- (Information) Paradox Lost
Tim Maudlin
arXiv:1705.03541 [physics.hist-ph]
Here is the problem. The dynamics of quantum field theories is always reversible. It also preserves probabilities which, taken together (assuming linearity), means the time-evolution is unitary. That quantum field theories are unitary depends on certain assumptions about space-time, notably that space-like hypersurfaces – a generalized version of moments of ‘equal time’ – are complete. Space-like hypersurfaces after the entire evaporation of black holes violate this assumption. They are, as the terminology has it, not complete Cauchy surfaces. Hence, there is no reason for time-evolution to be unitary in a space-time that contains a black hole. What’s the paradox then, Maudlin asks.
First, let me point out that this is hardly news. As Maudlin himself notes, this is an old story, though I admit it’s often not spelled out very clearly in the literature. In particular the Susskind-Thorlacius paper that Maudlin picks on is wrong in more ways than I can possibly get into here. Everyone in the field who has their marbles together knows that time-evolution is unitary on “nice slices”– which are complete Cauchy-hypersurfaces – at all finite times. The non-unitarity comes from eventually cutting these slices. The slices that Maudlin uses aren’t quite as nice because they’re discontinuous, but they essentially tell the same story.
What Maudlin does not spell out however is that knowing where the non-unitarity comes from doesn’t help much to explain why we observe it to be respected. Physicists are using quantum field theory here on planet Earth to describe, for example, what happens in LHC collisions. For all these Earthlings know, there are lots of black holes throughout the universe and their current hypersurface hence isn’t complete. Worse still, in principle black holes can be created and subsequently annihilated in any particle collision as virtual particles. This would mean then, according to Maudlin’s argument, we’d have no reason to even expect a unitary evolution because the mathematical requirements for the necessary proof aren’t fulfilled. But we do.
So that’s what irks physicists: If black holes would violate unitarity all over the place how come we don’t notice? This issue is usually phrased in terms of the scattering-matrix which asks a concrete question: If I could create a black hole in a scattering process how come that we never see any violation of unitarity.
Maybe we do, you might say, or maybe it’s just too small an effect. Yes, people have tried that argument, which is the whole discussion about whether unitarity maybe just is violated etc. That’s the place where Hawking came from all these years ago. Does Maudlin want us to go back to the 1980s?
In his paper, he also points out correctly that – from a strictly logical point of view – there’s nothing to worry about because the information that fell into a black hole can be kept in the black hole forever without any contradictions. I am not sure why he doesn’t mention this isn’t a new insight either – it’s what goes in the literature as a remnant solution. Now, physicists normally assume that inside of remnants there is no singularity because nobody really believes the singularity is physical, whereas Maudlin keeps the singularity, but from the outside perspective that’s entirely irrelevant.
It is also correct, as Maudlin writes, that remnant solutions have been discarded on spurious grounds with the result that research on the black hole information loss problem has grown into a huge bubble of nonsense. The most commonly named objection to remnants – the pair production problem – has no justification because – as Maudlin writes – it presumes that the volume inside the remnant is small for which there is no reason. This too is hardly news. Lee and I pointed this out, for example, in our 2009 paper. You can find more details in a recent review by Chen et al.
The other objection against remnants is that this solution would imply that the Bekenstein-Hawking entropy doesn’t count microstates of the black hole. This idea is very unpopular with string theorists who believe that they have shown the Bekenstein-Hawking entropy counts microstates. (Fyi, I think it’s a circular argument because it assumes a bulk-boundary correspondence ab initio.)
Either way, none of this is really new. Maudlin’s paper is just reiterating all the options that physicists have been chewing on forever: Accept unitarity violation, store information in remnants, or finally get it out.
The real problem with black hole information is that nobody knows what happens with it. As time passes, you inevitably come into a regime where quantum effects of gravity are strong and nobody can calculate what happens then. The main argument we are seeing in the literature is whether quantum gravitational effects become noticeable before the black hole has shrunk to a tiny size.
So what’s new about Maudlin’s paper? The condescending tone by which he attempts public ridicule strikes me as bad news for the – already conflict-laden – relation between physicists and philosophers.
Dear Tim,
ReplyDeleteWith your first point I absolutely agree.
Same holds for your second point and since you mentioned the letters let me add this: “Einstein’s point of departure is ‘realistic’ rather than ‘deterministic’”; “Einstein does not consider the concept of ‘determinism’ to be as fundamental as it is frequently held to be.”; “In particular it seems to me misleading to bring the concept of determinism into the dispute with Einstein” (Letter from Pauli to Born, 31 March 1954)
To your third point:
- Regarding the 1/r potentials: Historically when Einstein tried to include c into Newton´s gravitational potential and failed, he became aware of Galileo´s “all bodies are falling with the same acceleration”, which also finally led to his principle of equivalence.
(I have a small, not historical, but technical appendix "A.4 Classical 1/r potentials" in the linked pdf under my profile name. Interesting is that in the approximations to arrive the classical result from GR respectively QFT the role of the space and time components with respect to the metric respectively the photon propagator are exchanged)
- Regarding the preferred foliation: in the U/R-process in a U-patch (a tiny entangled state) there is also a kind of “preferred foliation” specified by the particles the U-patch consists of. But it is NOT a global preferred foliation (, which I guess Bohmian mechanics requires). It is restricted to this specific tiny entangled state, because it is dealing with these specific particles. So, the physical law still has the symmetry, but not this specific tiny temporary solution! This is the difference and answers your question ”why the preferred foliation cannot be empirically discovered” .
The answer to your second question "… why, despite the necessity of non-locality, we cannot send superluminal signals." is also straight forward. Since I am defending an indeterministic theory I can use QM randomness that prevents superluminal signals. The traced out density matrix for Bob does not change whatever Alice does. The not so nice feature (in terms of awareness) of the density matrix ρ - as I said here point 1.) - is, that it unfortunately also hides the spacelike correlation, the “non-locality” of QM by “squaring” the state |Ψ> to ρ=|Ψ>< Ψ|.
By the way the flashes in GRW, that in GRW have the bad habit to heat the system a little bit, correspond to the triggered reductions (R). But in the U/R-process there is no heating, because of the unitarity in between. (this is also the difference to the Lindblad eq.)
Tim Maudlin,
ReplyDeleteWhat both Werner and I have been "channelling" is basic facts about probability and QM (via von Neumann, Murray, Segal, Varadarajan, Mackey, ..., Landsman). I would (re-)answer your questions but you've made it very clear that your ignorance is wilful. Not to mention obnoxiously paraded. Your questions are answered and "basic texts" provided but you just declare the former nonsense and ignore the latter. You "simply ignore the classicality assumption and deride anybody as an idiot who does not share your blind spot", as Werner put it.
Paul Hayes
ReplyDeleteI certainly hope that any unbiased reader can see that you are doing nothing but avoiding answering a straightforward question—the very one that Werner also dodged—and being extremely obnoxious about it as well. You claim that EPR and Bell build some assumption of classicality into their arguments, where that assumption manifests by assuming that something or other is a simplex. So I rehearse the argument and ask you to identify exactly where said assumption occurs. And you assure us that you could indeed point it out but can't be bothered, hurling instead a string of insults. The intellectual dishnonesty and complete lack of seriousness of your post is be clear to all. So what is the point of it?
Reimond
ReplyDeleteGood. We already agree on a lot and can make progress on what is left.
It is true that my proposal is for a preferred universal foliation. As far as I can tell, your R process does break full Lorentz invariance, but somehow in a different way in the different local patches. Three observations:
1) Either there is, at a fundamental level, only the unique universal wavefunction, with the wavefunctions ascribed to subsystems definable in terms of the universal wavefunction and the other fundamental beables, or there are more than one fundamental wavefunction. The Bohmian approach is the first of these, with the conditional wavefunction of a subsystem definable from the universal wavefunction and the actual particle locations. I gather that you want to take the second approach. Can you say more about how many fundamental wavefunctions there are and how the tendency of systems to entangle is counteracted?
2) If each individual R process breaks Lorentz invariance, then any collection of them will define a unique preferred global frame (I discuss this in Quantum Non-Locality and Relativity). So you do not avoid a preferred global frame after all.
3) Indeed, the GRW hits do pump energy into the system. But it has been shown by explicit calculation that all the hits that would have ever occurred make only a fraction of a degree Kelvin difference to the temperature of the universe. So no empirical observation refutes GRW. Why the complaint, then, and how does your R process avoid adding energy?
Tim Maudlin,
ReplyDeleteAs far as the insults are concerned I don't think I've ever seen a blacker pot. I used to think your frequent accusations of intellectual dishonesty were projective too but now I think it's more likely a severe case of dysrationalia. Either way the answer to your last question is that under these circumstances there is no point to it. You have made it pointless. Unbiased readers who've been following closely enough can hardly have failed to see the absurdity in your claims that your questions have been dodged; that you haven't been shown* where the classicality assumption manifests itself etc.
* For the unbiased but click-lazy reader here's part of the Werner response which I've linked to several times already.
"In a classical theory this convex set [the probability state space] is a simplex, meaning that any state has a unique decomposition into extreme points, so can be understood as statistical mixture of dispersion free states: equivalently, any two measurements (POVMs, or decompositions of one into positive affine functionals) are the marginals of a joint measurement. We take these properties as a definition of classicality and it is this property I referred to as C in the introduction. How can such a technical criterion become a far reaching postulate? It is equivalent to the possibility of thinking of each individual system as completely described by one of the extreme points or, if one wishes, by one value of the system variables, or an appropriate list of logical predicates. These properties can be thought of as capturing the ‘real factual situation’ of the particle. We can reckon with these ‘facts of the matter’ as well-defined, even when they are unknown to us. A preparation just produces a random distribution of properties encoding our degree of ignorance, and measurements just lift this ignorance, usually only partially. So the physics of classical systems can be treated without ever referring to preparation or measurement. It is about the world and not about what we do with it."
... since I've left a potential (dishonest) exploitation of laziness undefended in that previous comment I suppose I should add this later bit from Werner's paper:
ReplyDelete"The first main point is the EPR criterion of ‘elements of reality’. From the outset of the EPR paper and from the flow of the argument it is clear that these elements of reality are supposed to be independent of what I choose to measure. They are clearly intended as classical in the sense of C. Quantum mechanics contains nothing of the sort. So if not containing such elements is to be incomplete, operational quantum mechanics obviously is incomplete in this sense."
Tim,
ReplyDelete1) “Can you say more about how many fundamental wavefunctions there are …”: In the U/R-process there is a single unique universal wavefunction (state) – mainly a bookkeeping device which particles are entangled. Important is that it is a product of tiny states (U-patches). Therefore, when one U-patch is reduced (R) the others, since it is a tensor product are unaffected as I said here “Separability”.
“… and how the tendency of systems to entangle is counteracted?”: By the reduction (R) – a triggered observer independent one. It will be triggered once the threshold of superposed mass/energy of a tiny state is reached. Only this individual tiny state is reduced, NOT the whole state, since it is already a product state.
2) ”If each individual [U/]R process breaks Lorentz invariance…”: E.g. in an EPR experiment let us first assume Alice and Bob do not move relative to each other and each has its own entangled electron. Both can sit comfortable in their common rest frame with their particle in front. The U-patch consists of the two entangled electrons and whatever particles (from the pointer) get further entangled to the U-patch. Beyond a certain threshold of entangled particles, a reduction (R) is triggered, in between all is unitary (U). Thus, in this single U-patch this frame of rest common to Alice and Bob is preferred.
If Allice and Bob are moving relative to each other then we have two frames of reference connected by a Lorentz transformation. Thus, two frames are preferred. But in other U-patches, i.e. other entangled particles, different frames are preferred, thus there is no preferred global frame. (But I will check in “Quantum Non-Locality and Relativity” what you mean with “collection”).
In other U-patches, no EPR, where e.g. a photon leaves A and arrives at B, real momentum is transferred, thus the two reference frames of A and B are related by the boost.
In the U/R-process the clear separation of U-patches, i.e. the whole state is a product of U-patches is all-important. The next all-important feature is the clear separation of unitary evolution (U) and reduction (R). This leads us to your third point.
But let me say first I have absolutely no complaints at all about GRW, it is very good, actually I went through many of the CSL models in here, even trace dynamics as a possible source for the random flashes in GRW, at least as far as I remember.
CONT.
3.) ”how does your [U/]R process avoid adding energy” Because the evolution between two reductions is unitary. There simply is no non-linear term. The dynamics does not result from e.g. a Newton-Schrödinger eq. with a non-linear term, but from pure unitary evolution (U) followed by triggered reduction (R) beyond a threshold.
ReplyDeleteIt is not an evolution exclusively in time, it is a process – this is the important point.
Just look at it from inside out – by all the changes, all the reductions with a bit of QM randomness, with their distributing mass/energy the process generates spacetime in the first place. In a way these changes are time. This is not far away from George Ellis’s crystalizing block universe. In Part III “General Relativity” I explain where the indeterminism enters into the block universe. (*)
I know we try to think of everything evolving in time, i.e. as integration of differential equations. This is more or less ingrained in our thinking, since Newton. And it is perfectly ok, but we should question whether the initial conditions are given in the very beginning of time, or whether it is a process where with every triggered reduction the initial condition for the next steps can change a bit with fundamental QM randomness.
Particles are redistributed a bit and here finally enters the non-linearity, because now the environment, i.e. the particles from previous steps can influence a tiny system by getting entangled. This enables the evolution of complex systems, consisting of myriads of tiny U-patches (interacting molecules, …) stabilized by feedback via myriads of U/R-process steps. I really tried to convey this idea in Part I “Third approach” (*)
This is not about reinventing QM (QFT, SM) and GR, but this is just a proposal how this fits neatly together.
We observe that QM and GR are working perfectly fine, but there is this tension between QM and GR. All the U/R-process does is to use this tension to solve the measurement problem and some other problems.
Basically, it is only a change in perspective.
-----------------
(*) In the pdf (link in profile name)
Tim,
ReplyDeleteMaybe I should add the following comparison with GRW to make it even more clear
1) “… and how the tendency of systems to entangle is counteracted?” :
In GRW one random flash in time and at a point in space acts on all states that are “localized” within a certain radius, thus all entanglement is reduced with respect to this region in space.
In the U/R-process in contrast only a specific U-patch is reduced (once it grows beyond a certain threshold). Other U-patches that are in spatial neighborhood are not affected. Thus, the reduction takes “place” with respect to the topology of the entanglement and not with respect to the spatial location.
This also might better illustrate point 3), why GRW is heating a tiny bit (no complaint, just to epitomize) in contrast to the U/R-process.
And to help to emphasize on non-locality: to determine the mass/energy in superposition of this U-patch, indeed a non-local mechanism is needed. But all QM non-locality is encapsulated in the U-patch. Only in EPR like situations the “non-local”, distant spacelike correlations after the reduction survive. But I would say, by just looking out of the window, the vast majority of process steps in our universe refer to transporting particles from there to here.
"Paul Hayes" (I use the quotation marks since I cannot find any evidence of a so-named actual person trained in a relevant branch of physics),
ReplyDeleteYour last post is an interesting combination of the sort of stuff we got from Dark Star (whose last piece of rhetoric before he was banned was also an accusation of mental illness) and a poster named Juan Manuel Jones Volunté (a real name, that one) who claimed that Bohr's response to the EPR paper was crystal clear. Since neither I nor John Bell could make head or tail of Bohr's response, I asked Volunté to explain what Bohr had in mind. He responded by simply quoting Bohr and again saying it was clear. So I asked him to explain what Bohr meant by a particular phrase, and specifically requested that he not just quote Bohr's paper, since I was already painfully aware of the sequence of words Bohr used, and was completely at sea about what that sequence of words was supposed to convey. Volunté responded by simply quoting more of Bohr again, despite my explicit request that he not do so. (I do not exaggerate: see the exchange here:
https://www.facebook.com/sabine.hossenfelder/posts/10156669764549574?comment_id=10156674554589574¬if_id=1530062053140602¬if_t=comment_mention .)
I went on to explain that if you really understand something, and are not just repeating back words like a well-trained parrot, you should be able to reformulate the point in different ways and make clear its meaning by answering sharply asked questions. So now you are playing Volunté's part to a tee, with Bohr replaced by Werner. That is a brilliant piece of casting, by the way. See Adam Becker's new book, which I have reviewed here:
http://bostonreview.net/science-nature-philosophy-religion/tim-maudlin-defeat-reason .
So let's see how much you understand by seeing if you can present Werner's argument in clear terms, something he never did.
In my post of 4:52 AM, June 27, 2018, I outlined the EPR argument in my own words, and asked you to point out where Einstein ever assumes that anything is a simplex. So I renew my request: just answer that question clearly, in your own words, without quoting either Bohr or Werner.
I eagerly await your response.
Reimond.
ReplyDeleteI am not following this response:
'”how does your [U/]R process avoid adding energy” Because the evolution between two reductions is unitary. There simply is no non-linear term. The dynamics does not result from e.g. a Newton-Schrödinger eq. with a non-linear term, but from pure unitary evolution (U) followed by triggered reduction (R) beyond a threshold.'
But the original GRW dynamics has precisely that form: unitary Schrödinger evolution punctuated at random times by collapses, and that dynamics is the one known to lead inevitably to heating. The degree of heating is controlled in that theory by a combination of the frequency of the collapses and the precise mathematical form of the collapses. In particular, GRW collapses are implemented by multiplying the wavefunction by a Gaussian, and the amount of heat injected by a collapse depends on the precise width of the Gaussian. As the Gaussian gets narrower in physical space the energy injection increases, which is why GRW does not and cannot use "position eigenstates" (i.e. Dirac delta "functions") in the collapse recipe. As far as I can tell, there is no way to introduce useful collapses without them leading to spontaneous heating. For one effect of the collapses must be to prevent the constant spreading of the wavefunction in position representation, and narrowing the wavefunction in position space increases the expectation value of its energy.
Clarifying this point in your approach would be very helpful.
In this sentence with regard to GRW “within a certain radius, thus all entanglement is reduced” I should have better said, instead of using the word entanglement, the following: “within a certain radius the positions are relocated with the help of a Gaussian.”
ReplyDeleteGo back to the classical experiment with red and blue marbles... In the quantum cases, the separated particles carry their entanglement with them across space and time.
ReplyDeleteThe non-classical aspect of quantum entanglement can’t be illustrated in terms of a single classically correlated attribute such as the marble colors you described. It involves choices of what measurements to perform. Suppose your marbles are all spinning, and the experimenters are free to measure the spins along any one of three fixed axes, 120 degrees apart. For whichever axes they choose to measure, each experimenter always gets either spin UP or spin DOWN (nothing in between) with 50/50 probability. When the two experimenters happen to measure along the same axis (for a given entangled pair) they always get opposite results, and when they measure along different axes they get equal results 3/4 of the time. As Bohr said, if you aren’t shocked by this, you haven’t understood it.
The problem is when the rejection of a preferred foliation is elevated into some sacrosanct principle… consider adding in a preferred foliation if that could yield a clearly articulated rational theory…. open our minds to the possibility that Relativity left some space-time structure out of account because when it was developed there was no empirical evidence of non-locality.
We should be careful not to give the impression that quantum entanglement somehow violates Lorentz invariance or special relativity, because of course it does not. In fact, the strict conformity to Lorentz invariance even of quantum entanglement phenomena is (in my opinion) one of the strongest affirmations of the “sacrosanct” status of the principle of local Lorentz invariance. The emergence of quantum field theory from the conviction that there should be a truly relativistic theory of the electron shows the heuristic power of the relativistic principle. A preferred foliation is as superfluous today as it always has been, because it introduces to the descriptions of events asymmetries that are not inherent in the phenomena (just like the conductor or the magnet moving in unipolar induction). The two spacelike-separated sides of an EPR experiment are perfectly symmetrical, and it makes no difference whether we work in a frame where one or the other occurs first. I don’t think a preferred foliation yields a more clearly articulated or a more rational theory. To the contrary, I think much of the perplexity over quantum entanglement is due to the neglect of the Lorentz invariant lightcone structure of spacetime, and the tendancy to still think in terms of spacelike foliations, even though we know better. It’s a hard habit to break. For example, even today people still get confused by the Coulomb gauge into thinking that the electric potential propagates instantaneously on our chosen foliation, even though it’s clear from the Lorentz gauge that it propagates on the light cone. The temporal symmetry of the fundamental laws (advanced and retarded solutions, etc.) is also important.
…the experimental context where two photons have been measured and the 3rd is still in flight…
I think it’s misleading to assign the spacelike measurements a definite temporal ordering, since the Minkowski metric imposes only a partial ordering of events. What you call the third measurement is actually the first in terms of some system of inertial coordinates. With this in mind, your question (“Why does the 3rd particle always do the right thing when measured?”) takes on a different flavor. In a frame in which the third particle is the first, the question becomes “Why does the first particle always do the right thing when measured?” I think this question is more interesting.
Tim,
ReplyDeleteSince you wrote your comment before you could read this and this I hope it became a little bit more tangible. And I am just reading your “Quantum Non-Locality and Relativity” and will give you in the next comment a corresponding picture within the U/R-process to your “Figure 7.3 ERP Experiment and Two Reference Frames”.
Amos,
ReplyDeleteThere is quite a lot in this paragraph. Let's go slowly.
"We should be careful not to give the impression that quantum entanglement somehow violates Lorentz invariance or special relativity, because of course it does not. In fact, the strict conformity to Lorentz invariance even of quantum entanglement phenomena is (in my opinion) one of the strongest affirmations of the “sacrosanct” status of the principle of local Lorentz invariance. The emergence of quantum field theory from the conviction that there should be a truly relativistic theory of the electron shows the heuristic power of the relativistic principle. A preferred foliation is as superfluous today as it always has been, because it introduces to the descriptions of events asymmetries that are not inherent in the phenomena (just like the conductor or the magnet moving in unipolar induction). The two spacelike-separated sides of an EPR experiment are perfectly symmetrical, and it makes no difference whether we work in a frame where one or the other occurs first. I don’t think a preferred foliation yields a more clearly articulated or a more rational theory. To the contrary, I think much of the perplexity over quantum entanglement is due to the neglect of the Lorentz invariant lightcone structure of spacetime, and the tendancy to still think in terms of spacelike foliations, even though we know better. It’s a hard habit to break. For example, even today people still get confused by the Coulomb gauge into thinking that the electric potential propagates instantaneously on our chosen foliation, even though it’s clear from the Lorentz gauge that it propagates on the light cone. The temporal symmetry of the fundamental laws (advanced and retarded solutions, etc.) is also important."
First, no one is claiming that entanglement per se breaks Lorentz invariance. But equally, entanglement per se does not explain how Bell's inequalities get violated. Entanglement plus wave collapse or objective reduction gets you somewhere, but then the reduction has to be implemented in a Lorentz invariant way, if you want to keep that sacrosanct. That is very, very tricky. Rodi Tumulka figured out how to do it for the flash process, but that is surely not what a standard person working in QFT has in mind. Many people take the ETCRs, which are part of standard QFT, as enforcing Lorentz invariance, but they do no such thing. They enforce no-signalling and observational Lorentz invariance, but Bohmian mechanics has those characteristics thanks to the use of a foliation and quantum equilibrium. So before claiming some victory for complete Lorentz invariance, you have to clearly spell out how your theory avoids the measurement problem. I'm all ears.
Your comment abut the light cones is puzzling to me. The light cone structure does not break the basic symmetries, so how can it help? Also, your appeal to Lorenz (N.B.: "Lorenz" not "Lorentz") gauge is odd. You think that the existence of Lorenz gauge proves that the propagation of the potential is "really" Lorentz invariant, but why not appeal to Coulomb gauge to prove just the opposite? Why should Lorenz gauge "win" to prove the "real" structure of the theory?
Tim,
ReplyDeleteI just realized that my account of GRW was wrong, the flashes act on single particles and has nothing to do with a radius/region in space. When the hit particle is entangled also the others in the entanglement get multiplied with the gaussian. Sorry, I messed up the GRW mechanism – it was some time ago that I looked at it.
I definitely need to read GRW again, because again I said something wrong about GRW: When the hit particle is entangled it just breaks the symmetry with the other entangled particles.
ReplyDeleteTim,
ReplyDeleteAfter having stirred more confusion than clarity with my ad hoc comparison with GRW, because of my faulty recollection of basic facts about GRW, I propose the following.
I need a couple of days recollecting GRW and go through “Quantum Non-Locality and Relativity” and then I give a comparison to the U/R-process based on the language of “flash ontology”. The random flashes and my trigger both map onto spacetime to recover more or less local beables, at least as I can see so far.
Tim Maudlin,
ReplyDeleteNice try but poisoning the well in an attempt to make yourself look like the credible authority and me the dunce doesn't hide that brazen evasion. It's my understanding that's in question? I don't think so. The role of crank, or heroic maverick - slayer of the conventional modern foundational wisdom - if you prefer, is all yours. You're the one who forces journal editors to commission responses to your "bad philosophy and bad physics", not me. So the onus is on you to clearly state exactly what you think is wrong in Werner's admirably clear explanation of this simple basic stuff. Maybe then we could at least get past you just parroting yourself.
Besides, Werner's explanation covers all the equivalent ways of stating the relevant and well-known differences between classical and quantum probability, and those of us who've tried one or another at a time before, here and elsewhere (in our own words and/or in numerous referrals to the literature), have found your response is always the same: continuing incomprehension. What a fool I was to hope I'd made some progress there by at least rescuing those poor lambdas from total oblivion at your hands.
Besides², this parrot isn't quite dead yet but it has just about lost the will to live.
"Your last post is an interesting combination of the sort of stuff we got from Dark Star (whose last piece of rhetoric before he was banned was also an accusation of mental illness)"
ReplyDeleteWhoa there, Tim! That's not what happened. Let's set things straight...
1. I have never been banned from this blog -- just gave up on Tim (as many others have now done). In fact I have engaged with other participants on this thread a couple of times since then.
2. In my last post to Tim (Jan 14) I accused him of intellectual dishonesty, not mental illness. But my money would be on NPD, for what it's worth.
"Paul Hayes" (whose only online presence appears to be that of a troll),
ReplyDeleteYour last post provides a wonderful example by which to explain the difference between just saying whatever and backing up a claim with actual evidence. Let's look at this claim, for example:
"You're the one who forces journal editors to commission responses to your "bad philosophy and bad physics", not me."
This clearly presents as fact a certain narrative: I (on request, by the way) wrote "What Bell Did" for the Bell 50th anniversary special issue of Journal of Physics A. (For anyone interested, it is open access, so here:
http://iopscience.iop.org/article/10.1088/1751-8113/47/42/424010/meta )
Your narrative is that the article was so horrible and the journal editors thought the paper so bad that they sought out and "commissioned" Werner to respond to it.
Here is a different narrative: Werner, made aware of my paper and realizing that it reveals what nonsense he has been writing, demands a chance to respond. The editors, out of a sense that this is a controversy that ought to be fully aired, allow him to respond but then grant me the right (as is only proper) to respond to his comment.
Now these two narratives are incompatible. If one is true than the other is false. So how can we figure out which is which?
Well, there is the obvious verifiable fact that the editors did give me the chance to respond, and squashed Werner's desperate attempt to respond to my response. That would suggest whose side the editors were on.
But completely decisively, there is this fact: my article was chosen by those very editors as a 2014 Highlight article. It was reproduced in a special collection of Highlight articles, and I was sent a certificate noting the selection that hangs on the wall of my office.
So: Narrative 1: The editors so disliked my article that they were "forced" to "commission" a response from Werner. They then went on to award this same dreadful article a notable distinction, make it widely available, and give it an award.
Narrative 2: The editors found my article to be provocative but clear and interesting, They either asked, or Werner himself demanded, to publish a response, because he could see that his nonsense was being revealed. The editors granted me the right to respond to Werner, and then selected my article as a Highlight article of the Year, bypassing other articles in the Bell volume.
There are competing, incompatible theories and there is empirical evidence. In this case the evidence completely favors Narrative 2 and is inconsistent with Narrative 1.
See how that works?
Now, one more time, please point out where in Einstein's EPR argument there is any tacit supposition that anything is a simplex. Still waiting.
Reimond
ReplyDeletePlease do go back and reacquaint yourself with GRW. When dealing with foundational question, it is always a huge benefit to understanding to have some clear concrete examples of theories that can recover the basic iconic quantum mechanical phenomena: 2-slit interference, the disappearance of that interference upon monitoring, violations of Bell's inequality, the Aharonov-Bohm effect, etc. The clearest such theories (which were both originally developed in the non-Relativistic setting) are Bohmian mechanics and GRW. For myself, I automatically ask, for some phenomenon, how it is explained in each of these theories. So take you time and don't rush. We have as much time as we need to get clear and come to some agreement.
Cheers,
Tim
Tim, Amos,
ReplyDeleteMaybe here I can add some clarity. This here is all about gauge including Lorenz. And here it is explained that the gauge invariance finally is based on the circumstance that external electrons are on mass shell (now we are back with Lorentz).
In a scattering process starting on mass shell and finally ending on mass shell one calculates amplitudes via a path integral (PI). For a PI a Lorentz invariant Lagrangian is used, but the propagators (virtual particles) in between can and most of the “time” do violate E²-p²=m² as I said here.
Now we look at a Feynman diagram that connects spacelike separated points, e.g. a more or less horizontally drawn electron propagator like this here and read the following 1/2 page about different reference frames.
The obvious/apparent difference to EPR is that the spacelike separated points are connected by an electron propagator. But what is common to this figure here and the Feynman diagram above (correctly anti-/symmetrized) is that both are entangled states and both give us absolutely correct probabilities in a measurement.
CONT.
The awareness of this “non-locality”(*) is indeed a little bit suppressed. For “a standard person working in QFT” non-locality means only faster than light signaling (see here) And indeed QFT does not violate this, but only after all amplitudes have been added up and we talk about probabilities. In between there is a hell of QM “non-locality” (hmm… or should I say non-locality…) going on. Also since MWI is wide spread, the awareness of the transition from amplitudes to probabilities (let me call it measurement) is also a little bit suppressed. (And decoherence does not help)
ReplyDeleteWith Amos´s “The emergence of quantum field theory from the conviction that there should be a truly relativistic theory of the electron shows the heuristic power of the relativistic principle” I absolutely agree. This is no paradox, when we clearly distinguish between unitary evolution (U) and reduction (R). Also, the power of GR and QFT(SM) was a big motivation for the U/R-process, which basically leaves QM and GR unaltered. But one needs to be very precise as Tim always justly demands.
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(*) “non-locality” in quotes to code spooky-action-at-a-distance, but no faster than light signaling.
You think that the existence of Lorenz gauge proves that the propagation of the potential is "really" Lorentz invariant, but why not appeal to Coulomb gauge to prove just the opposite? Why should Lorenz gauge "win" to prove the "real" structure of the theory?
ReplyDeleteThat was answered at a meeting of the British Association for the Advance of Science at Bath in 1888. According to Fitzgerald, the Maxwellians “murdered phi” at that meeting. They argued that the E and B field strengths are the observable "physical" entities of electromagnetic theory, since they represent the flow of causality (energy flux = E x B, etc), and of course changes in E and B unambiguously propagate at the speed of light. We have the same E and B fields for a given physical situation regardless of what gauge we choose, but the potentials are more like arbitrary computational artifacts in the sense that the same physical situation can be described by many different potential fields, depending on the chosen gauge. (Even Bell compared the “collapse of the wave function” with the “funny behavior of the scalar potential of Maxwell’s theory in Coulomb gauge”.) A good modern exposition is Jackson’s 2002 paper, “From Lorenz to Coulomb and other explicit gauge transformations". See also Brill and Goodman, Am J Phys, vol 35, 832, (1967).
Many people take the ETCRs, which are part of standard QFT, as enforcing Lorentz invariance, but they do no such thing. They enforce … observational Lorentz invariance…
Yes, I wouldn’t claim more than that.
Before claiming some victory for complete Lorentz invariance, you have to clearly spell out how your theory avoids the measurement problem.
I think local Lorentz invariance is a physical principle that, as far as we can tell, is observationally true without exception, regardless of what we think about the measurement problem. It’s similar to local energy and momentum conservation – it’s conceivable it could be violated, but that would raise far more problems than it solves (in my opinion).
Bohmian mechanics has those characteristics thanks to the use of a foliation and quantum equilibrium.
Again, I think a preferred foliation introduces asymmetries not inherent in the phenomena (and I don’t think Bohmian mechanics solves the measurement problem anyway).
Your comment abut the light cones is puzzling to me. The light cone structure does not break the basic symmetries, so how can it help?
I don't suggest to break basic symmetries, but to respect them. The light cone structure is essential for this, and for clarifying the causal topology.
Could you (all) please avoid trying to diagnose your mental illnesses, I think none of you is qualified to do that. Thanks,
ReplyDeleteB.
Amos,
ReplyDelete"That was answered at a meeting of the British Association for the Advance of Science at Bath in 1888. According to Fitzgerald, the Maxwellians “murdered phi” at that meeting."
The murder victim was miraculously resurrected by Aharonov and Bohm in 1959. Or at least, trying to discuss the invariance properties of electromagnetism without taking into account the Aharonov-Bohm effect, and thinking hard about how one's account of electromagnetism must change on account of that effect, is foolhardy. Aharonov and Bohm declared that the effect requires us to treat the potentials as physically real. You may disagree with that, but one thing sure: the 1888 view of the matter is a dead letter now.
"I think local Lorentz invariance is a physical principle that, as far as we can tell, is observationally true without exception, regardless of what we think about the measurement problem. It’s similar to local energy and momentum conservation – it’s conceivable it could be violated, but that would raise far more problems than it solves (in my opinion)."
Let's grant (which is of course not proven) that local Lorentz invariance is an exceptionalness observational symmetry. Now the job of the physicist is to look for theories according to which is comes out as an exceptionalness observational symmetry in a natural way. Such a theory must, of course, solve the measurement problem in a principled, physical way: until you solve the measurement problem you are in no position to make any claims about what the observational characteristics of the theory are.
If you are under the impression that how that will be done must be independent of how the measurement problem is solved, we know that that is incorrect. Roderich Tumulka's Relativistic version of GRW (and there are others now) certainly implies observational local Lorentz invariance because the whole theory is locally Lorentz invariant from beginning to end. Bohmian mechanics with a preferred foliation, in contrast, yields observational local Lorentz invariance via quantum equilibrium, which is the very same way it eliminates the possibility of superluminal signaling. Since equilibrium is the typical state of a system, and being out of equilibrium calls for explanation (e.g. the puzzle of the low entropy of the Big Bang), this is also a completely natural and satisfying explanation that uses no tricks or fine tuning.
Your comment that Bohmian mechanics does not solve the measurement problem is, to say the least, completely opaque. You would have to back that extraordinary claim up with some details in order for me even to comment on it.
Dark Star
ReplyDeleteMy bad! I apologize. I got you mixed up with someone else. Sorry about that.
Tim
Amos
ReplyDeleteAs a side comment, I would not bet my pension on conservation of energy and/or momentum, unless you are cheating a bit about the meaning of "local" here. As we all know, a very compelling account of the origin of these conservation laws is that they arise, via Noether's theorem, from space-time symmetries. But we know for a fact that the relevant symmetries are not globally realized, and hence are only approximately locally realized. In the actual universe there are, for example, no timelike global Killing fields, and so no reason to expect (and good reason not to expect) any definition of an energy that is globally conserved. And the same for translation invariance and linear momentum. I am writing a paper about this with Daniel Sudarsky and Elias Okon at the moment.
What about local conservation? Well, that could go just like the validity of Euclidean geometry on the surface of the Earth: it is good enough FAPP if you stay in your own back yard, and breaks down massively on the scale of 1,000 miles. But what if we go the other direction: to the ultra-microscopic? Will there be timelike Killing fields at Planck scale, for example? Not according to many approaches to quantum gravity, or at least this is what they say.
So if all you mean by local energy and momentum conservation is close-enough-to conserved-to-be-reliable-FAPP-on-a-scale-that-is-bounded-both-above-and-below, you have something that might be true. But even that highly hedged principle may well fail in some unusual circumstances, such as the final stages in the evaporation of a black hole. See—by odd coincidence—the very paper of mine that set off this whole thread.
Tim Maudlin,
ReplyDelete"Well, there is the obvious verifiable fact that the editors did give me the chance to respond, and squashed Werner's desperate attempt to respond to my response."
Journals aren't blog comment threads and the limitation to a triple - original article / counter (if any) / original article author's response - is standard journal practice is it not? Here, again, is Werner's "desperate" response to your desperate nonsense. Was it "squashed"? Was it even submitted?
"But completely decisively, there is this fact: my article was chosen by those very editors as a 2014 Highlight article. It was reproduced in a special collection of Highlight articles"
Along with Werner's corrective. Perhaps your certificate is bigger?
Whatever. You just repeat your evasion and this "dead parrot sketch" of a discussion is over* as far as I'm concerned.
* assuming no-one other than Tim Maudlin finds anything unclear in the explanations already given.
Tim, Amos,
ReplyDeleteIn QM + Maxwell and in QFT it is the potential A_μ, not E, B, which couples to ψ - coupled by the demand for local gauge symmetry (again see here (1)). Also the Aharonov-Bohm effect is all about the A_μ (and topology), not E, B. I know very well that many think, gauge freedom is just a mathematical redundancy and somehow reducing to "physical" entities will have a big benefit, but others like Carlo Rovelli (”Why Gauge?”) see in gauge a handle to couple different systems and this reveals the relational character of our world. [Disclaimer: and no, I do not buy Rovelli’s RQM nor LQG]
On to “Many people take the ETCRs, which are part of standard QFT, as enforcing Lorentz invariance, but they do no such thing. They enforce no-signalling and observational Lorentz invariance”.
Amos wants: “… as enforcing Lorentz invariance…”, which Tim excludes “… but they do no such thing …”
Tim´s statement is correct. But I really would like to add the clear distinction between unitary evolution (U) and reduction (R). Why? Look here. The ETCR (5) leads to the “ETCR” (12) of the creation/annihilation operators. As we saw here virtual particles are created at a point in spacetime, but then “travel”, according their propagator off mass shell most of the “time” (able to violate E²-p²=m², but still remembering Lorentz via the pole 1/( E²-p²-m²) in the propagator). This all “happens” in the unitary evolution (U). Now the key is observational Lorentz invariance, which needs a measurement/reduction (R). As always, my proposal is a triggered observer independent one.
In my previous comment I just wanted to address, that “non-locality”(*) is already implemented in QFT in Feynman diagrams like this here, but it is encapsulated in the unitary evolution (U). QFT=QM+SR does not lead to non-locality when regarded/observed after the measurement/reduction (R).
And yes, QFT is based on a “sacrosanct” Lorentz invariant Lagrangian, but in the propagators it is just the pole that remembers SR.
When we regard our world as the result of myriads of tiny U/R-process steps it is easy to understand.
(trying to understand our world as a single exclusively unitary evolution – at least for me - is hopeless)
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(*) “non-local” in quotes to code spooky-action-at-a-distance, but no faster than light signaling.
Entanglement and spooky-action-at-a-distance is the very essence of QM.
Tim,
ReplyDelete”When dealing with foundational question, it is always a huge benefit to understanding to have some clear concrete examples of theories that can recover the basic iconic quantum mechanical phenomena: 2-slit interference, the disappearance of that interference upon monitoring, … “ This is described in (*) under ‘Part II U/R-process in examples’ in ‘Double slit, bubble chamber, particle collider’ and further EPR is in ‘Entanglement, EPR and its "non-local" aspect’. ”violations of Bell's inequality, …” is in ‘A.20 Locality and QM’ and ”the Aharonov-Bohm effect, etc.” is at the end of ‘A.16 Superconductivity’ as an example of non-quantized flux.
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(*) In the pdf (link in profile name)
Amos,
ReplyDeleteSince you referred to this also have a look in this Jackson paper eq. (41) to connect to what I referred to here.
Steven, with some comments directed to “Paul Hayes”,
ReplyDeleteApologies for not responding sooner, I too have been taken up with other matters.
Steven, let’s continue discussion here, though I appreciate your offer to take it offline. I read your offer as a willingness to educate me (or point me in the direction of papers to achieve this), which is nice, but for the moment I am far from convinced that it’s me whose understanding of EPR-B and GHZ nonlocality is deficient. Of course, I admit that my mathematical and physical training is not the same as that of a working physicist, which I presume you are. But as Tim has argued several times above, that technical training with its associated socialization can make even brilliant physicists make mistakes on fundamental conceptual issues. So let’s keep an open mind about who’s missing the boat here.
I looked at the paper by Fuchs, DeBrota and Stacey that you mentioned, https://arxiv.org/pdf/1805.08721.pdf . It seems to me that they are playing around with equations with unclear and/or confused reasoning behind the play, and not revealing the real difference between classical physics (or classical probability) and quantum physics (or “quantum probability”, whatever this means). Their paper is based around Fig. 1, which shows a quantum state either being measured for D_j (some operator/measurement), or first measured for H_i, constituting state preparation in new state σ_i, followed by measurement for D_j. They introduce a formalism for codifying the conditional probabilities (D-measurement, conditional on prior H-measurement with outcome i) that involves a matrix �� which has some columns that are negative-valued. These are the “negative probabilities” that you mention in your last message. (Fuchs et al call them “quasiprobabilities”).
As far as I can see, they are just an artefact of the free mathematical play that they engaged in, with no direct physical meaning at all. They try to forge a meaning as follows: “What would it mean if �� were I? [I being the identity matrix.] This would be the case if the intermediate D_j measurement did not disturb the original state ⍴. This they then associate with “classicality”, via a completely specious argument.
“Put another way, we could behave as though measurements simply revealed a preexisting property of the system, as in classical physics where measurements
provide information about a system's coordinates in phase space.”
This is specious reasoning in two respects. First, because there is no conceptual guarantee of any kind that, in classical physics, measurements are non-disturbing. Rather the opposite, if you think about it, given that once you include gravity you see that as soon as you move a finger (literally) you affect the momentum of every other particle in the universe. True, classical physics has pre-existing values, that we can try to use measurements to [approximately] reveal. But that in no way implies that we can reveal them without disturbing them. Second, because Fuchs et al here presume that deviation from the ideal of pre-existing-values + non-disturbing-measurement is the chief characteristic making quantum physics different from classical, which ignores what we’ve been discussing for the past weeks: entanglement.
So, I’m afraid I didn’t see anything in this paper that made me think that I’m missing something important about “quantum probability”.
In the next message I will point out what I take to be your/Werner’s/Mermin’s mistake when discussing GHZ.
CONT.
Continued:
ReplyDeleteSteven, Paul Hayes,
Coming back to GHZ, I should give a nod to Amos and agree that, if we assume SR is correct about the true structure of spacetime, there is no saying which of 3 spacelike separated GHZ measurements is “last” and hence is the one that has to “know what to do”. This does not resolve the issue, however: collectively, the 3 particles have to “know what to do” in order to make the correlations come out right, and this is not possible if the only factors that can affect the 3 outcomes are local ones.
It is important to note, here, that we (me, Tim, Travis) are not making the mistake of inadvertently, tacitly assuming that GHZ measurements are revealing pre-existing values. The elegant thing about GHZ is precisely that you see, vividly, that it can’t be doing this, because there is no non-contradictory way to assign such pre-existing values that respects all the quantum probabilities (which in this case are all 0 or 1). Werner and others seem to accuse Bell and his devotees of making such an assumption when they introduce the dummy variable �� into the argument. That’s wrong. �� can stand for anything you like, including nothing, or the full entangled (initial) quantum state, which is inside the backward light cone of each measurement event. The point is that if you have got nothing local that tells you what settings were chosen for the distant measurements, you can’t generate outcomes that violate the Bell inequalities; conversely, if you do generate B-inequality-violating outcomes, you’ve got something nonlocal happening. I don’t presume to tell you which story is the right one to tell! I agree with the end of your last post, Steven: many interesting stories can be told, let people work on them if they have time and desire to do so. All I have been trying to insist is that those stories are going to involve something deserving of the title “nonlocality” in them, if they actually explain how the correlations are enforced rather than just waving the magic wand of “QM predicts them, that’s why. Oh, and QM doesn’t violate locality.” (To be rigorous: Either nonlocality, or something even weirder like backwards causation or conspiratorial initial conditions.)
So, to be clear: the inference from Bell-inequality violating experiments to genuine nonlocality in nature does not involve a tacit presupposition of pre-existing values, counterfactual definiteness, or anything of the sort. It also does not commit to a preferred temporal foliation, or the possibility of FTL signaling. I really don’t see why some physicists are so reluctant to accept the conclusion of the argument: nature is nonlocal in some way, even though it is not in a way that allows us to communicate FTL. What’s the psychological barrier to admitting this?
Cheers,
Carl
Apologies for the mystery characters; when I looked over my last 2 posts in preview mode, I didn't see anything going wrong. The first mystery character was a capital-PHI, the second one was (as I'm sure everyone could guess) lambda. (Not sure why Blogger is willing to let us use sigma and rho, but not these others. Maybe it was the font in Word that I used when drafting.)
ReplyDeleteCarl
"Paul Hayes"
ReplyDelete"Whatever. You just repeat your evasion and this "dead parrot sketch" of a discussion is over* as far as I'm concerned."
There is indeed something Monty Pythonesque about this at this point, because your desperation and simmering anger have become so extreme as to be comical.
Since it is you who I have repeated asked to point out where (as per Werner's nonsense) Einstein assumes anything is a simplex in the EPR argument, and it is you, who over and over again refuses to address this rather obvious and simple worry and evades the question, all you are doing is making yourself, and Werner with you, ever more ridiculous.
Now your narrative is this: the editors thought so horribly about my article that they "commissioned" Werner's response, and were so impressed with that response (and remember: still thought that my article was dreadful!) that they made my article a Highlight of the Year just so everyone could read Werner's response to it! Thereby advertising to the entire world how bad some of the articles they publish are! Well, that's exactly as plausible as everything else you have written.
There is a simple way to end a discussion. Stop continuing it. You are welcome to do so at any time. But if you think that you are going to post more of your tripe without any response you are once again deluded.
If you publish any further discussion, it better begin with a clear explanation of where in the EPR argument there is any tacit assumption that any anything is a simplex. Good luck with that.
And since a Google search for a "Paul Hayes" with any relevant qualifications comes up empty, how about a little more biographical information so we can know who we are dealing with here. I think you can find mine on my Wikipedia page.
Carl Hoefer,
ReplyDelete"not revealing the real difference between classical physics (or classical probability) and quantum physics (or “quantum probability”, whatever this means)."
Something we can agree on. In my view, the QBists' preference for the subjectivity-emphasising de Finetti-founded interpretation of probability over the objectivity-emphasising Cox-Jaynes-founded one is unfortunate, and so is the resort to quasiprobability proper.
I say "quasiprobability proper" because, despite it's sometimes being described as such, there really is nothing "quasi" about quantum probability [ / noncommutative probability]. It's a generalisation of probability which subsumes classical probability. In particular, it facilitates making the "on equal footing" direct comparison of QM and (probabilistic) CM which Max Born rightly suggested ought to be made. It really isn't wise to take your cues from someone who claims expertise in quantum foundations yet says things like "'quantum probability', whatever that means" (see e.g. this.)
"It is important to note, here, that we (me, Tim, Travis) are not making the mistake of inadvertently, tacitly assuming that GHZ measurements are revealing pre-existing values. The elegant thing about GHZ is precisely that you see, vividly, that it can’t be doing this, because there is no non-contradictory way to assign such pre-existing values that respects all the quantum probabilities (which in this case are all 0 or 1)."
That's right - it's not a mistake. It's a deliberate and doomed attempt to assign possessed values. And it's doomed because - how many more times? - the quantum probabilities are not all 0 or 1 and, unlike in classical probability, never can be.
"Werner and others seem to accuse Bell and his devotees of making such an assumption when they introduce the dummy variable [lambda] into the argument. That’s wrong."
Both Werner and I have clearly explained why it plainly isn't wrong. I beseech you, in the bowels of Christ, to think it possible that you may be mistaken; that you've been misled. Here's (yet another) source for you:
"A pretty standard framework for discussing such models has existed since John Bell’s work in the 1960’s, and almost everyone adopts the same definitions that were laid down then. The basic idea is that systems have properties. There is some space \Lambda of ontic states, analogous to the phase space of a classical theory, and the system has a value \lambda \in \Lambda that specifies all its properties, analogous to the phase space points."
It's a well-known fact that it's only in the classical case that probabilities can be distributed over ontic state spaces in this way (conversely, that there exists a Gelfand spectrum for probabilities to be distributed over). So again, the introduction of Lambda is - obviously - the imposition of the classicality assumption.
[…the Maxwellians “murdered phi”…] The murder victim was miraculously resurrected… Aharonov and Bohm declared that the effect requires us to treat the potentials as physically real.
ReplyDeleteThe Aharonov-Bohm effect involves the vector potential A, not the scalar potential phi. It's the scalar potential that is instantaneous in the Coulomb gauge, and considered non-physical (not a “beable”, as Bell put it). See Jackson 2002 for detailed explanation of propagation of the vector potential.
You may disagree with that, but one thing sure: the 1888 view of the matter is a dead letter now.
The referenced expositions of Brill and Goodman (1967) and Jackson (2002) give the modern explanation of the instantaneous propagation of the scalar (not vector) potential in the Coulomb gauge, and why this doesn’t actually represent the instantaneous propagation of anything “real”, and doesn’t represent any action at a distance - for essentially the same reason as given in 1888.
Let's grant (which is of course not proven) that local Lorentz invariance is an exceptionalness observational symmetry. Now the job of the physicist is to look for theories according to which it comes out as an exceptionalness observational symmetry in a natural way.
There can be different approaches to this. One approach is to take the observational symmetries as the actual symmetries (“that the argument of induction may not be evaded by hypotheses”). Another approach is to postulate some underlying symmetries different from the observed symmetries, and then try to explain why the postulated underlying symmetries are unobservable. It’s conceivable that a satisfying rationalization of phenomena might be constructed using some unobservable “hidden variables”, but I think answers are most likely to be found by focusing on the observational facts.
Such a theory must, of course, solve the measurement problem in a principled, physical way: until you solve the measurement problem you are in no position to make any claims about what the observational characteristics of the theory are.
We always face the conundrum that observations must be made within a theoretical framework but theoretical frameworks are founded on observations. It isn’t necessary to have a universally agreed resolution of the measurement problem in order to make observations and infer physical principles that any viable theory must respect. Local Lorentz invariance is one of the most thoroughly and precisely verified principles in physics, and it is also essential for the conceptual foundation of relativistic quantum theory, with massless energy propagating on null space-time intervals, etc.
I would not bet my pension on conservation of energy and/or momentum, unless you are cheating a bit about the meaning of "local" here.
Local conservation of energy and momentum (with the usual caveats related to quantum uncertainty), meaning the covariant derivative of the energy-momentum tensor vanishes, is not very controversial. As I said, it’s conceivable that it (or Lorentz invariance) might be violated, but that would raise more problems than it solves.
Amos
ReplyDeleteYour separation of the scalar from the vector potential in such a strict way is itself contrary to the Relativistic fundamentals: the Relativistic approach is, of course, to unite them into a potential four-vector. Then you still have to worry about the gauge freedom: different gauges with different symmetries (and lack of symmetries) are possible, and they all have exactly the same observational consequences. Of these many gauges, the decision to give deep ontological significance to Lorenz gauge as opposed to (e.g.) Coulomb gauge is just that: a decision, a free choice. Other choices are possible.
Your reference to "essentially the same reason as given in 1888" cannot possibly be correct. The 1888 view is that what is physically real is E and B (or H and D, or whatever),and all that A and phi are are convenient ways to code up information about E and B. So "real" changes are changes in E and B. And the whole point about the A-B effect is that you get an observational change outside the solenoid (the shift in the interference bands) without any change at all in E or B outside the solenoid. So the choices are either to reject E and B as the only physically real things or else embrace discontinuous action at a distance. Everyone chose the first option.
Your repeated claim that a certain approach "raises more problems than it solves" is just rhetoric until you look at a concrete proposal. Here's one: do a Bohmian approach, add a preferred foliation, and assume quantum equilibrium. Then prove that the foliation becomes observationally inaccessible. So there is observational Lorentz invariance.
That solves the problem of observational Lorentz invariance.What worse problem does it raise? Please be specific here.
Tim, Amos,
ReplyDelete@Amos: you are right, if you are not moving it is only A and not A_μ in the AB-effect. (sorry, copy&paste error)
Since both of you mentioned local conservation maybe I might add the following general remark:
In contrast to the covariant conservation of e.g. the electromagnetic current ∇,J’=0 (“,” = mu or nu), in good old GR the ∇,T’’=0 does not imply that energy-momentum cannot flow out of a spacetime volume, i.e. T’’ is not locally conserved. This difference is due to the fact that the covariant divergence of a tensor includes the additional term Γ,’’T’’ and this is finally due to the equivalence principle (see here or in A.13 in the pdf [link in profile name])
Tim,
ReplyDeleteProbably you ask yourself why I keep on talking about path integrals (PI) and probably you think we should work first with less fancy non-relativistic QM.
One reason is that PI is the generalization of ”… the basic iconic quantum mechanical phenomena: 2-slit interference …“. In many physics texts as you for sure know it is introduced like this.
Besides this generalizing feature of the PI, the Lagrangian used in the PI has another advantage - it is a Lorentz scalar, while the Hamiltonian in the canonical approach is the time component of a four-vector, i.e. the Hamiltonian is different in different frames. (see here and also in A.13 in the pdf [link in profile name])
Here is a recent comment, which refers to the 2-slit experiment based on this.
And here a talk by George Ellis - my hero - the lonely fighter against reductionism/determinism, the destroyer of the block universe.
He also favors like you a preferred global foliation, but not in the laws, but only in the solution (given by the specific distribution of matter in our universe).
Paul Hayes, & Steven if still interested,
ReplyDeletePH, your last message directed to me had many links, and I actually read the Leifer article explaining PBR (good stuff!) and Werner’s first and second replies to “What Bell Did”. I think I understand now much better why you think that obviously Bell makes an assumption besides locality, and why you think we must have a cognitive blind spot about the lambda in Bell’s proof.
I was thinking that Werner mistakenly accused Bell of tacitly presupposing classical hidden variables in the sense of something like pre-possessed values of observable quantities or properties. That misreading was strengthened by Werner’s use of the term “classicality” as a label for what Bell was presupposing. So, I thought Werner was simply wrong or confused about the presuppositions Bell made.
I now see that this was incorrect. What Werner means by “classicality” is actually “there exists a physical state of some sort or other”. And in his “Operational QM” this is rejected: quantum states are purely epistemic, mere prescriptions for probabilistic expectations; and [Operational] QM itself makes no claim about what’s “out there”, beneath/behind the observable stuff that we manipulate and record in our labs. With this clear, I will now concede that Werner is right: Bell presupposes “Realism” or “Classicality” in this sense. I think it’s kind of crazy not to make this presupposition, if you think through carefully all the implications of what you’re doing; but that is a debate for another day.
But Werner also equates “classicality” with some mathematical property of the state space being a simplex. Here’s his (alleged) translation of what Bell is assuming with his lambda : “He could have said, equivalently, but in a language that was not his or that of his supposed readership at the time: “Let us assume that the overall state space is a simplex, about which we will not make any further assumptions, and denote its extreme points by lambda ”.”
Werner gives no explanation of what this simplex property amounts to mathematically, nor why it is equivalent to positing ontic states that determine probabilities for measurement outcomes. And note that it would have been kind of nice to do so, given that if a normal physicist in the 1960s-1980s would not have understood such language, probably the readers of Tim’s and Werner’s papers will in general not either. I clicked on a couple of links to try to learn more about this simplex property, but I’m too busy to read long and mathematically dense papers looking for justification of Werner’s amazing translation of Bell’s lambdas assumption.
Rhetorically, it’s a great trick by Werner: claim that the extremely minimal assumption that Bell makes when he introduces his lambdas is in fact a huge one, and one explicitly rejected in QM (which he equates with Operational QM). And call this assumption “classicality” so that it seems that of course it’s an assumption we should naturally reject, knowing that we live in a quantum world. Victory! – on the cheap.
CONT.
Continued:
ReplyDeleteBut not much of a victory. First, this reader suspects that Werner is actually giving us a mistranslation rather than a faithful translation of Bell’s minimal assumption. Or if it is a faithful translation, then having a simplex state space turns out to be an extremely natural requirement for any physics that attributed actual states to systems in themselves (as opposed to epistemic states to agents).
Second, even if Bell did commit this assumption, EPR’s original argument did not. Tim challenged Werner, as well as PH, to point to exactly where in EPR’s argument the simplex assumption is made. Can’t be done - there is no such assumption.
Third, it’s a pyrrhic victory for someone whose theory contains only epistemic states. If the only states our theory has are epistemic states, then in particular the state we ascribe to Bob’s particle B sure as hell does undergo an instantaneous change when we see the result of Alice’s measurement on A. The violation of EPR-locality as defined by Maudlin (and Werner accepts the definition!) could not be clearer. (Maudlin also points this out, vividly, in his reply to Werner, and Werner’s reply to the reply fails utterly to fix things.)
Here, so no-one has to look it up, is that definition:
A physical theory is EPR-local iff according to the theory procedures carried out in one region do not immediately disturb the physical state of systems in suciently distant regions in any signicant way.
Now, I guess that PH and Werner will want to say: but the state at B is not changed by Alice’s measurement of A, unless/until there is some physical interaction. Hmmm. State at B? What's that? Notice the multiple ambiguities that arise when we go epistemic. Who is the agent whose knowledge is codified in the state? Is the state something that exists at a place, or does that notion not even make sense (unless the place is inside an agent’s head)?
For sure, Bob does not instantaneously know the result of Alice’s measurement – everyone agrees on that. That doesn’t mean his particle - or even, an ideal epistemic characterization of its potential behaviors, is not changed by Alice’s measurement taking place. It surely is.
[Here I stipulate that Alice’s measurement is timelike-related to Bob’s, and earlier, but no signal has passed between Alice’s region and Bob’s. Given some things Werner says, that means that no change in the state of B has happened. But this is foolish, and if he wants to stick to it, I have a nice gambling game I’d like to offer Werner to play with me...]
Tim, Amos,
ReplyDelete[resubmitted: I already submitted this yesterday, but it did not show up and since then other comments did appear]
@Amos: you are right, if you are not moving it is only A and not A_μ in the AB-effect. (sorry, copy&paste error)
Since both of you mentioned local conservation maybe I might add the following general remark:
In contrast to the covariant conservation of e.g. the electromagnetic current ∇,J’=0 (“,” = mu or nu), in good old GR the ∇,T’’=0 does not imply that energy-momentum cannot flow out of a spacetime volume, i.e. T’’ is not locally conserved. This difference is due to the fact that the covariant divergence of a tensor includes the additional term Γ,’’T’’ and this is finally due to the equivalence principle (see here or in A.13 in the pdf [link in profile name])
Tim,
ReplyDelete[resubmitted: I already submitted this yesterday, but it did not show up and since then other comments did appear]
Probably you ask yourself why I keep on talking about path integrals (PI) and probably you think we should work first with less fancy non-relativistic QM.
One reason is that PI is the generalization of ”… the basic iconic quantum mechanical phenomena: 2-slit interference …“. In many physics texts as you for sure know it is introduced like this.
Besides this generalizing feature of the PI, the Lagrangian used in the PI has another advantage - it is a Lorentz scalar, while the Hamiltonian in the canonical approach is the time component of a four-vector, i.e. the Hamiltonian is different in different frames. (see here and also in A.13 in the pdf [link in profile name])
Here is a recent comment, which refers to the 2-slit experiment based on this.
And here a talk by George Ellis - my hero - the lonely fighter against reductionism/determinism, the destroyer of the block universe.
He also favors like you a preferred global foliation, but not in the laws, but only in the solution (given by the specific distribution of matter in our universe).
Carl Hoefer,
ReplyDeleteOne step forward, several back. On just a couple of the latter...
"Werner gives no explanation of what this simplex property amounts to mathematically, nor why it is equivalent to positing ontic states that..."
Again, simply not true:
"In a classical theory this convex set is a simplex, meaning that any state has a unique decomposition into extreme points, so can be understood as statistical mixture of dispersion free states: equivalently, any two measurements (POVMs, or decompositions of one into positive affine functionals) are the marginals of a joint measurement. We take these properties as a definition of classicality and it is this property I referred to as C in the introduction. How can such a technical criterion become a far reaching postulate? It is equivalent to the possibility of thinking of each individual system as completely described by one of the extreme points or, if one wishes, by one value of the system variables, or an appropriate list of logical predicates. These properties can be thought of as capturing the ‘real factual situation’ of the particle. We can reckon with these ‘facts of the matter’ as well-defined, even when they are unknown to us. A preparation just produces a random distribution of properties encoding our degree of ignorance, and measurements just lift this ignorance, usually only partially. So the physics of classical systems can be treated without ever referring to preparation or measurement. It is about the world and not about what we do with it."
If there's something you don't understand about that explanation, please say what it is exactly. Don't claim that no explanation has been given. It's true that Werner simply states that a classical probability state space is a (Choquet) simplex, but even if you don't know what that is he tells you what it means in terms of some other properties - properties which surely every "normal physicist" knows quantum probability state spaces lack.
"Second, even if Bell did commit this assumption, EPR’s original argument did not. Tim challenged Werner, as well as PH, to point to exactly where in EPR’s argument the simplex assumption is made. Can’t be done - there is no such assumption."
Once again:
"The first main point is the EPR criterion of ‘elements of reality’. From the outset of the EPR paper and from the flow of the argument it is clear that these elements of reality are supposed to be independent of what I choose to measure. They are clearly intended as classical in the sense of C. Quantum mechanics contains nothing of the sort. So if not containing such elements is to be incomplete, operational quantum mechanics obviously is incomplete in this sense."
And Maudlin's reply is vividly fallacious:
"The epistemic state assigned to S1 certainly is changed, and disturbed, by the procedures carried out in S2. The experiment carried out in S2 provides information about how the experiment carried out in S1 will come out. So if one identifies the physical state with the epistemic state, as Werner explicitly and clearly does, the theory obviously fails to be EPR-local according to the cited definition."
"The physical / epistemic state"?! No! There's always more than one state of the epistemic and physical [objective] but not observer independent and ontic kind involved in this and similar settings (cf. my last reply to travis). I'll concede that Werner's partly to blame for not explicitly addressing and preempting this common and predictable error in his original response. Maudlin's spooky action question begging is easily fixed:
"The [local] epistemic state assigned to [the electron in] S1 [by Alice] certainly is [not] changed, [nor] disturbed, by the procedures carried out [by Bob] in S2. The experiment carried out [by Bob] in S2 provides information [to Bob] about how the experiment carried out [by Alice] in S1 will come out."
"Paul Hayes"
ReplyDeleteIt is maybe not so good to claim that a reply is "vividly fallacious" and then immediately have to remark that the argument being responded to is so inadequately written that it has to be fixed. So let's look at the magic fix to Werner's nonsense:
'"The physical / epistemic state"?! No! There's always more than one state of the epistemic and physical [objective] but not observer independent and ontic kind involved in this and similar settings (cf. my last reply to travis). I'll concede that Werner's partly to blame for not explicitly addressing and preempting this common and predictable error in his original response. Maudlin's spooky action question begging is easily fixed:
"The [local] epistemic state assigned to [the electron in] S1 [by Alice] certainly is [not] changed, [nor] disturbed, by the procedures carried out [by Bob] in S2. The experiment carried out [by Bob] in S2 provides information [to Bob] about how the experiment carried out [by Alice] in S1 will come out."'
If there is no "observer independent physical state" then there were no physical states before the existence of observers. But 13 billion years ago there were no observers, hence according to this claim there were no physical states and hence no physics. No Big Bang, no formation of the first neutral atoms which resulted in the CMB, no star formation, no galaxy formation, to nothing. Good luck with that.
All of your square-bracket editorial insertions to Werner's nonsense is of no avail. If the observer-dependent epistemic state *just is* the physical state (as your phrase "state of the epistemic and physical" implies), then when Bob measures his electron and updates the epistemic state he uses to make predictions about Alice's electron, he thereby changes the *physical* state of Alice's distant electron, the "physical" state that he himself attributes to it. Hence, according to him, the physical state of Alice's electron changes due to his experiment. Spooky action at a distance. Period.
Alice, of course, has her own epistemic state and hence what she regards as the physical state of Bob's electron, which also spookily changes when she does an experiment. You can keep multiplying "state[s] of the epistemic and physical" all you like: *every single one of them* will display spooky action at a distance. Every one. The only way out of that is the model of Bertlmann's socks, in which there is a *non-epistemic*, *non-observer-dependent* physical state of each electron, and all that Alice's or Bob's experiment does is provide them with information (which they lacked before the experiment) about that physical state. *That* model gets rid of any physical non-locality, and on that model both Alice's and Bob's representation of the particles is incomplete before they carry out their experiments. It is exactly because their epistemic states are incomplete that they can acquire more information about the system and change their epistemic state without there being a corresponding change in the physical state of the objects. But what GHZ proves is that the Bertlmann's socks model cannot possibly be right. So there is non-locality—spooky action at a distance—willy nilly.
Reimond
ReplyDeleteWe are drifting into new territory here—interesting territory, but new—so let me just respond briefly. I do not regard the path integral as some sort of theory or interpretation. It is just a mathematical technique for solving the Schrödinger equation. And it is a technique that is not even rigorously defined without a measure over path space, which typically does not even exist. So what do you have in mind by taking the PI as the basis of an understanding of the physics of quantum theory?
Paul Hayes,
ReplyDeleteMy bad about Werner's explanation of the simplex property; you are right, he gives one in one of the papers, and I guess I had the other paper fresher in my mind.
You ask if there is anything I don't understand in the longer explanation. Of course, plenty! - the whole mathematical first half. But no matter: let's focus on the plain-language translation Werner gives in the 2nd half:
It is equivalent to the possibility of thinking of each individual system as completely described by one of the extreme points or, if one wishes, by one value of the system variables, or an appropriate list of logical predicates. These properties can be thought of as capturing the ‘real factual situation’ of the particle. We can reckon with these ‘facts of the matter’ as well-defined, even when they are unknown to us. A preparation just produces a random distribution of properties encoding our degree of ignorance, and measurements just lift this ignorance, usually only partially.
This is ambiguous between two possible readings. On the first reading, the phrase “value of the system variables” refers to the sorts of physical properties, observables, that we may decide to measure: spin-x, position, etc. Assuming that [a complete set of] these things exist prior to measurement is indeed in conflict with QM, but Bell’s introduction of λ does not make any such assumption, so let’s set this reading aside. The second reading is that “value of the system variables” and “appropriate list of logical predicates” and “the real factual situation of the particle” are referring to, simply, the idea that there is a [mind-independent, future-measurement-choice-independent] physical state “out there” that the system possesses. Good. If this is what Werner is talking about, then yes, Bell does assume such a thing when he introduces his λ s. And I guess it does deserve to be called ‘Realism’, though not ‘Classicality’. Leifer calls this assumption ‘scientific realism’, though it would be more accurate, I think, to call it ‘metaphysical realism’. (Metaphysical realism is the doctrine that there is a mind-independent world out there whose features determine whether our statements about things are true or false.)
It’s important to note that it is a rather deceptive rhetorical move to call the assumption that there is some true, objective, non-epistemic physical state of things ‘Classicality’. First, because everyone understands ‘classical’ as the contrary of ‘quantum’, so if you can tar your opponent with the brush of “assuming classicality”, you make them look rather foolish. Second, because – again in virtue of the implicit classical/quantum divergence – you make it seem that QM itself renounces to attribute non-epistemic physical states to systems. But that’s false; it is only Operational QM (and its cousins) that do this. In particular, as I mentioned in earlier posts, the quantum state Ψ itself (entangled singlet state) could be the λ of Bell’s proof; and many physicists think that Ψ stands for a real physical state, not just an epistemic catalog of probabilities.
So, please, let’s call the assumption at issue ‘Realism’ rather than ‘Classicality’.
CONT.
Continued:
ReplyDeleteNow let’s get to the fun part of your last post, where you kindly disambiguate which epistemic state you are talking about, that does not change when Bob measures his particle.
"The [local] epistemic state assigned to [the electron in] S1 [by Alice] certainly is [not] changed, [nor] disturbed, by the procedures carried out [by Bob] in S2. The experiment carried out [by Bob] in S2 provides information [to Bob] about how the experiment carried out [by Alice] in S1 will come out."
I fully agree! But this is trivial. Everyone has always agreed that Bob’s state of knowledge is not immediately changed by the measurement of Alice’s distant particle. If that is all you mean when you assert that QM is local, then: sure, but big deal. Bell said that too.
But notice that you (and Werner) have now essentially conceded everything that Bell/Maudlin have been saying. Because the upshot of Bell’s theorem could be stated like this: Whatever the true physical description of reality may be, if the inequalities are violated then nature is non-local. You and Werner are trying to duck this conclusion by saying “Hang on, I deny that there is any true physical description of reality in itself; all there are are epistemic states that codify the epistemic probabilities of various observers at various places in spacetime.”
Fine! We now understand each other perfectly, and I’m content to let the matter rest here. Just do be aware that if you intend to hang on to your form of “locality” come what may, your renunciation of any future better/deeper/non-epistemic physics has to be permanent. To me this seems like an irrational commitment to make.
Typo here, it is Γ’,,T’’.
ReplyDeleteTim,
My remark about the PI was just the hint that with the introduction of an observer independent triggered measurement beyond a certain threshold all the extremely precise calculations done in QFT (standard model) would also be valid in the U/R-process. All the events in the LHC are of course just measurements/reductions (R).
[And further the cutoff needed in the renormalization in QFT could be nothing else than the threshold for the triggered measurement (some fraction of the plank mass). (Even further, also in curved spacetime e.g. when a U-patch touches a horizon, a measurement is triggered, the virtual particles are set on their mass shell (Cutkosky cutting). This would generate Hawking radiation and a tiny, tiny backreaction). Spacetime stays non-quantized.]
Thus, this very solving of the measurement problem would also bring QM and GR together.
But yes, with every triggered measurement QM randomness is added, thus the U/R-process is not a deterministic theory. But would not this also solve the BH info loss problem?
The evolution would simply not be an exclusively unitary one anymore, only between measurements it is time reversible.
This adding of QM randomness in every step also takes the pressure off the past hypothesis.
Here I describe how complexity can be generated and this talk by George Ellis and Stuart Kauffman about complexity is really worth watching.
Isn't "observer-dependent" properties just a specific form of "measurement-dependent" properties, which is in turn a specific form of "interaction-dependent" properties? That is, when the interaction is a measurement by an observer, the result can be called "observer-dependent", but without implying that observers are the only form of interaction. And don't physicists believe that quantum properties are interaction-dependent? For example, if you measure the x-spin, then the z-spin, the previous x-spin data is no longer guaranteed. I know some people take the term observer-dependence to mean that properties don't ever exist without conscious observers but I thought only woo-meisters believed that. (Personally I wish people would only say interaction-dependent, but I guess the fact that so far only humans are doing the quantum experiments that we know of, made observer-dependent seem natural.)
ReplyDeleteThe reading I am taking from this thread is not that Bell didn't make a good contribution, or that QM behavior isn't strange and non-intuitive, but that once you take on the possibility of interaction-dependence, and see how what we consider as classical behavior can emerge macroscopically from this, it begins to seem less strange; and perhaps some of the perceived paradoxes come from trying to make quantum behavior emerge from classical behavior, rather than the other way around.
Carl Hoefer,
ReplyDelete"It’s important to note that it is a rather deceptive rhetorical move to call the assumption that there is some true, objective, non-epistemic physical state of things ‘Classicality’."
It can only appear so to someone (still) unaware of why 'classicality' is often used in this sense. No-one's forgetting that CM, including probabilistic CM, is understood to be both local and realistic, and that the issue with QM is which one we should give up. The point is that this restricted use of 'classicality' is the natural one in investigations focusing on the probabilistic aspects: Nonlocality is certainly weird. Nonreality is equally weird... or is it? (Short answer: no.)
"Second, because – again in virtue of the implicit classical/quantum divergence – you make it seem that QM itself renounces to attribute non-epistemic physical states to systems. But that’s false; it is only Operational QM (and its cousins) that do this. In particular, as I mentioned in earlier posts, the quantum state Ψ itself (entangled singlet state) could be the λ of Bell’s proof; and many physicists think that Ψ stands for a real physical state, not just an epistemic catalog of probabilities."
Your misperceptions are not my doing. OQM certainly does not do that. It's a "systematic presentation of [standard] quantum mechanics which makes exhaustive use of the full probabilistic structure of this theory", not an interpretation. As far as the issue at hand - whether QM is best understood as either nonlocal or not (naively) realistic - is concerned, OQM 'merely' provides a deeper understanding. From its perspective the nonlocality option does appear (even) less attractive. The observation that many physicists choose ontic Ψ and the fact (which I've also mentioned in earlier posts) that \lambda can be just about anything you like are neither here nor there.
"So, please, let’s call the assumption at issue ‘Realism’ rather than ‘Classicality’."
No - let's stick to the usage appropriate to the context.
"I fully agree! But this is trivial."
Yet you also agree with its negation ("The epistemic state assigned to S1 certainly is changed, and disturbed, by the procedures carried out in S2"); Maudlin's "(Bell shows that) nature is nonlocal" nonsense.
"But notice that you (and Werner) have now essentially conceded everything that Bell/Maudlin have been saying. Because the upshot of Bell’s theorem could be stated like this: Whatever the true physical description of reality may be, if the inequalities are violated then nature is non-local. You and Werner are trying to duck this conclusion by saying “Hang on, I deny that there is any true physical description of reality in itself; all there are are epistemic states that codify the epistemic probabilities of various observers at various places in spacetime.”
Werner and I have conceded nothing. The upshot of Bell's theorem absolutely cannot be stated like that. Werner and I are refuting that false conclusion not trying to duck it. Even from the perspective of a (nonexhaustive) understanding of the probabilistic structure of QM - before one knows that, as a reference I gave earlier says, "the existence and basic properties of entangled states are actually quite generic features of all nonclassical probabilistic theories satisfying a basic “non-signaling” constraint." - it becomes clear that QM's nonlocal correlations can be and probably should be understood as purely probabilistic in origin rather than as indicative of mysterious nonlocal physical influences.
Well I've tried explaining as best I can, repeating points again and again and providing numerous references yet you still prefer the crank nonsense. So be it.
Carl Hoefer,
ReplyDeleteOne more thing (I'm afraid I just couldn't let the extreme pot-kettle-blackery in there go unchallenged):
"Just do be aware that if you intend to hang on to your form of “locality” come what may, your renunciation of any future better/deeper/non-epistemic physics has to be permanent. To me this seems like an irrational commitment to make."
One would think you'd read none of my comments and understood nothing of what this ridiculous dispute has been about. In case you hadn't noticed, I'm the one who's been warning against making irrational commitments here! I'm the one who's emphasised, time and again and in the face of a tsunami of (wilful) ignorance and irrationality, that the question of whether to ditch locality or (naive) realism is still an open one. I'm the one who's pointed out that that's understood even by (most of) those who'd prefer to keep realism and ditch locality! The false claim that in fact there is no choice; that locality is already a goner (killed by Bell), and the irrational commitment to nonlocality that follows from it, are not mine. The strongest claim I've made - and backed up with arguments coming from, among other things, consideration of what is (now) known about (quantum / general) probability - is that actually it's the ditching locality option that's the one nearest death these days.
"Paul Hayes"
ReplyDeleteRhetoric is rhetoric and facts are facts. Everyone agrees that computers that are not connected to through any wires or wireless modes of communication are effectively governed by local physics. And a computer can be programmed to simulate any sort of mathematical thing you want to call a "probability" you like. You want "negative probabilities"? Program the computer to calculate with negative numbers (a snap) however you want and base its behavior on the outcome however you like. You want to use complex numbers? Easy as pie.
So here is a really, really simple challenge. If you believe that any local physics can recover the GHZ phenomena using local physics, program three computes to simulate that local physics. Simulate however you like what the local physical state of the GHZ triple is, and share that among your three computers. Each computer is then to simulate the local physics governing one of the three particles. We will then separate the computers into three rooms, ensuring that all wireless communication is turned off. I then get to choose—by whatever means I like—to input into each machine either an "X" or a "Y", thereby simulating the choice of either an X or a Y spin experiment for that particle. I will bet you any sum of money you like at 100-1 odds that you cannot program the computers to replicate the GHZ statistics (and only with regard to the probability 1 features of those statistics) over 100 runs of the experiment.
If there is nothing non-local required to produce those statistics, then this is easy money for you. Put up or shut up.
Reimond
ReplyDeleteOf course, if you accept an objective reduction model, then you have no BH information loss problem to begin with, because one premise of the supposed paradox is that the dynamics is always unitary, or more generally retrodictable. So you don't so much solve the paradox but prevent it ever forming in the first place.
JimV
ReplyDeleteI was recently at a meeting of both physicists and philosophers who work on foundations, and I raised a very simple question: when people label some physics "classical" and other physics "quantum" what do they mean? What characteristics mark this supposed distinction? And no one in the meeting could offer a definition that could withstand 30 seconds scrutiny.
As a simple test case: Bohmian mechanics is a completely precise, mathematically well-defined physical theory. Is it a classical theory or a quantum theory?
Reflect for a while and see what definitions you can come up with. If you can't come up with any, then the question of whether "quantum" behavior can emerge from a "classical" underlying base, or vice-versa, is not even well posed.
Paul Hayes,
ReplyDeleteMy last post seems to have angered you for some reason, which is puzzling. Aside from the last sentence, mostly what I was doing was trying to express clearly what your position is and how I now see that it does, in a sense, evade the upshot of Bell’s theorem.
You seem to dislike my argument that it is more fair to call the implicit premise of Bell’s theorem that you and Werner reject “Realism” rather than “Classicality” – OK, have it your way if you like. But please tell us clearly, in your own words, what this assumption is. In your posts from July 8th you now call it “(naive) realism”. In my post of 7th July, I summarized it as clearly as I could after reading Werner: there is a [mind-independent, future-measurement-choice-independent] physical state “out there” that the system possesses. You seem to reject this, because you scornfully say ” Your misperceptions are not my doing. OQM certainly does not do that.” Please do tell me, in as plain language as possible, what is this assumption that Bell made and OQM rejects, which you now call “(naive) realism”. Try not to use the word ‘simplex’ or talk about extreme points of states in a convex space. My summary seems to fit the Werner quote that you gave in full perfectly well. But if you can improve it, please do.
About that last sentence of my July 8th post that seems to have pissed you off: glad to hear that you are not committed to denying non-locality come what may. I am not committed to insisting on it, nor am I committed to (naive) realism come what may, either. But if I am to contemplate embracing the denial of (naive) realism, first I have to understand what the alternative is. Hence my request that you clarify what it means, so I can see what I am being asked to give up clearly.
Carl Hoefer,
ReplyDeletemaybe it would help you to consider EPR or Bell in "many worlds interpretation". There is no collapse and every interaction is local, but, Bell's inequality is violated. I found this ppt that has some equations hard to make here http://people.umass.edu/blaylock/personal/MWI-BrynMawr-21Sep09.ppt , pages 7,9,14.
There is an example, so you can give up "realism" but keep locality and still violate Bell inequality. Therefore in Bell's argument must be an assumption of "realism" or classicality or counterfactual definiteness or whatever term you like.
Carl Hoefer,
ReplyDeleteI find it puzzling that you find that puzzling. Your second to last post 'framed me for a crime' - irrational commitment - perpetrated by others. Including yourself.* (You now say you're not committed to insisting on nonlocality. Well that's great, but sheesh!)
"You seem to reject this, because you scornfully say ” Your misperceptions are not my doing. OQM certainly does not do that.”"
No, that remark was a response to your "it is only Operational QM (and its cousins) that do this [renounce to attribute non-epistemic physical states to systems]" misperception, not a rejection of that definition of (naive) realism.
"Please do tell me, in as plain language as possible, what is this assumption that Bell made and OQM rejects, which you now call “(naive) realism”.
First let's deal with that misconception about the role of OQM. OQM is, roughly speaking, merely a particular mathematical formulation of standard QM. Werner wrote "(Operational) quantum theory" rather than "Operational quantum theory" for a reason. He invokes it in the passage Maudlin cites just to emphasise that QM is prima facie explicitly local (cf. my last reply to travis again). Not as "a conceit that Operational quantum physics is some newfangled theory"; an attempt to hide that it's "just plain old vanilla Copenhagen quantum physics".
Now here's Maudlin on Bell and EPR:
"Recall the dilemma posed by the EPR argument: if a theory predicts perfect correlations for the outcomes of distant experiments, then either the theory must treat these outcomes as deterministically produced from the prior states of the individual systems or the theory must violate EPR-locality. [...]"
(Naive) realism in plain language is the (usually explicit) assumption of the existence of "elements of reality". A classical substrate for a classical theory - doomed to violate EPR-locality. In the above Maudlin just leaves the assumption tacit, inviting "a theory" to be taken to mean "any theory"; turning a dilemma with a nonclassical EPR-locality preserving resolution into a false dilemma.
* "The combination of Bell's theorem plus experimental verification of violations of his inequality with spacelike separated measurements demonstrates that nature is nonlocal. Period. Bell understood this, as have thousands of physicists since 1964. If my understanding is deficient, so is that of thousands of your colleagues." (Carl3, 2:31 PM, June 05, 2018)
"Paul Hayes"
ReplyDeleteThank you for making the position finally clear. You have explicitly and publicly articulated a position that I have often discussed, but that is so absurd that to characterize it accurately sounds like satire, or an uncharitable reading. In your own words:
'(Naive) realism in plain language is the (usually explicit) assumption of the existence of "elements of reality"'.
Or as I like to present the position that you are Werner are trying to defend:
"Nothing is real, but thank God it's local".
It looks like all discussion of quantum black holes has evaporated for now. So until it recurs, thanks to all those who shared their insights.
ReplyDeleteMitchell,
ReplyDeleteSince you are lamenting that “all discussion of quantum black holes has evaporated” I simply cannot resist to say:
Well, in an indeterministic theory with a not exclusively unitary evolution, not only the black hole, but also the info loss paradox evaporates, or as Tim put it, if you accept an objective reduction, the paradox never gets off the ground.
Anonymous Physphil,
ReplyDeleteThe Many Worlds Interpretation does not provide a counterexample to Bell's theorem. There can be no counterexamples, because a theorem is a theorem.
Here is the theorem: no Einstein-local theory can predict regular violations of Bell's inequality for the outcomes of experiments done at spacelike separation. Therefore, if there are such regular violations seen in experiments done at spacelike separation. then the true physics of the world is not Einstein local, i.e. the world itself is not local.
How does MWI come in? Well, suppose Alice and Bob are in their labs. They each perform a spin measurement and the outcome is recorded. Now: does this constitute a violation of Bell's inequality at spacelike separation?
You can't tell yet. In Many Worlds, both outcomes occur on another side. What would it even mean for the two outcomes to the "correlated? How does one match a particular outcome on one side with a particular outcome on the other. Without this matching. talk of correlations is meaningless. Literally meaningless.
There are two possibilities here:
1) the outcomes are not matched until one side sends their result to the other and it is received on the other side. In this case, there need not be any non-locality, but also there is no violation of Bell's inequality for events at spacelike separation.
The second possibility is that the outcomes are already matched, even before the information is sent. The matching. for example, can be done by the wave function. But the wavelunction is not a local beable, so then you cannot maintain that it is a local theory.
In neither case is Bell's theorem violated. And in neither case does one claim that nothing is "real". Denying all reality is denying that physics even has a subject matter.
Carl,
ReplyDelete(I’m in the middle of a vacation, hence the delay in responding. I see many posts have appeared in the meantime but I’ll just post this reply to your reply to me.)
Here is a local story:
Suppose I have entangled two qubits, I keep one of them, Alice takes the other with her and travels far away from me for a whole year. Suppose we both manage to keep our qubits perfectly isolated during that year. Then, finally, Alice is going to perform a measurement on her qubit.
For me, my qubit is entangled with a simple degree of freedom associated with a 2-dim Hilbert space (Alice’s qubit). For one year, it stays like that. But then that degree of freedom is going to be mixed up with lots of degrees of freedom, all initially localized around Alice, as soon as she starts the measurement on her qubit. According to me, my qubit is still entangled in the same way as before, but the 2-dim Hilbert space has become a complicated 2-dim subspace of the much larger Hilbert space associated with Alice’s local degrees of freedom.
I still assign a superposition of two terms involving my qubit, one of which has a quantum state of Alice in it thinking the result of her measurement was ‘0’, the other a state corresponding to her result being ‘1’ . There is no interaction between me and Alice’s local degrees of freedom possible until some signal has traveled from Alice to me, and so there is no measurement I could possibly perform on the degrees of freedom with which my qubit is entangled until the arrival of a signal from Alice with which I can interact: only that (apart from me measuring my qubit directly) will collapse (for me) the state of my qubit.
In this story there are only local interactions and local effects.
The cost of avoiding non-locality is that Nature becomes observer dependent (this story, I think, can still accommodate QBists, Rovelli, and many-worlders).
In your version of this story Alice’s description of my qubit is promoted to being objective, as if there is a God-like view of the world that instantly changes as soon as she [I mean Alice, not God] does a measurement. Or, to put the emphasis a bit differently, *my* quantum description of Alice being entangled with my qubit is demoted in your story to a classical description of Alice definitely having found one measurement result and really collapsing the state of my qubit.
[Negative quasi-probabilities only show up when trying to fit the quantum formalism into the mold of a classical probabilistic description. You don’t really need them in the above story.]
I confess, I am addicted to physical theories that have 'elements of reality'.
ReplyDeleteTM asked "... when people label some physics "classical" and other physics "quantum" what do they mean? What characteristics mark this supposed distinction?"
ReplyDeleteWhat I consider the main distinction (for what that is worth, not that I'm the arbitrator) is the way probabilities of events are calculated. Where I got my understanding of this was from the following link:
https://www.scottaaronson.com/democritus/lec9.html
I believe it is commonly recognized that the quantum (amplitudes) method, when combined for a large number of particles in macroscopic events, gives rise to the classical statistics with which macroscopic experiment results are reported. Anyway, that would be the main example of deriving classical physics from quantum physics which I had in mind.
Unfortunately, language seems to be so ambiguous that often no two people can agree on what the words they are using to communicate mean, unless they are willing to use some charity in interpreting the other person. "Observer-dependent properties" might be an example. I expect that is why it is very difficult to get definitions that everyone agrees on.
Carl Hoefer,
ReplyDelete"I confess, I am addicted to physical theories that have 'elements of reality'. "
People were addicted to god, earth-centered system, determinism. Addiction is not healthy. Physics tries to teach us. Our job is to learn.
Tim,
ReplyDelete"The second possibility is that the outcomes are already matched, even before the information is sent. The matching. for example, can be done by the wave function. But the wavelunction is not a local beable, so then you cannot maintain that it is a local theory."
Those words are closer to actual QM evolution than your "first possibility". But, I maintain it is local theory. Operators commute at spacelike separation and all interactions are local (that is, at points). When Alice measures at spacelike separation there is no effect on wavefunction of Bob's particle or device. That is local.
Physphil
ReplyDelete"Those words are closer to actual QM evolution than your "first possibility". But, I maintain it is local theory. Operators commute at spacelike separation and all interactions are local (that is, at points). When Alice measures at spacelike separation there is no effect on wavefunction of Bob's particle or device. That is local."
1) There is no "wavefunction of Bob's particle or device". There is only a universal wavefunction, which is entangled between Alice and Bob. Since it is not a product state, the universal wavefunction cannot be analyzed into "the wavefunction of Bob's particle or device" and a distinct "wavefunction of Alice's particle or device". That's the point of entanglement.
2) If you want to attribute some sort of state solely to Bob's particle or device and some sort of state solely to Alice's particle or device, then your only option is to use the reduced density matrix for each. That will yield the correct statistical predictions for all "measurements" made solely on Bob's (respectively Alice's) particle. But that pair of reduced density matrices loses information from the entangled state, That is, given both of those reduced density matrices, you can't recover the pure state from which they were derived. And the missing information is precisely about correlations between Alice's and Bob's outcomes, i.e. precisely about the sort of data that Bell's theorem is all about.
3) This now threatens to devolve into a pointless debate over the word "local". By Bell's and Einstein's understanding of that word, QM is not a local theory: that's why Einstein always complained that standard QM employed "Spooky action at a distance". If you insist on using the word "local" in some other way, that's your business, but then your assertions cannot possibly show that anything Bell or Einstein said about the matter was mistaken: what you are doing is simply misinterpreting their claims by substituting your meaning for theirs.
4) As far as which meaning of "local" is correct, I again issue my challenge. Everyone agrees that a laptop computer with all wires unplugged and all wireless communications turned off is effectively governed by local physical laws. So program three laptops however you like, supply them all with whatever representation of the initial state of a GHZ triplet that you like. Place the three laptops in three separate rooms and allow me to input into each one—by whatever scheme I like—either an 'X' or a 'Y', representing making a spin "measurement" on that particle in either the X or Y direction. And your job is to make sure that your three computers display the same sorts of outcomes as a GHZ pair, over a run of, say, 1,000 trials. If those outcomes can be produced by any local physics, you should be able to simulate that local physics with your computers. I will again bet any amount of money at 100-1 odds that you cannot pass this test. And if you can't, then all the rest of the debate about the proper meaning of "local" is just gum-flapping. Recovering the actual predicted and observed behavior in this way is the acid test. And neither you nor anyone else can pass that test.
Tim,
ReplyDeleteMaybe I might provide another paradox for those who are missing to agonize about the black hole info loss paradox (which evaporates, if you drop one assumption: determinism).
The paradox is a clash between de Broglie and Galileo.
(We regress to non-relativistic physics just to state this paradox more easily, but non-relativistic versus relativistic is not important here).
Distances in Galilean transformation are invariant. So, when we look at a plane wave from a with velocity u moving frame of reference x’=ut+x; t’=t the wave number k=2π/λ does not change. Thus p’=ℏk’=ℏk=p stays the same. But on the other hand, we know very well, that the momentum must change like p’=p+mu. Thus, de Broglie clashes with Galileo.
And sure, here you all know that this paradox is only an apparent one. The answer again is connected to the measurement. “The solution lies in the observation that the wave-function itself is not invariant under a Galilean transformation.” (Quantum Non-Locality and Relativity)
(resolution in appendix A.12 in the pdf under the link in profile name)
By the way, the properties under Galilean transformation lead in Bohmian mechanics to the guiding equation - see here eq. (3.8). But here Tim is the expert.
ReplyDeleteTim,
ReplyDeleteI wrote " When Alice measures at spacelike separation there is no effect on wavefunction of Bob's particle or device. That is local."
You wrote "There is no "wavefunction of Bob's particle or device"."
Entanglement is defined only when Hilbert space is a product, H = Alice x Bob x .... My statement means Alice's measurement acts on Bob factor as identity. There is no confusion for anyone who understands QM.
"If you want to attribute some sort of state solely to Bob's particle or device"
Hilbert space is product. State is not. Alice measurement does not affect Bob. Math is crystal clear. If you are confused you have not understood this math.
"This now threatens to devolve into a pointless debate over the word "local"."
There is clear meaning of "local|". All interactions are point interactions. All operators commute outside lightcone. Measurements or operations of Alice act on Bob as identity (at least until future when lightcone intersects Bob). Alice measurements have no effect on Bob, and Bob none on Alice. If with all that you still claim non-local, we have no disagreement except word.
"laptop etc"
You do not understand. Programmed laptops are classical. Bell+GHZ proves only that world cannot be both local and classical. It cannot prove world is local.
Steven,
ReplyDeleteYou say:
" *my* quantum description of Alice being entangled with my qubit is demoted in your story to a classical description of Alice definitely having found one measurement result and really collapsing the state of my qubit"
I did have a short discussion with Lubos Motl about the non-realist view of QM. Unfortunately it is very difficult to disagree with the guy and still have him clearly describe his position, but my understanding was that, indeed, non-realism implies some sort of many-worlds. Everything remains in superposition. So, a direct implication would be this (I assume we have entangled photons that are correlated, as those produced by PDC sources):
Say Alice performs her measurement and gets 0. She is certain about it, she may publish a paper with that result, everybody agrees with her, etc. She also knows that Bob's result must also be 0. When Bob makes his measurement he might still get 0 or 1 with 50% probability. Say Bob gets 1. He also publishes his result, etc. According to him, Alice must have got a result of 1 as well. After some time in the future they meet and compare their results. And, they indeed find that they are in agreement. Alice finds out that Bob measured 0, just as she expected, while Bob hears from her that she obtained 1, just as he believed.
Is this correct?
Thanks!
Physphill,
ReplyDelete"When Alice measures at spacelike separation there is no effect on wavefunction of Bob's particle or device. [...]"
That depends. If Alice and Bob are each given half of a system prepared, for example, in the state ψ_P =(↑⊗↓ - ↓⊗↑)/√2 then that's the state they'll both assign. The trouble is that for a Bohmian it is the ontic state and Alice's and Bob's measurements will change it. The spooky action-proof epistemic state assignments are ψ_A = (↑⊗↓ - ↓⊗↑)/√2 and ψ_B = (↑⊗↓ - ↓⊗↑)/√2.
However, (some) Bohmians are like "Sleeping Beauty problem halfers": apparently simply ignorant of, or unable to understand, or fiercely ideologically opposed to the epistemic perspective ("Bohmians like Maudlin tend to confuse changes in distributions with a change in the world, because the notions of states and wave functions are reified, and considered as something real out there").
So pedantry - labelling every state assignment etc. - might help but TBH I doubt it. I was sloppy in my plain language definition of "(naive) realism)" (forgetting to e.g. put "even for properties described by incompatible observables" on the end of it) but I doubt doing so would've stopped the idiotic "the opposite of '(naive) realism' is 'nothing is real'" remarks.
Anonymous Physphil:
ReplyDeleteYou wrote " When Alice measures at spacelike separation there is no effect on wavefunction of Bob's particle or device. That is local."
I wrote "There is no "wavefunction of Bob's particle or device"."
You wrote: "Entanglement is defined only when Hilbert space is a product, H = Alice x Bob x .... My statement means Alice's measurement acts on Bob factor as identity. There is no confusion for anyone who understands QM."
I repeat: There is no "wavefunction of Bob's particle or device". Nor can the entangled wavefunction be divided into "Bob's factor" and "Alice's factor". In a Many Worlds setting, which you seem to be presenting, Alice's measurement produces a bifurcation in "Bob's wavefunction"—which is, of course the universal wavefunction. It does so non-locally and in a way no local physics can emulate.
Your comment about the computers is a transparent evasion. The issue is not how the classical computers work, but what they are capable of mathematically representing. By Church's thesis, they can represent the behavior of any computable physics, classical or non-classical.
Tim,
ReplyDeleteyou wrote "I repeat: There is no "wavefunction of Bob's particle or device". Nor can the entangled wavefunction be divided into "Bob's factor" and "Alice's factor". In a Many Worlds setting, which you seem to be presenting, "
Example. ψ_P =(↑⊗↓ - ↓⊗↑)/√2
First (left) factor in each term is Alice's particle, second (right) factor is Bob's. Understand now? It can be divided. If it could not, entanglement could not even be defined.
"Alice's measurement produces a bifurcation in "Bob's wavefunction"—which is, of course the universal wavefunction. It does so non-locally and in a way no local physics can emulate."
No. As I already told you, Alice's measurement does nothing to Bob's part of wavefunction, it acts as identity. Example:
(↑⊗↓ - ↓⊗↑)⊗(0A)⊗(0B) --> (↑⊗↓⊗(+A) - ↓⊗↑⊗(-A))⊗(0B)
0A means Alice's measuring device reads "0". +A means it measured up, -A down. Same for 0B etc. The --> is from no one measured to Alice measured.
Alice measurement has no effect on Bob part of state. In each term, Bob part remains exactl;y unchanged, ↓⊗(0B) and ↑⊗(0B) respectively. What measurement does is "bifurcate" (not good word) state of Alice's device only. Better to say, it entangles it with Alice's particle because it interacts with it. Everything is local.
Anonymous Physphil,
ReplyDeleteYou should enjoy having a content-free discussion with "Paul Hayes". You can praise each other and insult everyone else without fear of intervention from anyone who actually understands what is going on.
The wavefunction cannot be interpreted epistemically. That is the content of the PBR theorem, just as the impossibility of reliably and predictably violating Bell's inequality (or reproducing the GHZ correlations) for experiments done at space-like separation by any local physics is the content of Bell's theorem and the analog for GHZ. These are theorems, not mere opinion or empty rhetoric or guesses or biases. They are proofs. And you have never yet offered a single coherent objection to these proofs.
The both of you want to pretend that Bell and PBR contain, hidden away in some obscure corner, some other assumption beside the accuracy of the the predictions of quantum mechanics and, in the case of Bell, the locality of the physics. The only other assumption that both rely on is properly called "statistical independence", and the denial of that assumption is misleadingly called "superdeterminism" and more accurately called "hyperfine tuning" or "conspiracy theory". So if you want to hop on the hyperfine tuning train, along with 't Hooft and Sabine, be my guest. That particular train is going nowhere.
What about the assumption of "classicality" or "realism" or even "(naive) realism". Neither of you nor Werner has ever given a definition of what this supposed assumption is that holds water. I have asked and asked and asked, for example, for someone to point out where the EPR argument makes the assumption that anything is a simplex without a single response ever being offered by Werner or either of you (assuming that neither of you *is* Werner, which is something I guess we will never know). Until you can answer that simple question, leave the talk of simplexes behind.
What about "realism" or "(naive) realism"? What you do not seem to be aware of is that as the terms are used in philosophy of science they do not even characterize theories: they characterize *attitudes* towards theories. Is Newtonian mechanics a "realist" or "(naive) realist" theory? That question is literally nonsensical given the standard meaning of "realist". Person A can adopt a realist stance toward Newtonian mechanics, and person B can adopt an anti-realist stance toward it, and person C can be an especially naive realist about it, but the theory itself is neither one or the other. Similarly I can be skeptical about General Relativity, but that in no way make General Relativity a "skeptical theory".
So neither of you is using "realist" with its standard usage. What is the usage you are using? As far as I can tell, the most charitable guess is that a "realist" theory, as you mean it, postulates the existence of mind-independent physical states of the world. That is the best I can do to make ever a shred of sense out of your claims. And if we take that to be your meaning, then when you deny that any "realist" theory is acceptable, you are claiming that *there are no mind-independent states or features or properties in the universe*. So I guess you are some sort of weird idealists. but one thing sure: you just are not doing physics. Physics presupposes there is a physical world and that we have some reliable access to how it is. And what we know is that the physical universe existed and evolved, from the formation of the CMB through the formation of the first stars and galactic structures, without the benefit of the existence of any minds at all. If you want to deny that, man up (or woman up) and deny it. Or else provide a clear definition of "realism" as you are mis-using that term. Otherwise, just shut up.
Paul Hayes,
ReplyDeleteLet's see how your attempt at pedantry works out. I hereby fix your definition of (naive) realism as per your last message, combining it with the earlier statement:
“(Naive) realism in plain language is the (usually explicit) assumption of the existence of "elements of reality", even for properties described by incompatible observables.”
This new statement of "(naive) realism" does indeed make it look like it is not the same as what we understood, namely "there is a physical state of some sort 'out there'." Good. This protects you from having to own the position that Tim characterized as "Nothing is real, but thank God it's local."
Unfortunately, now it is clear that your charge against Bell fails. The λs of Bell's theorem do not amount to some hidden assumption of pre-existing values for incompatible observables. As I've said several times, λ could represent any sort of 'element of reality', including nothing or simply the initial entangled quantum state Ψ . (And I suppose you're not going to argue that the entangled quantum state is inadmissible as an 'element of reality'; if you do, we're back to "Nothing is real, ...")
So now we see clearly your and Werner's dilemma. Either your claim that Bell's conclusion is false is wrong, based on a misinterpretation of his λs, or you are able to deny Bell's conclusion, but only at the price of denying that there is any physical state out there in any sense. Which is it?
Bee, maybe this was lost.
ReplyDeleteTim,
you wrote "I repeat: There is no "wavefunction of Bob's particle or device". Nor can the entangled wavefunction be divided into "Bob's factor" and "Alice's factor". In a Many Worlds setting, which you seem to be presenting, "
Example. ψ_P =(↑⊗↓ - ↓⊗↑)/√2
First (left) factor in each term is Alice's particle, second (right) factor is Bob's. Understand now? It can be divided. If it could not, entanglement could not even be defined.
"Alice's measurement produces a bifurcation in "Bob's wavefunction"—which is, of course the universal wavefunction. It does so non-locally and in a way no local physics can emulate."
No. As I already told you, Alice's measurement does nothing to Bob's part of wavefunction, it acts as identity. Example:
(↑⊗↓ - ↓⊗↑)⊗(0A)⊗(0B) --> (↑⊗↓⊗(+A) - ↓⊗↑⊗(-A))⊗(0B)
0A means Alice's measuring device reads "0". +A means it measured up, -A down. Same for 0B etc. The --> is from no one measured to Alice measured.
Alice measurement has no effect on Bob part of state. In each term, Bob part remains exactl;y unchanged, ↓⊗(0B) and ↑⊗(0B) respectively. What measurement does is "bifurcate" (not good word) state of Alice's device only. Better to say, it entangles it with Alice's particle because it interacts with it. Everything is local.
Carl Hayes,
ReplyDelete"The λs of Bell's theorem do not amount to some hidden assumption of pre-existing values for incompatible observables. As I've said several times, λ could represent any sort of 'element of reality', including nothing or simply the initial entangled quantum state Ψ ."
That is not correct. Theorem of Bell combines probabilities classically. Probabilities for wavefunctions do not combine that way.
Physphill,
ReplyDeleteYour „It can be divided. If it could not, entanglement could not even be defined.“ is simply wrong.
You can “divide” a product state, but "The singlet state cannot be written as a product state." (Susskind, see here), thus you cannot separate, “divide” Alice and Bob.
You are probably used to trace out density matrices, which you also call state and use tensor networks to recover what you call entanglement entropy. I absolutely understand that this must be confusing when talking about EPR. But just go back to the basics.
Do not confuse a the state |Ψ> with the density matrix ρ=|Ψ>< Ψ| as Tim explained here.
Further you probably think that spacetime is quantized. If so, then in MWI when in the measurement |Ψ> splits into different branches, worlds, … whatsoever, then also spacetime splits. And in this situation, it should be clear that talking about locality or non-locality is meaningless.
In the same sense meaningless as Tim explained with respect to the correlations of the measurement outcome in MWI: ”How does one match a particular outcome on one side with a particular outcome on the other. Without this matching. talk of correlations is meaningless. Literally meaningless.”
If we forget about MWI, i.e. Alice and Bob still live in the same world after a measurement then it becomes meaningful again to talk about locality or non-locality and correlations.
And the experimentally verified fact is that the measurement results of Alice and Bob are spacelike correlated.
Why is it so hard to accept the experimentally verified “non-locality” (*) in EPR? The very essence of QM is to connect spacelike separated events in the state |Ψ> (not the traced out density matrix).
And yes, this is a conflict between QM and SR.
If you now say, but this conflict is already solved in rel. QFT then you are almost right. Something is still missing. So far, the measurement problem has not been solved.
-----------------
(*) “non-locality” in quotes as always to code spooky-action-at-a-distance, but no faster than light signaling.
Physphil
ReplyDeleteI really don't know what you are trying to accomplish, but what you actually are accomplishing is to demonstrate that you are both unable to grasp the most basic matters and unable to even vaguely gauge what other people do understand.
The entangled state you write is (of course) a linear combination of product states for Alice and Bob. And each of those product states (of course) ascribes a pure state of Alice and another pure state to Bob, so there is no problem talking about the "state of Alice's lab" and "the state of Bob's lab" when the universal state happens to be a product state. But the whole point of entanglement is that an entangled state cannot, in any way, be written as a product state in such a way, and therefore there is no pure state that counts as "the state of Alice's lab" or "the state of Bob's lab" when the universal state is entangled. The very idea that you would try to identify the state of Alice when the universal state entangled by writing "First (left) factor in each term is Alice's particle, second (right) factor is Bob's. Understand now? It can be divided. If it could not, entanglement could not even be defined." seems to be proof positive of a level on incomprehension that cannot be overstated. Try to write down—without any reference to Bob—Alice's state when the universal state is entangled in this way. Then write down—without any reference to Alice—Bob's state. Then do the same after changing the minus sign to a plus sign in the entangled state. Report the results.
Carl Hoefer,
ReplyDelete"Unfortunately, now it is clear that your charge against Bell fails. [...] So now we see clearly your and Werner's dilemma. Either your claim that Bell's conclusion is false is wrong, based on a misinterpretation of his λs, or you are able to deny Bell's conclusion, but only at the price of denying that there is any physical state out there in any sense. Which is it?"
Again, no it doesn't fail, and that is a false dilemma (one horn of which is utterly idiotic).
"The λs of Bell's theorem do not amount to some hidden assumption of pre-existing values for incompatible observables. As I've said several times, λ could represent any sort of 'element of reality', including nothing or simply the initial entangled quantum state Ψ ."
Yes, you do keep repeating that. You keep repeating it as though it were a fact of great significance that we non-Maudlinites had somehow missed or not understood. And we keep repeating that in fact we know it full well and, furthermore, that we understand its significance rather better than you do (because we have the advantage of that general conceptual and mathematical context which subsumes both the classical and the quantum). But instead of at least trying to understand this stuff - and it ain't exactly rocket science, as they say - you just dismiss it all with your "'quantum probability', whatever that means"s and your "I don't know what a simplex is but it can't possibly matter what it is"s etc. (accompanied by whining about "dense mathematics" in references that you can't be bothered to read). And then you have the gall to demand, without irony and in the tone of one who believes himself to be better-informed, that we provide answers to your ill-conceived and inapt questions.
This really does seem to be a case of the "Dunning-Kruger effect" which someone mentioned earlier. Not only do we (Werner and I and numerous others - philosophers included!) understand what Bell did - his demonstration that the attempt to explain classical CHSH-type inequality violating correlations in classical (probabilistic) terms fails - at least as well as any QPT/GPT-illiterate, we understand much better why it fails and, crucially, why it clearly doesn't entail "spooky action". (From an informed perspective it's actually rather bewildering that anyone would see anything "spooky" in the predictions (and observations) of correlations obeying the applicable, quantum version of the CHSH inequality).
Anyway, as I said before, this is a ridiculous dispute, and if you're just going to carry on parroting Maudlin's false claims and mindless mantras, in cranky, wilfully ignorant defiance of the wisdom of (modern) quantum foundations, it's over.
BTW, besides the paper itself and Matt Leifer's blog and review, Yemima Ben-Menahem's article is a good antidote to Maudlin's nonsense claims about the PBR theorem and psi-epistemic interpretation.
ReplyDeleteReimond,
ReplyDelete""Your „It can be divided. If it could not, entanglement could not even be defined.“ is simply wrong.
You can “divide” a product state, but..."
Again. Hilbert space must be a product, and so, is divided into factor for Bob and factor for Alice. State is not a product, if entangled.
Tim,
"The entangled state you write is (of course) a linear combination of product states for Alice and Bob. And..."
True. Hilbert space is product, state is not.
Now, did you see change when Alice measures? See how Alice measurement acts as identity on Bob's part of state?
(↑⊗↓ - ↓⊗↑)⊗(0A)⊗(0B) --> (↑⊗↓⊗(+A) - ↓⊗↑⊗(-A))⊗(0B)
This is local.
Anonymous physphil:
ReplyDeleteSo we have your error on display in two consecutive sentences:
"True. Hilbert space is product, state is not.
Now, did you see change when Alice measures? See how Alice measurement acts as identity on Bob's part of state?"
Since, as you acknowledge in the first sentence, the state is not a product state, there does not exist any such thing as "Bob's part of the state", which you mention in the second sentence. Checkmate.
"Paul Hayes", A.K.A. ???
ReplyDeleteI looked carefully for any actual physical or mathematical content in you response to Carl Hoefer (who really is Carl Hoefer) other than insults and a refusal to answer straightforward and clear questions. I could not find any. Perhaps you point out the sentence where any such content appears. If not, do us all the favor of stopping wasting our time.
Physphill,
ReplyDeleteI absolutely understand what you want to say with "Hilbert space must be a product, and so, is divided into factor for Bob and factor for Alice.”
And since your “State is not a product, if entangled" is correct, we have a common ground to shed light onto this issue.
(↑⊗↓ - ↓⊗↑)⊗(0A)⊗(0B) --> (↑⊗↓⊗(+A) - ↓⊗↑⊗(-A))⊗(0B)
--> (↑⊗↓⊗(+A) ⊗(-B) - ↓⊗↑⊗(-A) ⊗(+B))
In the last line the state further evolved unitarily and Bob also got entangled.
This state is entangled. Still no product. Still no dividing into factor for Bob and factor for Alice.
Probably what you try to articulate with “Hilbert space must be a product” is the underlying assumption of MWI that the branches, worlds, … whatsoever become independent of each other.
This independence assumption of MWI allows you to simply mentally “tear apart” a linear combination, a superposition of product states. This is what you call “divided into factor for Bob and factor for Alice”.
But here you have to be careful, where to specify the threshold to “tear apart” a linear combination, because if you tear it apart too early then you would not see interference in a 2-slit experiment. So, you better put the threshold on the level of the many Alices and Bobs.
Does this independence assumption of MWI solve the measurement problem?
Does it tell you how to correlate the many Alices and Bobs? Does it tell you what is local and non-local?
If you want to respond please report to this first:
“Further you probably think that spacetime is quantized. If so, then in MWI when in the measurement |Ψ> splits into different branches, worlds, … whatsoever, then also spacetime splits. And in this situation, it should be clear that talking about locality or non-locality is meaningless.”
Another way to “tear apart” a linear combination, a superposition of product states is to unentangle the state of the world.
(↑⊗↓⊗(+A) ⊗(-B) - ↓⊗↑⊗(-A) ⊗(+B)) ⊗(Rest of the world) -->
(↑⊗↓⊗(+A) ⊗(-B)) ⊗(Rest of the world)
OR
(-↓⊗↑⊗(-A) ⊗(+B)) ⊗(Rest of the world)
Now the reduced state of the world is a product of one Alice and one Bob.
Entanglement in a unitary evolution (U) is here only the first step. The reduction (R) of the state makes a decision according the probability amplitudes. This is the important part to get a product.
But now you have to pay a price. You need to distinguish between entanglement and measurement, the reduction again. A price you do not have to pay in MWI. Is the price too high? It depends on where you put the threshold when the reduction is triggered and what else you get for it.
The underlying assumption of MWI, the independence of branches, worlds … this very feature, which you embrace I would call a bug.
Why?
Because it makes you think, that the measurement problem is solved. But MWI does not solve the measurement problem, because it does not break the linearity of QM.
(And yes, I know you and many others will find this last remark sound peculiar, since you probably believe our world is an exclusively unitary evolution.)
Tim,
ReplyDelete"So we have your error on display in two consecutive sentences:
"True. Hilbert space is product, state is not.
Now, did you see change when Alice measures? See how Alice measurement acts as identity on Bob's part of state?"
Since, as you acknowledge in the first sentence, the state is not a product state, there does not exist any such thing as "Bob's part of the state", which you mention in the second sentence. Checkmate."
"Checkmate". This is truly idiotic.
Do you understand what it means that Hilbert space is product?
I will try to explain very very very slowly.
This state
↑⊗↓ - ↓⊗↑
is not product state. But, it is sum of terms ↑⊗↓, and ↓⊗↑. Each term is state in left part times state in right part. Left part of each term is Alice's factor. Right part is Bob's factor.
Alice measurement does not affect Bob's part of state just means Alice measurement is operator of form O⊗I. It acts on each term, non-trivial on Alice factor and trivial on Bob factor. That is local (if Alice and Bob are apart).
Do you understand now?
Reimond,
ReplyDelete"Probably what you try to articulate with “Hilbert space must be a product” is the underlying assumption of MWI that the branches, worlds, … whatsoever become independent of each other."
No. Hilbert space being product is necessary condition to discuss entanglement in QM (else, entanglement between what and what). It has nothing to do with interpretation.
"Paul Hayes"
ReplyDeleteRe your last two ad hominem posts responding to me: What a load of bluster! But if you subtract the mental diagnoses and links to things not written by you and self-aggrandizement, there's nothing new, and nothing left, other than your assurances that Werner and the other radical psi-epistemic guys understand what I'm too dumb to understand or too lazy to read.
If I were to carefully work through one of the many papers presenting “quantum probability”, I am pretty sure I would be able to spot where the formalism smuggles in nonlocality. I am pretty sure of this because I can’t see how Maudlin’s challenge fails to get the heart of the nonlocality question. Computers can model anything that can be expressed mathematically, given enough resources; that’s why they are called universal Turing machines. If the physics of the GHZ state measurements is truly local, then 3 isolated computers at locations A, B, and C, appropriately programmed, should be able to reproduce the GHZ correlations (with an external agent, e.g. Tim, providing the input of whether to “measure” X or Y). But we both know that neither you nor Physphill is going to take up Maudlin’s bet.
So here’s a different challenge. If you can explain clearly why Maudlin’s challenge is inappropriate, i.e., why an isolated computer might not be able to model a local physical process, then I will carefully read one of the articles you’ve linked that explain “quantum probability” and report back here what I find. But please note: “Computers are classical, quantum physics is quantum” is not a response. Computers can model any physics, whether classical, quantum, Cartesian, Aristotelian, or what have you.
I await your response.
Carl Hoefer,
ReplyDeletein QM, it is true you must give up either locality or that outcomes are unique. In Bell state, if you evolve total wavefunction including measuring device, you get
↑⊗↓⊗(+A) ⊗(-B) - ↓⊗↑⊗(-A) ⊗(+B)
This is one "world" where Alice measures + and Bob -, and another where Alice measures - and Bob +. These worlds do not interfere because macroscopic objects have negligible interference. So, to very good approximation you can ignore that one that does not describe your result. Doing so is Copenhagen. Or, you can keep both, it is not very expensive. That is "many worlds". Everything is local, wavefunction for Bob is not affected by Alice measurement, or Alice by Bob (if like Tim you do not understand what that means, see above). But, price is that result is not unique.
Tim's laptops can simulate this wavefunction, but they will have both worlds (or all for GHZ).
Physphill,
ReplyDeleteI agree with your last post! Given QM, we must give up either locality or unique outcomes.
For the past month or so when arguing with Paul Hayes and Steven, I have been assuming a one-world scenario, i.e. unique outcomes (as have they, and Tim). Hence, I've been saying that locality is out. If one prefers the Everett picture, then maybe one can maintain locality. (I looked at the powerpoint you mentioned several days ago. I realize that many physicists claim that the many worlds picture restores locality. I just haven't looked enough at the arguments on both sides to have a firm opinion.)
Anonymous Physphil
ReplyDeleteSo having been checkmated, you try to knock the pieces off the board and claim victory. Why am I not surprised?
Why you are trying to say so slowly something that everyone knows is beyond me. As we all know, an entangled state can be written (in many ways) as a superposition of product states. In fact, the definition of an entangled state is that it can *only* be written as the superposition of product states, not as a product state. And therefore, to repeat to the point to exhaustion, *there is no such thing as Bob's part of the state*. One more time: if you think there is such a thing, write it down. Display it. Give a formula for it.
Now: if there is no such thing as "Bob's part of the state", then there is no such thing as "an operation that does not change Bob's part of the state". That's just how the English language works. If there is no X, then there is no operation that either leaves X unchanged or that changes X. Period.
So instead of gracefully admitting defeat, and even more gracefully actually trying to learn something, you decide to try to shred the English language. You now want to insist that even though there is no such thing as Bobs part of the state, you can just pull out of thin air some completely different mathematical property and claim that it defines whether an operation is "local". Well, no you can't. Consider an operation that changes a singlet state to an m = 0 triplet state, i.e. an operation that, when the state is written in the right basis, changes the "-" in the singlet to a "+". By your criterion, such an operation does not "change Alice's part of the state" and also does not "change Bob's part of the state". But it sure as hell changes the state. So there must be something more than "Bob's part of the state"and "Alice's part of the state" that can be changed. Let's call that other part the entanglement of the state. So our operation changes the entanglement of the state without changing Bob's part and without changing Alice's part.
Now here's the kicker. By your stated criterion, the change is a local change because by your criterion it is the identity on *both* Alice and Bob's "parts"! But changing from singlet to m = 0 is a paradigm *non-local* change because it cannot be achieved by any local operator! You have so mangled the English language that what is manifestly a non-local change becomes a local change, and indeed apparently no change at all. If you try to define "up" as down or "black" as white you are going to get into a complete confusion, which is what you have done. I have patiently tried to get you unconfused, but your ego prevents you from either seeing the obvious or admitting that you see it.
Good call to remain anonymous.
Carl Hoefer,
ReplyDeletegood.
You write "If one prefers the Everett picture, then maybe one can maintain locality."
There is no maybe. I wrote this before:
"There is clear meaning of "local|". All interactions are point interactions. All operators commute outside lightcone. Measurements or operations of Alice act on Bob as identity (at least until future when lightcone intersects Bob). Alice measurements have no effect on Bob, and Bob none on Alice. If with all that you still claim non-local, we have no disagreement except word."
It is quite clear.
Tim,
ReplyDelete"Consider an operation that changes a singlet state to an m = 0 triplet state, i.e. an operation that, when the state is written in the right basis, changes the "-" in the singlet to a "+". By your criterion, such an operation does not "change Alice's part of the state" and also does not "change Bob's part of the state""
No, not true. It shows you still do not understand basics after very very very slow explanation.
"My criterion" for not changing either part is acting as identity on both parts. That does nothing, it does not change relative phase.
"Let's call that other part the entanglement of the state. So our operation changes the entanglement of the state without changing Bob's part and without changing Alice's part."
Sideways point, but this shows ignorance. Both singlet and m=0 triplet are maximally entangled.
With “Both singlet and m=0 triplet are maximally entangled” you probably wanted to articulate something like “Look, nothing changes!”.
ReplyDeletePhysphill, Nature prepared a show case extra for you and not to bother you too much with “non-locality” she even put both electrons into one atom. And believe me, you literally see the difference between para- and orthohelium, but this time be a bit more modest when looking into the sun.
Get out of your echo chamber, take a walk in nature and look around.
“You can see a lot by just looking” (Yogi Berra)
Reimond,
ReplyDelete"With “Both singlet and m=0 triplet are maximally entangled” you probably wanted to articulate something like “Look, nothing changes!”."
No, that is not what I said nor what I meant. Those two states are different, in fact they are orthogonal, but are both maximally entangled.
If an operation does not "change Alice's part of the state" and also does not "change Bob's part of the state"" it does nothing, it acts as identity on both parts. It does not change one of those states to other, identity cannot map one state to orthogonal state.
Clear facts are, unitary linear evolution by Schrodinger equation describing known physics laws is local. But, it creates superpositions of macroscopic measuring devices in different states. Then, two ways to proceed. One, keep all "branches". That is many worlds. Two, throw away all branches that do not agree with your observations. That is Copenhagen.
ReplyDeleteMany worlds is clearly local, but has no single "reality". Copenhagen? Read paragraph above. If many worlds is local, how can ignoring part of it for convenience, and only when accurate enough for necessary purposes, introduce nonlocality?
Anonymous physphil:
ReplyDelete"Clear facts are, unitary linear evolution by Schrodinger equation describing known physics laws is local."
Since the wavefunction is not a local beable, the standard Schrödinger dynamics for it is not local. Not in Bell's sense. Not in Einstein's sense. For example, if cannot be written as a differential equation *over physical space-time*.
The rest of your statement is therefore unjustified. Many worlds is not "clearly local". And no single world theory that violates Bell inequality is local. That's exactly what Bell proved.
Tim,
ReplyDeleteI already explain how it is local. Alice actions do not affect Bob at all, nor Bob Alice, at least until after lightcone intersects. Do you admit that now?
Bell assumed unique result, which is false in many worlds, so that result does not apply.
For wavefunction, in relativistic formulation it is not function of spacetime, it is functional of field configurations. So what?
Physphill,
ReplyDeleteTim may be too busy on another thread to answer, but I'm happy to predict that Tim does not admit that "Alice's actions do not affect Bob at all, nor Bob Alice, at least until after lightcone intersects".
Your reason for saying this (and others' above) is that spacelike separated operators commute, what Alice does doesn't change Bob's density function, etc. That is true, but irrelevant; it's like saying that Bob can't do any local test that reveal what measurement settings Alice has chosen, or what results she obtained. Yes, but so what. Neither Bell nor anyone else ever said EPR-type spooky action at a distance could be used for signalling (which it could, if Bob had the just-described ability).
Nonetheless, the QM account of what happens (in any single-world interpretation at least) is definitely nonlocal. If it was local, it should be able to be mimicked by spacelike-separated laptops running some physics-simulation program. But I notice that still nobody is taking up Tim on his bet from many posts above . . .
Carl,
ReplyDeletewe are discussing many worlds. In relativistic Schrodinger evolution it is simply mathematics fact that Bob and Alice measurements do not affect each other. It follows from commutators vanishing outside lightcone.
Above, you wrote "If one prefers the Everett picture, then maybe one can maintain locality." Do you still think "maybe"? What is your doubt?
Once you understand many worlds is local, you will want to think again why you say Copenhagen is not. Copenhagen is many worlds, where one ignores branches not consistent with your observation because it is good enough approximation. That approximation cannot introduce nonlocality!
Dr. Sabine,
ReplyDeleteHave youread this Tim Maudlin's book?
The math is too difficult for lay people, but you can fully understand it.