Where does non-locality originate in dBB theory?

[inflector]

(1) Sheldon Goldstein's crew believe that the initial conditions of the universe were such that, because our universe is 'typical', the particles were distributed as \Psi^2 right from the Big Bang. They aggressively promote the view that anyone who believes otherwise is an idiot.

Not that anyone cares about my opinion, but this seems self-evidently to be a crock of male bovine excrement.

Unless you can establish that the dynamics tend towards an equilibrium of \rho=|\Psi|^2 then the theory rests on shaky ground. That's the whole reason, I never liked the \rho=|\Psi|^2 distribution having to be specified as a postulate.

Who knows what the initial conditions were?

Besides, anytime I see an aggressive promotion that "anyone who believes otherwise is an idiot," on any subject, I have found that this generally indicates a lack of confidence and is often a substitute for intelligence and insight.

 

[zenith8]

Not that anyone cares about my opinion, but this seems self-evidently to be a crock of male bovine excrement.

Unless you can establish that the dynamics tend towards an equilibrium of \rho=|\Psi|^2 then the theory rests on shaky ground. That's the whole reason, I never liked the \rho=|\Psi|^2 distribution having to be specified as a postulate.

Who knows what the initial conditions were?

Besides, anytime I see an aggressive promotion that "anyone who believes otherwise is an idiot," on any subject, I have found that this generally indicates a lack of confidence and is often a substitute for intelligence and insight.

Well, quite..

 

[zonde]

If the electron density distribution is not equal to the square of the wave field, and the system is evolving according to the laws of QM, then it will become so distributed over the course of time. Once so distributed, it will stay like that for ever. Psi^2 is the only distribution with this property.

This is fine when you consider electrons. This is not fine if you consider photons.
Electrons are not moving at c and they can get feedback from environment and as a consequence undergo rapid decoherence. Photons on the other hand move at c.

There is even something from experiments that as I see directly contradicts with such picture for photons. Would you care to go into analysis of HOM effect?

 

[Demystifier]

There are two 'schools of thought' on this in the deBB community.

(1) Sheldon Goldstein's crew believe that the initial conditions of the universe were such that, because our universe is 'typical', the particles were distributed as \Psi^2 right from the Big Bang. They aggressively promote the view that anyone who believes otherwise is an idiot.

(2) Almost everyone else (including, for what it's worth, me) believes that one should show that \rho=\Psi^2 arises dynamically, irrespective of the initial conditions. This is what Valentini, Westman, Towler et al. appear to have done.

To me it's completely obvious that the second view is the correct one - assumptions about initial conditions can always be wrong.

You seem to be mixing up these two diametrically opposed point of view.

I agree that the Valentini et al camp uses a much nicer way of promoting their views than the Goldstein et al camp. Yet, I think that each of the approaches has certain advantages over the other. For example, in the relativistic-covariant Bohmian mechanics I am promoting, the Goldstein et al approach seems to work much better.

 

[DevilsAvocado]

Who knows what the initial conditions were?

Cosmologists.

See http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe" for more info.

 

[zenith8]

Cosmologists.
See http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe" for more info.

Quite right. Which is why Valentini et al. are looking for deviations in the CMB which are a signature of quantum nonequilibrium predicted by de Broglie-Bohm theory (this will probably have to wait for the higher accuracy results of Planck in 2012 or whenever).

See his talk at "http://www.vallico.net/tti/deBB_10/conference.html" " entitled "In search of a breakdown in quantum theory" for the details.

 

[DevilsAvocado]

Quite right. Which is why Valentini et al. are looking for deviations in the CMB which are a signature of quantum nonequilibrium predicted by de Broglie-Bohm theory (this will probably have to wait for the higher accuracy results of Planck in 2012 or whenever).

See his talk at "http://www.vallico.net/tti/deBB_10/conference.html" " entitled "In search of a breakdown in quantum theory" for the details.

Cool. I must read faster... information over-load right now... hopefully I’ll be back in a couple of days with some comments worth reading...

 

[inflector]

Cosmologists.

See http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe" for more info.

Well since we are currently lacking a coherent theory of quantum gravity, even cosmologists are guessing and back-extrapolating from when the universe was about 487,000 years old.

 

[inflector]

Iin the relativistic-covariant Bohmian mechanics I am promoting, the Goldstein et al approach seems to work much better.

Interesting. Can you explain what about the Goldstein approach makes it work better with your relativistic- covariant Bohmian mechanics?

 

[DevilsAvocado]

Well since we are currently lacking a coherent theory of quantum gravity, even cosmologists are guessing and back-extrapolating from when the universe was about 487,000 years old.

Well, the cosmologists are not the only ones 'guessing', right? At least they have 'some' data!

 

[nismaratwork]

Quite right. Which is why Valentini et al. are looking for deviations in the CMB which are a signature of quantum nonequilibrium predicted by de Broglie-Bohm theory (this will probably have to wait for the higher accuracy results of Planck in 2012 or whenever).

See his talk at "http://www.vallico.net/tti/deBB_10/conference.html" " entitled "In search of a breakdown in quantum theory" for the details.

Would the absence of those artifacts at the proper resolution falsify dBB?

 

[Maaneli]

Would the absence of those artifacts at the proper resolution falsify dBB?

There is no "proper" resolution. The absence of nonequilibrium signatures at a particular length and time scale would only put constraints on the possibility of nonequilibrium. DeBB theory, as it currently stands, does not require that nonequilibrium states should have existed in the early universe, only that they are possible states of the early universe.

However, it's worth mentioning that Valentini himself would find the deBB theory scientifically implausible if, after a 1,000 years of searching the universe, no evidence of quantum nonequilibrium were ever found.

 

[Maaneli]

Interesting. Can you explain what about the Goldstein approach makes it work better with your relativistic- covariant Bohmian mechanics?

Yes, Hrvoje, I'm also curious to know how the Typicality approach helps your covariant theory more than dynamical relaxation does.

 

[Demystifier]

Yes, Hrvoje, I'm also curious to know how the Typicality approach helps your covariant theory more than dynamical relaxation does.

It's actually very simple. In nonrelativistic BM, relaxation does not work for a stationary wave function which does not depend on t. Likewise, in relativistic BM with spacetime probabilistic interpretation, relaxation does not work for a wave function which does not depend on s. And of course, the relativistic wave function (in my approach) never depends on s.

 

[Maaneli]

It's actually very simple. In nonrelativistic BM, relaxation does not work for a stationary wave function which does not depend on t. Likewise, in relativistic BM with spacetime probabilistic interpretation, relaxation does not work for a wave function which does not depend on s. And of course, the relativistic wave function (in my approach) never depends on s.

I see your point, but then there seems to me a contradiction in your relativistic theory, since, in the NR limit of your theory, you get back the usual nonrelativistic deBB wavefunction where psi dynamically evolves with respect to the single time t. So it's as if in the relativistic case of your theory, you won't get dynamical relaxation, while in the nonrelativistic case, you would expect to get dynamical relaxation (with respect to t). That would suggest to me that one just has to think harder about how dynamical relaxation can occur in the relativistic case of your theory.

 

[zenith8]

That would suggest to me that one just has to think harder about how dynamical relaxation can occur in the relativistic case of your theory.

What about Holland's result that, if you consider the non-relativistic spin 1/2 theory as the limiting case of the relativistic Dirac theory, then this fixes the guidance equation uniquely (recalling there is a 'gauge freedom' in the standard one) and that this unique equation has a 'spin term' in addition to the gradient of the phase? With such a guidance equation, the electrons are no longer at rest in the stationary wave function case.

 

[Demystifier]

That would suggest to me that one just has to think harder about how dynamical relaxation can occur in the relativistic case of your theory.

I agree. And I would be very happy if I were not the only guy who is actually doing it (thinks hard about that).

 

[Demystifier]

What about Holland's result that, if you consider the non-relativistic spin 1/2 theory as the limiting case of the relativistic Dirac theory, then this fixes the guidance equation uniquely (recalling there is a 'gauge freedom' in the standard one) and that this unique equation has a 'spin term' in addition to the gradient of the phase? With such a guidance equation, the electrons are no longer at rest in the stationary wave function case.

The Holland's approach does not work for
1) particles with other spins (0, 1, ...)
2) systems of more than one entangled particles with spin 1/2

 

[zenith8]

The Holland's approach does not work for
1) particles with other spins (0, 1, ...)
2) systems of more than one entangled particles with spin 1/2

OK. Can you explain (2)?

 

[Demystifier]

OK. Can you explain (2)?

The Holland's paper
http://xxx.lanl.gov/abs/quant-ph/0305175
does not discuss the many-particle case at all.

A many-particle case (for spin 1/2) is studied in
http://xxx.lanl.gov/abs/quant-ph/9801070
where it was found necessary to introduce a preferred foliation of spacetime, which is certainly not unique.

The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s. But then, as I explained, the natural probabilistic interpretation does not seem compatible with the idea of dynamical relaxation towards the equilibrium. A typicality approach works much better.

 

[zenith8]

The Holland's paper
http://xxx.lanl.gov/abs/quant-ph/0305175
does not discuss the many-particle case at all.

A many-particle case (for spin 1/2) is studied in
http://xxx.lanl.gov/abs/quant-ph/9801070
where it was found necessary to introduce a preferred foliation of spacetime, which is certainly not unique.

The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s. But then, as I explained, the natural probabilistic interpretation does not seem compatible with the idea of dynamical relaxation towards the equilibrium. A typicality approach works much better.

For the many-particle case see section 10.5 of Bohm and Hiley's book or, for example, Timko and Vrscay's 'spin-dependent Bohmian electronic trajectories for helium' available at Found. Phys. 39, 1055 (2009) or on the usual web page.

Anyway, what's wrong with preferred foliations? Perfectly compatible with all known experimental results - it's just the neo-Lorentzian interpretation of relativity, no?

 

[Demystifier]

Anyway, what's wrong with preferred foliations? Perfectly compatible with all known experimental results - it's just the neo-Lorentzian interpretation of relativity, no?

Perhaps there is nothing wrong with it, but looks ugly. Too many possibilities are allowed, so how to know which foliation is the right one? In the absence of direct experimental evidence for a theory, simplicity and mathematical elegance should be the main guiding principles.

Besides, a preferred foliation is certainly not in the spirit of the Holland's approach that was first mentioned by you.

 

[Maaneli]

What about Holland's result that, if you consider the non-relativistic spin 1/2 theory as the limiting case of the relativistic Dirac theory, then this fixes the guidance equation uniquely (recalling there is a 'gauge freedom' in the standard one) and that this unique equation has a 'spin term' in addition to the gradient of the phase? With such a guidance equation, the electrons are no longer at rest in the stationary wave function case.

Btw, Holland wasn't the first to recognize this in the literature. Hestenes and Gurtler did way back in the 70's:

Consistency in the formulation of the Dirac, Pauli, and Schroedinger theories
Journal of Mathematical Physics, 16 573–584 (1975).
http://geocalc.clas.asu.edu/pdf/Consistency.pdf

Also, I independently derived this result as an undergrad, which suggests that it's been independently rediscovered by others countless times.

 

[Maaneli]

Perhaps there is nothing wrong with it, but looks ugly. Too many possibilities are allowed, so how to know which foliation is the right one? In the absence of direct experimental evidence for a theory, simplicity and mathematical elegance should be the main guiding principles.

But if you take the possibility of quantum nonequilibrium seriously, then there's nothing fundamentally problematic about that underdetermination of foliations - we just happen to be stuck in a special state (the quantum equilibrium state) that prevents us from observing the correct foliation.

 

[Maaneli]

The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s.

Though it isn't popular among deBB theorists, another logical possibility is to introduce retrocausation a la Sutherland's model:

Causally Symmetric Bohm Model
Rod Sutherland
http://arxiv.org/abs/quant-ph/0601095

 

[Demystifier]

But if you take the possibility of quantum nonequilibrium seriously, then there's nothing fundamentally problematic about that underdetermination of foliations - we just happen to be stuck in a special state (the quantum equilibrium state) that prevents us from observing the correct foliation.

I completely agree. Yet, it does not change the fact that the theory itself is ugly. It's hard to take seriously a theory that looks ugly, unless there is a direct experimental evidence supporting the theory.

For example, there are many alternatives to the classical Einstein theory of gravity, compatible with existing experimental data. Yet, the Einstein theory is the most popular. Why? Because neither of the alternatives is so elegant.

Another example is the Standard Model of elementary particles. It is in perfect agreement with all experiments. Yet, many physicists search for alternatives (GUTs, supersymmetries, strings, ...). Why? Because the Standard Model is terribly ugly.

 

[Maaneli]

I agree. And I would be very happy if I were not the only guy who is actually doing it (thinks hard about that).

Yeah, I'm thinking about it. One possibility I have in mind is to allow that a nonequilibrium version of your relativistic psi does initially depend on s, and then a stochastic Markov process dynamically relaxes the wavefunction to an equilibrium state with respect to s (much like in the Parisi-Wu approach to stochastic quantization). Then, it is only in this stochastic equilibrium state that your relativistic psi appears to be independent of s, and thus not allow for relativistic nonequilibrium states thereafter.

On the other hand, if you want to insist on deterministic dynamics, you might insist that your relativistic psi should always depend on s, in which case, your relativistic deBB theory becomes a deBB version of the Stueckelberg proper time formulation of relativistic QM.

 

[Demystifier]

Though it isn't popular among deBB theorists, another logical possibility is to introduce retrocausation, a la Sutherland's model:

Causally Symmetric Bohm Model
Rod Sutherland
http://arxiv.org/abs/quant-ph/0601095

Thanks, I didn't know about this. But it also seem to require a preferred frame [Eq. (60)].

 

[Demystifier]

Yeah, I'm thinking about it. One possibility I have in mind is to allow that a nonequilibrium version of your relativistic psi does initially depend on s, and then a stochastic Markov process dynamically relaxes the wavefunction to an equilibrium state with respect to s (much like in the Parisi-Wu approach to stochastic quantization). Then, it is only in this stochastic equilibrium state that your relativistic psi appears to be independent of s, and thus not allow for relativistic nonequilibrium states thereafter.

That seems interesting, but I don't like the idea that I must add a stochastic process by hand.

On the other hand, if you want to insist on deterministic dynamics, you might insist that your relativistic psi should always depend on s, in which case, your relativistic deBB theory becomes a deBB version of the Stueckelberg proper time formulation of relativistic QM.

Irrespective of dBB, the Stueckelberg equation does not seem to be in agreement with observations. In particular, we do not observe a continuous mass spectrum. (See however
http://xxx.lanl.gov/abs/0801.4471 )

 

[Maaneli]

I completely agree. Yet, it does not change the fact that the theory itself is ugly. It's hard to take seriously a theory that looks ugly, unless there is a direct experimental evidence supporting the theory.

For example, there are many alternatives to the classical Einstein theory of gravity, compatible with existing experimental data. Yet, the Einstein theory is the most popular. Why? Because neither of the alternatives is so elegant.

Another example is the Standard Model of elementary particles. It is in perfect agreement with all experiments. Yet, many physicists search for alternatives (GUTs, supersymmetries, strings, ...). Why? Because the Standard Model is terribly ugly.

I would agree that it is reasonable to take more seriously alternative models, if those alternative models can make all the same predictions as the standard theory, but with fewer and more physically plausible assumptions. However, I still think it's dubious to say that the standard deBB theory is hard to take seriously because it has this feature which seems "ugly" (or even fugly) to you.

In the 19th century, positivistic physicists like Mach criticized Boltzmann's statistical mechanics on similar grounds, saying for example that for molecules in thermal equilibrium, one could double the number of particles composing a gas, but halve their volume and masses (or something like that), and make all the same predictions. Of course, we now know that Mach's criticism is wrong because we understand (and can empirically observe) that equilibrium dynamics masks important microscopic details of particle dynamics, and that equilibrium dynamics is only a special case of a more general nonequilibrium dynamics. So even though Boltzmann's statistical mechanics has this feature which would probably seem ugly to you if you were living in that time, we can see that nature can still conform to such ugly features.