Exploring the Relationship Between Schroedinger and Bohm's Quantum Mechanics

[Haelfix]

Look, I think we all agree QM is correct in producing calculations and correct results, at least in the domain of validity that has been probed experimentally.

The correct interpretation however is still up in the air IMO, and there are theoretical and consistency problems with *ALL* interpretations that simply won't go away. In fact, depending on the interpretation, some things in the actual mechanics of the theory could change, so again the whole story is not known entirely.

I don't understand why some people must insist that the theory is 100% complete, its not, and indeed serious people are still working on it years after the initial formulations.

Again, I don't expect quantum mechanics to be entirely solved for quite some time still, as I suspect there are still some fundamental pieces deep down in the chain that elude us. But you know what... They *have* to be there, if we subscribe to the tenets of logic.

 

[Rothiemurchus]

NRQED:

Im my opinion (and that's just that, a very personal opinion), the nonlocality exhibited in Bohm-Aharonov...

Rothie M:

It is Bohm-Aharonov that convinces me that there is a significant piece of
a jigsaw to be found.The results of toroid experiments could be due to some kind of particles passing through the toroid material and then interacting with electrons and changing the phase of electron interference patterns.
We know that at least 95 per cent of the mass of the universe is unaccounted for,so this is not such an unreasonable proposition.

 

[ZapperZ]

Well, although I agree of course that the final judge is and should be experiment, using beauty contest arguments in order to find inspiration for new ideas is something that has been successfully used in the past. Dirac even went to say that he preferred a beautiful equation over a correct one

cheers,
Patrick.

But you also have to admit that what Dirac and Einstein termed to be "beautiful" is distinctly different than what is being used within the context of this thread here. Logical consistency of a theory is beautiful. I find QM that is filled with that! However, as you said, this also cannot be the definitive "proof" that such a theory is valid. There are many gorgeous idea and theories that went nowhere.

Zz.

 

[humanino]

Evo's signature lastly :
"The great tragedy of Science - the slaying of a beautiful hypothesis by an ugly fact." - Thomas H. Huxley

 

[nrqed]

That last part is clearly incorrect. The fact that there are still experiments being done, both in testing the violation of Bell inequality up to higher sensitivity, the continuing increase in size of detecting quantum superpostion as done by SQUID experiments, and especially the study of decoherence of a quantum state into classically familiar values, all these point to the fact that the validity of QM are continually being tested. So to argue that physicists especially are satisfied or "done" with testing QM is simply absurd based on such evidence. The same can be said with the continuing tests on the various postulates of Special Relativity, including more accurate determination of the upper limit of the photon mass (if any).

Thanks for your feedback.

I never meant to imply that people are not testing QM anymore! I was talking about the *conceptual* foundations of the theory. See below please.

However, note that in these cases, we have CONCRETE stuff to test and to measure! In none of these are we testing something vague and ambiguous such as "it doesn't feel right" or "it is conceptually difficult". To argue that QM is incomplete or incorrect because it doesn't feel or look right makes it sound as if this is a beauty contest. This is what I have been arguing against. I am NOT insisting that we stop testing and prodding QM to see if and where it might fail! Being an experimentalist, that's what I do and in the end, that is the ONLY thing that will convince me one way or the other.

Zz.

I think this is where we might have different points of view. To paraphrase, you are saying that if a theory is mathematically consistent, the only worthwhile questions to focus on are the things that can be tested experimentally. All other considerations are vague, ambiguous and a waste of time.

That's where I would disagree. I think that even though it is indeed vague and somewhat ambiguous, being guided by notions of "beauty", "naturalness" etc is still a worthwhile direction. In other words, you would probably say: unless there is an internal mathematical inconsistency in a theory (this is still subjective since it assumes that the mathematics we have developped are appropriate to undertsand the universe! But I digress), or unless there is an experiment disproving a theory, then we should not waste our time trying to undercover something deeper. If it ain't broke, don't fix it!



That's where I would disagree. Again, there were no experimental contradictions to Kepler's laws (at the time of Newton), so why the need to develop a theory of gravity? Only the need for something deeper that would explain in a "unified" way all three laws of planetary notion. If that's not a consideration of beauty and naturalness I don't know what is.

If I understand your point of view, you would have said: let's focus on experiments to test the validity of Kepler's laws. Let's measure the positions of the planets with ever increasing precision. Talking about new principles without experimental discrepancies would have been misdirected. It's only when discrepancies with the Kepler's laws that you would have felt warranted the search for a new theory.

On the other hand, just the feeling that "there must be something that we are missing" was enough for Newton. And it turned out he was right.

Of course, it's not enough to simply say "I feel something's wrong". One should come up with alternatives or gedanken experiments, etc. But on such an informal forum (it's not the lanl archives, after all), I think it's at least important to say that QM might not be the final word and that people should keep thinking about what could be deeper principles. I think we should not wait for discrepancies in experimental results to consider new conceptual ideas. This is where maybe we should agree to disagree.

Maybe QM could be the final word. But I find this whole business of nonlocality and measurement very disturbing. It seems to me that it is in conflict with the entire machinery of mathematical physics we have been developping over almost 400 years. Locality is a key element of almost all of our equations, and it's easy to just say, well no information (in the conventional sense) is exchanged so there is no problem. But I still feel that that it's not a satisfactory answer. I agree, though, that it's very subjective.


So maybe we should agree to disagree. But I still think that we should not wait for experimental discrepancies to consider new physical principles.

My sincere regards

Pat

 

[nrqed]

Look, I think we all agree QM is correct in producing calculations and correct results, at least in the domain of validity that has been probed experimentally.

The correct interpretation however is still up in the air IMO, and there are theoretical and consistency problems with *ALL* interpretations that simply won't go away. In fact, depending on the interpretation, some things in the actual mechanics of the theory could change, so again the whole story is not known entirely.

I don't understand why some people must insist that the theory is 100% complete, its not, and indeed serious people are still working on it years after the initial formulations.

Again, I don't expect quantum mechanics to be entirely solved for quite some time still, as I suspect there are still some fundamental pieces deep down in the chain that elude us. But you know what... They *have* to be there, if we subscribe to the tenets of logic.

Thanks for your input. I totally agree with what you wrote. Especially your sentence "I suspect there are still some fundamental pieces deep down in the chain that elude us". I feel the same exactly the same way. And this is all I was trying to say in this thread.

Personally, what especially makes me feel this way is the nonlocality issue. I know that people say "no information is exchanged, no energy is transferred, so there is no problem to it. End of story"... But *there* is correlation between the measurements and either we are missing some principle that will clarify this or we have to change our understanding of the physical laws in a deeper way. For example, we would need to rewrite SR in a way that would make clear when two light-like events cannot be correlated and when they can be correlated. But people keep repeating "no energy is transferred, information in the usual sense can't be transmitted so ther is no problem"! And this bothers me.

Anyway, just my two cents.

I don't think I can add to the discussion anything constructive so I'll stop posting.

Thanks to all for their input!

Pat

 

[ttn]

As far as Bohm's pilot wave formulation of QM, I have mentioned this before in another thread, but anyone who professes to be a fan of such a formulation seem to have swept under the carpet the zoo of problems that come with such formulation. This includes the still troubling inability to formulate a correct QFT-like formalism (meaning no creation/desctruction of particles) and the fact that the first attempt to do that resulted in a non-lorentz invariant form! Is this "conceptually easier" to accept?!
Zz.

I don't think it is at all fair to suggest that fans of Bohm's theory "have swept under the carpet the zoo of problems that come with such formulation." In fact, if anyone is guilty of such sweeping, it is the advocates of the standard interpretation of QM. This is known to be plagued by the measurement problem, for example, yet most of the advocates of the standard interpretation simply ignore this. John Bell described the reliance of the standard interpretation on the concept of "measurement" as "unprofessionally vague and ambiguous." Why? Because the theory contains two different rules for how wave functions evolve in time, but fails to give any coherent account of when the rules apply. (The two rules are of course Schroedinger's equation and the collapse postulate.) And for a theory which claims to provide a complete description of physical reality, that is a serious problem.

It also frustrates me to hear the argument that Bohm's theory cannot be made consistent with relativity (i.e., put in a lorentz invariant form). It's true that consistency with relativity is a major issue for Bohm's theory, but it is no more and no less an issue for Bohm than for the standard interpretation of QM. After all, that standard interpretation includes a postulate about the "collapse of the wave function" which is supposed to occur instantaneously (presumably across some space-like hypersurface, though this is not typically even mentioned as an issue) when a measurement is made. So if one regards the wave function as a complete description of the physical system, the wave function collapse process evidently describes a kind of relativity-violating action at a distance no more and no less spooky than the non-local effects in Bohm's theory.

On the other hand, if one rejects the claim that the description provided by the wave function is complete, one immediately finds oneself in the company of Bohm fans and other "hidden variable theory" advocates. And since Bell proved that any experimentally viable hidden variable theory must include non-local effects, the lesson is that non-local effects must be included in any experimentally viable formulation of QM, period. Bell said this quite clearly and quite explicitly, but people seem to have a difficult time hearing and understanding him. See, for example, quant-ph/0408105 at www.arxiv.org.

One can of course say what one wants about the strange features of Bohmian mechanics. But it cannot be reasonably asserted that the advocates of that theory deliberately blind themselves to its problems. Indeed, to again cite the great John Bell (who was, by the way, the principal advocate of Bohm's theory for several decades!), it is to the great credit of Bohm's theory for bringing out in a clear way some strange features (such as non-locality) that had been inside QM all along, but which had been hidden away behind the "unprofessionally vague and ambiguous" fuzz of the standard interpretation.

 

[ttn]

Strangely enough, EVERYONE who works in the field that does this EPR-type study, finds no such alarm. This is because for there to be a violation of SR, there has to be a TRANSFER of information via a continuous displacement over space from one location to another. QM indicates that there is no such thing! There is no info flowing from one location to another in an entanglement measurement. If there is, wouldn't you think this is widely mentioned in physics journals already and highly debated, considering this would cause two MAJOR physics principles (Relativity and QM) to be at odds with each other? <snip>
Zz.

Ummm, does John Bell count as someone "who works in the field that does this EPR-type study"? Because he DEFINITELY found the kind of alarm you refer to here, namely, a reason to worry that the non-locality of quantum theory was in conflict with relativity. Here are his words:

"For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory..." (from J.S. Bell, "Speakable and Unspeakable...", page 172.)

Note also that it represents a confusion to discuss "information transfer" in this context. Do we really want to commit to the idea that the only thing relativity says can't go faster than light is "information"? For one thing, this would make orthodox QM and Bohmian mechanics equally consistent with relativity. For another thing, what the heck is "information"? Whose information, and information about what? Put bluntly, "information" is just not the kind of "stuff" that relativity or any other physical theory ought to be talking about. It is just way too mental. At least, that's what most of the people who have scrutinized these questions carefully believe.

At this point, it probably won't surprise anyone that Bell was among these careful scrutinizers:

"Do we then have to fall back on 'no signaling faster than light' as the expression of the fundamental causal structure of contemporary physics? That is hard for me to accept. ...the 'no signaling' notion rests on concepts which are desperately vague, or vaguely applicable. The assertion 'we cannot signal faster than light' [i.e., 'we cannot transmit information faster than light'] immediately provokes the question:

Who do we think we are?

We who can make 'measurements', we who can manipulate 'external fields', we who can 'signal' at all, even if not faster than light? Do we include chemists, or only physicists, plants, or only animals, pocket calculators, or only mainframe computers?" (from Bell's article "La Nouvelle Cuisine", reprinted in the 2nd edition of "Speakable and Unspeakable...")

 

[vanesch]

Who do we think we are?

We who can make 'measurements', we who can manipulate 'external fields', we who can 'signal' at all, even if not faster than light? Do we include chemists, or only physicists, plants, or only animals, pocket calculators, or only mainframe computers?" (from Bell's article "La Nouvelle Cuisine", reprinted in the 2nd edition of "Speakable and Unspeakable...")

This is indeed exactly the kind of reasoning that lead me (only half jokingly) to say that QM with the projection postulate leads to a kind of solipsism. The only "measurement" that is undeniable and necessary is my conscious observation. Only mine, because I'm not sure whether yours gives rise to a true measurement or simply a decoherence, in the same way as I'm not sure a measurement device has applied the projection postulate or is just correlated with the environment in such a way that when *I* observe it, it collapses into a state which has a recorded history compatible with the Born rule.
So the only true, necessary "collapse of the wave function" is introduced by my consciousness.
The problem with the above statements is that it will for sure trigger reactions such as: "come on, a postulate in a fundamental physical theory cannot have anything to do with the existence or not of a consciousness", or "this is not science" or...
However, if you think about the measurement problem as formulated in standard QM, together with decoherence that confirms Born's idea that we can put the "cut" anywhere in between the observed system and the human observer, will lead you in one way or another to considerations of the kind I mention. It solves also the problem of the vague definition of what is a measurement: it is *my conscious observation*, period. ALL the rest is unitary quantum theory. And it solves, in a way, the non-local aspects: after all, my consciousness can only observe locally.

As I said before, I'm the first one to say that these metaphysical considerations on a purely scientific question make me feel uneasy ; one shouldn't be forced into such considerations in order to try to make sense of a theory, no ?

cheers,
Patrick.

 

[ZapperZ]

I don't think it is at all fair to suggest that fans of Bohm's theory "have swept under the carpet the zoo of problems that come with such formulation." In fact, if anyone is guilty of such sweeping, it is the advocates of the standard interpretation of QM. This is known to be plagued by the measurement problem, for example, yet most of the advocates of the standard interpretation simply ignore this. John Bell described the reliance of the standard interpretation on the concept of "measurement" as "unprofessionally vague and ambiguous." Why? Because the theory contains two different rules for how wave functions evolve in time, but fails to give any coherent account of when the rules apply. (The two rules are of course Schroedinger's equation and the collapse postulate.) And for a theory which claims to provide a complete description of physical reality, that is a serious problem.

But notice above that the way you present your argument against my assertion that Bohm's theory problem have been swept under the carpet is to blast away against CI. You didn't present anything to show that my original assertion about Bohm's theory isn't true.

It also frustrates me to hear the argument that Bohm's theory cannot be made consistent with relativity (i.e., put in a lorentz invariant form). It's true that consistency with relativity is a major issue for Bohm's theory, but it is no more and no less an issue for Bohm than for the standard interpretation of QM. After all, that standard interpretation includes a postulate about the "collapse of the wave function" which is supposed to occur instantaneously (presumably across some space-like hypersurface, though this is not typically even mentioned as an issue) when a measurement is made. So if one regards the wave function as a complete description of the physical system, the wave function collapse process evidently describes a kind of relativity-violating action at a distance no more and no less spooky than the non-local effects in Bohm's theory.

This is NOT what I meant when I said it can't be put in a lorentz invariant form. This is in reference to a recentely published PRL paper that tried to formulate a QFT-equivalent form of Bohm's theory.[1] The lack of a QFT-equivalent form is a major drawback of Bohmian mechanics - everyone who works in that field acknowledged this. The authors of this paper basically tried to show how Bohmian mechanics can be extended to QFT. There are still problems, though. The theory isn't Lorentz invariant, so there is a "preferred" reference frame. But they claim that there can be no experiment that would determine which frame is the preferred one. (Oy vey!) THIS is what I meant as a non-lorentz invariant problem!

On the other hand, if one rejects the claim that the description provided by the wave function is complete, one immediately finds oneself in the company of Bohm fans and other "hidden variable theory" advocates. And since Bell proved that any experimentally viable hidden variable theory must include non-local effects, the lesson is that non-local effects must be included in any experimentally viable formulation of QM, period. Bell said this quite clearly and quite explicitly, but people seem to have a difficult time hearing and understanding him. See, for example, quant-ph/0408105 at www.arxiv.org.

One can of course say what one wants about the strange features of Bohmian mechanics. But it cannot be reasonably asserted that the advocates of that theory deliberately blind themselves to its problems. Indeed, to again cite the great John Bell (who was, by the way, the principal advocate of Bohm's theory for several decades!), it is to the great credit of Bohm's theory for bringing out in a clear way some strange features (such as non-locality) that had been inside QM all along, but which had been hidden away behind the "unprofessionally vague and ambiguous" fuzz of the standard interpretation.

Let's be clear about one thing here. I referred to "fans of Bohmian mechanics" as the people in this forum who continuously advocated this version of QM. Practically all the postings I've seen regarding this on here has been devoid of the glaring problems with this version of QM. I am NOT referring to people, some of whom I know of personally, who work and advocate this formulation. In fact, I have been avidly studying this for the past 4 years ever since I became seriously interested in it, and thus my contact with people who are actively involved in it.

If this forum is full of CI fans who does nothing but tout its "superiority", I would also stand up and start rattling off a bunch of problems with it. But I don't need to do that. There's enough CI bashing going on without my help. So please, try not to equate my pointing out the problems with Bohm theory as an indication that I dislike it. If I dislike it THAT much, I wouldn't have followed and read almost every single paper on it that I can find.

Zz.

[1] D. Durr et al., PRL v.93, p.090402 (2004).

 

[ZapperZ]

Ummm, does John Bell count as someone "who works in the field that does this EPR-type study"? Because he DEFINITELY found the kind of alarm you refer to here, namely, a reason to worry that the non-locality of quantum theory was in conflict with relativity. Here are his words:

"For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory..." (from J.S. Bell, "Speakable and Unspeakable...", page 172.)

Note also that it represents a confusion to discuss "information transfer" in this context. Do we really want to commit to the idea that the only thing relativity says can't go faster than light is "information"? For one thing, this would make orthodox QM and Bohmian mechanics equally consistent with relativity. For another thing, what the heck is "information"? Whose information, and information about what? Put bluntly, "information" is just not the kind of "stuff" that relativity or any other physical theory ought to be talking about. It is just way too mental. At least, that's what most of the people who have scrutinized these questions carefully believe.

At this point, it probably won't surprise anyone that Bell was among these careful scrutinizers:

"Do we then have to fall back on 'no signaling faster than light' as the expression of the fundamental causal structure of contemporary physics? That is hard for me to accept. ...the 'no signaling' notion rests on concepts which are desperately vague, or vaguely applicable. The assertion 'we cannot signal faster than light' [i.e., 'we cannot transmit information faster than light'] immediately provokes the question:

Who do we think we are?

We who can make 'measurements', we who can manipulate 'external fields', we who can 'signal' at all, even if not faster than light? Do we include chemists, or only physicists, plants, or only animals, pocket calculators, or only mainframe computers?" (from Bell's article "La Nouvelle Cuisine", reprinted in the 2nd edition of "Speakable and Unspeakable...")

1. What exactly does Bell theory (or that infamous inequality) tell us? Is it really that there are NO hidden variables of all kind, or a test of what is now known as local realism, as defined within the CHSH[1] reformulation of Bell's theory? The violation of Bell's (or more accurately, CHSH's) inequality can only rule out, at best, local realism scenario. This is as far as what those EPR-type experiments can tell us! We have no clue if there is such a thing as non-local hidden variables, which would then make SR, not QM, to be the one in deep doo doo.

2. Consider the following CLASSICAL scenario. A body is at rest in a reference frame, and no net angular momentum. At time t=0, it explodes into 2 separate pieces. The 2 pieces fly off in opposite direction. Piece A reaches a detector on the other side of the galaxy and its angular momentum was measured. Instantaneously, the measurer automatically knows the angular momentum of Piece B that is on the opposite side of the galaxy because he/she was told of the original set up. Was there any "signal" or "information" traveling between the two?

The difference between this classical scenario and the EPR-type experiment is the existence of the superposition of various states before a measurement. So while the classical scenario has a "predermined" orientation before a measurement, the QM scenario does not! The orientation for both pieces are still in an undetermined superposition of states. But in both cases, when a measurement is made, it is a "joint" measurement, meaning the orientation of both pieces are instantaneously determined. They are not separable, both semanticly (is this a word?) and mathematically. If there are no obvious problem with the classical scenario, why would there be with the QM scenario?

3. I have gone back and double checked all the papers by Aspect, Zeilinger, etc., and in NONE of them were there any claims of violation of SR. I will continue to look some more and see if I can come up with a few things I can quote.

Zz.

[1] J.F. Clauser et al., PRL v.23, p.880 (1969).

 

[ttn]

This is indeed exactly the kind of reasoning that lead me (only half jokingly) to say that QM with the projection postulate leads to a kind of solipsism.

I can sympathize with the reasoning here, though not the conclusion. I mean, you're certainly right that one way to solve the measurement problem is to come up with a clear, physically-grounded definition of what is and isn't a "measurement" (and hence, a clear definition of when wf's evolve by the Sch eq and when they undergo collapse). And since everything on the "outside" of consciousness appears to be essentially the same in terms of its being constructed from the same electrons, protons, etc., the only semi-plausible place to hypothesize there might be a real difference is between matter and consciousness.

But I also agree with what you said about this being pretty crazy and being, probably, the kind of thing that reasonable physicists shouldn't even be taking seriously. (I would only add this spin: since the standard interpretation of QM seems to almost inevitably lead here, perhaps it's that interpretation itself that reasonable people shouldn't take seriously.)

Let me also note that Bohm's theory provides a completely different (and in my opinion far superior and eminently scientific) answer to the measurement problem. Since, in that theory, there is a fact of the matter about where particles are at all times, there is no need to postulate a mysterious collapse process. We simply find particles where they are when we look, period. I can't go into too much detail here, but I would encourage people to look at some of the literature on Bohmian Mechanics to find out more about exactly how the theory unambiguously solves the measurement problem. See, for example the wonderful article by Sheldon Goldstein at:

http://plato.stanford.edu/entries/qm-bohm/

 

[ttn]

But notice above that the way you present your argument against my assertion that Bohm's theory problem have been swept under the carpet is to blast away against CI. You didn't present anything to show that my original assertion about Bohm's theory isn't true.

Fair enough. And, being new to this forum, I don't know much about the context of your remarks (e.g., the fact that maybe there are some ignorant bible-thumping Bohmians here!). So I apologize if my earlier post had an unjustly confrontational tone. I didn't mean for it to come across that way, and I'm delighted to hear that you are sincerely interested in the Bohm theory since you are obviously a knowledgeable and thoughtful physicist.

But given your interest in Bohmian mechanics, I think your critical comments about Bohm's theory are potentially misleading. Here's the best analogy I could come up with: suppose someone criticized G.W. Bush for being inconsistent and dancing around all sides of every issue and never really taking a definite stand on anything. Now, that *is* true of Bush to some extent, so it's not, strictly speaking, an invalid criticism. But unless the person specifically states otherwise, every person reading the criticism will infer that the person supports Bush's opponent, Kerry. And to support Kerry *on those grounds* would be, I think, quite preposterous.

The fact is, people have been dismissing Bohm's theory on the sorts of grounds you raised (it isn't lorentz invariant, it requires a preferred reference frame that is unobservable, there's no clean Bohmian version of QFT, etc.) for decades. Yet every single one of these criticisms, I maintain, is equivalent to the Bush/Kerry analogy. So it is simply misleading to criticize Bohm's theory *on these grounds* unless one simultaneously and explicitly makes crystal clear that, despite these issues, Bohm's theory is *no worse off on precisely these grounds* than any other formulation of QM. And when you throw into the mix the fact that Bohm's theory unambiguously solves the measurement problem (and provides a wonderful, visualizable, intuitive picture of quantum phenomena to boot) it seems downright bizarre to be criticizing Bohm's theory in this way.

This is NOT what I meant when I said it can't be put in a lorentz invariant form. This is in reference to a recentely published PRL paper that tried to formulate a QFT-equivalent form of Bohm's theory.[1] The lack of a QFT-equivalent form is a major drawback of Bohmian mechanics - everyone who works in that field acknowledged this. The authors of this paper basically tried to show how Bohmian mechanics can be extended to QFT. There are still problems, though. The theory isn't Lorentz invariant, so there is a "preferred" reference frame. But they claim that there can be no experiment that would determine which frame is the preferred one. (Oy vey!) THIS is what I meant as a non-lorentz invariant problem!

There are lots of preliminary attempts to formulate a Bohm-like theory of relativistic particle phenomena; the paper you mentioned being merely one recent one. I agree with you that there is no single, clean theory here yet. But I don't think it's legitimate to dismiss Bohmian mechanics (considered as a theory of non-relativistic quantum phenomena) on these grounds. For the same objection would have applied in the 30's to orthodox QM. How did the standard theory in fact achieve a relativistic (particle / field theory) extension? Through lots of hard work by lots of very talented physicists. I believe that it is confusing cause and effect to reject Bohmian mechanics on the grounds that a fully-worked-out relativistic extension does not yet exist. Perhaps it is precisely *because* the community has (in my opinion, unjustifiably) rejected Bohm's theory for 50 years that more progress in this direction hasn't been made.

 

[ZapperZ]

There are lots of preliminary attempts to formulate a Bohm-like theory of relativistic particle phenomena; the paper you mentioned being merely one recent one. I agree with you that there is no single, clean theory here yet. But I don't think it's legitimate to dismiss Bohmian mechanics (considered as a theory of non-relativistic quantum phenomena) on these grounds. For the same objection would have applied in the 30's to orthodox QM. How did the standard theory in fact achieve a relativistic (particle / field theory) extension? Through lots of hard work by lots of very talented physicists. I believe that it is confusing cause and effect to reject Bohmian mechanics on the grounds that a fully-worked-out relativistic extension does not yet exist. Perhaps it is precisely *because* the community has (in my opinion, unjustifiably) rejected Bohm's theory for 50 years that more progress in this direction hasn't been made.

But then again, I don't think I've ever said anything about rejecting Bohmian mechanics. The very reason I studied it was because of the potential of using it for certain cases when it is more convenient than using the straightforward propagator method in many-body physics.

Dan Styer has a very useful paper on the 9 different formulations of QM.[1] His most important comment, to me, is that fact that no one formulation is convenient all the time. I shift quite often between 2nd quantization and path integral whenever one sucks and the other becomes more useful. I have yet to adopt Bohmian mechanics seriously enough to actually use it in my work, because using it simply because it is "conceptually easier" doesn't cut it, especially when other formulations are well-tested. There simply aren't many application of it yet to describe complex phenomena that we study, even non-relativistic ones.

Zz.

[1] D. Styer et al. Am. J. Phys., v.70 p.288 (2002).

 

[ttn]

1. What exactly does Bell theory (or that infamous inequality) tell us? Is it really that there are NO hidden variables of all kind, or a test of what is now known as local realism, as defined within the CHSH[1] reformulation of Bell's theory? The violation of Bell's (or more accurately, CHSH's) inequality can only rule out, at best, local realism scenario. This is as far as what those EPR-type experiments can tell us! We have no clue if there is such a thing as non-local hidden variables, which would then make SR, not QM, to be the one in deep doo doo.

The issue of "realism" is a complete red-herring. Violations of Bell's inequality shows that hidden variable theories (i.e., theories according to which the quantum description of reality is incomplete) cannot be local. And the EPR argument shows that if quantum mechanics itself is complete (as Bohr claimed) than it is non-local. So pick your poison. You must face non-locality (i.e., the "deep doo doo" of conflicting with SR) no matter what.

2. Consider the following CLASSICAL scenario. A body is at rest in a reference frame, and no net angular momentum. At time t=0, it explodes into 2 separate pieces. The 2 pieces fly off in opposite direction. Piece A reaches a detector on the other side of the galaxy and its angular momentum was measured. Instantaneously, the measurer automatically knows the angular momentum of Piece B that is on the opposite side of the galaxy because he/she was told of the original set up. Was there any "signal" or "information" traveling between the two?

I don't know exactly what "signals" and "information" are, but the answer is almost certainly: no. More importantly, there was surely no physical, causal influence exerted on Piece B by the observation event on Piece A.

The difference between this classical scenario and the EPR-type experiment is the existence of the superposition of various states before a measurement. So while the classical scenario has a "predermined" orientation before a measurement, the QM scenario does not! The orientation for both pieces are still in an undetermined superposition of states.

Excellent. So, after the measurement at A, the piece at B suddenly does have a definite state. If it had it all along, the pre-measurement quantum description (a "superposition of various states" as you said) was an incomplete description of the state of particle B, i.e., some hidden variable theory is true. If, on the other hand, the state of Piece B changed, because of the measurement at A, to a state with a definite angular momentum value, then quantum mechanics is non-local. That's the EPR dilemma. QM is either incomplete, or it's non-local.

Which do you think it is? Or do you think the argument for the dilemma is flawed?

But in both cases, when a measurement is made, it is a "joint" measurement, meaning the orientation of both pieces are instantaneously determined. They are not separable, both semanticly (is this a word?) and mathematically. If there are no obvious problem with the classical scenario, why would there be with the QM scenario?

Because the standard interp of QM asserts that the quantum description of reality is complete!

3. I have gone back and double checked all the papers by Aspect, Zeilinger, etc., and in NONE of them were there any claims of violation of SR. I will continue to look some more and see if I can come up with a few things I can quote.

The conflict with SR is sufficiently subtle that it's possible for people to fail to see it for a variety of reasons. A careful reading of "Speakable and Unspeakable" will, I think, clear up any doubts. Tim Maudlin's book ("Quantum NonLocality and Relativity") is also an excellent, and highly accessible, text.

 

[ZapperZ]

The issue of "realism" is a complete red-herring. Violations of Bell's inequality shows that hidden variable theories (i.e., theories according to which the quantum description of reality is incomplete) cannot be local. And the EPR argument shows that if quantum mechanics itself is complete (as Bohr claimed) than it is non-local. So pick your poison. You must face non-locality (i.e., the "deep doo doo" of conflicting with SR) no matter what.

Ah, but now I think that "non-locality" is also a red herring. This is because it is uncertain if we mean superluminal motion or the "spooky action at a distant", or other beasts. I think I am being consistent with my other stance by only restricting to only what can be determined. The CHSH refinement of Bell's theorem indicates, by people who are experts in this field, that all the experimental results so far have been inconsistent with local realism. Unlike you, I don't think that just because someone criticizes Bush, he/she is automatically for Kerry. The logical path has not been established the way Bell did that this is an "either-or" situation.

I don't know exactly what "signals" and "information" are, but the answer is almost certainly: no. More importantly, there was surely no physical, causal influence exerted on Piece B by the observation event on Piece A.

Excellent. So, after the measurement at A, the piece at B suddenly does have a definite state. If it had it all along, the pre-measurement quantum description (a "superposition of various states" as you said) was an incomplete description of the state of particle B, i.e., some hidden variable theory is true. If, on the other hand, the state of Piece B changed, because of the measurement at A, to a state with a definite angular momentum value, then quantum mechanics is non-local. That's the EPR dilemma. QM is either incomplete, or it's non-local.

Which do you think it is? Or do you think the argument for the dilemma is flawed?

Because the standard interp of QM asserts that the quantum description of reality is complete!

The conflict with SR is sufficiently subtle that it's possible for people to fail to see it for a variety of reasons. A careful reading of "Speakable and Unspeakable" will, I think, clear up any doubts. Tim Maudlin's book ("Quantum NonLocality and Relativity") is also an excellent, and highly accessible, text.

Bell's book is well read and well cited by these EPR papers. I am very skeptical that these prominent people simply ignored such clear contradiction between QM and SR. And I have no problem with QM being non-local without violating SR. There is simply no evidence that I know of of any superluminal effects of any kind.

Here's a question: do you think this has deteorated into simply an argument based on a matter of taste? If it has, I see it going nowhere.

Zz.

 

[selfAdjoint]

So, after the measurement at A, the piece at B suddenly does have a definite state. If it had it all along, the pre-measurement quantum description (a "superposition of various states" as you said) was an incomplete description of the state of particle B, i.e., some hidden variable theory is true. If, on the other hand, the state of Piece B changed, because of the measurement at A, to a state with a definite angular momentum value, then quantum mechanics is non-local. That's the EPR dilemma. QM is either incomplete, or it's non-local.

There's a third altrnative: Piece B DIDN'T HAVE the property in question until a measurement took place. The superposition wasn't just a combination of properties but a complex propensity for Piece B to have property 1 if Piece A had property 2 and vice versa. This complex propensity was created before the two particles separated and has spread, quite causally, with them. When a measurement takes place, no matter at which particle, it gives the other particle the appropriate property, just as quantum states always project into the properties in the real world.

You say that if Piece B didn't have its property all along then QM is incomplete. But that's just the point. QM is complete and it is NOT realist, either local or otherwise. It's not a bug, it's a feature!

 

[ZapperZ]

There's a third altrnative: Piece B DIDN'T HAVE the property in question until a measurement took place. The superposition wasn't just a combination of properties but a complex propensity for Piece B to have property 1 if Piece A had property 2 and vice versa. This complex propensity was created before the two particles separated and has spread, quite causally, with them. When a measurement takes place, no matter at which particle, it gives the other particle the appropriate property, just as quantum states always project into the properties in the real world.

You say that if Piece B didn't have its property all along then QM is incomplete. But that's just the point. QM is complete and it is NOT realist, either local or otherwise. It's not a bug, it's a feature!

Er... selfadjoint, your posting quoted me. But what you quoted didn't come from me at all. :)

Zz.

P.S. Er.. it was probably my fault. I messed up the quote commands in my previous posting.

 

[ttn]

Bell's book is well read and well cited by these EPR papers. I am very skeptical that these prominent people simply ignored such clear contradiction between QM and SR.

Fair enough. I'd be very skeptical too if I didn't know this field very well for myself.

But I'm curious what you think of the Bell quote I gave earlier, the one where he says quite explicitly that, in his opinion, there is a fundamental conflict between relativity and quantum theory. Surely Bell understood Bell at least as well as all the folks writing papers on EPR. Are you also "very skeptical" that Bell himself could fundamentally misunderstand his own result?

I know both possibilities are difficult to believe. But either Bell himself didn't understand the significance of Bell's theorem, or a bunch of the subsequent commentators didn't understand it. (Of course, many others *do* understand it: David Albert, Tim Maudlin, Sheldon Goldstein, etc.) It's one or the other (or, I suppose, both) since Bell believed his theorem proved a deep inconsistency between QM (in any formulation) and relativity.

And I have no problem with QM being non-local without violating SR.

I don't understand this. Could you clarify what you take SR to require or prohibit... and what you take "non-locality" to mean?

There is simply no evidence that I know of of any superluminal effects of any kind.

How to you account for Bell's belief to the contrary?

Here's a question: do you think this has deteorated into simply an argument based on a matter of taste? If it has, I see it going nowhere.

A matter of taste? No way. Absolutely not. It's a matter of replacing the "unprofessionally vague and ambiguous" interpretation that is currently dominant with something that is clear and consistent. I mean, I guess you can call that a matter of taste. But I would say anyone who prefers the taste of subjectivity and vagueness and inconsistency, doesn't deserve to be called a scientist.

 

[ttn]

There's a third altrnative: Piece B DIDN'T HAVE the property in question until a measurement took place.

So the transition from a state in which it doesn't have the property in question, to a state in which it does, isn't a change in the state of the piece?

It's a simple yes/no question. And it's precisely the EPR dilemma.

When a measurement takes place, no matter at which particle, it gives the other particle the appropriate property...

Sounds like a non-local action at a distance to me.

You say that if Piece B didn't have its property all along then QM is incomplete. But that's just the point. QM is complete and it is NOT realist, either local or otherwise. It's not a bug, it's a feature!

Here's a question: if QM denies realism (which I assume means the idea that there is some real, objective world "out there" which is referred to by the theory) then what does it mean to claim, as you did, that "QM is complete"? I always thought completeness meant that the theory provided a complete account of the physical state of the real, objective system. If there is no such real system, then there would seem to be nothing for QM to provide a complete description *of*.

 

[ZapperZ]

Fair enough. I'd be very skeptical too if I didn't know this field very well for myself.

But I'm curious what you think of the Bell quote I gave earlier, the one where he says quite explicitly that, in his opinion, there is a fundamental conflict between relativity and quantum theory. Surely Bell understood Bell at least as well as all the folks writing papers on EPR. Are you also "very skeptical" that Bell himself could fundamentally misunderstand his own result?

I know both possibilities are difficult to believe. But either Bell himself didn't understand the significance of Bell's theorem, or a bunch of the subsequent commentators didn't understand it. (Of course, many others *do* understand it: David Albert, Tim Maudlin, Sheldon Goldstein, etc.) It's one or the other (or, I suppose, both) since Bell believed his theorem proved a deep inconsistency between QM (in any formulation) and relativity.

I have no response against what Bell has mentioned, the very same way that I have no response against Einstein when he claim that QM is incomplete. This is because these were not based on any physical findings. I have not seen, nor has Bell indicated, of any observables that has superluminal transmission. This comes back again to the very argument of information transfer - is there anything being transferred from one location to another? The very same way that the phase velocity of light can be of ANY speed but carries no information, a measurement made in an EPR type experiment transfers no info about a measurement in one location to the other EPR pair. If there is, then this will be a clear violation of SR. In ALL of the EPR experiments, there has been no insistance that this is the case.

I don't understand this. Could you clarify what you take SR to require or prohibit... and what you take "non-locality" to mean?

How to you account for Bell's belief to the contrary?

A matter of taste? No way. Absolutely not. It's a matter of replacing the "unprofessionally vague and ambiguous" interpretation that is currently dominant with something that is clear and consistent. I mean, I guess you can call that a matter of taste. But I would say anyone who prefers the taste of subjectivity and vagueness and inconsistency, doesn't deserve to be called a scientist.

But if it is subjective, vague, and inconsistent, it should not work. And it should not work this spectacularly. However, I'm a bit confused. You appear to have completely accepted Bohmian mechanics, even when faced with the problem of non-lorentz invariant. I know you have argued that, hey, it is only the beginning, they'll work this out, but aren't you a bit too certain about it? The Dirac/Klein-Gordon equation has successfully dealt with the relativistic aspect of the Schrodinger equation, so to argue that this is still a problem with the conventional QM that is being ignored is highly inaccurate. And yet, you think it is perfectly OK to abandon what HAS worked, and jump onto a bandwagon that is still untested and struggling to plug a lot of unsolved problems. And we're not just talking about conceptual problems either such as the "measurement" problem.

I like the way Bohm's idea has evolved, and continue to evolve. But is it actually read for Prime Time? I hardly think so. I have one test I use to see if a certain formulation is ready to be used - deriving the BCS theory of superconductivity. As a punishment to myself, I have derived this via variational method, field-theoretic method, and even "fudged" perturbation method. I have presented this as a challenge to a couple of people who are big advocates of Bohmian mechanics. Until this can be shown to work, I have no confidence in using it as a tool to solve real research problems.

Zz.

 

[ttn]

I have no response against what Bell has mentioned, the very same way that I have no response against Einstein when he claim that QM is incomplete. This is because these were not based on any physical findings.

What do you mean by "physical findings"? Direct experimental results? Well, OK, but then aren't you essentially saying that all of theoretical physics is hot air, and all that matters or is meaningful is the "raw" uninterpreted data of experiment? I think this attitude is mistaken; for example it would leave one unable to prefer the Copernican model of the solar system to the old Greek Ptolemaic theory. Moreover, I find it a bit offensive to essentially accuse two of the greatest physicists of the last century as basically being full of hot air.

This comes back again to the very argument of information transfer - is there anything being transferred from one location to another? The very same way that the phase velocity of light can be of ANY speed but carries no information, a measurement made in an EPR type experiment transfers no info about a measurement in one location to the other EPR pair. If there is, then this will be a clear violation of SR. In ALL of the EPR experiments, there has been no insistance that this is the case.

You're certainly right that none of the experiments literally saw a physical thing flying faster than c. No doubt. Yet despite this, Bell still firmly believed that there was a fundamental conflict between QM and relativity. Why do you think he believed this? And why do you think all the other smart people I mentioned earlier agree with Bell on this point?

But if it is subjective, vague, and inconsistent, it should not work. And it should not work this spectacularly.

What's subjective, vague, and inconsistent is the orthodox interpretation of the quantum formalism. It's the formalism itself which has demonstrated spectacular success. But nobody thinks the equations are wrong. I just think Bohr was dead wrong in virtually everything he said about what those equations *meant* about the way the world works.

However, I'm a bit confused. You appear to have completely accepted Bohmian mechanics, even when faced with the problem of non-lorentz invariant. I know you have argued that, hey, it is only the beginning, they'll work this out, but aren't you a bit too certain about it?

That wasn't my argument at all. I agree with Bell that *any* -- that is, *every* -- sharp formulation of quantum theory suffers from non-locality. So the non-locality of Bohm's theory isn't a problem to be worked out. It is a feature that must be present in any theory which accurately describes nature -- i.e., non-locality is a fact of nature. And (again like Bell) I believe non-locality and relativity are at odds. If nature is non-local, then relativity is wrong or broken or needs to be re-interpreted or something like that. So the fact that, e.g., attepts to formulate Bohmian versions of QFT require a preferred frame, does not appear to me to be a problem. It is just one of the possible ways of fixing up whatever it is that's broken with relativity. (Incidentally, at the risk of sounding like a broken record, this is the "fix" that Bell himself preferred, at least at times: see his wonderful article on "How to Teach Special Relativity" for example.)

The Dirac/Klein-Gordon equation has successfully dealt with the relativistic aspect of the Schrodinger equation, so to argue that this is still a problem with the conventional QM that is being ignored is highly inaccurate.

Wait, now you're the one failing to distinguish equations from interpretation. (If I recall, you stressed the importance of that distinction at the beginning of this thread.) The Dirac or KG equations are fine, and the usual recipes for using them are obviously correct. But the standard "story" that goes along with the use of these equations contains all the same vagueness about measurement and wave function collapse as is present in regular old non-relativistic QM. The equations are lorentz covariant, but the conceptual problems remain. Turning it around, the mere fact that the equations work doesn't prove that the currently dominant interpretation is correct (any more or any less than it proves any other interpretation is correct).

And yet, you think it is perfectly OK to abandon what HAS worked, and jump onto a bandwagon that is still untested and struggling to plug a lot of unsolved problems.

That's not true. The equations work great, and I'm all for keeping them. It's mostly Bohr's verbiage about completeness and measurement and collapse that I want to abandon -- precisely because those things haven't "worked" at all!

And we're not just talking about conceptual problems either such as the "measurement" problem.

Did you intend these as scare quotes? I don't follow you. Are you denying that the measurement problem is a real problem? You think it's just semantics or metaphysics or something?

I like the way Bohm's idea has evolved, and continue to evolve. But is it actually ready for Prime Time? I hardly think so.

I do. I have all sorts of questions about it -- there's lots of work left to be done, lots of interesting paths to pursue. But in my opinion it's the best thing available at present. So it's ready for prime time, baby. =)

I have one test I use to see if a certain formulation is ready to be used - deriving the BCS theory of superconductivity. As a punishment to myself, I have derived this via variational method, field-theoretic method, and even "fudged" perturbation method. I have presented this as a challenge to a couple of people who are big advocates of Bohmian mechanics. Until this can be shown to work, I have no confidence in using it as a tool to solve real research problems.

The various formulations you mention here aren't different interpretations of the quantum formalism, they're just different mathematical tools or perspectives on that formalism. So I don't see the point of your challenge. Any valid quantum mechanical derivation of the BCS theory could be understood from a Bohmian point of view, or a Copenhagen point of view (to the extent that's possible), or a MWI point of view, or whatever. They all share the same core formalism.

 

[ZapperZ]

Then I'm COMPLETELY confused. I could have sworn that I read a while back of your criticism of the "conventional" QM by pointing out the fact that the Schrodinger eqn. is also not covariant under lorentz transformation. When you said that (unless I imagined it), then I took it that you were disagreeing with the formalism of QM as presented in the conventional manner, NOT the interpretation.

Honestly, and I've said this a long time ago on here so someone else can verify this, I have little patience for "interpretation" philosophy. I view it as part of a necessary evil (inconvenience?). And the fact that people often confuse the interpretation with the formalism makes this even more annoying.

If you are unhappy with CI, then be my guest. I have absolutely ZERO problem with that unhappiness. However, the Schrodinger wavefunction approach is a different formulation of QM with compared to the Bohmian pilot wave formulation, which is then different then Feynman path integral approach, which is then different than the Heisenberg Matrix formulation, etc...etc. (Ref. to Dan Styer's paper). I thought that these difference in formulations are what we're debating on, not interpretation. It is why I used the BCS theory as the test case of any of these formulations to be shown as workable.

Zz.

 

[Rothiemurchus]

A slight diversion:

Could the Pauli exclusion principle be due to superconductivity -
assuming space around electrons in atoms is occupied by some highly ordered arrangement of charged particles?

The hyperphysics website repeats the assertion that Schrodinger equation cannot be
derived.It says:

"Though the Schrodinger equation cannot be derived, it can be shown to be consistent with experiment. The most valid test of a model is whether it faithfully describes the real world. "

 

[humanino]

The hyperphysics website's statement is not very precise : it cannot be derived outside the axioms of QM.

The Pauli principle is more fundamental. Besides, why would other states outside the the atom explain statistics ?

 

[ZapperZ]

A slight diversion:

Could the Pauli exclusion principle be due to superconductivity -
assuming space around electrons in atoms is occupied by some highly ordered arrangement of charged particles?

Not that I know of, and I've studied superconductivity for almost all of my college student years. Note that if it is due to superconductivity, then it shouldn't occur in atoms, in light, in the deBoer effect of Nobel gasses, etc., where there are no superconductivity.

The hyperphysics website repeats the assertion that Schrodinger equation cannot be
derived.It says:

"Though the Schrodinger equation cannot be derived, it can be shown to be consistent with experiment. The most valid test of a model is whether it faithfully describes the real world. "

I love the hyperphysics site and cite it regularly. However, they have made several inaccurate statements before and this would be one of them. [The other being that the energy gap in a superconducting density of states leads to the zero resistivity property. This is not correct - these two are correlated, but the gap is not the cause of zero resistance].

Zz.

 

[ttn]

Then I'm COMPLETELY confused. I could have sworn that I read a while back of your criticism of the "conventional" QM by pointing out the fact that the Schrodinger eqn. is also not covariant under lorentz transformation. When you said that (unless I imagined it), then I took it that you were disagreeing with the formalism of QM as presented in the conventional manner, NOT the interpretation.

No, I'm sorry, maybe I wasn't very clear before. The non-locality in the orthodox formulation of QM is not to be found in the Schroedinger equation. That has just the right sort of relativity (namely, Galilean invariance) to be a good non-relativistic dynamical equation (just as the Dirac and KG equations have the correct sort of invariance to be good relativistic dynamical equations). The non-locality is to be found, rather, in the collapse postulate. It's the collapse of the wave function which I believe violates the prohibitions of relativity (if we regard QM as complete).

Of course, one could get rid of the non-locality (and lots of the vague talk about "measurement") by simply jettisoning the collapse postulate. But then one's theory simply predicts the wrong thing, e.g., that the pointers on (what we call) measuring instruments end up pointing in definite directions at the ends of experiments.

So... just to clarify, I'm not at all against the formalism of QM. Of course that is correct -- it's been verified to an amazing degree by decades of experiments, many of which were specifically designed to test what people thought might be its weak points. My main goal in this discussion was simply to object to using the non-locality in Bohmian mechanics as an argument against Bohmian mechanics. I don't think this is a valid objection, since all other interpretations of QM (leaving aside many worlds, which has plenty of other problems to contend with) are non-local too.

(That was the point of the Bush/Kerry analogy. It's not that I think anyone who hates Bush must love Kerry. I just don't think it's appropriate to criticize Bush for a characteristic he shares with the other contenders in the ring -- at least, not without making it clear that one is aware of that fact.)

Honestly, and I've said this a long time ago on here so someone else can verify this, I have little patience for "interpretation" philosophy. I view it as part of a necessary evil (inconvenience?). And the fact that people often confuse the interpretation with the formalism makes this even more annoying.

I agree with the last part, but I guess, unlike you, I see interpretation as an absolutely central and essential part of the progression of science. Where would astronomy be without Copernicus' interpretation of the data about the solar system (or, if you like, the proto-equations that summarized all this data)? Where would physics be without Boltzmann's interpretation of the physical basis for the laws of macroscopic thermodynamics?

If you are unhappy with CI, then be my guest. I have absolutely ZERO problem with that unhappiness. However, the Schrodinger wavefunction approach is a different formulation of QM with compared to the Bohmian pilot wave formulation, which is then different then Feynman path integral approach, which is then different than the Heisenberg Matrix formulation, etc...etc.

Probably this is mostly just a dispute over terminology. But I don't think the difference between Standard QM and (say) Feynman Path Integrals, is the same as the difference between Standard QM and Bohmian mechanics. Path Integrals are just another mathematical tool for evolving wave functions forward in time (or, if you like, calculating matrix elements). They are mathematically equivalent to the Sch equation (or whatever the basic dynamical equation is of whatever type of quantum theory one is talking about) but they are sometimes computationally more elegant or more practical. Bohm's theory, on the other hand, provides a physical interpretation of the meaning of the equations -- one very different from the "standard" interpretation due to some superposition of Bohr, Heisenberg, and von Neumann.

(Ref. to Dan Styer's paper).

I know the paper you mean. I wouldn't recommend Styer as an expert on these issues, however. In his paper on "common misconceptions regarding quantum mechanics" (AmJPhys 64, 31-34) he basically dismissed Bohm's theory (and all other hidden variable type theories) by saying that the whole idea that the wave function represents an incomplete description of reality "was rendered untenable by tests of Bell's theorem which show that no deterministic model, no matter how complicated, can give rise to all the results of quantum mechanics."

This is really a terrible and false statement about what Bell's theorem shows. It's just not right at all. Indeed, Bohm's theory is an explicit counterexample to his claim, for it is a deterministic model (not even all that complicated) which gives rise to all the results of QM.

 

[humanino]

I am not saying the discussion is useless.

I see interpretation as an absolutely central and essential part of the progression of science.

I agree very much with that statement for instance.
But when it comes to

I think anyone who hates Bush must love Kerry

that kind of analogy, I must say I feel the discussion is not very scientific.

The EPR "paradox" has been discussed many times. QM is not intuitive, but it is rigorous.

Path Integrals are just another mathematical tool for evolving wave functions forward in time (or, if you like, calculating matrix elements). They are mathematically equivalent to the Sch equation (or whatever the basic dynamical equation is of whatever type of quantum theory one is talking about) but they are sometimes computationally more elegant or more practical.

The all mystery of the quantum world is in the path integral. Is it not ?

 

[wm]

Bell's theorem refuted; Bohmian possibilities

Here's what I know: Every version of Bell's theorem (BT) known to me is flawed. The probabilistic versions are based on BE (Bell's error); non-prob versions are based on ME (Mermin's error). These errors may be associated with the EPRCM (EPR's category mistake) but are (imo) best named as above for clarity.

Here's what follows: A local realistic QM is valid, in full accord with Einstein's ideas re relativity, locality & separability, and a commonsense view of reality; a reality that justifies the term "hidden variables" because the sub-stratum reality is (often) "hidden" or "veiled" from us due to perturbative measurement effects.

Here's what I suspect: That the quantum potential in Bohm's work might be re-interpretable as a logical consequence of the initial conditions. This suspicion arises from (so-called) "non-local effects" in other theories being replaced by logical consequences in a fully local-realistic theory. PS: I have little interest in this direction (wanting to focus elsewhere), but am sure that my refutation of BT (with little more than high school maths and logic) will encourage others to dig a little deeper with Bohm.

If anyone's interested, I suggest we start four new threads (to provide focus): EPRCM: EPR's category mistake? BE: Bell's error? ME: Mermin's error? BTR: Bell's theorem refuted? Could be fun.

 

[ttn]

Here's what I know: Every version of Bell's theorem (BT) known to me is flawed.

I would be interested to hear what you think the flaw is. But let's just say I'm not holding my breath.

Here's what follows: A local realistic QM is valid, in full accord with Einstein's ideas re relativity, locality & separability, and a commonsense view of reality; a reality that justifies the term "hidden variables" because the sub-stratum reality is (often) "hidden" or "veiled" from us due to perturbative measurement effects.

A local hidden variable theory that agrees with QM's predictions?! Let's see it!

 

[vanesch]

When do complex numbers arise?
Is there a well established theory already for what type of equations produce complex numbers as solutions?

One should study things in order
You talk about quantum gravity and then you ask the above question ; I don't want to sound offending, but it is a bit as if you subscribed to Formula 1 contests, and ask the technician on the starting line, what do people mean by "changing gears" ?
But I can understand that this comes from reading lots of popular science books. There is a not to be underestimated pleasure to be gained in doing things in the right order. Do you know real calculus ? (integrals, differentials etc...) We can take that maybe as a starting point.

cheers,
Patrick.

 

[Rothiemurchus]

vanesch:
But I can understand that this comes from reading lots of popular science books. There is a not to be underestimated pleasure to be gained in doing things in the right order. Do you know real calculus ? (integrals, differentials etc...) We can take that maybe as a starting point.

Rothie M:
It might surprise you to know that I know calculus of variations, Hamilton's principle,
how to solve differential equations and just about any useful mathematical procedure you can think of that relates to classical mechanics.I also know much of the maths of relativity - general and special relativity.I have studied complex numbers in detail - years ago - but I do not think they provide a reasonable or satisfactory description of reality.Physics is about ideas - not mathematics.Einstein said the maths will always follow from a good idea.
A mastery of mathematics does not guarantee an understanding of anything.
The trouble with quantum mechanics is this -
It has taken causality away from the world.It is de a defeatist point of view:it says " there are some things that just can't be understood in terms of the commonsense world."
Where is the proof of this? The most important question to ask about qm - in my opinion - is this:why is Max Born's guess ( that the wavefunction x complex conjugate of wavefunction is proportional to the probability of finding a particle at a certain position in space) so useful - what is a wavefunction? It must be something physical like Bohm's pilot wave.
There is a way to resolve the problem's associated with Bell's Theorem
and to restore causality to the world and that is to assume a signal exists that travels faster than light.But because such an idea shakes the foundations of relativity people will not get their heads around it.
But there was a time when nobody would have believed that the speed of a light wave catching up with the Earth equals the speed of a light wave approaching the Earth.

 

[vanesch]

Rothie M:
It might surprise you to know that I know calculus of variations, Hamilton's principle,
how to solve differential equations and just about any useful mathematical procedure you can think of that relates to classical mechanics.I also know much of the maths of relativity - general and special relativity.I have studied complex numbers in detail - years ago - but I do not think they provide a reasonable or satisfactory description of reality.

Well I then offer my apologies, but you have to understand that it is somehow contradictory to read the above, and:

When do complex numbers arise?
Is there a well established theory already for what type of equations produce complex numbers as solutions?

Do you see what I mean ?

cheers,
Patrick.

 

[ZapperZ]

The trouble with quantum mechanics is this -
It has taken causality away from the world.It is de a defeatist point of view:it says " there are some things that just can't be understood in terms of the commonsense world."

But you see nothing wrong in demanding that the world behaves only in ways that you approve DESPITE of all the experimental observations?

Where is the proof of this? The most important question to ask about qm - in my opinion - is this:why is Max Born's guess ( that the wavefunction x complex conjugate of wavefunction is proportional to the probability of finding a particle at a certain position in space) so useful - what is a wavefunction? It must be something physical like Bohm's pilot wave.
There is a way to resolve the problem's associated with Bell's Theorem
and to restore causality to the world and that is to assume a signal exists that travels faster than light.

I can play the same game as you do and ask you "Where is the proof of this"?

We didn't just make things up just so we can feel good about it and sleep comfortably at night. If you insist that there ARE signals traveling faster than light, then describe the nature of the signal so that it can be measured and proven to exist, and then be proven that it DOES travel faster than c. Till then, you're just making things up as you go along.

But because such an idea shakes the foundations of relativity people will not get their heads around it.
But there was a time when nobody would have believed that the speed of a light wave catching up with the Earth equals the speed of a light wave approaching the Earth.

The difference being that there were existing TANGIBLE, experimental observations that simply did not fit the old notion of how light speed behave. These were not based on simply a matter of tastes, which is all you have stated. There have been NOTHING, no clear experimental observation, to indicate violation of any of SR's postulates so far. You should not equate what have been done to advance our knowledge of light with what you are trying to do here, because they are not even close to being the same.

Zz.

 

[Rothiemurchus]

Zapper Z:
But you see nothing wrong in demanding that the world behaves only in ways that you approve DESPITE of all the experimental observations?


Rothie M:

I do not doubt that the mathematical predictions of qm match experiment and
that any theory challenging qm must explain why.
As for my piece on superluminal signals:are we left with any alternative to them to
explain what Einstein called " ghostly action at a distance."
Everything else seems to have been tried.
I would say that your attitude is "I think that unfortunately the world is just
incomprehensible at some level."
That could be true but there is no harm in challenging it.
And as you have said previously people test qm all the time - just in case.
And people were very surprised by the results of Michelson and Morley
on the speed of light relative to the Earth.

Vanesch:
No need to apologise, I do have a habit of asking what people call
"naive" questions.