worlds interpretation of quantum mechanics in quantum cosmologyinQuantum Concepts of Space and Timeeds 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 edsQuantum Theory and MeasurementPrinceton 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 ZurekDecoherence 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 ZurekPreferred States, Predictability, Classicality, and the Environment-Induced DecoherenceProgress of Theoretical Physics, Vol 89 #2 281-312 (1993) A fuller expansion of [7a] [8] Max JammerThe Philosophy of Quantum MechanicsWiley, 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 WaltherQuantum optical tests of complementarityNature, 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 alsoThe Duality in Matter and LightScientific American, (December 1994) [10] Murray Gell-Mann, James B HartleQuantum Mechanics in the Light of Quantum CosmologyProceedings 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 DeutschQuantum theory as a universal physical theoryInternational 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 DeutschThree connections between Everett's interpretation and experimentQuantum 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 DeutschQuantum theory, the Church-Turing principle and the universal quantum computerProceedings of the Royal Society of London, Vol. A400, 96-117 (1985). [13] David DeutschQuantum computational networksProceedings of the Royal Society of London, Vol. A425, 73-90 (1989). [14] David Deutsch and R. Jozsa _Rapid solution of problems by quantum computationProceedings of the Royal Society of London, Vol. A439, 553-558 (1992). [17] Julian BrownA Quantum Revolution for ComputingNew 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:<psi'|(|psi1>*a_1 + |psi2>*a_2) = <psi'|psi1>*a_1 + <psi'|psi2>*a_2where 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>|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).|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_dMore 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_4This 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 therelative 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.

Michael Clive Price

February 1995