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

"A Philosopher Looks at Quantum Mechanics (Again)" (2005), 126147 in my Philosophy in an Age of Science, and

"Quantum Mechanics and Ontology" (2012), 148161, in the same volume

Apr 16
 
to David Albert, Shelly Goldstein, Tim Maudlin and Roderich Tumulka 
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 spacetime, 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 spacetime is MInkowskian. And BM is wedded to Euclidean spacetime. It derived, after all, from De Broglie's attempt to see the psifunction as the description of a wave in flat 3+1 spacetime.
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 psifunction 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 spacetime in which cosmological processes take place is general relativistic; the "theater" can't be flat 3+1 space, or even Minkowski spacetime. 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 spacetime 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

Apr 17



Dear Hilary,
You invited remarks, and I would have a few. It's not a big difference for
the foundations of QM whether spacetime is flat or curved. GRW theory
with flashes works just as well in curved spacetime, and Bohmian
mechanics does, too, once we allow that a certain foliation of spacetime
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 spacetime (i.e., a given nonflat 4metric) is
not yet full GR, where matter influences curvature, and furthermore it is
unclear in which sense we will have a 4metric 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

Apr 17



Hi Hillary,
Just saw your note, and Roddy's response  and what Roddy says sounds just right to me.

Apr 17



Dear Rodi,
You write, "Of course, using a curved spacetime (i.e., a given nonflat 4metric) is not yet full GR, where matter influences curvature, and furthermore it is unclear in which sense we will have a 4metric 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 "intermolecular forces". The sense in which "we will have a 4metric" in the future "full (quantum mechanical) GR" may be very surprising.
I would happy to receive references. Is one of them the CallenderWeingard "The Bohmian Model of Quantum Cosmology"? What do you think of it?
Best wishes,
Hilary

Apr 17



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 “lowgrade wood”, i.e. the Stressenergy 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 spacetime 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 fourdimensional geometry plus a foliation would give the resources to specify a Bohmtype dynamics, and we could get dynamical and variable spacetime geometry.
If the combination of QM and GR demands more extensive revision of the GR picture (e.g. if spacetime 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 spacetime 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

Apr 17



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 nonempirical speculation around. But thanks for your responses.
Warm regards,
Hilary

Apr 17



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 spacetime, including spacetime itself, seriously. Thus there should be local beables in some sort of spacetime, 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, 275289 (Cambridge University Press, 2001), quantph/9902018
Best, Shelly

Apr 17



Thanks to you as well!
I certainly think a Bohmian version is possible. But Newtonian spacetime was very different from Minkowskian spacetime, and GR from Minkowskian, and it is possible that (GR+QM) spacetime will turn out to be very different as well. I admit that I am suspicious of the idea of nonrelativistic trajectories hidden from us so they can't be observed, which is what historically Bohmian trajectories are.
Best,
Hilary

Apr 17



Yes, hidden shmidden, but can you give some indication of what it is about the new spacetime 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?

Apr 17



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 superspace and a cosmic time or not, whether the Bohmian theory appropriate to this future theory (if there is one)
will still be based on positionrepresentation 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 SpaceTime recently brought back to me how unanticipated the next picture of space time and causality was at each of the stages:GalileoDescartesLeibnitz, Newton, EinsteinSR, and EinsteinGR. 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

Apr 17



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 functionsor 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.

Apr 17



Then for you "Bohmian" just means "sensible nonromantic interpretation". I wasn't expressing skepticism about the idea that that is what we need.

Apr 17



On 4/17/2014 8:59 PM, Hilary Putnam wrote:
Then for you "Bohmian" just means "sensible nonromantic interpretation".
Yes. It's surprising that that is so very accurate.

Apr 23



Dear Hilary,
I agree that we don't know whether the final theory of quantum gravity
will have a 4metric 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 4metric.
The references I had in mind are mainly about the formulation of Bohmian
mechanics and GRW in curved spacetime; they spell out the equations and
prove that the theories work.
Bohmian mechanics:
o Sections 4.5 and 4.6 of R. Tumulka:
Closed 3Forms and Random World Lines.
Ph. D. thesis, LudwigMaximilians University, Munich (2001).
o Section 2 of R. Tumulka:
Bohmian Mechanics at SpaceTime Singularities. II. Spacelike
Singularities.
General Relativity and Gravitation 42: 303346 (2010).
GRWf:
o Section 3 of R.Tumulka:
A relativistic version of the GhirardiRiminiWeber model.
Journal of Statistical Physics 125: 821840 (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: 155227 (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: 623631 (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
Welcome to the blogosphere! Now you just need to add some Everettians to your list of correspondents.
ReplyDeleteAn interesting read. IMHO the compelling scientific realist picture that answers the collapse dilemma is akin to the optical Fourier transform. A photon is an extendedentity wave, when you detect it with an electron which is another wave, you see a dot on the screen. But photons and electrons are as pointlike as seismic waves and hurricanes.
ReplyDeleteAs for what psiwavefunction is, see weakmeasurement work by Aephraim Steinberg et al and Jeff Lundeen et al. Mindful of LIGO think "displacement current", think "spacewarp".
Unifying GR and QM is nice, but a red herring. A photon conveys inertia from the emitting body to the absorbing body, and inertial mass equates to active gravitational mass, so the virtual photon is a virtual graviton too. Besides, remember the current in the wire? The electromagnetic forces largely cancel, but not quite. Then when you stop that current, they still don't.
Cosmological processes don't take place in spacetime, they take place in space. Spacetime is static. The map is not the territory. And curved spacetime relates to inhomogeneous space. Remember Wheeler's geons? The strong curvature regime isn't down near the event horizon. It's nothing to do with gravity. It's everything to do with electromagnetism. I kid ye not. Check out Percy Hammond.
John Duffield
My objection for BM starts with its treatment of the Hydrogen atom: the electron is stationary at a fixed distance from the proton (otherwise the electron would radiate energy). Now in BM trajectories are surreal, so this is not a problem, but why is this distance distinguished from any other distances? Because God made it so? Something is fundamentally wrong here.
ReplyDeleteI think the problem of quantum mechanics interpretation is illposed: what is needed is to reconstruct quantum mechanics from first principles. Then the right QM interpretation will follow naturally. What would those principle be? I have a proposal (which I am in the process of writing up for publication):
1. laws of nature are invariant under time evolution
2. laws of nature are invariant under tensor composition (if system A is described by QM, and system B is described by QM then the composite system A tensor B is described by quantum mechanics as well)
3. positivity (ability to have a state space)
4. nature violated Bell's inequalities (technical postulate needed to distinguish between classical and quantum mechanics)
The full QM in the C* algebra formalism follows as a mathematical theorem from those 4 postulates, nothing more, nothing less.
Hi Florin,
Deletethe hydrogen situation in BM is only so for the ground state. In different states the electron would  according to BM  move e.g. in circles or even quite chaotically (e.g. in superpositions of different eigenstates, see the illustration at http://bohmc705.uibk.ac.at/ ).
So if you want to model a situation in BM in which the electron moves around the core, you should better choose the wave function accordingly. Otherwise you just refer to a different physical situation than you inteded to.
The possibility to radiate and fall into the core depends on a mechanicsm that would allow this. The normal Schrödinger equation for the hydrogen atom simply does not include such a term. So an electron that is modeled by this equation also cannot do this.
Don't apply the intuition about a different (and classical) theory here!
Best, Matthias
My first thought on this question was that Bell's theorem works on a sufficiently neutral basis (mostly independent of actual QM theory) so as to let us reflect on the measurement problem without bothering too much of issues such as the reconciliation of QM and GR.
ReplyDeleteHowever after a second thought... Bell's theorem involves at least space time.
Moreover recent research seems to establish a conceptual link between quantum entanglement and wormholes in GR. See
http://mobile.extremetech.com/#/extreme/575wormholesarejustquantumentangledblackholessaysnewresearch
I do not know what it's worth but it might occur that a deeper connection exists between spacetime geometry and the measurement problem after all, which a new physical theory would uncover?
Thanks for posting this interesting discussion. Maybe someone here can answer a question that's been bugging me ever since I read von Neumann's Mathematical Foundations of Quantum Mechanics.
ReplyDeleteVon Neumann uses a "filter argument" in his derivation of the quantum mechanical entropy. The filter argument says that if there is any physical difference between two systems, then a filter can be created that will let one pass through but not the other.
Applied to Bohmian QM, the filter argument says that if the Bohmian position variables have any physical effect, then we can create a filter that will sweep up a subset of the systems that are represented by a particular pilot wave. But sweeping up a subset in this way would lead to an ensemble that has a nonquantum mechanical distribution, so Bohmian QM would make different predictions from standard QM.
On the other hand, if the Bohmian position variables have absolutely no physical effect, then they are unphysical by definition, and can be dropped from the theory.
This seems to put an end to Bohmian QM. But none of the discussions I've read of Bohm's approach make any mention of von Neumann's filter argument. (Note this argument is completely different from the one set out in von Neumann's "no hidden variables proof.")
Does anyone know of a response to this objection?
Dear Robert,
DeleteI am not a supporter of BM, but I will attempt to give an answer in BM spirit (the real Bohmians please jump in and correct me if I am saying something wrong). The way the question is posed is unclear. What does "create a filter that will sweep up a subset of the systems that are represented by a particular pilot wave." actually mean? How is the filter going to be implemented in practice?
Let me speculate on the filter implementation in a particular case: in a double slit experiment. Let us block one of the slits (filtering out the paths that go thorough there). Then what happens? The interference pattern vanishes. What is the BM explanation? The quantum potential changes. Therefore the assertion "But sweeping up a subset in this way would lead to an ensemble that has a nonquantum mechanical distribution" is false.
Therefore the solution to your objection is to consider contextuality: whenever one changes the experimental setting, the quantum potential in BM changes as well and no predictions contradicting standard QM predictions are possible. In fact it is a mathematical theorem that BM recovers exactly the standard QM predictions.
Thanks for your response, Florin, but I think you missed the point. BM asks us to consider an ensemble of systems which all have the same pilot wave but different initial values of the position variable (let's call it q). If the q values has any physical effect, it must be possible to separate out a subset of the original ensemble: let's say all those initial q values that result in the particle going through the top slit. Then we have a new ensemble that violates the predictions of QM (100% probability of top slit vs. 50%).
DeleteIf it is not possible to use the q values to create such a subensemble, then the q values have no physical reality  they have no physical effect.
As far as the theorem you mention, it holds under the assumption that the initial distribution of q values corresponds to the square modulus of the pilot wave. If the filtering process is possible, then this assumption is violated and the so the theorem doesn't hold.
Von Neumann wrote a paper showing that the filtering process must be possible if the quantity has any physical effect. (He describes the process as creating a membrane that is permeable to systems with some values of the variable (q) and impermeable to others.) I don't have the reference at hand but you can find it in a footnote in his book.
Hi Robert,
Delete" If the q values has any physical effect, it must be possible to separate out a subset of the original ensemble"
I think this is not correct for BM. Let me illustrate why:
"Having a physical effect" could mean e.g. that the initial position influences where the particle ends up in the experiment. This is so in BM.
Why should it therefore be possible by the experimental (and statistical means) that you can *control* the position directly? In fact, one can prove that for BM this is not possible in the generic situation of quantum equilibrium. See http://arxiv.org/pdf/quantph/0308039v1.pdf, ch. 11 "Absolute Uncertainty" (pp. 46).
The simple argument that particle positions are physical in BM is that you need something to represent what is happening in physical space in your theory. Otherwise (strictly speaking and not accepting tacit assumptions or conventions) the theory is an empty mathematical formalism.
Best, Matthias
Hilary Putnam: “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 psifunction 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; … 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 …”
ReplyDeleteIndeed, ‘theater’ before anything else.
Let us consider only 3playertheater (time, space and particles). While all the three have the dualitypersonality, I would like to ‘simplify’ the issue as below.
Space, 99% wave.
Time, 99% wave.
Particle (such as electron), 99% particle.
That is, the wavefunction of electron is actually describing a ‘particle’ floating on the spacetimewave. Electron as a ‘particle’ is always as a ‘whole’ while its ‘position and momentum’ are depending upon the spacetimewave (described by the electronwave function). Thus, there is no ‘collapse’ issue as there is nothing to collapse about. The visualized collapse of electron in our measurement is caused by the spacetime wave which is ‘structured’ by the spacetime force.
F (spacetime Force) = K ħ/ (delta S x delta T); the ‘theater’.
K (coupling constant, dimensionless); ħ (Planck constant); S (space); T (time).
Then, delta P (linear momentum) = F x delta T = K ħ/ (delta S)
So, delta P x delta S = K ħ
When, K is near to 1 (but a bit smaller than 1), then delta P x delta S > ħ (the uncertainty principle).
When K ħ is near to (0 ħ), the F is ‘gravity’.
Dear authors of the blog,
ReplyDeleteis it really so clear that one needs a preferred (albeit dynamical) foliation of spacetime into spacelike hypersurfaces for relativistic BM?
To me, the situation seems to be more complicated: the foliation is not necessary to formulate a Lorentz covariant and nonlocal law of motion (this could e.g. be done by forward and backward light cones as well, see http://arxiv.org/abs/quantph/0105040 for a similar idea).
The crucial argument in favor of a foliation then seems to be that one has no idea how to statistically analyze laws of motion different from ones generated by velocity vector fields.
This argument is, however, just a "human" one: one does not know better at the moment. Could it not be that for relativistic physics of N nonindependent particles, the way how to do statistics has to be changed in general?
An indication that this might be so is WheelerFeynman electrodynamics (http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.21.425, http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.17.157): Its laws of motion are very natural from a certain perspective but can also not be formulated using a velocity vector field. Consequently, no way of analyzing the statistics is known.
In the expectation that many people might object to the theory because of its unusual view towards "causality", it is in any case an example for how the question of the analyzability of law that are not of a velocity vector field type arises, also in a context different from relativistic BM.
I'm sometimes wondering why this line of thought is not discussed more intensely when it comes to relativistic BM...
Best, Matthias
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