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The reality of Configuration space

  1. Nov 27, 2011 #1
    Someone suggested to me that this stuff may be more appropriate in the QM section (I’m not sure?). I think others on here have brought this up before but I thought I’d post some stuff I’ve come across that may be useful to some as a kind of an introductory reading on the ontology of configuration space. These authors have tried to present an ontology of configuration space (and the wave function). I thought these skeptical quotes by Einstein regarding this topic is an interesting introductory quote on the topic:


    If QM is supposed to be more “fundamental” than classical physics, does this suggest that configuration space is more "fundamental" than normal 3-space or (4 dimensional space-time)? If it’s more fundamental, why does the world appear to evolve in 3-space or (4 dimensional space-time)? What is the nature of this configuration space where the wave function lives in? Goldstein writes:

    Reality and the Role of the Wavefunction in Quantum Theory

    On the Metaphysics of Quantum Mechanics
    http://www.niu.edu/~vallori/Allori-OnTheMetaphysicsOfQuantumMechanics.pdf [Broken]

    I’ve been reading over the various models and trying to better understand them and here is a brief summary of my basic understanding. If I messed up please correct them because I’m no expert on these views!

    1. David Albert: Configuration (3N-dimensional) space realism.
    The space we live in, the space in which any realistic understanding of quantum mechanics is necessarily going to depict the history of the world as playing itself out...is configuration-space. And whatever impression we have, to the contrary (whatever impression we have, say, of living in a three-dimensional space, or in a four-dimensional space-time) is somehow flatly illusory... In reality, there is just a single 3N-dimensional wavefunction, and the division of reality into separate three-dimensional objects, including organisms, is just the product of our internal representation. Thus, for Albert objects exist as single points, evolving one way or another in this very high-dimensional space.

    Wave function Ontology

    Problems: Why does the world appear 3-dimensional (or 4-dimensional if space-time) to us? What does N represent in 3N space (what is the space a configuration of, if not the particles)? Maudlin finds this view hard to swallow because he finds it "obscure how something happening at a point (such as a particle occupying a point or a field being concentrated near a point) could have complexly structured physical state of affairs...it is not easy to understand how those physical structures could constitute cats, or chairs, or people."

    2. Monton/Lewis: 3-dimensional space is fundamental. The 3N-dimensional space is an illusion/false and wave function is only a mathematical tool.
    While their arguments are somewhat different, both claim that the world really is 3-dimensional and the 3N-dimensional space is a kind of an illusion for different reasons. While Monton flatly rejects the reality of 3-N space ("the wave function is no more real than the numbers-such as 2 or p"), Lewis rules out the reality of configuration space by arguing that the "dimensionality" of configuration space defining the wavefunction is not really "spatial".

    Problem: Predictions of QM depend on the 3N-dimensional space that get lost in the 3-dimensional representation (e.g. information about correlations among different parts of the system, that are experimentally observed are left out).

    QM and 3-N Dimensional Space
    http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/qm 3n d space final.pdf

    Against 3-N Dimensional space

    Dimension and Illusion

    Life in Configuration space

    3. T. Maudlin/Goldstein: While 3N-dimensional space is a mathematical tool the wave function is "real" (in a unique way)
    There are two distinct fundamental spaces (3-dimensional and 3N-dimensional), each with its own structure. What’s more, each space must possess additional structure beyond what is normally attributed to it. Further structure is needed to ground the connections between the two fundamental spaces, saying which parts and dimensions of the high-dimensional space correspond to which parts and dimensions of ordinary space, and which axes of configuration space correspond to which particle.

    Problem: Adds additional fundamental structure, making it less elegant/far more complex.

    Maudlin argues, that's fine, because such structure is needed to make an informationally complete description, from which "every physical fact about the situation can be recovered". With respect to the wavefunction structure, Maudlin doesn't make a commitment but suggests that it may be unlike anything else (sorta "physical"/real but in a unique/different way), kind of "in its own metaphysical category". These authors appear (if I understand them) to regard configuration space as only a mathematical tool and the wave function as nomological (a law of nature). Thus, they seem to regard the wave function as more than just a probability wave. And even though we don't have direct “access” to it, this doesn't bother them as Maudlin writes: "If our only access to the wavefunction is via its effect on the particles, and if the connection to the lived world is primarily through the particles, then we are not constrained about the physical nature of the wavefunction."

    Maudlin video-Can the world be only wave-function?

    Reallity and the role of the wave function in QT

    4. Bohm/Hiley: The 3N-dimensional space is a "real" objective information space.
    So, 3-N space is an abstract multi-dimensional "informational space" that guides a particle evolving in 3-dimensional space.

    Problem: How can an "informational field" guide the particle? How does it interact with it to inform it? The field acts on the particles but particle doesn't act on the field. Brown has argued that this goes against Einstein's action-reaction principle. Einstein wrote it is "contrary to the mode of scientific thinking...to conceive of a thing...which acts itself, but which cannot be acted upon." Regardless this ontology requires far greater intrinsic complexity to be given to particles like electrons, etc. This leads to russian dolls and problem of infinite regress at. Bohm writes:

    Can Mind Affect Matter Via Active Information?

    Meaning and Information

    From the Heisenberg Picture to Bohm: a New Perspective on Active Information and its relation to Shannon Information

    5. Antony Valentini: Configuration space is "real" where wave function, a new causal agent, evolves. (his position seems somewhere in between Albert’s, Bohm's and Maudlin/Goldstein?)
    He accepts reality of configuration space but not Bohm's/Hiley's 'quantum potential'. He disagrees with Goldstein and thinks the wave function is not just nomonological (a law of nature). Valentini suggests that configuration space is "real" (like Albert, it seems) and argues that the quantum wave is a new type of "causal" agent that may take some time for us to understand it, in the same way scientists had difficulties accepting the concept of "fields" when they were first introduced. So he sees an evolution (see slides in video) from forces to fields to this non-local quantum wave (which does not vary with distance and appears to be completely unaffected by matter in between). So in his scheme, the configuration space is always there where the pilot wave (a radically new kind of causal agent that is more abstract than conventional forces or fields in 3-D space) propagates.

    Problem: Mixture of above ones.

    Valentini video- from Perimeter Institute The nature of the wave function in deBroglie’s pilot wave theory
    http://streamer.perimeterinstitute.ca/Flash/3f521d41-f0a9-4e47-a8c7-e1fd3a4c63c8/viewer.html [Broken]
    Last edited by a moderator: May 5, 2017
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  3. Nov 28, 2011 #2

    Ken G

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    I have no objection to pointing out ontological advantages to thinking in configuration space, but I see a basic inconsistency in any claim that boils down to "the ontological entities of our previous physical theories were not the real ones, but the ontological entities of our present theories are the real ones." Come on, how can any deep thinker fall into such an obvious trap?
    Same trap again, only reversed. This one boils down to "the ontological entities of our new theories can't be real because they aren't the comfortable ontological entities we had gotten used to in our previous theories, including the ones most humans develop prior to any scientific training." No traction there either, I fear!
    An abstraction guides a particle? That doesn't sound coherent. I know Bohm's views are generally self-consistent, so I'm not sure where he got this idea from. He has the pilot wave to guide the particles, but I would have to say that the pilot wave doesn't actually guide anything, the particles behave as if guided by the pilot wave-- that way our concepts are not pushing particles around in anything but how we think about the particles.

    What I keep coming back to is, it is fine to imagine ontological elements as we do science. But there is never any reason to imagine these elements are real, absolute, or uniquely determined. They vary with the theory, and science shouldn't want it any other way.
  4. Nov 28, 2011 #3
    Dear bohm2,

    Let me add the following. nightlight noticed that the Fock space (which is a direct sum of configuration spaces for all numbers of particles) can be just an artefact of Carleman linearization (see, e.g., http://www.akhmeteli.org/akh-prepr-ws-ijqi2.pdf (an article in Int. Journ. Quantum Inf.), starting with the words "as for second-quantized theories, nightlight..." on p. 6, and the relevant references).
  5. Nov 28, 2011 #4
    Here's a historical argument why taking a "realist"/ontological approach (at least provisionally) may be useful. Consider the unification of chemistry with physics, before QM. At that time physicists dismissed a lot of the models the chemists had developed as "fictions" (non-real) because they could not be accomodated with Newtonian physics. The problem was not so much that the models were not "real" but the reduction base (Newtonian physics) was wrong.

    The argument, I think, is that by treating some of these mathematical objects as ontological (more "real"), it may give some insight into what direction science/physics needs to adopt in order to progress? Again, I'm not sure but it seems reasonable to me. So, for example, the contextuality and non-locality/non-separability forced upon us by the properties of this mathematical object we call the wave function (if we take the ontological view) may be trying to tell us something about the way nature/reality may be (and I'm denying our epistemic limitations here).


    http://www.journalofphilosophy.org.myaccess.library.utoronto.ca/articles/issues/106/4/1.pdf [Broken]
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  6. Nov 29, 2011 #5

    Ken G

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    But I would point to that exact same insightful example as the reason why we should not regard our ontic elements as absolute! That was the problem, the physicists were taking the Newtonian ontology as absolute, and doing wrong reasoning from that. Intead, we should treat all our ontic elements (those of both physics and chemistry) as provisional to the context in which they are useful, and further, we should always seek unification of these ontic elements. There is no law that says unifying ontic elements should work if they are absolutely true and not work if they are merely effective mental constructs! The goal of effective mental constructs is unification.
    I absolutely agree, but note your crucial use of "treat as real". You did not say "regarding these mathematical objects as absolutely more real" than some others, for that was exactly the mistake the physicists made. It's fine to "treat" our ontic elements as real, that's just what we do in science, it's a very useful device. The point is that the understanding we achieve, using that device, is always provisional and contextual, and we should not expect to be able to transport it outside its context of usefulness. Granted, it is never obvious what the "context of usefulness" actually is, but discovering that is very much a goal of science, it is not something we need to pretend we aren't doing.

    I feel it is very much trying to tell us something, but one of the messages we should be listening to most closely is "when is this lesson applicable, and when will it lead us down a closedminded dead end?" That must always be the question in the back of the scientist's mind, when confronting ontology of any stripe.
  7. Nov 29, 2011 #6


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  8. Nov 30, 2011 #7
    Given the unification of chemistry with QM and the unification of molecular biology with chemistry (more recently), do you see any hope/hint of similar unification of mental phenomena with present-day physics or do you think that this can't happen until major changes occur in a future physics (assuming you think this can ever happen)? Do you think that perhaps by noting "some sort of theoretical inference from the character of phenomenal properties" to their underlying constituents, it may help us decide what would be required by a future theory of physics for unification to occur? I'm having trouble focusing and expressing my thoughts, so I'm not sure if this makes sense. Consider Eddington's remarks:

    I think McGinn hints at this where he writes he writes:

  9. Dec 1, 2011 #8


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    This probably isn't what you want to hear but in http://pirsa.org/08100049 Smolin argues against the justification of timeless eternal laws and timeless state spaces (he calls the newtonian scheme), and how this relates to to "the poisoned gift of mathematics to physics".

    I think the essence of that talk is that in the quest for "objectivity", there are TWO ways to think about it.

    Either you just ASSUME some ontological (ie. that CAN not be scientifically inferred; and the whole meaning of ONTOLOGICAL is that you don't REQUIRE it to be!). Ie. you assume that there are eternal laws that determined the evolution of the system in time, in a timeless statespace. the argument is that this is the poisoned gift of mathematics, and it is not empirical justified science.

    Or you consider an inferred consensus that is valid between the observer and it's environment or the system it interacts with. This is a epistemological construct, which gives objectivity in the sense of consensus between different observers. But this is then an emergent expectation, not a constraint - In this view, state spaces and the LAWS that rule evolution in them are merely rationally inferred empirical expectations. APPARENT objectivity is just the result of TUNING between interacting observers. But we're not talking about mysterious ad hoc fine tuning, because the TUNING is not a conicidence, it follows from the interaction.

    In that talk analogis are made from social theory (which is where Unger comes in). In social systems, laws are NOT forcing constraints you can't break. They are merely expectations from the environment that unless you obey then has a price. These laws are always in motion and is the result of an negotiation process that takes place locally througout the universe. Nothing guarantees global consensus except as a kind of equilibrium.

    however, such radical ideas must explain by correspondence principle the success of the newtonian scheme. And Smoling argues in that paper that the newtonian scheme does indeed work for limiting cases: small sybsystems in QM/QFT, and then of course classical mechanics (for different reasons).

    All ideas are certainly not worked out the paper, but the conceptual perspective as well as some obvious problems with newtonian scheme is introduceed.

  10. Dec 1, 2011 #9

    Ken G

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    I do think it can ever happen, and I do think you are characterizing it correctly-- it is a type of unification that is needed. I think we might be a ways off yet though-- I doubt I'll see it. But I do think that some future physics is going to account much more completely for the role of the physicist in the physics, and that is when the unification you speak of might be possible. Of course, who knows what new mysteries might be raised by that kind of perspective! I don't think it will go much past that unification, it might not get to an understanding of consciousness itself. How does something understand itself, does a mirror not distort and reverse?
    A line I like from that is "Things in space can generate consciousness only because those things are not, at some level, just how we conceive them to be; they harbour some hidden aspect or principle." I believe this statement points to the fundamental paradox of physics: when it is the similarities between how we conceive things, and however they are, that dominate our attention, then we can make progress in the conventional way, but when we take aim at the differences between our conceptions and what is, when we look for what is hidden, we face a much more difficult task. It might not just be the task of asking the right question-- it might be the task of letting go of the very things that got us this far. We may reach the end of the line of what science can do before we get to the end of what we want science to do, and if that happens, we'll need a breakthrough akin not to any in science, but instead akin to the invention of science itself.
  11. Dec 1, 2011 #10

    Ken G

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    That's funny, I just gave a seminar in which I referred to the "cult of numerogical determinacy" that essentially dates all the way back to Pythagoras, and its legacies of both value and impediment to science. It sounds like Smolin is saying something similar about the pitfalls of the newtonian scheme.
  12. Dec 2, 2011 #11


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    I think Smolins and in particular Ungers (which is not a physicist, but the more radical of the two it seems) points are important, although controversial.

    What Smolin has been struggling with though (and not quite succeeded with IMO) is to make something constructive and testable about of this (so as to make it a scientific statement). His Cosmological Natural Selection idea is rooted in these ideas, but I think there are better not yet unravelled ways to implement these ideas.

    These ideas are particularly hard for people that seek determinsm and realism. But what if nature itself is undecidable about it's own actions, then it's a serious mistake to try to impose more decidability in our models. Not to mention that we are lead to initial value problems as well as "landscape problems" in the sense that the empistemoligal perspective simply is unable to determined WHICH deerministic rules there are (so in the end we still have undecidability).

    I think the lession is to try to not project more decidability onto nature than what simply follows from a rational expectation in the empirist view.

    Smolin mentions several examples and analogies that are though provocing. For example how can it possible even make SENSE to talk about eternal laws of physics, if the universe is only 14 billion years old.

    The point is that the empirist context, constraints the possible confidence and thus decidability in any inference.

    Now, if we can couple this idea to how nature ACTS, then we have a scientific prediction that can be tested. Smoling argues that it CAN be tested... his CNS was his attempt, now while I'm not so impressed aobut hte CNS, I am still convinced that there is alot of things to gain here.

    But in most discussions here I see that this is a "hard to convey" thinking. The "newtonian scheme"-dogma is quite cemented into the minds of many physicists.

  13. Dec 2, 2011 #12

    Ken G

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    Right, and I would object to the often-made claim that "realism" requires such decidability. That's not realism, it's "decidism", close to both "determinism" and "reductionism." When realism is equated with reductionism and determinism, it isn't realism any more, it is a very narrow, almost myopic, version. That is also the objection to the PBR "mild assumptions" about a "complete set of properties" that I keep returning to. Since when is reductionism a mild assumption, or worse, a requirement of realism?

    I don't want to sidetrack into a discussion of the "landscape", but it gives an example of the epistemological morass one gets into when one mistakes reductionism for realism. If one swallows the claim that realism must be reducible to some complete set of physical properties, then one immediately wonders why those properties are what they are, instead of some other possible set. Instead of seeing this for what it is (the reason that the concept of a complete set of properties is an unscientific assumption because it leads to a dead end for scientifically determining why those properties are what they are), the need is felt to make the question simply go away by introducing the landscape. It's fine to make pesky questions go away, but only if it empowers the next theory by doing so (like how GR makes the pesky question "why are inertial observers special" go away). I just don't see how the landscape is a scientific theory, it smells like pure philosophy to me.

    Yes, that's the key point. The old model that nature somehow "contains" an infinite amount of information in any local box, but we can only access and process a finite amount of it, is logically incoherent. Information is defined by what we do with it, it has no ontological meaning.
    Yes, and then there's also the "shut up and calculate" types who might not recognize that a calculation is itself a kind of epistemological stance, so even characterizing what we are doing there needs to be made consistent with some larger epistemological framework. Refusing to undertake that project is accepting that we will never be able to say what we are doing, we will only be able to do it. I think that's more than the "shut up" camp is really willing to bargain for, it's a little too quiet, and nobody is really willing to be that quiet about what science is!
    child: "Daddy, what do you do for a living?"
    Daddy: "I shut up and calculate, so I can't tell you."
    Last edited: Dec 2, 2011
  14. Dec 2, 2011 #13


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    Thanks bohm2, for the links and an interesting question. I have to start where you ended - I’m absolutely no expert on these views! (And maybe I’m making a fool of myself, but who cares ;)

    Configuration space? What is that?? :shy:

    In classical mechanics, Configuration space is the space of possible positions that a physical system may attain, and has the structure of a manifold (aka the configuration manifold).

    So in the 'classical world', Configuration space would be the 3-dimensional Euclidean space (ℝ3), right? And in Special Relativity, ℝ3 is embedded in 4-dimensional spacetime (ℝ1,3), called Minkowski space, right?

    In QM we use Hilbert space (or state space) for the wavefunction (aka state vectors), described by the Schrödinger equation, which could be time-dependent or time-independent.

    What’s the problem!? :confused:

    Well, if the wavefunction is considered a mathematical tool and not real; there’s no problem at all (afaict). The Schrödinger equation describes the behavior of ψ, and Born interpreted ψ as related to the probability amplitude |ψ|2, i.e. the probability density of possible positions for the particle. This is the physical meaning of the wavefunction.

    Two stationary states and a superposition
    state at the bottom

    But, what about this "n-dimensional space"?? That *must* create problems!? :grumpy:

    I’m not sure it does... Hilbert space includes a generalized notion of classical Euclidean space... so this should be okay, I think... And if we consider the wavefunction as just a mathematical tool, we should be very okay, I think...

    Historically, Schrödinger replaced the outdated Bohr (atomic) model, with a wave equation for the electron, and standing waves representing eigenvalues λn (n = 1,2,3,...), which this lady can explain much better than me:

    Spherical harmonics for the Hilbert space

    Check out the Hydrogen Atom Applet in 3D for more configurations (click, drag & release, to rotate in 3D).


    2D Quantum Well Simulation for the time-dependent Schrödinger equation

    So, what happens IF the wavefunction one day turns out to be REAL!?!? :devil:

    Then we got problems... to begin with; what IS a real wavefunction (and probability amplitude)? Could probabilities be something 'real' or 'material'?? :bugeye:

    I have no idea... and then this 'thing' with entanglement and (what then must be) non-local 'causal correlations'... and then the 'extra dimensions'... it looks tough indeed...

    And to be frank – we (they) already got 'interesting problems' in finding a solution for Quantum gravity (QG), with or without real wavefunctions:
    How do we describe the fundamental degrees of freedom when there is no fixed background space? -- Carlo Rovelli

    General relativity is said to be background independent, i.e. there is no fixed spacetime background. QM, including quantum field theory, relies on a fixed background (non-dynamic) structure.

    This is really advanced science at the frontline, and I don’t understand that much... quantization of both space and time at the Planck scale... 4D spacetime at large scales, but 2D spacetime near the Planck scale, and a fractal structure on slices of constant time... Gosh I’m lost...

    If you’re interested, here’s info on Quantum geometry and different possible solutions in pipeline. (Causal Dynamical Triangulation looks fascinating)

    Okay, but what is the conclusion then?? :rolleyes:

    My view is that the ordinary Joe Six-pack "We all live in yellow 3D submarine, yellow 3D submarine" is already a dead parrot.


    We already know that ℝ3 is an illusion. Einstein’s theory of relativity shows that time dilation (difference of elapsed time between two events as measured by two observers) arises not from technical aspects of the clocks, nor from the fact that signals need time to propagate, but from the nature of spacetime itself. Both relative velocity time dilation and gravitational time dilation has been confirmed experimentally (and corrected for in the GPS system), and these phenomena will never "go away", no matter what theory comes in the future, and the same goes for other relativistic effects, like Gravitational lensing (spacetime around a massive object is curved):

    Where is my yellow 3D submarine!? :cry:

    So how could we ever 'cope' with a fundamental reality based on 'points' on a 2D plane with any finite or infinite number of dimensions, if this turns out to be the result in unify QM & GR...??

    I have no good answer... maybe we could hope to make 'parallels' to Claude Monet. If you get up close at one of his later paintings, it looks like a '2D accident', without any meaning:


    But take a few steps back, and a beautiful bridge to the '3D world' emerges:


    The answer to all this could probably not be given before we know the true nature of "space", and QM + GR = True... I think...

    Finally: Can we always trust our senses? Is what we perceive what’s really there? Is this a bulletproof mechanism that always gives "The Right Answer"?

    Well, talking about points on a 2D plane, check this out:

    Stare at the center cross for at least 30 seconds to
    experience the three phenomena of the illusion

    When you stare at the cross for about 30 seconds or so, you will see three different things, in this sequence:
    1. A gap running around the circle of lilac discs.

    2. A green disc running around the circle of lilac discs in place of the gap.

    3. The green disc running around on the grey background, with the lilac discs having disappeared in sequence.
    It’s an illusion, you’re cheated! What you see is not "THE TRUTH"!! :yuck: (:wink:)

    (If you want to try in full screen and/or other colors, speeds, go here.)

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  15. Dec 3, 2011 #14
    Do you think that there are good reasons why one should treat the wave function as more of a mathematical tool compared to the electric and magnetic fields of classical electromagnetism? What I mean, is there any reason why one should treat the "field" concept as more ontological/real than the wavefunction? Wasn't it really the non-locality that was largely responsible for turning off physicists (e.g. Einstein) from taking the wave function as an ontological entity/"real". Is there any reasonable way of really avoiding this non-locality/non-separability?
  16. Dec 3, 2011 #15

    Ken G

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    No, because the correlations that quantum mechanics predicts are found to hold in experiments. Hidden variables approaches require nonlocality to match that, independently of any wave function issues.
  17. Dec 3, 2011 #16
    I think there might be (see the article cited in post 3 in this thread, although the approach for the Dirac equation there can be dramatically improved - see the article in the Journ. Math. Phys. http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf ). Other people strongly disagree though (you may find a lengthy and sometimes fierce discussion at https://www.physicsforums.com/showthread.php?t=369328 )
  18. Dec 3, 2011 #17
    Thanks akhmeteli. What's your opinion on PBR and how do you think it affects your model?

    The quantum state cannot be interpreted statistically
    Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
    Completeness of quantum theory implies that wave functions are physical properties

    Quantum theorem shakes foundations

    Last edited: Dec 3, 2011
  19. Dec 3, 2011 #18
    I am not sure I have any opinion on PBR work, and I don't think PBR affects my model directly, as the model is not statistical. It can positively affect the model indirectly though by eliminating some alternative (statistical) interpretations.
  20. Dec 3, 2011 #19
    I never understood that. I mean consider the double-slit experiment. How does one understand individual quantum processes or measurement? The whole issue of the projection postulate, etc. Isn't that non-local? One wants to say that the wave function is epistemic to avoid wave collapse as real physical process but how can one explain the interference effects without also treating the wave function as ontic?

    In Bohmian mechanics, although it's argued that position is the hidden variable it's actually the wave function that's hidden because it's never "observed", except indirectly by how it affects/guides the particle (which is "observed"). But I don't understand why position measurements assume pre-existing particle positions in Bohmian while everything else is contextual: spin, momentum, energy, and other non-position “observables”.

    While the dualism is arguably a problem de-Broglie/Bohmian models some argue that the Orthodox (Copenhagen) has even greater problems:

    http://www.niu.edu/~vallori/Allori-OnTheMetaphysicsOfQuantumMechanics.pdf [Broken]

    I think another weirdness in the Bohmian interpretation (BM) are the 2 characteristics below. For some reason the first part doesn't bother me as much as the "empty waves" part:

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  21. Dec 3, 2011 #20


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    I understand what you mean and it’s a good question, but just to make sure to avoid any 'confusion'; I’m not an expert and this is just my 'personal view' (for what it’s worth). Furthermore, I’m not in any 'camp' advocating this or that stance, except when there are experiments confirming what is accurate or not.

    I think there are reasons in favor for the "Just a Mathematical Tool" standpoint:
    • Originally, Schrödinger did not know the nature of ψ only that his equation describes the behavior of ψ, and he tried to interpret it as a charge density (which was wrong). One would like to think that if ψ was real, this would not have been a 'problem'... it would have come 'naturally' from the logic...

    • Schrödinger used calculus for his "wave mechanics" and Werner Heisenberg used linear algebra for his "matrix mechanics". Strange enough, they both work in describing the atomic model. Schrödinger showed that the two approaches were equivalent. I don’t know if this common in science; that two different mathematical approaches could describe the same "real thing" with the same efficiency...? Nevertheless, if Schrödinger’s "wave mechanics" is real, then must also Heisenberg’s "matrix mechanics" be real... (or I am missing something very basic?). Two 'real things' describing the same 'thing'!? Huh... :uhh:

    • I don’t know about Heisenberg’s "matrix mechanics", but in Schrödinger’s ψ there is one imaginary part (i = √-1) and the square root of a negative number does not have a solution (only complex numbers).

    • If ψ is real and |ψ|2 gives the probability density of possible positions for the particle, then "the square root of the probability density" must represent something real... what on earth is that...? Could √probabilities be real?? :bugeye:

    As for electric and magnetic fields of classical electromagnetism, I think there’s big difference – We can observe the effect of these fields directly.





    (With the reservation the electromagnetic force can be described by the exchange of virtual photons...)

    Until this day; no one has ever measured or observed ψ directly, only the end result in particles like electrons and photons, etc.

    However there are claims like Wave function directly measured but when you read it you’ll see that they are talking about is "weak measurements", and one of the physicists says "Measuring the wave function itself is not really thought to be a possible thing [...] It’s not really thought to be something physical".

    Yes, I think you’re right. For Einstein "real non-locality" would not have been appealing, considering SR, and I guess non-realism wasn’t attractive either... The ironic thing is that EPR in the extension of EPR-Bell kinda 'backfired' on Einstein ...

    ... because Ken G is 100% right. Local Realism is a dead parrot waiting for the Grand Funeral. What’s left is non-locality and/or non-realism (non-separability).

    Edit: I changed my mind, it’s 50% right, because if you dump Realism then Locality could be saved. (Don’t ask me how this works! :smile:)

    Having said this, it might look like I’m in the "Just a Mathematical Tool" camp, but I’m not, because there are things that look 'strange' even in this camp:
    • Take the Double-slit experiment. We know that a wave, interfering with itself, has to pass the two slits to generate this pattern – but this wave is not real!? How does this work?? :eek:

    • Take the EPR-Bell experiment. If the wavefunction is not real, how on earth does this 'unreal thing' manipulate a particle to be correlated with its entangled twin? How does this work? What’s the name of this 'unreal mechanism'?? :confused:

    • According to the new PBR theorem a ψ-epistemic ontological model does not work, therefore if the wavefunction is not real, any hidden variables are automatically excluded, i.e. at the fundamental level; the world is unreal... and that must mean that our measuring apparatus is also unreal... which means that we are verifying our physical theories with something that is unreal = end of science...? :bugeye:

    It’s quite strange...

    P.S. Ask anyone who claims that Local Realism is still an option for the name of one reputable PhD who is active at an reputable institution, and involved the foundations community, who has published at least one paper in a professional peer-reviewed journal the last 10 years, claiming Local Realism is still alive.
    Last edited by a moderator: Sep 25, 2014
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