Article 73331 of sci.physics: From: rmaimon@husc9.Harvard.EDU (Ron Maimon) Newsgroups: sci.physics Subject: Re: Bell's theorem, asumptions? Date: 6 Dec 1994 20:50:29 GMT Organization: Harvard University, Cambridge, MA Lines: 38 Sender: rmaimon@husc9 (Ron Maimon) Distribution: world Keywords: Bell, EPR, FTL y91magpa@ida.liu.se (Magnus Paulsson) writes: |> |> I know some QM :-), but almost nothing about relativistic QM. |> I've been thinking some about EPR, Bell-inequality and Aspens |> experiment. |> I've only come across different |> sorts of explanations saying "IT IS LIKE THIS" or "Random is random". |> Does anybody have an explanation? Yes- it's pretty obvious what's going on in the Everett picture. If you are recieving a superposed wave of half spin up and half spin down, you are cast into a superposition of states upon observing it, similarly, a far away friend is also cast into a superposition of states when he observes the other electron. so now there are two versions of each of you, one who observed spin up and one who observed spin down. When you both come to meet each other, the spin up version of you only can interact with the spin down version of your friend, and similarly, the spin down version of you can only interact with the spin up version of your friend. Both versions are shocked that they always see the "opposite" guy. Nothing nonlocal is going on, just something non-single- universal. If Everett makes you queasy, you can think about it in a subjective Copenhagen way too. If you and your friend are observing two correlated particles, it is a _mistake_ for you to assign a definite state to your friend before he talks to you. If you are consistent in attaching collapse of the wavefunction to subjective gain in knowledge about the results of experiments _you_ perform, not just any observer, you can rid your mind of any illusions of nonlocality. Article 74340 of sci.physics: Newsgroups: sci.physics From: price@price.demon.co.uk (Michael Clive Price) Path: beaux!kiki.icd.teradyne.com!netcomsv!netcomsv!ix.netcom.com!howland.reston.ans.net!pipex!demon!price.demon.co.uk!price Subject: Re: John Mc Carthy's request re: Penrose (mechanisms for consciousness) References: <503@glare.in-chemnitz.de> <3c63p2$g88@ixnews2.ix.netcom.com> <3cdsoh$qms@nntp1.u.washington.edu> Reply-To: price@price.demon.co.uk X-Newsreader: Demon Internet Simple News v1.29 Lines: 150 X-Posting-Host: price.demon.co.uk Date: Tue, 20 Dec 1994 11:54:49 +0000 Message-ID: <787924489snz@price.demon.co.uk> Sender: usenet@demon.co.uk Penrose (quoted): >> .. the many-worlds viewpoint provide no explanation for the >> extremely accurate wonderful rule whereby the squared moduli >> of the complex-number weighting factors miraculously become >> relative probabilities..." JS: >> Actually I thought Everett and then DeWitt did have such a proof, >> but, evidently Penrose does not think those proofs are right. He >> does not mention them however. "Lamont Granquist" writes: > I'd be interesting in hearing their proofs. Q23 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 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. Hilbert space vectors with zero norm don't exist (see below), thus we, as observers, only observe the familiar, probabilistic predictions of quantum theory. Worlds where probability breaks down are never realised. Strictly speaking Everett did not prove that the usual statistical laws of the Born interpretation would hold true for all observers in all worlds. He merely showed that no other statistical laws could hold true and asserted the vanishing of the Hilbert space "volume" or norm of the set of maverick worlds. DeWitt (with Graham) later published a longer *derivation* of Everett's assertion [4a], [4b], closely based on an earlier, independent demonstration by Hartle [H]. What Everett asserted, and DeWitt/Hartle derived, is that the collective norm of all the maverick worlds, as the number of trials goes to infinity, vanishes. Since the only vector in a Hilbert space with vanishing norm is the null vector (a defining axiom of Hilbert spaces) this is equivalent to saying that non-randomness is never realised. All the worlds obey the usual Born predictions of quantum theory. That's why we never observe the consistent violation of the usual quantum statistics, with, say, heat flowing from a colder to a hotter macroscopic object. Zero-probability events never happen. Of course we have to assume that the wavefunction is a Hilbert space vector in the first place but, since this assumption is also made in the standard formulation, this is not a weakness of many-worlds since we are not trying to justify all the axioms of the conventional formulation of QM, merely those that relate to probabilities and collapse of the wavefunction. In more detail the steps are: 1) Construct the tensor product of N identical systems in state |psi>, according to the usual rules for Hilbert space composition (repeated indices summed): |PSI_N> = |psi_1>*|psi_2>*...... |psi_N> where |psi_j> = jth system prepared in state |psi> = |i_j> (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>... 2) Quantify the deviation from the "expected" Born-mean for each component of |PSI_N> with respect to the above |i_1>|i_2>...|i_N> basis by counting the number of occurrences of the ith eigenstate/N. Call this number RF(i). Define the Born-deviation as D = sum(i)( (RF(i) - ||^2)^2 ). Thus D, loosely speaking, for each N length sequence, quantifies by how much the particular sequence differs from the Born-expectation. 3) Sort out terms in the expansion of |PSI_N> according to whether D is less/equal to (.LE.) or greater than (.GT.) E, where E is a real, positive constant. Collecting terms together we get: |PSI_N> = |N,"D.GT.E"> + |N,"D.LE.E"> worlds worlds for which for which D > E D <= E 4) What DeWitt showed was that: < 1/(NE) (proof in appendix of 4b) Thus as N goes to infinity the right-hand side vanishes for all positive values of E. (This mirrors the classical "frequentist" position on probability which states that if i occurs with probability p(i) then the proportion of N trials with success i approaches p(i)/N as N goes to infinity [H]. This has the immediate benefit that sum(i) p(i) = 1.) The norm of |N,"D.LE.E">, by contrast, approaches 1 as N goes to infinity. Note: this property of D is not shared by other definitions, which is why we haven't investigated them. If, say, we had defined, in step 2), A = sum(i)( (RF(i) - ||)^2 ), so that A measures the deviation from |psi|, rather than |psi|^2, then we we find that does not have the desired property of vanishing as N goes to infinity. 5) The norm of the collection of non-random worlds vanishes and therefore must be identified with some complex multiple of the null vector. 6) Since (by assumption) the state vector faithfully models reality then the null vector cannot represent any element of reality, since it can be added to (or subtracted from) any other state vector without altering the other state vector. 7) Ergo the non-random worlds are not realised, without making any additional physical assumptions, such the imposition of a measure. Note: no finite sequence of outcomes is excluded from happening, since the concept of probability and randomness only becomes precise only as N goes to infinity [H]. Thus, heat could flow from a cold to hotter object, but we might have to wait a very long time before observing it. What *is* excluded is the possibility of this process going on forever. The emergence of Born-style probabilities as a consequence of the mathematical formalism of the theory, without any extra interpretative assumptions, is another reason why the Everett metatheory should not be regarded as just an interpretation. (See "Is many-worlds (just) an interpretation?") The interpretative elements are forced by the mathematical structure of the axioms of Hilbert space. [H] JB Hartle _Quantum Mechanics of Individual Systems_ American Journal of Physics Vol 36 #8 704-712 (1968) Hartle has investigated the N goes to infinity limit in more detail and more generally. He shows that the relative frequency operator obeys RF(i) |psi_1>|psi_2>.... = ||^2 |psi_1>|psi_2>.... Hartle regarded his derivation as essentially the same as Everett's, despite being derived independently. [1] Hugh Everett III _The Theory of the Universal Wavefunction, Princeton thesis_ (1956?) The original and most comprehensive paper on many-worlds. Investigates and recasts the foundations of quantum theory in information theoretic terms, before moving on to consider the nature of interactions, observation, entropy, irreversible processes, classical objects etc. 138 pages. Only published in [5]. [2] Hugh Everett III _"Relative State" Formulation of Quantum Mechanics_ Reviews of Modern Physics Vol 29 #3 454-462, (July 1957) A condensation of [1] focusing on observation. [4a] Bryce S DeWitt _Quantum Mechanics and Reality_ Physics Today, Vol 23 #9 30-40 (September 1970) One of the earlier, and more accurate, popularisations of Everett's work. The April 1971 issue has reader feedback and DeWitt's responses. [4b] Bryce S DeWitt _The Many-Universes Interpretation of Quantum Mechanics_ in _Proceedings of the International School of Physics "Enrico Fermi" Course IL: Foundations of Quantum Mechanics_ Academic Press (1972) Michael Price price@price.demon.co.uk Article 75226 of sci.physics: Newsgroups: sci.physics From: price@price.demon.co.uk (Michael Clive Price) Path: beaux!kiki.icd.teradyne.com!netcomsv!netcomsv!ix.netcom.com!howland.reston.ans.net!pipex!demon!price.demon.co.uk!price Subject: Re: many minds,many histories Distribution: world References: <3ddcko$sg9@nef.ens.fr> Reply-To: price@price.demon.co.uk X-Newsreader: Demon Internet Simple News v1.29 Lines: 25 X-Posting-Host: price.demon.co.uk Date: Fri, 30 Dec 1994 20:27:18 +0000 Message-ID: <788246814snz@price.demon.co.uk> Sender: usenet@demon.co.uk "Ioan Mitrea" writes: > Is anyone out there acquainted with quantum mechanics > intepretations like "many minds" of David Albert,or > "many histories" of Hartle and Gell-Mann? 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]. 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. (Fine-grained histories effectively relax the irreversible criterion.) Mathematically the many-histories approach is isomorphic to Everett's many-worlds. The worlds split or "decohere" from each other when irreversible events occur. (See "Why do worlds split?" and "When do worlds split?".) Correspondingly many-histories defines a multiply-connected hierarchy of classical histories where each classical history is a "child" of any parent history which has only a subset of the child defining irreversible events and a parent of any history which has a superset of such events. Climbing up the tree from child to parent moves to progressively coarser grained consistent histories until eventually the top is reached where the history has *no* defining events (and thus consistent with everything!). This is Everett's universal wavefunction. The bottom of the coarse-grained tree terminates with the maximally refined set of decohering histories. The classical histories each have a probability assigned to them and probabilities are additive in the sense that the sum of the probabilities associated a set classical histories is equal to the probability associated with the unique parent history defined by the set. (Below the maximally refined classical histories are the fine grained or quantum histories, where probabilities are no longer additive and different histories significantly interfere with each other. The bottom level consists of complete microstates, which fully specified states.) The decoherence approach is useful in considering the effect of the environment on a system. In many ways the environment, acting as a heat sink, can be regarded as performing a succession of measurement-like interactions upon any system, inducing associated system splits. All the environment basis is is a basis choosen so as to minimise the cross- basis interference terms. It makes any real-worlds calculation easy, since the cross terms are so small, but it does not *uniquely* select a basis, just eliminates a large number. 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 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 "Do worlds diverge or 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 Albert's April 94 Scientific American article.) The two theories should not be confused. Michael Price price@price.demon.co.uk Article 75227 of sci.physics: Newsgroups: sci.physics From: price@price.demon.co.uk (Michael Clive Price) Path: beaux!kiki.icd.teradyne.com!netcomsv!netcomsv!ix.netcom.com!howland.reston.ans.net!news.sprintlink.net!pipex!demon!price.demon.co.uk!price Subject: Re: John Mc Carthy's request re: Penrose (mechanisms for References: <9412201651.ab23090@dispatch.demon.co.uk> X-Posting-Host: price.demon.co.uk Date: Fri, 30 Dec 1994 00:00:00 +0000 Message-ID: <788743556snz@price.demon.co.uk> Sender: usenet@demon.co.uk Lines: 92 <3dlo9h$lko@senator-bedfellow.MIT.EDU> Date: Thu, 29 Dec 94 23:25:56 GMT Reply-To: price@price.demon.co.uk X-Newsreader: Demon Internet Simple News v1.29 Lines: 51 Me: > John, as usual, misrepresents Everett, who did not share Baez's > selective aversion to metaphors. Everett did not shy away from > saying that observers split. "John Baez" writes: > I am far from books at the moment so if there is some sentence where > Everett says something like "observers split" it would be nice to > see it. Since this has come up a number of times, I have stuck it in my FAQ: Q32b Was Everett a "splitter"? ------------------------- Some people believe that Everett eschewed all talk all splitting or branching observers in his his original relative state formulation [2]. This is contradicted by the following extract: [...] Thus with each succeeding observation (or interaction), the observer state "branches" into a number of different states. Each branch represents a different outcome of the measurement and the *corresponding* eigenstate for the object- system state. All branches exist simultaneously in the superposition after any given sequence of observations.[#] The "trajectory" of the memory configuration of an observer performing a sequence of measurements is thus not a linear sequence of memory configurations, but a branching tree, with all possible outcomes existing simultaneously in a final superposition with various coefficients in the mathematical model. [...] [#] Note added in proof-- In reply to a preprint of this article some correspondents have raised the question of the "transition from possible to actual," arguing that in "reality" there is-as our experience testifies-no such splitting of observers states, so that only one branch can ever actually exist. Since this point may occur to other readers the following is offered in explanation. The whole issue of the transition from "possible" to "actual" is taken care of in the theory in a very simple way- there is no such transition, nor is such a transition necessary for the theory to be in accord with our experience. From the viewpoint of the theory *all* elements of a superposition (all "branches") are "actual," none are any more "real" than the rest. It is unnecessary to suppose that all but one are somehow destroyed, since all separate elements of a superosition individually obey the wave equation with complete indifference to the presence or absence ("actuality" or not) of any other elements. This total lack of effect of one branch on another also implies that no obsever will ever be aware of any "splitting" process. Arguments that the world picture presented by this theory is contradicted by experience, because we are unware of any branching process, are like the criticism of the Copernican theory that the mobility of the earth as a real physical fact is incompatible with the common sense interpretation of nature because we feel no such motion. In both case the arguments fails when it is shown that the theory itself predicts that our experience will be what it in fact is. (In the Copernican case the addition of Newtonian physics was required to be able to show that the earth's inhabitants would be unware of any motion of the earth.) [2] Hugh Everett III _"Relative State" Formulation of Quantum Mechanics_ Reviews of Modern Physics Vol 29 #3 454-462, (July 1957) A condensation of [1] focusing on observation. > Anyway, what I was ineptly trying to say is that, regardless of > whether Everett saw it this way, his work demonstrates that there > is no need to supplement quantum theory with any sort of extra > theory about how "perceiver's states split", along the lines of > theories Granquist was proposing -- e.g. that they "pick the branch > in which they have the longest life," most sex, or what have you. > Quantum mechanics is all ya need. Of course. > I don't care if people using quantum mechanics use the "split" > metaphor as long as it doesn't drive them nuts and make them start > wondering how their consciousness picks which branch to go along, > like someone sledding down a branching network of paths. Sorry, John, but not using the "split" metaphor isn't going to clear things up for them, but, instead, makes it look like you either have failed to understand their concerns (which I know isn't true) or are delibrately avoiding the issue. Michael Price price@price.demon.co.uk Article 75797 of sci.physics: Newsgroups: sci.physics From: price@price.demon.co.uk (Michael Clive Price) Path: beaux!kiki.icd.teradyne.com!netcomsv!netcomsv!ix.netcom.com!howland.reston.ans.net!news.sprintlink.net!demon!price.demon.co.uk!price Subject: Re: John Mc Carthy's request re: Penrose (mechanisms for Distribution: world References: <9412201651.ab23090@dispatch.demon.co.uk> X-Posting-Host: price.demon.co.uk Date: Thu, 5 Jan 1995 00:00:00 +0000 Message-ID: <789207381snz@price.demon.co.uk> Sender: usenet@demon.co.uk Lines: 292 <788743556snz@price.demon.co.uk> <1994Dec30.235640.11449@galois.mit.edu> <3e4a0o$5f@mtnmath.mtnmath.com> Date: Wed, 04 Jan 95 08:16:21 GMT Reply-To: price@price.demon.co.uk X-Newsreader: Demon Internet Simple News v1.29 Lines: 22 "Paul Budnik" writes: > [Baez] is deliberately avoiding the issue [of the quantum spltting > of worlds in the many-worlds interpretation] because unlike [Price] > he understands that there is no solution to this problem > within the formalism of the existing theory. Only hearing what you want to hear, as usual, eh? > In a sense you have the better position. If you keep trying to > understand how the split emerges from the existing > formalism you may in time recognize that QM is an incomplete theory. Everett explained how splits emerged. John and I both think Everett solved it completely. > As long as Baez avoids the issue he will remain a hopeless case. As long as you remain so clueless, ignorant and arrogant you will remain a hopeless case. Go and read Feynman vol III to address one of these. **************** for the interested ***************** Q3 What is 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? Q3 What is many-worlds? -------------------- AKA as the Everett, relative-state, many-histories or many-universes interpretation or metatheory of quantum theory. Dr Hugh Everett, III, its originator, called it the "relative-state metatheory" or the "theory of the universal wavefunction" [1], but it is generally called "many- worlds" nowadays, after DeWitt [4a],[5]. Many-worlds comprises of two assumptions and some consequences. The assumptions are quite modest: 1) The metaphysical assumption: That the wavefunction does not merely encode the all the information about an object, but has an observer-independent objective existence and actually *is* the object. For a non-relativistic N-particle system the wavefunction is a complex-valued field in a 3-N dimensional space. 2) The physical assumption: The wavefunction obeys some standard linear deterministic wave equation 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. Measurement and observation 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. The histories form a branching tree which encompasses all the possible outcomes of each interaction. (See "Why do worlds split?" and "When do worlds split?") Every historical what-if compatible with the initial conditions and physical law is realised. 2) That the conventional statistical Born interpretation of the amplitudes in quantum theory is *derived* from within the theory rather than having to be *assumed* as an additional axiom. (See "How do probabilities emerge within many-worlds?") Many-worlds is a re-formulation of quantum theory [1], published in 1957 by Dr Hugh Everett III [2], which treats the process of observation or measurement entirely within the wave-mechanics of quantum theory, rather than an input 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, after the subsystems have jointly interacted, henceforth correlated with, or dependent upon, each other. Each element of the superposition - each a product of subsystem states - evolves independently of the other elements in the superposition. The states of the macrosystems are, by becoming correlated or entangled with each other, impossible to understand in isolation from each other and must be viewed as one composite system. It is no longer possible to speak the state of one (sub)system in isolation from the other (sub)systems. Instead we are forced to deal with the states of subsystems relative to each other. Specifying the state of one subsystem leads to a unique specification of the state (the "relative state") of the other subsystems. If one of the systems is an observer and the interaction an observation then the effect of the observation is 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 inducing local splitting or decoherence of branches of the universal wavefunction [7a], [7b], [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 embedded within it. All outcomes exist simultaneously but do not interfere further with each other, each world having split into mutually unobservable but equally real worlds. Q4 What is a "world"? ------------------ Loosely speaking a "world" is a complex, partially closed set of interacting sub-systems which doesn't significantly interfere with the 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 the latter is reserved the totality of worlds. 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 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 (the measured system) by a Geiger counter (the measuring apparatus) leads to the generation of a "click" (high-level change). The absence of a charged particle does not generate a click. The interaction is with those elements of the charged particle's wavefunction that passes *between* the charged detector plates, triggering the amplification process (an irreversible electron cascade or avalanche), which is ultimately converted to a click. A measurement, by this definition, does not require the presence of an observer. Q6 Why do worlds split? --------------------- What is decoherence? -------------------- Worlds, or branches of the universal wavefunction, split when different components of a quantum superposition "decohere" from each other [7a], [7b], [10]. Decoherence refers to the loss of coherency or absence of interference effects between the elements of the superposition. For two components or worlds to interfere with each other all the atoms, subatomic particles, photons etc, in each world, have to be in the same state, usually in the same place. For small microscopic systems it is quite possible for all their components to match at some future point. In the double slit experiment, for instance, it only requires that the divergent paths of the diffracted particle overlap again at some point for an interference pattern to form, because only the single particle has been split. For more complex systems overlapping becomes harder because all the constituent particles have to overlap with their counterparts simultaneously. For a macroscopically sized system such future coincidence of positions in all the components is virtually impossible. Irreversible processes, in particular, will destroy almost any possibility of interference effects being restored in the future. An irreversible process is one in, or linked to, a system with a large number of internal, unconstrained degrees of freedom. Once the process has started then alterations of the values of the many degrees of freedom leaves an imprint which can't be removed. If we try to intervene to restore the original status quo the intervention causes more disruption elsewhere. In QM jargon we say that the components (or vectors in the underlying Hilbert state space) have become permanently orthogonal due to the complexity of the systems increasing the dimensionality of the vector space, where each unconstrained degree of freedom contributes a dimension to the state space. In a high dimension space almost all vectors are orthogonal, without any significant degree of overlap. Thus vectors for complex systems, with a large number of degrees of freedom, naturally decompose into mutually orthogonal components which, because they can never significantly interfere again, are unaware of each other. From the point of view of the complex systems they have split into different, mutually unobservable worlds. According to thermodynamics each activated degree of freedom acquires kT energy. This works the other way around as well: the release of approximately kT of energy increases the dimensionality available to the system. Even the quite small amounts of energy released by a irreversible frictive process are quite large on this scale, increasing the size of the associated Hilbert space. Contact between a system and a heat sink is equivalent to increasing the dimensionality of the state space, because the description of the system has to be extended to include all parts of the environment in causal contact with it. This is, therefore, 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. An irreversible process will always produce decoherence which splits worlds. (See "Why do worlds split?", [7a], [7b], [10] 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 in the particle's wavefunction. The Geiger counter splits when the amplification process became irreversible. (See "What is a measurement?") 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. 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 "Why do worlds split?") Decoherence [7a], [7b] occurs when irreversible macro-level events take place and the macrostate description of an object admits no single description. (See "Does the EPR experiment prohibit locality?" for a fully worked out example of this.) 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 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. 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, completly isolates the cat from its environment and vice versa. After a while an investigator 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 onlooker is split into two copies only when the box is opened and they are altered by the state 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 just split off world. The investigator can deduce, after the event, by examining the cyanide mechanism, that the cat split prior to opening the box. Michael Price price@price.demon.co.uk Article 75822 of sci.physics: Path: beaux!kiki.icd.teradyne.com!netcomsv!netcomsv!ix.netcom.com!howland.reston.ans.net!gatech!bloom-beacon.mit.edu!uhog.mit.edu!nntp.club.cc.cmu.edu!cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!fas-news.harvard.edu!scws17.harvard.edu!mcirvin From: mcirvin@scws17.harvard.edu (Matt McIrvin) Newsgroups: sci.physics Subject: Re: Have hidden-variable explanations been disproven? Date: 5 Jan 1995 21:41:52 GMT Organization: Harvard University, Cambridge, Massachusetts Lines: 37 Message-ID: <3ehp30$3hf@decaxp.harvard.edu> References: NNTP-Posting-Host: scws17.harvard.edu In article , DOYLE PATRICK wrote: > I recall reading somewhere that hidden-variable explanations for quantum >effects had been disproven. In other words, no matter what kind of hidden- >variable scheme one comes up with, it simply will not correspond to >observation. The actual statement is rather less strong: it applies only to *local* hidden-variable theories which attempt to explain EPR correlations without any faster-than-light transmission of information. It was once thought that such theories could reproduce all the predictions of quantum mechanics, but J. S. Bell showed that this was not the case. There was a statement known as "Bell's inequality" that was satisfied by these theories and violated by quantum mechanics. The best experimental tests of Bell's inequality have come out on the side of quantum mechanics; the most famous of these was performed by Alain Aspect's group in Paris in the early 1980s. David Bohm's *nonlocal* hidden-variable theory is completely consistent with observations; in it information about correlations is transmitted instantaneously (in a special frame) by the "quantum potential." Of course, this theory fails to possess the desired qualities that provoked Einstein, Podolsky, and Rosen to propose hidden-variable theories in the first place, but it does have the (possible) advantage of being a deterministic theory. One good popular description of EPR correlations and Bell's inequality is in Heinz Pagels' _The Cosmic Code_. N. David Mermin has written many excellent, somewhat more technical _Physics Today_ columns bearing on the subject as well, and there's a fairly good description of it in Sakurai's _Modern Quantum Mechanics_ (though it assumes that you know all about the formalism of spin in quantum mechanics). The best exposition of Bohm's theory is Bohm and Hiley, _The Undivided Universe_. -- Matt 01234567 <-- Indent-o-Meter McIrvin ^ Harnessing tab damage for peaceful ends!