Pilot wave theory, fundamental forces

[Frame Dragger]

Concerning the arbitrariness, perhaps this thread
https://www.physicsforums.com/showthread.php?t=252491
might convince you that it is not so arbitrary as it looks at first sight.

That is fascinating, and is part of dBB's ability to outlive virtually every respectable theory. However, between the highly reductionist TCI, and dBB... TCI seems more in line with LESS "added" elements. Non-Local HV's, a purely theoretical pilot wave... it all makes for a theory that keeps up with TCI, but the one argument I haven't seen properly defended is just Occam's Razor. I read one defense of that one linked by Zenith, but while TCI is incredibly WEIRD, it doesn't make as many assumptions to stay deterministic.

I don't believe that TCI is a fully accurate description of quantum behaviour, or how it becomes macroscropic... however, the word of Interpretations is the world of metaphysics. I suppose dBB strikes me as slightly more contrived than TCI, and therefore less useful as a working theory.

 

[zenith8]

I suppose dBB strikes me as slightly more contrived than TCI, and therefore less useful as a working theory.

Yeah - TCI is massively useful. For example:

"From these arguments we must conclude that it is meaningless to assign to the free electron a magnetic moment" (c) Bohr, Heisenberg et al. (1928)

People were still telling Hans Dehmelt up to the 1980s to stop trying to measure it because Bohr had 'proved' using the Copenhagen interpretation that it couldn't be done. Today the magnetic moment of the electron is probably the best measured number in the whole of science and Dehmelt has got a very nice prize sitting on his mantelpiece.

Perception shapes thinking.

 

[Frame Dragger]

Yeah - TCI is massively useful. For example:

"From these arguments we must conclude that it is meaningless to assign to the free electron a magnetic moment" (c) Bohr, Heisenberg et al. (1928)

People were still telling Hans Dehmelt up to the 1980s to stop trying to measure it because Bohr had 'proved' using the Copenhagen interpretation that it couldn't be done. Today the magnetic moment of the electron is probably the best measured number in the whole of science and Dehmelt has got a very nice prize sitting on his mantelpiece.

Perception shapes thinking.

True, but utility leads to progress, and as strange and unlikely as TCI is it has lead to progress. Let's face it however, it's issues just such as the ones you cite that have more and more people like me, listening to people like you. Once upon a time I would have had to burn you at the stake! ;)

I think I'll stay on the fence... with a tilt towards TCI. Not for the sake of rhetoric, but they both are so clearly incomplete that I'm happy to examine both ideas and keep them in mind when confronting cardinal issues of apparent QM behaviour.

Edit: To be fair, the magnetic moment of the electron was not a TYPICAL blunder by Bohr, although it was typically Bohr. TCI has a better record of producing results (whatever you attribute that to, teaching/student bias included) although it has its major problems. So does dBB... but dBB is just that little bit more... "complete". At this point, completion in the dBB Interpretation smacks of bias towards a more classicist and deterministc view. Not for everyone, but many. TCI is just... the math without apoligies or meaningful philosphophy... which probably makes it the least metaphysical, and therefore the most valuble.

 

[zenith8]

True, but utility leads to progress, and as strange and unlikely as TCI is it has lead to progress.

You have no evidence whatsoever that more progress wouldn't have been made if people had believed deBB from the start. It's the same mathematics but a clearer conceptual picture, so I rather suspect there would have been.

Non-Local HV's, a purely theoretical pilot wave... it all makes for a theory that keeps up with TCI, but the one argument I haven't seen properly defended is just Occam's Razor. I read one defense of that one linked by Zenith, but while TCI is incredibly WEIRD, it doesn't make as many assumptions to stay deterministic..

.. I suppose dBB strikes me as slightly more contrived than TCI, and therefore less useful as a working theory.

(1) Occam: Just for the record, deBB adds no math that is not already there - everything follows from one semantic change in the meaning of the word 'probability'. It also eliminates the - to most people uncompelling - postulates about measurement (so it actually has fewer premises..). It gives a completely new interpretation of quantum phenomena in which e.g. probability plays no fundamental role. The descriptive content is identical but the theories are not equivalent at all. There is no basis to apply Occam here.

(2) You can't moan about the theory being non-local unless you yourself can explain entanglement in a better way. And you can't - we already discussed this. In fact, I seem to recall you said 'I believe in nonlocality'.

(3) As for being contrived - OK, let's work this through. For a start, you're confusing Copenhagen with instrumentalism/shut-up-and-calculate.

Let's start with the equations of quantum mechanics (the Schroedinger equation, say). Here are three typical choices:

* Instrumentalism: assume that we can never know what the mathematical objects in the theory represent (or that we don't care) and just look at the probabilities of experimental results. Perfectly reasonable if you just want to build stuff.

* deBB: assume that the mathematical objects in the theory correspond to things that actually exist. This is also perfectly reasonable if you want to build stuff (it's the same maths) but it makes completely clear what is happening in an individual quantum event and hence guides thinking.

* TCI: because we are in thrall to the latest 1920s philosophical fashion which we heard in a Danish pub assume that one of the two mathematical objects in the theory corresponds to something (God knows what?) that exists er.. only when humans look at it, and insist (with no evidence whatsoever) that nature must be fundamentally probabilistic. Allows you to build stuff but makes everyone who studies it utterly confused (witness the hordes of students posting here).

Now, if we asked a panel of independent witnesses to say which of those options is more contrived, what do you think they would say?

Not for everyone, but many. TCI is just... the math without apoligies or meaningful philosphophy... which probably makes it the least metaphysical, and therefore the most valuble.

But who says metaphysics is not useful? Take the guy in the https://www.physicsforums.com/showthread.php?t=372423" who's going on about the momentum being imaginary in classically-forbidden regions. His whole argument (though he won't have noticed this because he will have been taught that philosophy is pointless) is based on the idea that an actual particle is tunneling through the barrier and that it has an actual momentum given by quantizing the expression 'mv'.

Now of course, if you do assume that particles exist (deBB) then an examination of the Schroedinger current tells you that their momentum is not given by the quantum equivalent of mv but by something else (because of the existence of the quantum force or particles being pushed around by the wave field). So the quantum-mechanical 'momentum' operator only gives the true momentum of a particle in the classical limit i.e. when the wave component is passive. Thus when you 'measure' the momentum in a quantum system, you are not in fact measuring anything at all. This is what people mean by 'contextuality'. So when people make physical arguments about 'the uncertainty in the momentum' they always talk as if they mean the actual uncertainty in the actual momentum of some particle even though, strictly speaking, [tex]\Delta p[/tex] as defined by Heisenberg refers to one component of the stress tensor of the wave field.. (see Peter Holland's deBB textbook). Ho hum.

With hindsight we can now see how impractical, inhibiting ideas came to dominate and distort the entire development of quantum theory. The early quantum physicists attributed to nature a limitation we can now see was simply a deficiency of contemporary thought. [Holland, 1993]

 

[Frame Dragger]

You have no evidence whatsoever that more progress wouldn't have been made if people had believed deBB from the start. It's the same mathematics but a clearer conceptual picture, so I rather suspect there would have been.



(1) Occam: Just for the record, deBB adds no math that is not already there - everything follows from one semantic change in the meaning of the word 'probability'. It also eliminates the - to most people uncompelling - postulates about measurement (so it actually has fewer premises..). It gives a completely new interpretation of quantum phenomena in which e.g. probability plays no fundamental role. The descriptive content is identical but the theories are not equivalent at all. There is no basis to apply Occam here.

(2) You can't moan about the theory being non-local unless you yourself can explain entanglement in a better way. And you can't - we already discussed this. In fact, I seem to recall you said 'I believe in nonlocality'.

(3) As for being contrived - OK, let's work this through. For a start, you're confusing Copenhagen with instrumentalism/shut-up-and-calculate.

Let's start with the equations of quantum mechanics (the Schroedinger equation, say). Here are three typical choices:

* Instrumentalism: assume that we can never know what the mathematical objects in the theory represent (or that we don't care) and just look at the probabilities of experimental results. Perfectly reasonable if you just want to build stuff.

* deBB: assume that the mathematical objects in the theory correspond to things that actually exist. This is also perfectly reasonable if you want to build stuff (it's the same maths) but it makes completely clear what is happening in an individual quantum event and hence guides thinking.

* TCI: because we are in thrall to the latest 1920s philosophical fashion which we heard in a pub assume that one of the two mathematical objects in the theory corresponds to something (God knows what?) that exists er.. only when humans look at it, and insist (with no evidence whatsoever) that nature must be fundamentally probabilistic. Allows you to build stuff but makes everyone who studies it utterly confused (witness the hordes of students posting here).

Now, if we asked a panel of independent witnesses to say which of those options is more contrived, what do you think they would say?


But who says metaphysics is not useful? Take the guy in the https://www.physicsforums.com/showthread.php?t=372423" who's going on about the momentum being imaginary in classically-forbidden regions. His whole argument (though he won't have noticed this because he thinks philosophy is pointless) is based on the idea that an actual particle is tunneling through the barrier and that it has an actual momentum given by quantizing the expression 'mv'.

Now of course, if you do assume that particles exist (deBB) then their momentum is not given by the quantum equivalent of mv but by something else (because of the existence of the quantum force or particles being pushed around by the wave field). So the quantum-mechanical 'momentum' operator only gives the true momentum of a particle in the classical limit i.e. when the wave component is passive. Thus when you 'measure' the momentum in a quantum system, you are not in fact measuring anything at all. This is what people mean by 'contextuality'. So when people make physical arguments about 'the uncertainty in the momentum' they always talk as if they mean the actual uncertainty in the actual momentum of some particle even though, strictly speaking, [tex]\Delta p[/tex] refers to one component of the stress tensor of the wave field.. (see Peter Holland's deBB textbook). Ho hum.

With hindsight we can now see how impractical, inhibiting ideas came to dominate and distort the entire development of quantum theory. The early quantum physicists attributed to nature a limitation we can now see was simply a deficiency of contemporary thought. [Holland, 1993]

"...This allows you to build stuff." When it comes down to it, this is what matters right now. You see the formalism of TCI or Instrumentalism as restrictive, and the coherent explanation of dBB is freeing. I don't. I see the concrete, but unlikely conjectures (not the math, but the interpretation of what that means) made by dBB as supporting a more anthropic and comfortable view of physics. TCI essentially says that the math is an accurate description of the system, and therefore whatever the math says is true. Hence, dead-cat, live-cat, +observer in box with cat, etc...

Is it confusing? Yes. Does it seem likely? I don't know. You say things like, "Corrosponds to something (God knows what?)", but that shows a human fallacy. Why do you take your intuitive experience to be more reliable than the math which allows us to, as you say, "build stuff"? I suppose I'm Instrumentalist willing to work with TCI, or even dBB and MWI, but I don't buy any of them. I DO believe that there is a description beyond the utility of the math, but I don't think we're at the point of forming a coherent description.

Given that dBB is a coherent description of apparently QM behaviour in a manner that is not purely probabilistic, I suppose you could say that in my eyes that makes it wrong from the outset. Yes, dBB is a construction that CURRENTLY holds up, but it wouldn't take much experimental or observational evidenence for it to be brushed aside. In my view, dBB (as I've said before) is more of an "option" waiting in the wings if TCI and Instrumentalism stop panning out. The thing is... they haven't yet, and the margin by which dBB can rely on Pilot Waves and particles instead of a true duality is slim. The fact that TCI is also a shakey theory or borne of academia is purely tu quoque. If the situation were reversed, a person positing TCI could make the same argument about exlusionist practictices, etc. In essence, they are both worth considering, and then the terms cancel.

EDIT: What if the universe operates in such a way that we can only ever hope to come CLOSER to a meaningful Interpretation, but ultimately can only guess and "build stuff" (which from a philosphical POV and not a physics one, is not unlikely or unreasonable). In addition, I do believe you apply Occam's Razor to the CONCEPTS which are introduced to explain the math in dBB/QM. TCI just says that the math which clearly shows everything being a function of probabilities, is literally right. This may seem counterintuitive, or silly, but it introduces no unecessary concepts not mandated by the math. dBB introduces a Pilot Wave and (now) non-local hidden variables. To say that I must give a better explanation of non-locality (entanglement) is also tu quoque. My response is that it is a poorly understood phenomenon, not yet well explained by any existing interpreation, and therefore the Instrumentalist approach is best.

What is so wrong with accepting the conditional and fluid nature of theory and knowledge? If medicine progresses as expected, we may all live long lives; long enough to see more than one theoretical framework be born and die. Get too wedded to one at your own peril, which may be the best argument for practicality of all time.

 

[Demystifier]

argument I haven't seen properly defended is just Occam's Razor. I read one defense of that one linked by Zenith, but while TCI is incredibly WEIRD, it doesn't make as many assumptions to stay deterministic.

Occam razor is a vague argument, because the notion of "simplicity" is not well defined.
Anyway, if you accept the argument that purely probabilistic interpretation of QM is simpler than Bohmian QM, then, by the same argument, you should also accept that a purely probabilistic interpretation of CLASSICAL mechanics is simpler than the standard deterministic view of classical mechanics. For the details see
http://xxx.lanl.gov/abs/quant-ph/0505143 [Found.Phys.Lett. 19 (2006) 553]
http://xxx.lanl.gov/abs/0707.2319 [AIPConf.Proc.962:162-167,2007]
So, would you say that a purely probabilistic interpretation of classical mechanics is better or more convincing than the standard view of classical mechanics?

 

[SpectraCat]

But who says metaphysics is not useful? Take the guy in the https://www.physicsforums.com/showthread.php?t=372423" who's going on about the momentum being imaginary in classically-forbidden regions. His whole argument (though he won't have noticed this because he will have been taught that philosophy is pointless) is based on the idea that an actual particle is tunneling through the barrier and that it has an actual momentum given by quantizing the expression 'mv'.

Hmm .. I guess you mean me. Interesting that you seem to think you know my (or anyone else's) opinions on philosophy without discussing them with me.

For the record, I definitely do not think philosophy is useless ... and I have no preference for either TCI or dBB (so far). I am a bit confused about why people seem to think one has to have a favorite. I have found it incredibly instructive to see how the different interpretations deal with different problems in Q.M. Perhaps my point of view will change as I learn more about dBB ...

 

[Frame Dragger]

Occam razor is a vague argument, because the notion of "simplicity" is not well defined.
Anyway, if you accept the argument that purely probabilistic interpretation of QM is simpler than Bohmian QM, then, by the same argument, you should also accept that a purely probabilistic interpretation of CLASSICAL mechanics is simpler than the standard deterministic view of classical mechanics. For the details see
http://xxx.lanl.gov/abs/quant-ph/0505143 [Found.Phys.Lett. 19 (2006) 553]
http://xxx.lanl.gov/abs/0707.2319 [AIPConf.Proc.962:162-167,2007]
So, would you say that a purely probabilistic interpretation of classical mechanics is better or more convincing than the standard view of classical mechanics?

That definitely seems like reductio ad absurdum to me... Classical mechanics was a stepping stone on the way to notions of relativity and probability. Simplicity is relative within a given system. That said, of course arguments can be made for both sides; that's why dBB is around when virtually all of its compatriots died in the great "Bell's Theorem Pogrom" ;) and subsequent 'cuts'.

Like SpectraCat, I don't HAVE to stick to one Interpretation in my daily life (a luxury, I realize), so I don't. If I had to choose, I've shown that I'm ultimately Instrumentalist/Phenomonologist/Skeptic. It's not the most comfortable state of mind, but it works for now.

 

[zenith8]

Like SpectraCat, I don't HAVE to stick to one Interpretation in my daily life (a luxury, I realize), so I don't. If I had to choose, I've shown that I'm ultimately Instrumentalist/Phenomonologist/Skeptic.

Indeed, you were a Copenhagenist this morning.

 

[Frame Dragger]

Indeed, you were a Copenhagenist this morning.

Play nice now... It's not easy to find your way in the world of interpretations of quantum theory. I still consider myself essentially an adherent of TCI, however from a practical point of view I'm obviously flexible. Part of that flexiblity is that none of the existing interpretations are without their gaping holes, or assumptions. A Pilot Wave and hidden variables, or wavefunction collapse and entanglement... it's not really the greatest choice of all time. That said, as counterintuitive as it may be, TCI seems to require the fewest additional elements to work. If I were to be in any situation outside of a debate over interpretations, I would generally just leave it as metaphysics and move on.

Beyond that, I refer to my earlier posts on the subject, and would simply say that the best description for QM is the most effective at describing the system and making predictions. dBB seems more concerned with just keeping alfoat.

 

[SpectraCat]

Ok, it's clear I need to do some homework to keep up with these discussions. I am looking for a good text on Bohmian mechanics. Would anyone recommend the recent book by Durr and Teufel? Is there a better choice? I would appreciate recommendations by zenith, maaneli and demystifier, or anyone else who is an expert on the subject.

 

[Frame Dragger]

Ok, it's clear I need to do some homework to keep up with these discussions. I am looking for a good text on Bohmian mechanics. Would anyone recommend the recent book by Durr and Teufel? Is there a better choice? I would appreciate recommendations by zenith, maaneli and demystifier, or anyone else who is an expert on the subject.

I'll second that. Feel free to make it a big reading list.

 

[zenith8]

Ok, it's clear I need to do some homework to keep up with these discussions. I am looking for a good text on Bohmian mechanics. Would anyone recommend the recent book by Durr and Teufel? Is there a better choice? I would appreciate recommendations by zenith, maaneli and demystifier, or anyone else who is an expert on the subject.

Even though it's modern, I find Duerr and Teufel's book pretty poor - too much of the wrong sort of mathematics - not enough physics. And there's something about the pompous tone of the book that makes you want to hit them.

Peter Holland's 1993 book 'The Quantum Theory of Motion' is an exhaustively detailed presentation of the whole theory - essentially recalculating every result in standard QM from this new perspective. If you don't mind the excessive detail, it's great for the non-relativistic stuff. It's less good for the relativistic stuff (which wasn't that well developed back then anyway but never mind). D+T don't touch the relativistic stuff at all.

There's a new book by Peter Rigg called "Quantum Causality" which is a really good little discussion monograph - I like it. He unfortunately tries to rename the theory as the 'Causal theory of quantum mechanics' so no-one will actually know what it's about from looking at the title.

You could also read Bohm + Hiley's 'The Undivided Universe' from the same year as Holland, but I wouldn't bother yet (they're too clever to bother with boring details, and they mix in far too much speculative nutter stuff to make it a good introductory textbook).

If you just want a decent summary, [PLAIN]http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" is good (there's also a 60+ slide popular lecture on the same site which I really like). Obviously he lacks the detail of a proper textbook but he manages to pack a surprising amount in (he doen't get very far into the relativistic theory either).

Antony Valentini is apparently writing a comprehensive textbook that should be out this year. This won't help you at the moment obviously but it will be the one to read, I'm sure. His recent historical study "Quantum Theory at the Crossroads: reconsidering the 1927 Solvay Conference" (2009) - also available online - was a revelation to me regarding the historical context.

A final decent option might be reading some of the review articles. There is a comprehensive list of Bohm/pilot-wave references with links on Towler's [PLAIN]http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" (Click 'Further Reading' in the right hand column).

 

[Maaneli]

Even though it's modern, I find Duerr and Teufel's book pretty poor - too much of the wrong sort of mathematics - not enough physics. And there's something about the pompous tone of the book that makes you want to hit them.

Peter Holland's 1993 book 'The Quantum Theory of Motion' is an exhaustively detailed presentation of the whole theory - essentially recalculating every result in standard QM from this new perspective. If you don't mind the excessive detail, it's great for the non-relativistic stuff. It's less good for the relativistic stuff (which wasn't that well developed back then anyway but never mind). D+T don't touch the relativistic stuff at all.

There's a new book by Peter Rigg called "Quantum Causality" which is a really good little discussion monograph - I like it. He unfortunately tries to rename the theory as the 'Causal theory of quantum mechanics' so no-one will actually know what it's about from looking at the title.

You could also read Bohm + Hiley's 'The Undivided Universe' from the same year as Holland, but I wouldn't bother yet (they're too clever to bother with boring details, and they mix in far too much speculative nutter stuff to make it a good introductory textbook).

If you just want a decent summary, [PLAIN]http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" is good (there's also a 60+ slide popular lecture on the same site which I really like). Obviously he lacks the detail of a proper textbook but he manages to pack a surprising amount in (he doen't get very far into the relativistic theory either).

Antony Valentini is apparently writing a comprehensive textbook that should be out this year. This won't help you at the moment obviously but it will be the one to read, I'm sure. His recent historical study "Quantum Theory at the Crossroads: reconsidering the 1927 Solvay Conference" (2009) - also available online - was a revelation to me regarding the historical context.

A final decent option might be reading some of the review articles. There is a comprehensive list of Bohm/pilot-wave references with links on Towler's [PLAIN]http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" (Click 'Further Reading' in the right hand column).

I agree with zenith's recommendations. And Towler's further reading list is in fact the most comprehensive archive on the subject available anywhere.

 

[Frame Dragger]

Thanks very mich Zenith, Maaneli.

 

[Demystifier]

Here is my opinion about the books:

Duerr and Teufel - too mathematical for my taste

Bohm and Hiley - good, but slightly too philosophical for my taste

Riggs - also good, but slightly too philosophical for my taste

Holland - very physical, i.e., the best for my taste

 

[Maaneli]

Seems interesting.

I will talk about making Bohmian nonlocal particle mechanics compatible with relativity and particle creation/destruction. It will be based on
http://au.arxiv.org/abs/0811.1905 [Int. J. Quantum Inf. 7 (2009) 595]
http://au.arxiv.org/abs/0904.2287 [to appear in Int. J. Mod. Phys. A]
but some new insights will also be presented.

I've read the first paper before, and I liked it very much. But I still don't understand how you've managed to get around the need for a preferred frame or spacetime foliation, in your effort to construct a fundamentally Lorentz invariant deBB dynamics.

 

[Demystifier]

That definitely seems like reductio ad absurdum to me...

Yes, that was the intention.

If I had to choose, I've shown that I'm ultimately Instrumentalist/Phenomonologist/Skeptic. It's not the most comfortable state of mind, but it works for now.

That is certainly a reasonable attitude too.

 

[Demystifier]

I've read the first paper before, and I liked it very much. But I still don't understand how you've managed to get around the need for a preferred frame or spacetime foliation, in your effort to construct a fundamentally Lorentz invariant deBB dynamics.

Thanks for asking it. But before giving you an answer, I'll ask YOU a question. Do you see a need for any preferred foliation in Eqs. (17)-(19)?

The point is the following. Even though for each s there may exist a particular (s-dependent) Lorentz frame with respect to which the force between two particles is instantaneous, such a Lorentz frame is by no means special or ``preferred''. Instead, such a particular Lorentz frame is determined by covariant equations of motion supplemented by a particular choice of initial conditions X_a^{\mu}(0).

See also this thread:
https://www.physicsforums.com/showthread.php?t=354083
especially posts #1 and #109.

If you still have questions, I will be happy to answer them.

 

[Maaneli]

Thanks for asking it. But before giving you an answer, I'll ask YOU a question. Do you see a need for any preferred foliation in Eqs. (17)-(19)?

The point is the following. Even though for each s there may exist a particular (s-dependent) Lorentz frame with respect to which the force between two particles is instantaneous, such a Lorentz frame is by no means special or ``preferred''. Instead, such a particular Lorentz frame is determined by covariant equations of motion supplemented by a particular choice of initial conditions X_a^{\mu}(0).

See also this thread:
https://www.physicsforums.com/showthread.php?t=354083
especially posts #1 and #109.

If you still have questions, I will be happy to answer them.

Thanks, I'll read those posts and get back to you ASAP.

Edit: I have read the posts, and reread the relevant sections of your paper, and I have comments and questions - but they will have to wait until (hopefully) tomorrow, on account of it being very late at night here in New York.

 

[SpectraCat]

Thank you very much for the recommendations! I will buy Holland, and I will look at some of the review papers on Towler's list.

 

[Demystifier]

Thank you very much for the recommendations! I will buy Holland, and I will look at some of the review papers on Towler's list.

That's a good strategy IMHO.

 

[yoda jedi]

Seems interesting.

I will talk about making Bohmian nonlocal particle mechanics compatible with relativity

http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.0177v1.pdf

 

[yoda jedi]

I've read the first paper before, and I liked it very much. But I still don't understand how you've managed to get around the need for a preferred frame or spacetime foliation.

it does not

http://arxiv.org/PS_cache/quant-ph/pdf/0607/0607124v1.pdf

Since the existence of a time foliation would be against the spirit of relativity, several attempts have been undertaken at obtaining a relativistic Bohm-like theory without a time foliation. I briefly describe four such proposals in this subsection, items (i)–(iv) below. However, (i)–(iii) are not satisfactory theories, and (i) and (iv) both involve some foliation-like structure, something just as much against the spirit of relativity as a time foliation.

(i) Synchronized trajectories [11, 21, 56]. Define a path s 7→ X(s) in (space-time)N as the integral curve of a vector field jψ on (space-time)N, with jψ a suitably defined current vector field obtained from a wave function ψ on (space-time)N. The path
X(s) =(X1(s), . . . ,XN(s)) defines N paths in space-time, parametrized by a joint parameter s, which are supposed to be the particle world lines. This approach is based on a naive replacement of space with space-time. Apparently, it does not possesses any equivariant measure, and thus does not predict any probabilities.
Moreover, it does introduce a foliation-like structure: The joint parametrization defines a synchronization between different world lines, as it defines which point on one world line is simultaneous to a given (spacelike separated) point on a second world line. Indeed, the synchronization is encoded in the world lines since, if N non-synchronous points X1(s1), . . . ,XN(sN) on the N world lines are chosen, then the integral curve s → Y (s) of jψ starting from Y (0) =(X1(s1), . . . ,XN(sN)) will generically lead to different world lines than X.

11.-Berndl, K., Durr, D., Goldstein, S., Zangh`ı, N.: Nonlocality, Lorentz invariance, and Bohmian quantum theory. Phys. Rev.A 53: 2062–2073(1996).
21.-Dewdney, C., Horton, G.: A Non-Local, Lorentz-Invariant, Hidden-Variable Interpretation of Relativistic Quantum Mechanics Based on Particle Trajectories. J. Phys. A: Math. Gen. 34: 9871–9878 (2001).
56.-Nikolic, H.: Relativistic Quantum Mechanics and the Bohmian Interpretation. Foundations of Physics Letters 18: 549–561 (2005).










Foliation independent:

http://arxiv.org/PS_cache/quant-ph/pdf/0607/0607124v1.pdf

The GRW theory can be made relativistic, without a time foliation or any similar structure, when using the flash ontology [72] [74].


The foliation independence of the model can be expressed in the following way: With every spacelike 3-surface epsilon in the future of epsilon ₀ there is associated a wave function ψ _epsilon on epsilon^N , the conditional wave function, which depends on all flashes between epsilon₀ and epsilon, as well as on the seed flashes before epsilon₀ and, of course, on the initial wave function. (Indeed,the conditional wave function collapses at every flash.)


.-72 Tumulka, R.: A Relativistic Version of the Ghirardi–Rimini–Weber Model. To appear in J. Statist. Phys. (2006).
.-74 Tumulka, R.: Collapse and Relativity.On the Present Status of Quantum Mechanics, AIP Conference Proceedings 844, 340–352. American Institute of Physics (2006).

 

[SimonA]

Maaneli

You clearly have a strong grasp of the pilot wave theory, can you explain your understanding to a waitress? I'm concerned about time in the quantum world, not gravity. Gravity in quantum terms, if you forget the standard model that will be proven accurate but hugely misinterpreted eventually, can be easily described in quantum-relavatistic terms that are equivalent to recent experiments where blobs of oil find their way around a maze. Mass creates a potential difference in the background fabric. The mechanism is beyond current theories, but it's most certainly not any Higgs particle that imparts mass to itself. Until we accept that the background fabric is more than minowski spacetime, and that our post-enlightenment view is a barrier in terms of understanding that our physics is looking at a holographic plate from the perspective of both the surface image and the projected image, we will hide under Bohr's clever arguments. We need to connect the holographic principle with non locality in QM. We need to really understand the inside out view we have of reality where relativity says that there is no such thing as time for photons and electrons.

We think of relativity as the enemy of QM. In reality, Einstein gave us a theory that was ahead of it's time.

 

[Frame Dragger]

Maaneli

You clearly have a strong grasp of the pilot wave theory, can you explain your understanding to a waitress? I'm concerned about time in the quantum world, not gravity. Gravity in quantum terms, if you forget the standard model that will be proven accurate but hugely misinterpreted eventually, can be easily described in quantum-relavatistic terms that are equivalent to recent experiments where blobs of oil find their way around a maze. Mass creates a potential difference in the background fabric. The mechanism is beyond current theories, but it's most certainly not any Higgs particle that imparts mass to itself. Until we accept that the background fabric is more than minowski spacetime, and that our post-enlightenment view is a barrier in terms of understanding that our physics is looking at a holographic plate from the perspective of both the surface image and the projected image. We need to connect the holographic principle with non locality in QM. We need to really understand the inside out view we have of reality where relativity says that there is no such thing as time for photons and electrons.

We think of relativity as the enemy of QM. In reality, Einstein gave us a theory that was ahead of it's time.

All fine notions, if true, but science does not embrace the assumption first and then seek to disprove. The process may be slow, and further retarded by the near-impossiblity of testing some notions (The Holographic Principle is fascinating, but there is NOTHING to show it's true yet). There is a difference between the physics and the metaphysics, and it's just that fine line (clear and bright though it is) that has had Insturmentalism and TCI as the primary working notions in QM. They work. It's implicit in many such interpretations that the reality they describe is not a perfect or absolute description, but the work is done in the math, and for that steps must be taken in sequence. If you want breakthroughs in unifying posits, conjectures and notions... the breakthrough is going to emerge from experimental evidence or a mathematical/computing breakthrough.

Barring that, this is a field of incrementalism because it works.

EDIT: Other than the unecessary comment about female waitstaff being less than crisp, why should a coherent theory of QM or SR/GR or what supercedes them be explicable to a layperson at all? I'm fairly sure that THP is beyond the average career waiter/waitress unless you use shadow-on-landscape analogies and leave it at that.

 

[Maaneli]

it does not

http://arxiv.org/PS_cache/quant-ph/pdf/0607/0607124v1.pdf

Since the existence of a time foliation would be against the spirit of relativity, several attempts have been undertaken at obtaining a relativistic Bohm-like theory without a time foliation. I briefly describe four such proposals in this subsection, items (i)–(iv) below. However, (i)–(iii) are not satisfactory theories, and (i) and (iv) both involve some foliation-like structure, something just as much against the spirit of relativity as a time foliation.

(i) Synchronized trajectories [11, 21, 56]. Define a path s 7→ X(s) in (space-time)N as the integral curve of a vector field jψ on (space-time)N, with jψ a suitably defined current vector field obtained from a wave function ψ on (space-time)N. The path
X(s) =(X1(s), . . . ,XN(s)) defines N paths in space-time, parametrized by a joint parameter s, which are supposed to be the particle world lines. This approach is based on a naive replacement of space with space-time. Apparently, it does not possesses any equivariant measure, and thus does not predict any probabilities.
Moreover, it does introduce a foliation-like structure: The joint parametrization defines a synchronization between different world lines, as it defines which point on one world line is simultaneous to a given (spacelike separated) point on a second world line. Indeed, the synchronization is encoded in the world lines since, if N non-synchronous points X1(s1), . . . ,XN(sN) on the N world lines are chosen, then the integral curve s → Y (s) of jψ starting from Y (0) =(X1(s1), . . . ,XN(sN)) will generically lead to different world lines than X.

11.-Berndl, K., Durr, D., Goldstein, S., Zangh`ı, N.: Nonlocality, Lorentz invariance, and Bohmian quantum theory. Phys. Rev.A 53: 2062–2073(1996).
21.-Dewdney, C., Horton, G.: A Non-Local, Lorentz-Invariant, Hidden-Variable Interpretation of Relativistic Quantum Mechanics Based on Particle Trajectories. J. Phys. A: Math. Gen. 34: 9871–9878 (2001).
56.-Nikolic, H.: Relativistic Quantum Mechanics and the Bohmian Interpretation. Foundations of Physics Letters 18: 549–561 (2005).

Good timing, I was just about to cite this paper and this exact section, as this synchronized trajectories approach to Bohm-Dirac theory is exactly what Demystifier proposes in equations (17)-(19) in his paper.

So, Demystifier, you asked if I see the need for a preferred foliation in equations (17)-(19), and my answer would be yes, because of the reasoning given above by Tumulka.

Another problematic issue for the synchronized trajectories approach seems to be the statement that it "apparently does not possesses an equivariant measure". I'm sure Demystifier will disagree with that, so perhaps it's best to go straight to the argument given in the 1996 Berndl et. al paper, for why this is so:

-Berndl, K., Durr, D., Goldstein, S., Zangh`ı, N.: Nonlocality, Lorentz invariance, and Bohmian quantum theory. Phys. Rev.A 53: 2062–2073(1996).
http://arxiv.org/abs/quant-ph/9510027

They argue (see section 4) that the reparameterization invariant Dirac current velocity (see equation 32), is not Lorentz invariant because it is not of the form J_k/rho for more than one particle. Thus, equivariance does not hold in any obvious way for a multi-particle, multi-time Bohm-Dirac theory.

On the other hand, Demystifier seems to suggest that equivariance does hold by writing the multi-time, multi-particle Dirac wavefunction in polar form, assuming that the polar decomposition of the N-particle multi-time Dirac equation goes through, and then looking at the relativistic continuity equation for the multi-time, multi-particle Dirac four-current (which seems to imply equivariance). It is unclear to me which argument is correct, and hopefully Demystifier will address Berndl et. al's point.

 

[Maaneli]

Maaneli

You clearly have a strong grasp of the pilot wave theory, can you explain your understanding to a waitress? I'm concerned about time in the quantum world, not gravity. Gravity in quantum terms, if you forget the standard model that will be proven accurate but hugely misinterpreted eventually, can be easily described in quantum-relavatistic terms that are equivalent to recent experiments where blobs of oil find their way around a maze. Mass creates a potential difference in the background fabric. The mechanism is beyond current theories, but it's most certainly not any Higgs particle that imparts mass to itself. Until we accept that the background fabric is more than minowski spacetime, and that our post-enlightenment view is a barrier in terms of understanding that our physics is looking at a holographic plate from the perspective of both the surface image and the projected image, we will hide under Bohr's clever arguments. We need to connect the holographic principle with non locality in QM. We need to really understand the inside out view we have of reality where relativity says that there is no such thing as time for photons and electrons.

We think of relativity as the enemy of QM. In reality, Einstein gave us a theory that was ahead of it's time.

Not sure why I was singled out, but I basically agree with Frame Dragger's response to your waitress question.

 

[Demystifier]

Yoda jedi and Maaneli,

The question of equivariant probability density is indeed the crucial question. My answer to this question is better explained in my second paper
http://xxx.lanl.gov/abs/0904.2287 [to appear in Int. J. Mod. Phys. A]
Appendix B.
The point is the following. There is no equivariance in the sense of Eq. (127). However, there IS equivariance in the sense of Eq. (125).
Berndl et al consider only the equivariance of the form of (127) [actually generalized to the case of many particles] and do not consider the equivariance of the form of (125) [which can also be generalized to the case of many particles]. Therefore, their conclusion that there is no equivariance has only a partial validity. The crucial difference between (127) and (125) is that the latter treats time and space on an equal footing (which is very relativistic in spirit), while the former does not treat time and space on an equal footing.

To conclude, my claim is that time should be treated on an equal footing with space, and that this, among other things, solves the problem of equivariance.

 

[Demystifier]

i
Moreover, it does introduce a foliation-like structure:

Yes, but it does not introduce a PREFERRED foliation-like structure. Instead, such a structure is determined dynamically, through the choice of initial conditions.

It is analogous to the fact that a planet also defines a particular Lorentz frames (the one with respect to which it is at rest), but it does not mean that classical laws of physics describing the motion of the planet are not relativistic covariant.

 

[Demystifier]

On the other hand, Demystifier seems to suggest that equivariance does hold by writing the multi-time, multi-particle Dirac wavefunction in polar form, assuming that the polar decomposition of the N-particle multi-time Dirac equation goes through, and then looking at the relativistic continuity equation for the multi-time, multi-particle Dirac four-current (which seems to imply equivariance).

That's not what I suggest at all. I do not use the Dirac current. Not even for spin-1/2 particles. (See Sec. 3.4 and Appendix A of the second paper.)

 

[Maaneli]

That's not what I suggest at all. I do not use the Dirac current. Not even for spin-1/2 particles. (See Sec. 3.4 and Appendix A of the second paper.)

I think that may be a semantic misunderstanding, because all I meant is that you use a four-current whose divergence is equal to zero, namely, the relativistic continuity equation obtained from the Dirac equation under polar decomposition (equation 17 of the first paper).

 

[Maaneli]

Yes, but it does not introduce a PREFERRED foliation-like structure. Instead, such a structure is determined dynamically, through the choice of initial conditions.

It is analogous to the fact that a planet also defines a particular Lorentz frames (the one with respect to which it is at rest), but it does not mean that classical laws of physics describing the motion of the planet are not relativistic covariant.

But aren't you introducing an absolute simultaneity surface (a hypersurface across which all the particle positions are simultaneously defined, even at spacelike separations), by virtue of the fact that you have to synchronize the initial positions of the particles at a common time s, and that this synchronization has to hold for all future s, even when they are spacelike separated? And isn't that simultaneity surface unique?

Also, the issue (in my view at least) is not whether the equations of motion are relativistically covariant, but whether the spacetime structure introduced is consistent with "fundamental Lorentz invariance" (which I take to mean the constraints on dynamics imposed by the causal structure of Minkowski spacetime). And a simultaneity surface that introduces spacelike causal influences does not seem to me to be consistent with fundamental Lorentz invariance in that sense.

Also, when considering the possibility of nonequilibrium particle distributions in the multi-time Bohm-Dirac theory (assuming also for the moment that such a theory is in fact equivariant), I don't see anything in the synchronized trajectories approach that stops it from allowing superluminal signaling, as Valentini has demonstrated is possible with nonequilibrium particle distributions; and superluminal signaling is the most explicit violation of fundamental Lorentz invariance that I can possibly think of.

 

[Demystifier]

I think that may be a semantic misunderstanding, because all I meant is that you use a four-current whose divergence is equal to zero, namely, the relativistic continuity equation obtained from the Dirac equation under polar decomposition (equation 17 of the first paper).

The semantic misunderstanding must be more than that, because in that paper I do not use Dirac equation, but Klein-Gordon equation.

Besides, not also that, even though I use a four-current whose divergence is equal to zero, that's not exactly the content of Eq. (17). Instead, Eq. (17) is a combination of TWO facts, one that the divergence of the four-current is zero, and the other that psi does not depend on s. In other words, the left-hand side of (3) contains two zeros, i.e., (3) is a consequence of the trivial fact that 0+0=0.

Anyway, that's not essential. The essential stuff is presented in post #64.

 

[Maaneli]

The semantic misunderstanding must be more than that, because in that paper I do not use Dirac equation, but Klein-Gordon equation.

Crap, you're right! I must have confused the equations in your paper with those of Berndl and co.. My mistake.