On the Many-Worlds-Interpretation Comments on the Everett FAQ An analysis of Everett's original paper is given in a separate entry in this FAQ, called ''Circularity in Everett's measurement theory''. The main conclusion is that Everett's analysis simply derives the projection postulate by having assumed it, without any discussion, in disguise. Thus his ''interpretation'' explains nothing. The commentary below is a very old entry (from 1999, with a few later amendments) regarding a particular, low quality but popular, version of Everett's ''many worlds'' interpretation. My response here (in contrast to the analysis mentioned above) is at the same superficial level. ------------------------------------------------------------------------ The Everett FAQ by Michael Clive Price, available at http://www.hedweb.com/manworld.htm claims to show ``how quantum paradoxes are resolved by the "many-worlds" interpretation or metatheory of quantum mechanics.'' The following quotes refer to the version I downloaded on Sept. 29, 1999. My comments show that quantum paradoxes are not resolved by the version of the "many-worlds" interpretation of quantum mechanics promoted by the Everett FAQ; instead, the latter is full of home-made puzzles and ambiguities. ------------------------------------------------------------------------ Q1 Who believes in many-worlds? many-worlds is most popular amongst scientists who may rather loosely be described as string theorists or quantum gravitists/cosmologists. It is less popular amongst the wider scientific community who mostly remain in ignorance of it. The paper http://arxiv.org/PS_cache/quant-ph/pdf/0101/0101077v1.pdf contains results of a poll at a quantum computation conference. "Which interpretation of quantum mechanics is closest to your own? (a) Copenhagen or consistent histories (including postulate of explicit collapse): 4 (b) Modified dynamics (Schroedinger equation modified to give explicit collapse): 4 (c) Many worlds/consistent histories (no collapse): 30 (d) Bohm (an ontological interpretation where an auxiliary ''pilot wave'' allows particles to have well-defined positions and velocities): 2 (e) None of the above/undecided: 50 This very uninformative questionnaire is used to support the MWI. The dominant statistical interpretation is not even mentioned (and might figure under either (c) or (e)). The consistent history interpretation has nothing to do with Everett's MWI, but both are classified together in the single choice (c). No collapse does not imply either of many worlds or consistent histories, but this seems to be suggested by the choices. In any case, this gives an upper bound of 30/90 = 33% on supporters of MWI in the particular sample taken, while the only deducible lower bound is 0%. A slightly earlier (1977) poll recorded in http://arxiv.org/pdf/quant-ph/9709032v1 gives the table Copenhagen 13 Many Worlds 8 Bohm 4 Consistent Histories 4 Modified dynamics (GRW/DRM) 1 None of the above/undecided 18 giving a percentage of 8/48=17% supporters of MWI. 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. But how can an interaction be irreversible if the evolution of the wave function is unitary? Q6 Why do worlds split? What is decoherence? Any system complex enough to be described by thermodynamics and exhibit irreversible behaviour is a system complex enough to exclude, for all practical purposes, any possibility of future interference between its decoherent branches. An irreversible process is one in, or linked to, a system with a large number of internal, unconstrained degrees of freedom. Once the irreversible process has started then alterations of the values of the many degrees of freedom leaves an imprint which can't be removed. But how many particles needs a system to deserve being called complex? What happens with a system with one particle less, why should it be different? In a mathematically consistent interpretation, one may not use concepts like `for all practical purposes' unless one specifies exactly what that should mean. In a high dimension space almost all vectors are orthogonal, without any significant degree of overlap. Thus vectors for complex systems, with a large number of degrees of freedom, naturally decompose into mutually orthogonal components which, because they can never significantly interfere again, are unaware of each other. they decompose only into nearly mutually orthogonal components. How close must the angle be to 90 degrees before we may say that irreversibility (and hence measurement) has taken place? Clearly, Nature must have such a criterion to know when it should split. Without such a demarkation, the concept of measurement is vague and no explanation of how Nature works has been given. The same problems as in the Copenhagen interpretation remain, namely the ambiguity of what constitutes a measurement... Q7 When do worlds split? 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. How can irreversibility be subjective if it defines what a measurement is and when worlds split? It would imply that when worlds split is also a subjective matter. But then it is observer-dependent, the very thing the interpretation is trying to avoid. 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.) Again, this requires the observer to define accessible external characteristics. Q8 When does Schrodinger's cat 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. Indeed, this confirms that splitting is a subjective process not affecting the world at large. Otherwise the number of worlds could not depend on the point of view? Or is it to be understood as follows: As the cyanide/no-cyanide interacts with the cat the world is split into two, one containig a dead cat and the other one that is alive? And each of these two worlds splits again as the onlooker opens the box? But then we have 4 worlds, two of which corresponding to nonexistent possibilities (e.g., the world with the dead cat which is found alive on opening the box). Thus only one split should have occured, and the `explanation' is nonsense. 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. This is funny since it implies a fractional number of worlds unless the ensemble of worlds is microcanonical. But then each world is equally probable, and we must be puzzled why we are in a world where the unlikely happens rarely... The entropy formula employed only counts the number of energetically accessible energy eigenstates (not the number of all possible states at a given energy, which is infinite), and is applicable only to a bounded volume of matter in equilibrium. But the many worlds interpretation must consider the whole universe as the physical system, and the latter is neither in equilibrium nor (most likely) bounded. Q14 Is many-worlds a relativistic theory? First quantisation: the wavefunction of an N particle system is a complex field which evolves in 3N dimensions as the solution to either the many-particle Schrodinger, Dirac or Klein-Gordon or some other wave equation. External forces applied to the particles are represented or modelled via a potential, which appears in the wave equation as a classical, background field. many-particle Dirac or Klein-Gordon equation?? Unfortunately no one so far has found an N particle Dirac or Klein-Gordon equation that approximates reality... Many-worlds has no problems incorporating QFT, since a theory (QFT) is not altered by a metatheory (many-worlds), which makes statements about the theory. This is funny, too, conflicting with the asserted deterministic nature of MWI since there is no deterministic QFT of interacting fields. All QFT has to offer is the S-matrix that defines probability amplitudes... Q17 Why don't worlds fuse, as well as split? Do splitting worlds imply irreversible physics? 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. According to the Liouville equation (that follows from the Schr"odinger equation assumed valid in MWI), the state of the universe at any chosen moment evolves unitarily and hence reversibly. Irreversibility can be introduced only as an approximation in a coarse grained sense which corresponds to choosing time and space scales to avoid the Poincare recurrence theorem. A metatheory such as MWI that depends on such uncontrolled approximations in its most basic tenets cannot be very fundamental... Q22 Does many-worlds violate conservation of energy? energy is conserved within each world and also across the totality of worlds. But in an irreversible world, energy is not conserved but dissipates. The presence of such arguments that flatly contradict other statements shows that MWI is a smokescreen without a consistent mathematics behind. Q23 How do probabilities emerge within many-worlds? Strictly speaking Everett did not prove that the usual statistical laws of the Born interpretation would hold true for all observers in all worlds. He merely showed that no other statistical laws could hold true and asserted the vanishing of the Hilbert space "volume" or norm of the set of "maverick" worlds. And he cannot prove it since statistics makes no sense in MWI as everything that can happen, happens. Consider measuring a sequence of orthogonal idempotent observables e_0, e_1, ... in a state psi with = 0.001 for all i. After each measurement, the world splits into two, corresponding to the two eigenvalues 0, 1 of e_i. After N measurements we have 2^N worlds, half of them having e_0=0, and half of them having e_0=1. But there should be only one thousendth of the latter... The formal proof involves a weighting of the world according to probabilities. But these weights have no influence on what happens in a world. How to distinguish a world with weight 0.9999 from one with weight 1e-100000000000? The only way is that the latter world contains lots of improbable historical imprints while the former does not. But this leaves us to explain why we happen to perceive a world of large weight throughout our entire life... 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. As the previous argument shows, Born-style probabilities emerge at best in a formal way, but not with a natural interpretation as probabilities. Q25 Why am I in this world and not another? Why does the universe appear random? The Copenhagen interpretation posits that observers collapse wavefunctions, but is unable to define "observer". Without a definition of observer there can be no mechanism triggered by their presence. Actually it posits that measurements collapse wavefunctions, but is unable to define "measurement". Without a definition of measurement there can be no mechanism triggered by its presence. Another popular view is that irreversible processes trigger collapse. Certainly wavefunctions appear to collapse whenever irreversible processes are involved. And most macroscopic, day-to-day events are irreversible. The problem is, as with positing observers as a cause of collapse, that any irreversible process is composed of a large number of sub-processes that are each individually reversible. To invoke irreversibility as a mechanism for collapse we would have to show that new fundamental physics comes into play for complex systems, which is quite absent at the reversible atom/molecular level. The same two arguments apply against splitting, with the conclusion that there is no mechanism for splitting worlds since neither measurement nor irreversibility can be clearly demarcated. Q26 Can wavefunctions collapse? The simplest conclusion, which is to be preferred by Ockham's razor, is that wavefunctions just don't collapse and that all branches of the wavefunction exist. An even simpler conclusion, which is to be preferred by Ockham's razor, is that wavefunctions neither collapse nor branch. ======================================================================= Some recent papers on the arxiv about Many Worlds Interpretations: hep-th/0403008 gr-qc/9703089 gr-qc/9309012 gr-qc/9704039 quant-ph/0312157 quant-ph/0312136 quant-ph/0303114 quant-ph/0303050 quant-ph/0211104 quant-ph/0209055 quant-ph/0112081 quant-ph/0112077 quant-ph/0111072 quant-ph/0111047 quant-ph/0108070 quant-ph/0001057 quant-ph/9910108 quant-ph/9904004 quant-ph/9709032 quant-ph/9703008 quant-ph/9609006 and some related papers: gr-qc/9901024 gr-qc/9810078 gr-qc/9412067 gr-qc/9208001 quant-ph/9805065 quant-ph/9704006 quant-ph/9603008 ======================================================================= The above just criticises the Many Worlds interpretation, but does not hint at what interpretation is better. For my constructive views on the interpretation problem, see: A. Neumaier, Ensembles and experiments in classical and quantum physics, Int. J. Mod. Phys. B 17 (2003), 2937-2980. quant-ph/0303047, http://www.mat.univie.ac.at/~neum/papers/physpapers.html#ensembles and the links in the FAQ entry Quantum mechanics without mysteries http://www.mat.univie.ac.at/~neum/physfaq/topics/born.html ======================================================================= A theoretical physics FAQ http://www.mat.univie.ac.at/~neum/physics-faq.txt Physics links by Arnold Neumaier http://www.mat.univie.ac.at/~neum/physics.html