Wednesday, October 21, 2009

MWI proposals that include modifications of physics

Previous: Decision Theory and other approaches to the MWI Born Rule, 1999-2009

The greatest appeal of the Everett-style Many-Worlds Interpretation of QM - that is, the wave equation alone, or standard MWI - is its simplicity in terms of mathematics and physics. While all other interpretations need to add extra things to the wave equation - adding in hidden variables with dynamics of their own, or modifying the wave equation itself to include random wave collapse processes - the Everett MWI states that the standard wave equation alone can explain everything we observe.

Yet, despite numerous attempts and claims to the contrary (and putting aside the possibilities for my own approach for now), the Born Rule probabilities have not been derived from the Everett picture. Thus, it may prove necessary to add new physics to our description of QM after all.

However, some approaches attempt to retain much of the advantage in simplicity of the MWI, as well as its multiple-worlds character, while making such modifications. It's a promising idea, and these MWIs certainly take inspiration from the Everett-style MWI, but they add too much to the pure wave picture to satisfy true Everett-style MWI partisans.

a) Hidden variables introduce complexity not only because of the extra dynamic equations, but because they require some choice of initial conditions. The wavefunction of QM also requires initial conditions, of course, but there is reason to hope that some simple equation could govern those initial conditions; the Hartle-Hawking 'no boundary' condition for the wavefunction of the universe is a well-known example of such a proposal (though it has problems of its own). Particle-like hidden variables do not seem amenable to such simple specification of initial conditions. However, if all possible sets of hidden variable initial conditions are equally real, then the overall simplicity of initial conditions for the multiverse is restored.

'Continuum Bohmian Mechanics' (CBM) is the best-known example of this approach. Like the Pilot Wave Interpretation, it has particle-like hidden variables; but instead of just one set of them, it has a continuous distribution of such sets, which act much like a continuous fluid. In addition to the possibility of simpler initial conditions, CBM may be immune to the fatal flaw of the PWI, which is being 'many-worlds in denial'. In other words, in the 'single-world' PWI, with one set of hidden variables, most of the observers will end up being implemented by the many worlds of the wavefunction, so the hidden variables won't matter. With CBM, the number of hidden variable sets is also infinite, so a typical observer could depend on the hidden variables after all. (This latter claim still needs to be proven compatible with computationalist considerations, but it is plausible.)

The hidden variables in the PWI follow the Born Rule, so CBM should be OK in that regard. But CBM retains the other features of the PWI that many physicists dislike, namely non-locality and a preferred reference frame. It is also not clear how well a relativistic version of the PWI works, and CBM inherits such problems. (Granted, no physics that works for quantum general relativity is known yet.) Also, even CBM is not as simple as the standard MWI.

I regard CBM (and more generally, MWI's with hidden variables) as something useful to keep in mind, as it is one of the few interpretations of nonrelativistic QM that seems to actually work in terms of being compatible with the Born Rule and not having an 'MWI in denial' problem. But other possiblities must be thoroughly explored before I would consider endorsing CBM as being likely to be true.

b) Another approach is to retain a pure wavefunction picture as in Everett's MWI, but to make the wavefunction be discrete instead of continuous. Discrete space is not what is meant here, but rather a discrete nature of the wavefunction itself. Buniy et al advocate such an approach.

The most obvious way to do that might be to assume that the wavefunction is represented by an integer function on configuration space rather than a continuous function. (If configuration space is also discrete, that is one way an approximate discrete numerical representation of a continuous wave function might be done on a digital computer.)

Buniy et al propse a somewhat different different assumption, in which wavefunctions seperated by a term of some mimimum squared amplitude are condidered to be the same.

Because the wave function (or perhaps I should say its 'populated' region) is constantly and rapidly expanding into new areas of configuration space (e.g. as entropy increases), its numerical value is constantly imploding. I will call this the Wavefunction Value Implosion (WVI). If the universe is finite, then this effect will be finite, but exponentially large as a function of the number of particles in the universe. Thus, a discrete wavefunction could not be detected experimentally if its discrete nature is small enough, until such time as the WVI brings the populated part of the wavefunction below that scale, and then presumably time evolution will radically change or effectively stop; I will call this the Crash.

Discrete physics has a certain appeal to some people, independent of any possible role in quantum mechanics. Wolfram's book "A New Kind of Science" discusses such views. Also, the idea that all possible mathematical universes physically exist (the Everything Hypothesis, which will be discussed in a later post) may be somewhat more tractable if it is restricted to digital systems (though, despite its undeniable appeal, it still has problems even then).

If the wavefunction is discrete, would that help explain the Born probabilities? Buniy et al argue that it would, by shoring up the old "frequency operator" attempted derivation by extending it to finite numbers of measurements rather than infinite. This argument notes that, after repeated measurements, terms in the wavefunction which don't have the Born frequencies have much smaller amplitudes than the terms with the 'right' frequencies. With a minimum amplitude cutoff, most of the un-Born terms would be eliminated. This argument does not seem very satisfactory, as we are interested in situations with small numbers of meaurements, and thus small factors of difference in amplitude, while the digital cutoff would have to be very far from a significant fraction of the total amplitude if the Crash is not yet upon us. In practical situations, other factors would affect amplitudes much more. For example, entropy production is not associated with low probability, but it results in numerous sub-branches each of which shares a fraction of the original squared amplitude.

Shoring up the 'Mangled Worlds' argument would seem a more promising approach. There are many sub-branches comprising each macroscopically distinguishable world, and they tend to have a log-normal distribution in squared amplitude. As Hanson showed, a cutoff in the right range of squared amplitudes would lead to Born Rule probabilities. This cutoff must be uniform across branches, which Hanson's 'mangling' mechanism by larger branches actually fails to provide, but a digital cutoff could provide it. I will tentatively say that this is a possible mechanism for the Born Rule, though I need to study it more before I can say for sure that there are no problems that would ruin it. In particular, if the number of worlds changes too much over time or the era in which the Born Rule holds is too short, that would indicate a problem.

c) Another mechanism that improves on 'Mangled Worlds' is my own idea in which random noise in the initial wavefunction means that larger volumes in configuration space per implemented computation are required for low-amplitude sub-branches, which can lead to the Born Rule. This requires new physics in the form of special initial conditions, but hopefully not in terms of time evolution. It is possible that this leads to a Boltzmann Brains problem. I will discuss this, as well as an alternative in which the Born Rule is due to a special way to count computations (which avoids new physics - if it can be justified) in later posts.

d) The Everything Hypothesis (that all possible mathematical stuctures exist) can be used directly in an attempt to predict what a typical observer would observe. Some have argued that this explains what we observe, including the Born Rule. The Everything Hypothesis will be discussed in a post of its own.

e) Other MW schemes for modifying physics have been proposed.

One example is Michael Weismann's idea involving sudden splitting of existing worlds into proposed new degrees of freedom, with a higher rate of such splitting events for higher amplitude worlds. The problem with it is that if new worlds are constantly being produced, then the number of observers would be growing exponentially. The probability of future observations, as far into the future as possible, would be much greater than that of our current observations. Thus, the scheme must be false unless we are highly atypical observers, which is highly unlikely.

David Strayhorn had an idea based on general relativity, in which different topologies correspond to different sub-branches of the wavefunction. This approach is not well-developed as of yet and it has problems that I think will prevent it from working. I discussed it in various post on the OCQM yahoo group.

26 comments:

  1. Do you have a link regarding your suggestion that "random noise in the initial wavefunction means that larger volumes in configuration space per implemented computation are required for low-amplitude sub-branches"?

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  2. Perhaps email me at rhanson@gmu.edu?

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  3. The only link I have for that right now is my MCI paper: http://arxiv.org/abs/0709.0544

    Basically, we can make many independent mappings by dividing up configuration space. The idea is that 'noise' ruins the reliable transitions that computations need for mappings from the wavefunction to formal states. This can be overcome by using a mapping from a larger volume of configuration space because the "noise" would be random, with a net effect that grows as the square root of the volume, while the "signal" would all be pulling in the same direction and its effect would grow linearly with the volume.

    Thus if you have 1/2 the "signal" amplitude, you need to use on average four times as much "real estate" per implementation (and so have 1/4 as many implementations) in order to overcome the same amplitude of noise.

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  4. What do you think of Wallace's "emerging branches" model? Do you think it is sufficient to give rise to a ontology?

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  5. An ontology for a model is just that which exists according to the model. In Wallace's case, it's clear that he uses the standard MWI ontology that the wavefunction is what exists. Branching is not fundamental in the MWI ontology; the Shrodinger equation is all you need. What he lacks is a correct derivation of the Born Rule.

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  6. Great blog Mallah.

    I do have two objections though.

    1) The "empty branches" would not neccesarily have to give rise to any observers.
    Have you read Peter J. Lewis's paper where he adresses this exact issue without taking sides?

    2) You say that if MWI had been able to derive Born Rule then the case for MWI would have been made beyond a reasonable doubt.
    I think 99% of physicists and philosophers involved in QM would strongly disagree with this statement.
    MWI still has some other issues:
    Maudlin's chapter in the Many Worlds? 2010 book
    David Alberts narratability objection to Everett
    Adrian Kent raises more than just the probability issue in his 2 papers

    And more recently Miroljub Dugic has shown that there is severe conflict with entanglement relativity and the "splitting" that takes place in the Neo-Everettian interpretation.

    -

    I loved your post on "Everything hypothesis" and look forward to your next post!

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  7. Thanks, qpdb.

    1. Yes, I read Lewis' paper and was not impressed. He basically makes 2 arguments.

    The first amounts to 'PWI has problems with 'empty branches' being real, but so does MWI with other stuff, so PWI is still a viable option'. It's pathetic.

    His second argument is a bit more interesting. He notes that there is no agreed-upon definition of the patterns that functionalist theories of mind rely upon, so we can choose the definition in a way that makes the PWI viable.

    Well, we could, but that would be totally dishonest of us unless we would have found a definition like that at all plausible if we weren't just doing it to save the PWI. And I would have to say that I certainly wouldn't have, and I don't think too many others honestly would have.

    Gotta go, so I'll address your other comments later.

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  8. Thanks, can't wait for the answers:)

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  9. BTW, Lewis' paper can be found here:
    http://philsci-archive.pitt.edu/3145/

    A couple more answers:

    > Maudlin's chapter in the Many Worlds? 2010 book

    Maudlin argues that the appearance of classical mechanics has not been derived from the wavefunction-only MWI.

    What he's missing is that the wavefunction implements many of the _same_ computations as would be the case in classical mechanics. The world appears classical to us because that's the sort of computation that our brains perform.

    > David Albert's narratability objection to Everett

    Albert argues that in relativistic QM, knowing the wavefunction's history in one reference frame doesn't tell you everything about its history in other frames; he calls this non-narratability. He doesn't like this, and thinks that the MWI may need a preferred frame so we won't have to worry about it. But that supposedly negates the locality advantage of the MWI.

    Most people don't share Albert's aversion to non-narratability, so it may not be much of an issue on that account. But there's a better reason why it's a non-issue.

    If we're talking about the wavefunction evolving in time, then we're using the Schrodinger picture of QM. (A 'picture' in QM is a version of the equations.) This picture very explicitly and obviously has a preferred reference frame and a preferred time variable, and is usually used for nonrelativistic QM.

    If you want to put QM (and the MWI) in a Lorentz-invariant and local framework, then you have to use the Heisenberg picture of quantum field theory. Because it's local, non-narratability does not arise in that picture.

    Personally I prefer the simpler Schrodinger picture (the usual wavefunction picture) and I think the preferred reference frame is a feature, not a bug, which has advantages for quantum gravity. The big advantage of the MWI is not lack of a preferred frame, but simplicity and the fact that it doesn't ignore the "other branches" of the wavefunction as for example the PWI does. However, even though the Shrodinger picture is nonlocal, the fact that it _is_ in some sense "dual to" the local Heisenburg picture is surely a plus for it.

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  10. > Adrian Kent raises more than just the probability issue in his 2 papers

    As it happens, a paper that argues against Kent's views (which is not a particularly difficult task!) was recently posted on the arxiv.

    http://arxiv.org/abs/1111.2563

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  11. Thanks for the answers.
    I must say I disagree with the response to Kent, but that was not even the point.
    Kent raises other issues regarding MWI besides the probability probem that this paper does not adres at all.

    If you are ok with a preferred reference frame, then you have to agree that the interpretation doe not have a upper hand to other realist interpretation like Bohm that postulate a preferred foliation...

    Atleast Bohm derives Born Rule and like Lewis shows, the argument by MWI'ers that the empty branches are worlds is not neccesary...

    Did you check out the paper by Miroljub?

    Also why do you believe in MWI when you clearly see it's insoluble problem with probability?
    Whatever MWI that would end up working would surely be way uglier than a single universe interpretation

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  12. qpdb wrote:

    > Kent raises other issues regarding MWI besides the probability probem that this paper does not adres at all.

    Could you be specific as to the issue you think is important? Much of Kent's work is just attacking the decision theoretic "derivation" of the probabilities, and as you know, I agree that "derivation" doesn't work.

    > If you are ok with a preferred reference frame, then you have to agree that the interpretation doe not have a upper hand to other realist interpretation like Bohm that postulate a preferred foliation...

    No. Did you not read my reply above? The MWI has a huge upper hand due to simplicity and taking the "other branches" into proper account.

    > At least Bohm derives Born Rule and like Lewis shows, the argument by MWI'ers that the empty branches are worlds is not neccesary...

    No. As I explained, Lewis' argument fails completely. The so-called empty branches implement computations that should be conscious; or in his less sophisticated language, they have the patterns that functionalist hypotheses about minds require. This conclusion can only be evaded by being totally dishonest and implausible about deciding on criteria for those things.

    > Did you check out the paper by Miroljub?

    Yes; I'll comment on that later.

    > Also why do you believe in MWI when you clearly see it's insoluble problem with probability?

    Who said it's insoluble? It's not easy to solve, and we may need more information on quantum gravity to get the correct solution, but as you know I have made proposals already on how to solve it.

    On the other hand, trying to get ANY non-MWI to work seems UTTERLY hopeless. Hidden variable models, like the PWI, will ALWAYS fail due to the presence of the other branches which should give rise to observers. Collapse models such as GRW don't fully eliminate the other branches either; they just make them small. They are also way more complicated. In ANY model, we still need an account of observers, measure of consciousness, and their relation to physical systems.

    The Born Rule problem is the only criticism of the MWI that isn't easy to dismiss despite the many criticisms that have been attempted. That, in itself, speaks very well of the MWI. But of course, we still need to solve it.

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  13. Jack Mallah wrote:

    >Could you be specific as to the issue you think is important? Much of Kent's work is just attacking the decision theoretic "derivation" of the probabilities, and as you know, I agree that "derivation" doesn't work.

    Yes, check his paper in 1997 on the preferred basis problem etc.

    >> Did you check out the paper by Miroljub?

    >Yes; I'll comment on that later.

    Do so, it is a slam dunk against MWI.
    Even if one takes Wallace's route of vague approximate splitting etc. (which has no root in known physics, pure speculation) you still can't escape the conclusions...



    >Who said it's insoluble? It's not easy to solve, and we may need more information on quantum gravity to get the correct solution, but as you know I have made proposals already on how to solve it.

    Most people I have ever discussed this with (amongst physicists) agree that it is indeed insoluble and I agree.
    MWI has no way of making sense of Born Rule "naturally".

    >On the other hand, trying to get ANY non-MWI to work seems UTTERLY hopeless. Hidden variable models, like the PWI, will ALWAYS fail due to the presence of the other branches which should give rise to observers. Collapse models such as GRW don't fully eliminate the other branches either; they just make them small. They are also way more complicated. In ANY model, we still need an account of observers, measure of consciousness, and their relation to physical systems.

    I agree that collapse is hopeless, but there are quite a lot of other options ranging from new physics, hell with the neutrino experiment and the fact that we know next to nothing about quantum gravity indicates that it is almost inevitable that we will not have to rethink our models in PROFOUND ways.

    Even if you were to insist on keeping quantum mechanics today as "the last word" I think QM implies a form of retrocausality way more than it implies many worlds.

    A single outcome from a single effect is unquestionably the most natural thing and the fact that MWI can't solve the Born rule, preferred basis or the new issues now raised by Miroljub just use a nailgun on the coffin.

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    1. Dear Jack,

      i couldn't detect your arguments against relevance of my (and my co-authors') refutation of the Everett MWI. Could you please elaborate it a bit?

      Delete
  14. Also, let's say the argument is right, the branches in dBB yields worlds (assuming the pilot wave is ontological and not nomological).
    Why wouldn't this Many Worlds view be better than that of Deutsch et al?

    In the Pilot Wave Worlds you have no intersecting of branches or splitting of any kind...
    Here the Born Rule would obviously come in the form of frequency of branches...

    so why wouldn't you rather prefer this to the Everettian?

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  15. qpdb, you've seen my email reply to Dugic. Of course that discussion will continue for a bit, but I think I've made it clear in my emails why his paper is irrelevant to the MWI. If you want to follow up on that, do it in the emails.

    Of course the wavefunction (and don't call it by any other name: it is the standard wavefunction of QM) in the PWI would be ontological, which is only to say that it would exist; it's part of the mechanics. Anyone who fails to see that is only fooling himself.

    The regular PWI is thus FAPP the same as the regular MWI; it would have mostly the same observers.

    You must be thinking of Continuum Bohmian Mechanics, which is the PWI but with infinitely many sets of hidden variables instead of just one. That is an honest MWI version of the PWI, in which the hidden variable observers could outnumber the ones in the wavefunction and thus would be relevant.

    CBM seems like it could work, though I should study it in more detail. It deserves an honorable mention and I gave it one.

    Being that the wavefunction is the same in the PWI/CBM as in the MWI, there would be exactly the same branching and so on. I guess what you mean is that the Born Rule would come from counting the sets of hidden variables in CBM. That's a nice feature, yes.

    But I don't think it's right. Those hidden variables seem a lot like Ptolemaic epicycles to me. They're jury-rigged to give the right answer to match what we've observed, but provide no insight as to why things would be like that.

    For example, one of the neat things about QFT is that there are really no particles, just quantized waves, which can behave a lot like particles. But because they're not really particles, it's not surprising that exchanging them with each other gives a symmetry. We pull a trick by symmetrizing the wavefunction with respect to exchanges (or anti-symmetrizing for fermions) in order to pretend we have particles. This leads to new behaviors such as Bose-Einstein condensation and so on. Waves can also be produced or destroyed, so we have things like pair production that we never could have had with actual particles instead of waves.

    In the PWI, bosons have hidden variable fields associated with them, while fermions have actual particle-style hidden variables. There are infinitely many "dormant" fermion particle hidden variables, which we can put in motion when we need them in pair production.

    Does that work? Probably (the PWI still has technical issues with QFT). But is it pretty? No. It just seems like overkill. We start with a perfectly good set of wavelike dynamics - the wavefunction - which would already lead to observers, even if the probabilities would be different from what we know. On top of that we add both fields and particles, and assume that the equations are just what we'd need to get them to explain our observations.

    I'd rather see what other possibilities are out there before buying into such a model.

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  16. I have you ask you one question before I can go on to comment on the rest of the post.

    If one is to postulate that the wavefunction is real and one believes one can get all the necessary structure extracted from it to account for 3Space and all things existing within it, then why doesn't all of his already exist in Hilbert Space?

    A branch in the WF (an area in H-space where the WF is non-zero) manifests in the form of a "world", while areas in H-space where the WF is zero (yet the "structure" is still there, as that's part of H-space!) do not.

    _WHY?_

    If one is going to attack the pilot wave interpretation by saying that "all the other branhes give rise to worlds" by appealing to functionalism, then why is functionalism not good enough when it comes to hilbert space?

    Also:
    The initial conditons will always seem "jury rigged" unless you posit that _EVERYTHING_ exists ala Tegmark's MUH.
    The initial conditions of any potential MWI will also be jury rigged, admittedly less than that of a single world, but I do not think that is enough argument to reject the single world..

    From what I gather, you also reject the Mathematica Universe Hypothesis or "The Everything Hypothesis" so you know that simpler does not equal correct.

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  17. qpdb, yes, that structure would exist in areas where the WF is zero, but there would be no dynamics - no change over time - and thus no functioning.

    A much more interesting problem is that there wouldn't actually _be_ any areas where the WF is zero! Due to tunneling, every part of the Hilbert space would get at least a _very_ tiny amplitude. We need to explain why typical observers aren't found in those VAST areas (which as we now know are mainly dominated by huge black holes with their high entropy).

    If we have the Born rule, then the problem is solved, because the total squared amplitude in those areas is very small. Without it we would need another way to get rid of those very small amplitude observers, and suggestions include "mangling" by random noise (as my proposal that I mentioned already includes) (but would that be enough?), or that the wavefunction takes on discrete values (e.g. is digitized) and so really is zero in those places where it would be very small. I consider this one of the most important open problems for deriving the Born Rule in the MWI. I'll be discussing these issues more later as I get further into the posts I plan for the blog.

    I reject the "MUH / Everything Hypothesis" but only because such a mathematical model apparently can not be well defined. It would need to be unique, including having a unique measure distribution, but with an infinity of elements the order in which they are listed contributes to the measure distribution. If it were not for this problem, I would prefer the Everything Hypothesis, which would have been the simplest possible thing.

    Even so, I think the totally of whatever exists probably includes everything and is probably "relatively simple", such as you might get by just picking a "simple" rule for the order in which to list the elements of everything. It's a lot like the Everything Hypothesis FAPP, but sadly, it can't claim Platonic necessity.

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  18. Hmmm, I have to think a little more about whether that is a good enough explanation to say why we should disregard the structre in hilbert space.

    However, yes the Born Rule problem becomes very apparant when you think about it in that context.
    Which again just tells me how wrong MWI actually is...

    I want to know out of curiosity: what would it take for you to give up trying to save MWI?
    Or at least accept that if a MW picture are going to fit reality it will need radical changes, such as for instance Many Bohm worlds ?

    On Everything Hypothesis, ok that's fair.
    I think you should write a seperate article on Tegmark's arguments directly before a lot of people start adopting it.

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  19. What it would take for me to think that a single-world model is more likely is that it would need to be simpler, consistent with my views of consciousness (unlike single world PWI), give the Born Rule, and explain as much as a corresponding many worlds version. I don't think that's possible.

    I'm open to the idea that there will need to be changes to the physics. This blog post was all about such possibilities.

    Many Bohm worlds is an MWI with hidden variables, but based on generalizing what was intended to be a 'single world' model. Maybe a simpler model could be obtained by making a hidden variable model that is meant to be an MWI to start with. For example, it has been speculated that the Schrodinger equation could emerge as the "hydrodynamic limit" of a condensed-matter-like model. If such a model were a simple MWI with hidden variables and gave the Born Rule, I would find that quite attractive. Such a model might also have a built in source of 'noise' and/or a natural reason for the wavefunction to have discrete values. That said, I doubt it is true since the wavefunction lives in such a high-dimensional configuration space.

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  20. But there is nothing hindering the possibility that the wavefunction is not ontological, so then what would be inconsistent with your views of consciousness?

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  21. qpdb, I can hardly believe that you're still proposing such nonsense.

    Saying that something is "not ontological" is just saying that it doesn't exist.

    In the PWI, the WF obviously does exist and affects the particles.

    Saying that "the WF in the PWI is not ontological" is saying that it exists (since it is part of the PWI) but it doesn't exist. It is an obvious contradiction.

    You might want to read (if you haven't already) the debate between me and I. Schmelzer in the comments on here:
    http://onqm.blogspot.com/2009/07/why-mwi.html

    To quote myself "If it has real effects, it's real. The WF in the PWI is real. Any other view is doublethink at best, and makes no sense at all."

    BTW, if computation is to be a meaningful notion (and if it isn't, we are stuck with dualism about consciousness), then even "laws of physics" must exist in just as strong of a sense as dynamical variables do.

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  22. I was not talking about PWI at all in that comment, I was talking in general, QM might not have a ontological wavefunction in its final explanation..

    So my question still remains, if the wavefunctino ends up not being ontological, what is the problem of consciousness?

    how does your view differ from functionalism?

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  23. qpdb, I'm not sure exactly what you're getting at.

    If there is a model which doesn't have a WF in it, I'd treat it no differently from one that does in terms of consciousness.

    Of course, given the predictive power and central dynamical role of the wavefunction, it would be very surprising if there could be any model which doesn't have the WF at least as an approximate or emergent structure.

    For example, if the underlying physics is a world where classical Newtonian mechanics holds, and Bob has a super computer in his basement where as a hobby he plays with alternative physics simulations such as QM, and our universe is one of his simulations, then the WF is an emergent structure in the classical switches in Bob's computer; as such it exists and implements computations.

    There are different varieties of functionalism. My view is one of them, but more precise than most.

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  24. Yes, but my point is there could be some other forms of hidden variables.
    Or perhaps cellular automata, Gerard 't Hooft describes this in a very recent paper (dec 2011) http://de.arxiv.org/PS_cache/arxiv/pdf/1112/1112.1811v1.pdf

    In these interpretations the wavefunction would not be a "wave" actually existing in 3N space or any other space.

    This is not in conflict with functionalism at all.

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  25. The model 't Hooft describes there is based on the Shrodinger equation, not on cellular automata, while supposedly avoiding 'collapse' and MWI.

    It doesn't surprise me that 't Hooft's paper is full of hand waving and vague hopes. It does surprise me, a little, that he would stoop to endorsing the grossly implausible idea of 'conspiracy theory' initial conditions to explain away Bell's theorem.

    But what really amazes me is that a physicist of his stature would make so elementary a mistake about quantum mechanics as to claim that 'parallel worlds' and collapse could both be avoided by choosing the right initial conditions for the Schrodinger equation.

    Suppose we pass a spin 1/2 atom through a Stern-Gerlach device and find that its spin is in the +z direction. We confirm that by passing it through a second SG device, also in the z direction; it always passes inspection. We then send it through an SG device pointed in the y direction, and measure that its spin is either +y or -y. Suppose we find that it's +y.

    If 't Hooft's idea were right, then there would be no branch where it's -y; it must have been +y before it reached the last SG. But that's inconsistent with the fact that it was prepared as +z, and with the fact that there was no branching in the middle SG device.

    Consider it also in the time-reversed picture. In the MWI, there are +y and -y branches, which in the time reversed picture 'merge'; the interference between +y and -y leads to a net result of +z, which explains why it passes unchanged through the middle SG device. Or, in the time-reversed collapse picture, the -y component spontaneously appears.

    't Hooft's model has neither so it's just +y. In the time-reversed picture, when that +y hits the middle SG device, it will have to branch into +z and -z components. Since this is a time-reversed picture, the -z component would have to have been sent from a different MWI-style 'world' in order to be consistent with the Schrodinger equation and the fact that we knew the spin was +z in our world.

    So there's no way to avoid parallel worlds if you keep the Schrodinger equation; if you insist that the final state has only one macroscopically distinct world, then all you end up doing is making worlds merge instead of split.

    It's nothing at all like the case of classical probability distributions where if you know the final state, you can obtain that final state by the right choice of an initial state, avoiding any spreading out of the probability distribution. Wavefunctions are waves, not probability distributions.

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