Exploring the Relationship Between Schroedinger and Bohm's Quantum Mechanics

[nrqed]

You know, a lot of this depends on how you want to axiomatize your system. Non relativistic Quantum mechanics does have a rigorous mathematical interpretation that is self consistent, but I does not start from the Schroedinger equation right from the get go, or indeed even where the paper in post #2 starts from.

Von Neumann's text is probably where you want to start.. But ultimately, its the nice properties of the the Wiener measure that makes things work out.

There are still mysteries though, particularly when you jump into relativistic material. There you have to axiomatize completely differently, and in a non intuitive way, in order to have any hope for progress... And unfortunately, there is still a lot that needs to be done, it is by no means a full theory yet.

I mean, I could just as well take as a postulate that classical Hamiltonian mechanics is correct.. And then, indeed, I can *derive* Newtonian physics as an isomorphism between theories.

Very true and very interesting. Thanks for your input.

Regards

Pat

 

[ZapperZ]

Marlon:
That is very untrue for the simple reason that QM is not trying to describe gravity.

Rothie M:

In the real world all physical processes take place in the presence of gravity -
qm must depend on gravity and therefore in some sense describe it (gravity can be put into the potential energy term of the schrodinger equation but because it is very weak compared to EM it is not, but that does not describe reality - just a useful approximation to it).

Take note that the quantum effects of gravity HAS been verified for at least a couple of years already![1]

Humanino:
But the Schrodinger equation has a mass parameter ! Even : you cannot apply the Schrodinger equation to a massless particle, which is relativist, since the mass term is in a denominator !

Rothie M:
You are talking about an infinity here?
But even a photon might have a small mass - people are trying to
determine what it is.



I would like to emphasize that the only problem I have with QM is that nobody has ever justified squaring the amplitude of the wavefunction to get a probability.
There could be something fundamental underlying why this is the right thing to do.

Using the rubber sheet analogy for spacetime in GR:
If I stretch the sheet it would gain potential energy.
Could the Schrodinger wavefunction be a measure of the amplitude of the stretching
of spacetime with an electron most likely to be where the stretching is greatest
(which for a hydrogen atom would be close to the proton at 0.52 Angstroms).

This is where I clearly said early in this thread that QM has a set of postulates.[2] Most of these postulates assign a PHYSICAL meaning to certain mathematical operations! However, it is incorrect to think that the wavefunction as a real, physical wave. This is one of the most popular misconception of QM. Other than the fact that the wavefunction itself is complex, the wavefunction sits in a "configuration space", not in real space (except for a single-particle special case).

This hypothesis of assigning a part of the wavefunction to the location of an electron borders on an unverified personal theory. Unless we be careful, that will cause this whole thread to be dumped into the Theory Development section, which will end my participation (that may not be such a bad thing to some people).

Zz.

[1] V.V. Nesvizhevsky et al., Nature v.415, p.297 (2002).
[2] http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qm.html

 

[humanino]

Rothie M:
You are talking about an infinity here?
But even a photon might have a small mass - people are trying to
determine what it is.

I am not talking about infinity.

There are not many things we know with such an accuracy as the vanishing of the photon mass. Who is seriously trying to show that it is non-zero ? QED relies on a gauge theory which is not broken and for which the mass of the boson is zero. For all purpose the mass of the real photon is experimentally and theoretically zero in physics today.

Of course, something very nice about this mass, is that although introducing a mass term spoils the gauge invariance, you can still do it in the calcultaions and set it to zero in the end of the day. There are non-trivial reasons for the gauge invariance to be recovered.

We are not having a very constructive discussion here. All of us agree on the fact that QM is mysterious at some point, when you think about it. Yet it is working perfectly fine. All the rest is speculations so far unfortunately. I wish thise speculations could lead somewhere.

 

[vanesch]

But I am surprised by your statement that Newton found F=ma experimentally. I'd love to see something more specific about this (what experiment did he actually use? What was his reasoning?)

He used an apple tree
His reasoning went like "aaauw"

cheers,
patrick.

 

[nrqed]

He used an apple tree
His reasoning went like "aaauw"

cheers,
patrick.

You are right but that's the "experiment" he used to discover the universal law of gravitation, not F=ma...

Pat

 

[Rothiemurchus]

Humanino:
We are not having a very constructive discussion here. All of us agree on the fact that QM is mysterious at some point, when you think about it. Yet it is working perfectly fine.

Rothie M:
Yes it works fine.But perhaps finding out why it works could be a useful thing to know.

ZAPPER Z:
it is incorrect to think that the wavefunction as a real, physical wave. This is one of the most popular misconception of QM. Other than the fact that the wavefunction itself is complex, the wavefunction sits in a "configuration space", not in real space (except for a single-particle special case).

Rothie M:
In Bohm's theory it is not incorrect to think of the pilot wave as a physical wave.

The magnitude of the wavefunction squared in standard qm is real even if the wavefunction itself is complex.This is of interest because in the analogy with the intensity of a light wave both the amplitude squared and the amplitude are real numbers.The analogy isn't that good is it?

 

[bd1976]

hmmm...

Again, this is an objection based on a matter of tastes.

Secondly, when you say something is "conceptually difficult", what does that mean? I know of MANY things which I found to be "conceptually difficult" to comprehend until I actually learned about those things. Then they became conceptually easy to understand! Are we basing it on intuition? If so, then this isn't a valid foundation to use since our intuition changes with our accumulated knowledge! So when you say something is conceptually difficult, how would you know the problem isn't with you or your understanding of it?

First of all I think that quantum mechanics as a theory is fundamentally different to other physical theories. Yes its true that sometime you gain knowledge ideas become easier to understand, however I think that qm is an example of completely the opposite the more knowledge you gain the more challenging the conceptual problems become. I'm sure there’s a quote from Schrödinger that goes something like - anyone who claims to have understood qm hasn't understood it at all!

First of all there's the problem of measurement. QM is a theory based around "measurements". However what a "measurement" actually is not understood!

Secondly there is the problem of instantaneous information exchange - violating the principle of relativity! Now since there is no experiment which can preformed that violates relativity it has to be said that such a conflict is a serious cause for alarm.

Finally there is the problem of complex numbers. Now don't get me wrong complex number theory is (in my humble opinion) the most beautiful piece of mathematics I have ever encountered. However that doesn't get over the "pie" problem. Integers are whole pies, rational numbers allow for slices of pies.. but what is a complex pie? The answer is that there is no such thing! Complex numbers have no physical correspondence. So here we have a theory where the main object - "the wave-function" has no physical meaning at all and that does separate qm from the other theories in physics.

Please address any comments on complex numbers inthis thread Integral

 

[humanino]

You guys are addressing here questions which we would like to have an answer to. So please, discuss here and find it. I don't have it. In the meantime, if you could find a simple geometrical TOE, don't hesitate, I'd be glad too. Ho, and elixir of long life would be fine as well.

 

[ZapperZ]

First of all there's the problem of measurement. QM is a theory based around "measurements". However what a "measurement" actually is not understood!

But we CONTINUE to study it. However, this doesn't detract from the validity of QM because it only states what CAN be measured. The mechanism of a measurement (if there is any) is part of something QM can't say unless one has a clear definition and idea of what to look for. QM can't make up things out of the air simply to satisfy something that may or may not be there.

And lest we ignore one important thing: there is ALSO a measurement problem in classical mechanics. Think about it. What you measure will depend on how accurately you measure it. At some point, the accuracy of your measurement will bump into the quantum regime. If you don't believe me, look at the diffraction from a single slit. It only APPEARS that what you measured gave you a "good" value because of the coarseness of your measurement.

Secondly there is the problem of instantaneous information exchange - violating the principle of relativity! Now since there is no experiment which can preformed that violates relativity it has to be said that such a conflict is a serious cause for alarm.

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? If you read ALL the EPR-type papers, be it theoretical or experimental (any paper by Anton Zeilinger would suffice), in NONE of them are there any claims of superluminal transfer of information.

Finally there is the problem of complex numbers. Now don't get me wrong complex number theory is (in my humble opinion) the most beautiful piece of mathematics I have ever encountered. However that doesn't get over the "pie" problem. Integers are whole pies, rational numbers allow for slices of pies.. but what is a complex pie? The answer is that there is no such thing! Complex numbers have no physical correspondence. So here we have a theory where the main object - "the wave-function" has no physical meaning at all and that does separate qm from the other theories in physics.

Then you must also have major problems in accepting electrical engineering, classical E&M, etc. So why are we picking on QM alone?

Zz.

 

[nrqed]

...
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? If you read ALL the EPR-type papers, be it theoretical or experimental (any paper by Anton Zeilinger would suffice), in NONE of them are there any claims of superluminal transfer of information.


Zz.

First, let me thank you for your input in this thread.

I agree with what you are saying, but I must still admit that I do feel very uneasy about this entanglement stuff. I know that no information, in the ordinary sense, is transfered, but still there *is* a correlation between the measurements. I know that my position is not a popular one among physicists but I am deeply dissatisfied with the conventional point of view that there is nothing bothersome there and that if one is wondering about whether "something" is exchanged (maybe in some way that would require a rethinking of spacetime), then that person either does not understand the formalism or is a crackpot.



I guess that maybe we should simply say "our formalism is consistent and it agrees with experiments so let's just accept that our comprehension has reached its limits (as opposed to our ability to do calculations) and let's stop asking certain types of questions". But it's hard for me to accept. These EPR type experiments are, imho, the most intriguing and mind blowing aspects of modern physics and I am suprised that most physicists just go "that's neat and strange but we "understand" what's going on, it's all in the formalism. let's move on to other things". I, on the other hand, can't help feeling that I am missing something. That's there something more to the story. Of course, I am not saying that I'll be coming up with a new revolutionary theory, I am just saying that I find it amazing how other people find it easy to accept this aspect of the theory.


Regards,

Pat


(PS:In his book on QFT, Weinberg defines the cluster decomposition principle as the principle that says that "distant experiments yield uncorrelated results. " Well, one should probably define more clearly what "uncorrelated results" means but it would seem that Bell type experiments would violate this principle!)

 

[vanesch]

I, on the other hand, can't help feeling that I am missing something. That's there something more to the story. Of course, I am not saying that I'll be coming up with a new revolutionary theory, I am just saying that I find it amazing how other people find it easy to accept this aspect of the theory.

I have exactly the same feeling. In fact, I came to a peace of mind with this by considering very seriously solipsism.
(look at http://www.iep.utm.edu/s/solipsis.htm)

I cannot help but relate the quantum measurement problem to the hard problem of consciousness. I discussed this a while ago in the philosophy forum.

However, I don't take myself very seriously there :-)

cheers,
Patrick.

 

[humanino]

So according to solipsism, I am the cause of all those annoying people in my neighborhood. I must be pretty masochist

... sorry :shy:

 

[vanesch]

So according to solipsism, I am the cause of all those annoying people in my neighborhood. I must be pretty masochist

It doesn't matter. You don't even exist

cheers,
patrick.

 

[humanino]

Yourself !

 

[Rothiemurchus]

nrqed:
These EPR type experiments are, imho, the most intriguing and mind blowing aspects of modern physics and I am suprised that most physicists just go "that's neat and strange but we "understand" what's going on,

Rothie M:

Einstein certainly thought that instantaneous action at a distance was a problem.
I think most physicists would be delighted if it is shown that a signal can travel faster than light because it would make the world more interesting and it would restore causality to it.

 

[bd1976]

hmm...

I think most physicists would be delighted if it is shown that a signal can travel faster than light because it would make the world more interesting and it would restore causality to it.

I for one very much like the idea that the universe can not be understood. One of the quantum principles is that our knowedege of the universe will always be limited and I think that's strangely appealing. We are not God and shouldn't believe that we can ever approach the divine! (sounds catchy hey!)

Anyway can someone have a crack at explaining why quantum mechanics is more dodgy fundamentally than say classical E.M. I have thought a bit about it but I'm worried that if I am the first one to put my toe in the water I might be the who is drowned!

 

[humanino]

QM is a framework. It defines a general formalism into which observable are operators. EM is a physical interaction. As other interactions, when requiring a high accuracy or more precisely when dealing with phenomena involving a small action, it must conform to QM.

 

[nrqed]

I for one very much like the idea that the universe can not be understood. One of the quantum principles is that our knowedege of the universe will always be limited and I think that's strangely appealing. We are not God and shouldn't believe that we can ever approach the divine! (sounds catchy hey!)

The thing is that up until now, this has never been the correct approach. I mean what if Newton had said "well, there are these Kepler laws and maybe we can not understand them, we have reached the limit of our comprehension so let's just accept them as empirical laws. That's the way Nature is. They work well and that's all we should care about"

Instead he went "I'm sure I can figure this out"... and he did, to a certain extent.

We could repeat this pattern for many major discoveries. And so on.

So why somehow should we reach this point now and say "we can't understand this correlation business. That's just the way things are. It works well and that's all that matters" ?

Maybe QM is the end of the road. Maybe QM is fundamental the way it is and we'll never uncover a deeper principle. But I would not bet on it.

Anyway can someone have a crack at explaining why quantum mechanics is more dodgy fundamentally than say classical E.M. I have thought a bit about it but I'm worried that if I am the first one to put my toe in the water I might be the who is drowned!

Well, classical E&M can be recovered from QED so this is clear.

But, if you are asking "why is QM fundamental", I would have to say that there is no reason to be sure of that! It might well be a kind of approximate theory to something else (maybe even more weird). I am my opinion (and that's just that, a very personal opinion), the nonlocality exhibited in Bohm-Aharonov, Bell's inequality type of experiments, which way experiments, etc are the strongest hints that we should think about some more fundamental principle. I am apparently almost alone in this . It sounds as if most people just say "well, no information (in the usual sense) is transmitted, no energy is transmitted so everything is fine. End of story. Whereas I think that a more fundamental theory would present a more clear picture of the measurement process, of the collapse of the wavefunction, etc.

But it seems that people have got so used to the weirdness of QM that it does not elicit much desire to dig deeper.

Pat

 

[ZapperZ]

The thing is that up until now, this has never been the correct approach. I mean what if Newton had said "well, there are these Kepler laws and maybe we can not understand them, we have reached the limit of our comprehension so let's just accept them as empirical laws. That's the way Nature is. They work well and that's all we should care about"

Instead he went "I'm sure I can figure this out"... and he did, to a certain extent.

We could repeat this pattern for many major discoveries. And so on.

So why somehow should we reach this point now and say "we can't understand this correlation business. That's just the way things are. It works well and that's all that matters" ?

Maybe QM is the end of the road. Maybe QM is fundamental the way it is and we'll never uncover a deeper principle. But I would not bet on it.




Well, classical E&M can be recovered from QED so this is clear.

But, if you are asking "why is QM fundamental", I would have to say that there is no reason to be sure of that! It might well be a kind of approximate theory to something else (maybe even more weird). I am my opinion (and that's just that, a very personal opinion), the nonlocality exhibited in Bohm-Aharonov, Bell's inequality type of experiments, which way experiments, etc are the strongest hints that we should think about some more fundamental principle. I am apparently almost alone in this . It sounds as if most people just say "well, no information (in the usual sense) is transmitted, no energy is transmitted so everything is fine. End of story. Whereas I think that a more fundamental theory would present a more clear picture of the measurement process, of the collapse of the wavefunction, etc.

But it seems that people have got so used to the weirdness of QM that it does not elicit much desire to dig deeper.

Pat

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).

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.

 

[vanesch]

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.

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.

 

[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!