Thursday, May 29, 2014
The measurement problem in QM
In 1976, when I delivered the John Locke Lectures at Oxford, I often spent time with Peter Strawson, and one day at lunch he made a remark I have never been able to forget. He said, "Surely half the pleasure of life is sardonic comment on the passing show". This blog is devoted to comments, not all of them sardonic, on the passing philosophical show.
HILARY PUTNAM
This first post is an exchange (which I have received permission from all the participants to include) on the measurement problem in QM.
For background, see my
HILARY PUTNAM
This first post is an exchange (which I have received permission from all the participants to include) on the measurement problem in QM.
For background, see my
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"A Philosopher Looks at Quantum Mechanics (Again)" (2005), 126-147 in my Philosophy in an Age of Science, and
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"Quantum Mechanics and Ontology" (2012), 148-161, in the same volume
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Apr 16
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Dear David.
I recall that you have said (more than once, in fact) that I give too much weight to (the failure of) Lorentz invariance as an objection to Bohmian mechanics (BM). If Special Relativity (SR) were the state of the art description of space-time, the fact that the violations of Lorentz invariance in BM are undetectable according to BM itself, might be a way of mitigating, if not wholly disposing of, that objection. But Special Relativity is not the state of the art description; the best description we have (pending a theory that reconciles General Relativity (GR) with QM) is GR. The standard model in cosmology is soaked with GR—expansion, inflation, black holes, etc., etc. are all GR phenomena. And GR implies that while SR is wrong globally, it is right locally; as we all know, in infinitesimal regions, the space-time is MInkowskian. And BM is wedded to Euclidean space-time. It derived, after all, from De Broglie's attempt to see the psi-function as the description of a wave in flat 3+1 space-time.
I have been following the apparent detection of gravitational waves (caused by quantum fluctuations of the vacuum during inflation, assuming the BICEP2 observations hold up, as seems very likely) with fascination. This leads me to wonder if the difficulty over many decades of finding a compelling scientific realist picture that answers the "collapse" dilemmas is not, at bottom, due to the fact that we are prematurely trying to say what the psi-function is and how it figures in the dynamics before physics has come up with a good account of what its "theater of operation" really is; prematurely, as long as we don't know how to unify GR and QM. One thing is sure, I think: the space-time in which cosmological processes take place is general relativistic; the "theater" can't be flat 3+1 space, or even Minkowski space-time. This makes me suspicious not just of BM, but of GRW as well. Even if Roderich has produced an SR version of GRW for a special case, the "theater" is a Minkowski space-time in which there are bunches of "flashes". As I said (typed) a moment ago, that can't be the true theater of operations, and it may well be premature to try to resolve the "collapse/no collapse" problem until we have a theory that fits GR, at the very least.
Remarks welcome from all.
Best,
Hilary
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Apr 17
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Dear Hilary,
You invited remarks, and I would have a few. It's not a big difference for
the foundations of QM whether space-time is flat or curved. GRW theory
with flashes works just as well in curved space-time, and Bohmian
mechanics does, too, once we allow that a certain foliation of space-time
into spacelike hypersurfaces, possibly selected in a covariant way, plays
a special dynamical role.
(The use of a preferred foliation may be regarded as going against the
spirit of (special or general) relativity, but that is largely a matter
of taste. Other things being equal, I'd prefer a theory that doesn't
involve a preferred foliation, but in this case other things are not
equal. Also, note that inhabitants of a Bohmian world can't find out which
foliation is the preferred one.)
Of course, using a curved space-time (i.e., a given nonflat 4-metric) is
not yet full GR, where matter influences curvature, and furthermore it is
unclear in which sense we will have a 4-metric in the correct theory of
quantum gravity. Nevertheless, I expect that, once we have a full quantum
gravity theory, the options for the foundations will be similar to the
ones we have today: a Bohmian version that involves a preferred foliation
and a collapse version that does not (but is more complex).
I can give you references if you like.
Best, Rodi
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Apr 17
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Hi Hillary,
Just saw your note, and Roddy's response - and what Roddy says sounds just right to me.
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Apr 17
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Dear Rodi,
You write, "Of course, using a curved space-time (i.e., a given nonflat 4-metric) is not yet full GR, where matter influences curvature, and furthermore it is unclear in which sense we will have a 4-metric in the correct theory of
quantum gravity. Nevertheless (sic), I expect that, once we have a full quantum
gravity theory, the options for the foundations will be similar to the
ones we have today: a Bohmian version that involves a preferred foliation
and a collapse version that does not (but is more complex)."
The "nevertheless" is just where I have my doubts. I am reminded of how Lorentz thought his transformations would be explained by the action of velocity relative to the ether on "inter-molecular forces". The sense in which "we will have a 4-metric" in the future "full (quantum mechanical) GR" may be very surprising.
I would happy to receive references. Is one of them the Callender-Weingard "The Bohmian Model of Quantum Cosmology"? What do you think of it?
Best wishes,
Hilary
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Apr 17
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HI All,
I’m with Rodi and David here. It is, of course, not possible to say anything rigorous about how quantum theory and GR are going to come together, but one can take the attitude that the real problem is with the part of Einstein’s field equation that he himself characterized as “low-grade wood”, i.e. the Stress-energy tensor as the mathematical representation of the matter. IF some decent (local!) representation of the matter distribution (or energy distribution, if you like) is forthcoming, then the space-time geometry can be made to depend on that in something like the usual way.One has to focus, as Bell would say, on the local beables here. That four-dimensional geometry plus a foliation would give the resources to specify a Bohm-type dynamics, and we could get dynamical and variable space-time geometry.
If the combination of QM and GR demands more extensive revision of the GR picture (e.g. if space-time becomes discrete rather than continuous), then there have to be more adjustments to the GR side. (I have some ideas about how to do this, but you have to rewrite all the physics using the Theory of Linear Structures, so that’s a long story). But even there, it looks to me that space-time geometry + foliation provides the resources to write down the dynamics, and having the geometry itself be a product of the dynamics is not problematic (if the dynamics is Markov).
I also would not really demand that the foliation in such an approach be unobservable. I would rather try to find the mathematically most natural way to write a theory that has the right limiting behavior. I would not, having done that, be very surprised if the foliation turned out to be unobservable, but also not surprised if it had, in principle, observable features.
Cheers,
Tim
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Apr 17
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Thanks all!
On the plus side, the existence of Bohmian dynamics (and GRW if Rodi succeeds in extending what he was working on to a full QM) does show that we don't need to take seriously the idea of "changing the logic" (as I once thought) or invoking consciousness - no need for "romantic" interpretations, as Bell called them, to get at least one "realist" interpretation.
But lacking a theory with testable predictions, I am still inclined to think it is premature to speculate on what the right story will turn out to be. (What with the "multiverse" talk, the present state of string theory, etc.., there is enough and more than enough non-empirical speculation around. But thanks for your responses.
Warm regards,
Hilary
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Apr 17
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Hi Hilary. I agree more or less with everything that Rodi, David and Tim wrote, and don't know whether there is anything more that needs to be said. But I'll say the following, though I'm not sure whether it's "anything more":
For me, a Bohmian version of a quantum theory is more or less a version in which one takes structure in space-time, including space-time itself, seriously. Thus there should be local beables in some sort of space-time, which could well be discrete and dynamical. I can't imagine why, if we live in a quantum world, it could not be Bohmian in this sense. (Of course, the way I've described Bohmian here, probably too broadly, it's hard to imagine it could fail to be Bohmian.) It seems to me that the burden of proof should be on someone who claims that a Bohmian version is impossible, and not on someone who maintains it should be possible.
Here's a possible relevant link:
- Quantum Spacetime without Observers: Ontological Clarity and the Conceptual Foundations of Quantum Gravity, with S. Teufel, in Physics meets Philosophy at the Planck Scale, edited by C. Callender and N. Huggett, 275-289 (Cambridge University Press, 2001), quant-ph/9902018
Best, Shelly
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Apr 17
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Thanks to you as well!
I certainly think a Bohmian version is possible. But Newtonian space-time was very different from Minkowskian space-time, and GR from Minkowskian, and it is possible that (GR+QM) space-time will turn out to be very different as well. I admit that I am suspicious of the idea of non-relativistic trajectories hidden from us so they can't be observed, which is what historically Bohmian trajectories are.
Best,
Hilary
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Apr 17
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Yes, hidden shmidden, but can you give some indication of what it is about the new space-time and its very different nature that should be relevant to making a Bohmian version unlikely. Exactly what sort of worry do you have in mind?
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Apr 17
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Briefly, that we don't even know how space time metrics are to be superimposed (apart from ideas that go back to Wheeler, et al in 1973), whether this will involve a background super-space and a cosmic time or not, whether the Bohmian theory appropriate to this future theory (if there is one)
will still be based on position-representation and probability currents, etc., etc., I think that you guys are betting that the picture re interpretations of QM will not be changed drastically, but I am reluctant to bet on that, although I do expect that in time physics will make sense of what is going on. Reading Robert DeSalle's fine Understanding Space-Time recently brought back to me how unanticipated the next picture of space time and causality was at each of the stages:Galileo-Descartes-Leibnitz, Newton, Einstein-SR, and Einstein-GR. I see no reason to think the next such picture won't be as orthogonal to the picture we have now as GR is to Newton plus Maxwell. And I suspect theories [string theory in particular] for which the arguments are all apriori (as of now, of course).
Warm regards,
Hilary
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Apr 17
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I guess I'm unclear about what you mean by a theory that is Bohmian or a theory that is not Bohmian. For me one that is not Bohmian would involve only wave functions---or would involve fundamental axioms about measurement or observation. So for me GRW is a kind of Bohmian theory. At least, relative to this discussion, I don't see a relevant difference.
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Apr 17
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Then for you "Bohmian" just means "sensible non-romantic interpretation". I wasn't expressing skepticism about the idea that that is what we need.
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Apr 17
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On 4/17/2014 8:59 PM, Hilary Putnam wrote:
Then for you "Bohmian" just means "sensible non-romantic interpretation".
Yes. It's surprising that that is so very accurate.
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Apr 23
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Dear Hilary,
I agree that we don't know whether the final theory of quantum gravity
will have a 4-metric and, if not, what replaces it. But at least it seems
clear that on the macroscopic scale, and outside of extreme conditions
such as in black holes, it is a good approximation to pretend there is a
Lorentzian 4-metric.
The references I had in mind are mainly about the formulation of Bohmian
mechanics and GRW in curved space-time; they spell out the equations and
prove that the theories work.
Bohmian mechanics:
o Sections 4.5 and 4.6 of R. Tumulka:
Closed 3-Forms and Random World Lines.
Ph. D. thesis, Ludwig-Maximilians University, Munich (2001).
o Section 2 of R. Tumulka:
Bohmian Mechanics at Space-Time Singularities. II. Spacelike
Singularities.
General Relativity and Gravitation 42: 303--346 (2010).
GRWf:
o Section 3 of R.Tumulka:
A relativistic version of the Ghirardi-Rimini-Weber model.
Journal of Statistical Physics 125: 821--840 (2006).
o Sections 4.1 and 4.2 of R. Tumulka:
The Point Processes of the GRW Theory of Wave Function Collapse.
Reviews in Mathematical Physics 21: 155--227 (2009).
GRWm:
o D. Bedingham, D. Durr, G.C. Ghirardi, S. Goldstein, R. Tumulka, and
N. Zanghi:
Matter Density and Relativistic Models of Wave Function Collapse.
Journal of Statistical Physics 154: 623--631 (2014).
About whether a preferred foliation violates the spirit of relativity:
o D. Durr, S. Goldstein, T. Norsen, W. Struyve, and N. Zanghi:
Can Bohmian mechanics be made relativistic?
Proceedings of the Royal Society A 470: 20130699 (2014).
I don't know the paper of Callender and Weingard that you mentioned.
Best, Rodi
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