Noesis

The Journal of the Mega Society

Number 96

August 1994

EditorRick Rosner

5139 Balboa Blvd #303

Encino CA 91316-3430

(818) 986-9177

IN THIS ISSUE

FREQUENTLY ASKED QUESTIONS ABOUT THE

MANY-WORLDS OR RELATIVE STATE FORMULATION

OF

QUANTUM MECHANICS

ANSWERS COMPILED BY MICHAEL CLIVE PRICE

1 What are the problems with quantum theory?

2 What is the Copenhagen interpretation?

3 What is many-worlds?

4 What is a "world"?

5 What is a measurement?

6 Why do worlds split?

7 When do worlds split?

8a What is sum-over-histories?

8b What is many-histories?

9 How many worlds are there?

10 Is many-worlds a local theory?

11 Is many-worlds a deterministic theory?

12 Is many-worlds a relativistic theory?

13 Is many-worlds (just) an interpretation?

14 What are the alternatives?

15 Is many-worlds testable?

16 Could previously separate worlds diverge rather than split?

17 What is many-minds?

18 Does many-worlds violate Ockham's Razor?

19 Does the multiplication of worlds violate conservation of energy?

20 How do probabilities emerge within many-worlds?

21 Does many-worlds allow free-will?

22 Why am I in this world and not another?

23 Can wavefunctions collapse?

24 Is physics linear?

25 Can we determine what other worlds there are?

26 Who was Everett?

27 Who believes in many-worlds?

30 Does the EPR experiment prohibit locality?

31 References and further reading

Q1 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, and despite his early contributions to the subject, was never reconciled with assigning the act of observation a physical significance, which QM requires. 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 in the axioms, as they are in the Copenhagen interpretation. Yet the Copenhagen interpretation is the most popular interpretation of quantum mechanics. (See "What is the Copenhagen interpretation?")

Q2 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, instantaneously, with the probability of any particular outcome given by the Born formula, determined by the wavefunction. This is known as the collapse of the wavefunction. The problems with this approach are: (1) The collapse is an instantaneous process across an extended region ("non-local"). This is in conflict with relativity, which states that no processes can be transmitted faster than the speed of light. (Nevertheless it has been shown that no information can be transmitted faster than light by the collapse process). (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?")

Q3 What is many-worlds?

AKA as the Everett, relative-state, many-histories or many-universes interpretation. Dr Hugh Everett III, its originator, called it the relative-state metatheory or the theory of the universal wavefunction [1], but, after DeWitt [4a],[5], it is generally called many-worlds nowadays.

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 information about an object, but has an observer- independent objective existence. For an N-particle system the wavefunction is a complex-valued field in a 3-N dimensional space. In quantum field theory the state vector spans a space of an indeterminate number of dimensions.

2) The physical assumption: The wavefunction obeys some standard deterministic wave equation at all times. The observer plays no special role in the theory and, consequently, there is no collapse of the wavefunction. Measurement and observation are modelled by applying the wave equation to the joint subject-object system. For non-relativistic systems the Schrodinger wave equation is a good approximation to reality. (See "Is many-worlds a relativistic theory?" for the more general case.)

The rest of the theory is working out consequences of the above assumptions. Some consequences are: 1) That each measurement causes a decomposition or decoherence of the universal wavefunction into non-interacting and non-interfering branches or worlds. History forms 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 an 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 henceforth correlated with 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, by becoming correlated or entangled, meaning that it no longer possible to speak the state of one system in isolation from the other subsystems. Instead we are forced to only speak of the relative states of the subsystems, with respect to the other subsystems. Specifying the state of one subsystem leads to the state of the other subsystems. In this sense the states of the subsystems are determined only relative to each other, hence Everett's original designation of his theory.

If one of the systems is an observer and the interaction an observation then observer has been split into a number of copies, each copy observing just one of the possible results of a measurement and unaware of the other results and its own observer-copies. Interactions between systems and their environments, including communication between different observers in the same worlds, transmits the correlations, inducing local splitting or decoherence of branches of the universal wavefunction [7],[10]. 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 within it. All outcomes exist simultaneously but do not interact further with each other, each world having split into mutually unobservable but equally real worlds or branches of the universal wavefunction.

Q4 What is a "world"?

Loosely speaking a "world" is a complex, partially closed set of interacting sub-systems which don't significantly interfere with other elements in a quantum superposition. Any complex system and its coupled environment, with a large number of internal degrees of freedom, counts 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. The worlds all exist simultaneously in a non- interacting linear superposition.

Sometimes "worlds" are called "universes", but more usually this is reserved the totality of worlds, or "histories" (Gell-Mann/Hartle's phrase, see "What is many-histories?").

Q5 What is a measurement?

A measurement is an interaction between subsystems that triggers an amplification process, typically within an object (which we often designate as the measuring apparatus) with many internal degrees of freedom, leading to a change in the higher-level structure of the object (which might be the recording apparatus). The trigger is sensitive to some (often microphysical) parameter of the one of the subsystems, which we designate the measured system. Eg the detection of a charged particle by a Geiger counter leads to the generation of a "click". The absence of a charged particle does not generate a click. The measured system is the charged particle. 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 observer.

Q6 Why do worlds split?

Worlds, or branches of the universal wavefunction, split when different components of a quantum superposition "decohere" from each other [7], [10]. Decoherence refers to the loss of coherency or absence of interference effects between the elements of the superposition. For two components or worlds to interfere with each other all the atoms, subatomic particle, photons etc in each world have to be in the same state, in the same place. For small systems this is quite possible. In the double slit experiment, for instance, it only requires that the divergent paths of the diffracted particle overlap again at some point, because only the single particle has been split. For more complex systems overlapping becomes harder because all the constituents particles have to overlap with their counterparts simultaneously.

In QM jargon we say that the components (or vectors in the underlying Hilbert space) have become permanently orthogonal due to the complexity of the systems increasing the dimensionality of the Hilbert space. In a high dimension space almost all vectors are orthogonal. Each time a new degree of freedom is activated the dimensionality of the space which the different components move through increases. Thus vectors for complex systems, with a large number of degrees of freedom, naturally decompose into mutually orthogonal components which, because they never interfere again, are unaware of each other. From the point of view of the complex systems they have split into different, mutually unobservable worlds.

Q7 When do worlds split?

Worlds irrevocably "split" at the sites of measurement-like interactions associated with thermodynamically irreversible processes. An irreversible process will always produce decoherence which splits worlds. (see "Why do worlds split?", [7], [10])

In the example of a Geiger counter and a charged particle (see "What is a measurement?") 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 in the particle's wavefunction. The Geiger counter split when the amplification process became irreversible.

The splitting is local (ie 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. (The event has become irreversible.)

Consider Schrodinger's Cat. A cat is placed in a sealed box with a device that releases a lethal does of cyanide if a radioactive decay is detected. After a while an observer opens the box to see if the cat is alive or dead. According to the CI 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. 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. As the device/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 unlucky and late copy. The external observer is split into two copies only when the box is opened and is altered by the state of the cat.

In the language of thermodynamics the decay of the atom and the amplification of its detection by a Geiger counter, the release of the cyanide and the death of the cat are all irreversible events. These events have caused the decoherence (see "Why do worlds split?") of the different branches of the wavefunction of the cat + device + box. Decoherence [7] 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 is irreversible and forward-time-branching, following the increase with entropy. Like all irreversible processes, though, there are exceptions even at the coarse- grained level and worlds will occasionally fuse. A necessary, although not necessarily sufficient, precondition for fusing is for all records, memories etc that discriminate between the pre-fused worlds or histories be lost.

Q8a What is sum-over-histories?

The sum-over-histories or the path integral formalism was developed by Feynman in the 1940s [F] as an alternative 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 PI formalism offers some interesting insights into many-worlds. In the PI picture the single particle wavefunction at (x',t') is built up of contributions of all possible paths from (x,t), where each path's contribution weighted by a (phase) factor of exp(i*Action[path]/hbar) * wavefunction at (x,t). The Action[path] is the time-integral of the lagrangian (roughly: the kinetic minus the potential energy) along the path from (x,t) to (x',t'). The final expression is thus 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 are over a 3-N space.

Feynman developed his PI formalism further for his work on quantum electrodynamics, QED, with his Feynman diagrams, in parallel with Schwinger and Tomonoga who developed a less visualisable form of QED. Dyson showed that these approaches were all equivalent.

It is quite natural when analysing systems from the PI point of view to think of the particle continually splitting apart and fusing together to explore every possible intermediate configuration between the specified start and end states. For this reason the 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 therefore that they all have equal reality. Perhaps we shouldn't be surprised that Feynman, therefore, 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 sharing the same thesis supervisor, John A Wheeler.

[F] Richard P Feynman, Space-time approach to non-relativistic quantum mechanics, Reviews of Modern Physics, Vol 20 267 (1948)

Q8b What is many-histories?

There is considerable linkage between thermodynamics and many-worlds, explored in the "decoherence" views of Zurek [7] and Gell-Mann and Hartle [10], Everett [1] and others [4b].

Gell-Mann and Hartle 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. (Fine-grained histories effectively relax the irreversible criterion.) Physically the many-histories approach is isomorphic to Everett's many-worlds, although Gell-Mann and Hartle choose not to accept Everett's metaphysical stance that each history corresponds to an element of reality.

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.)

Q9 How many worlds are there?

It so happens that we can use the thermodynamic Planck-Boltzmann relationship to count the branches at each splitting, at the lowest, maximally refined level of Gell-Mann's many-histories tree (See "What is many-histories?"). The bottom level consists of microstates which can be counted by the formula W = exp (S/k), where S = entropy, k = Boltzmann's constant (approx 10²² 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 worlds splits into at the site of an irreversible event is exp(dS/k), where dS = entropy of the defining event. Because k is very small a great many worlds split off at each macroscopic event.

Q10 Is many-worlds a local theory?

The simplest way to see that the many-worlds metatheory is local 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 locally 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?" for more details and "When do worlds split?")

Q11 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 are embedded within the universal wavefunction although each observer, split by acts of 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.

Q12 Is many-worlds a relativistic theory?

It is trivial to relativise many-worlds because all relativistic theories of physics are still quantum theories with linear wavefunctions. There are three or more stages to developing a fully quantum relativistic theory. Simplifying slightly gives:

First quantisation: the wavefunction is a complex field which evolves in 3N dimensions which represent N particles. The wavefunction is a solution of either the many-particle Schrodinger, Dirac or Klein-Gordon equation or some other wave equation.

Second quantisation: AKA quantum field theory, which handles the creation and destruction of particles by quantising fields as well as particles. (Each particle type corresponds to a field, in QFT. Eg the electromagnetic field's particle is the photon, but the number of particles involved is indeterminate.) Again many-worlds has no problems handling QFT. The wavefunction of a collection of particles and fields exists in a Fock space, where the number of dimensions varies from component to component.

Third quantisation. The gravitational metric is quantised, along with (perhaps) the topology of space-time. The physics of this is incomplete, but there is no reason for thinking that many-worlds can't be extended to cover this as well. (One of the original motivations of Everett's scheme was to provide a system for quantizing the gravitational field within quantum cosmology to yield a complete description of the universe.)

Q13 Is many-worlds (just) an interpretation?

No, for four reasons:

First, many-worlds has testable implications (see "Is many-worlds testable?") and interpretations, generally, do not have testable differences from each other.

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. Therefore 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?")

Four, the interpretative side of many-worlds, like the subjective probabilistic elements, are derived from within the theory, rather than added in 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, as Everett pointed out, since it makes statements that are applicable across a range of theories. Many-worlds is the unavoidable implication of any quantum theory which obeys some type of wave equation, linear with respect to the wavefunction it operates on.

Q14 What are the alternatives?

There is no other quantum theory, besides many-worlds, that is scientific 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 physics than the non-observer. (A return to vitalism.) The definition of 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 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 he 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 potential. 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. The particles can, therefore, 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 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 "probability amplitude" and thus why we are justified in collapsing the complex probability as if it were a classical probability.

[M] W Muckenheim A review of extended probabilities Physics Reports Vol 133 339- (1986)

[Y] Saul Youssef __ 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 forms between the first single slit and one of the double slits and another transaction forms between the same double slit and the point of screen where the photon lands.

[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?")

Q15 Is many-worlds testable?

Yes, it is. There are two forms of tests: retrodictions (theory follows data) and predictions (data follows theory).

A) 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 data 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 "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?")

B) A prediction occurs when a theory suggests new phenomena.

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. See a guide to QM.)

According to many-worlds worlds split with the operation of every thermodynamically irreversible process. The operation of our minds are irreversible, carried along for the ride, and divide with the worlds. Normally, therefore, 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 will doable by 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 dissipates much less than kT of energy is reversible. (This implies that frictive or dissipative forces are absent.) 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 10¹⁷ bits/sec, based on the number of neurons (approx 10¹⁰) per human brain, average number of synapses per neuron (approx 10⁴) and the average firing rate (approx 10³ 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 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 measurements 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, 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.

Q16 Could previously separate worlds diverge rather than split?

This is definitely not permissable in many-worlds. 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/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 all comes out wrong. Also the divergence theory stops being deterministic, in contradiction to the wave equations which are deterministic, since we have a

AAAAAAAAAAAAAAABBBBBBBBBBBBBBB ===========> time

Worlds diverge

AAAAAAAAAAAAAAACCCCCCCCCCCCCCC

situation, rather than:

BBBBBBBBBBBBBBB

B

AAAAAAAAAAAAAA Worlds splitting

C

CCCCCCCCCCCCCCC

Additionally the divergence model has to explain why:

AAAAAAAAAAAAAAABBBBBBBBBBBBBBB

AAAAAAAAAAAAAAABBBBBBBBBBBBBBB

doesn't happen! This false divergence model, at the mental level, seems favoured by adherents of many-minds. (See "What is many-minds?")

Q17 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 the associated minds are thought of as diverging rather than splitting. The motivation for this brain-mind dichotomy seems purely to avoid talk of minds splitting and talk instead about the divergence of pre-existing separate mental states. There is no physical basis for this interpretation, which is incapable of an operational definition. Indeed the divergence 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 "Could previously separate worlds diverge rather than split?")

In many-minds the role of the conscious observer is accorded special status, with its fundamental axiom about infinities of 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 April 94.)

The two theories should not be confused.

Q18 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 multitude 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, 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 theory because it proposes that same laws of physics apply to animate observers as inanimate objects. The multitude of worlds predicted by the theory is not a weakness for many-worlds, any more than stars are for astronomy, 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. Again they were confusing the notion of vastness with complexity [15].)

Q19 Does the multiplication of 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 weighted averages or of expectation values. Conservation of energy is expressed by saying that the time derivative of the expectation of the energy operator vanishes. This statement can be scaled up to includes the whole universe. Each world has an approximate energy, but the energy of the total wavefunction (of 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 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 smaller and smaller slices, as measured in the Hilbert space.

Q20 How do probabilities emerge within many-worlds?

Everett demonstrated [1],[2] that observations in each world obey all conventional statistical laws predicted by the probabilistic Born interpretation by showing that the Hilbert space's inner product or norm supplies a unique measure or "volume" to each world or set of worlds. The norm 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 the limit. Vectors with zero norm, where probability breaks down, don't exist (see below), thus we, as observers, observe the familiar predictions of quantum theory expressed as probabilistic events.

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 would hold true and asserted the vanishing of the Hilbert space volume of the set of non-random worlds. DeWitt (with Graham) later published a longer *derivation* of Everett's assertion [4a],[4b]. What Everett asserted and DeWitt 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 axi