Why Explore the Bohmian Interpretation of Quantum Mechanics?

[Demystifier]

But I tihnk for bohmian notion to get more attention the approache needs to take things further and solve things the ortodox approach doesn't.

This is exactly what in
http://arxiv.org/abs/quant-ph/0406173
is done.

 

[Fra]

Hmmm... I wonder about these philosophical discussions, I suspect nonone gets any wiser at any side LOL Mentz I don't follow your conclusion. "Objective reality" is barley in my dictionary. I am not a bohmist, and not even close, but I was showing some sympathy to Demystifier for the lack of feedback. OTOH, You're certainly free to make your customer interpretations of my statements :) but your feedback on my feedback sort of doesn't add up in my head :)

/Fredrik

 

[Mentz114]

Fra, re-reading your post #49, I admit my response was off-target. As you say, you're not guilty of ascribing 'object reality' to anything.

 

[Cane_Toad]

In my humble opinion, Fra, you are ascribing reality to mathematical ideas. There's no complex phase, no wave function, no phase space. They do not have any objective reality so analysing them in detail will take you further from reality, not closer.

I can't be sure, but I think I might beg to differ with this

So much of observable QM phenomona can only be understood in mathematical terms, i.e. wave-particle duality, that I'm on the way to believing that the reality might be the mathematics (which mathematics is debatable).

This doesn't preclude an objective reality, though, just one that has a function oriented substructure.

 

[Mentz114]

So much of observable QM phenomona can only be understood in mathematical terms, i.e. wave-particle duality, that I'm on the way to believing that the reality might be the mathematics (which mathematics is debatable).

I'm sure you'll never fall into that trap. Look what happens to forces when we go from Newtonian dynamics to GR. GR is a fine theory which makes many correct predictions, but it is not a complete description of reality.. ditto QM.

Maybe when/if there is a complete theory, the mathematics will be the reality. Than again, maybe pigs can fly.

 

[Fra]

This is exactly what in
http://arxiv.org/abs/quant-ph/0406173
is done.

I agree that some of QM contains a lot of logical issues that is ignored and motivated by "it still works", and I do not believe the fundamental formulation of QM ends with plugging the p -> -i\hbar\frac{\partial}{\partial q} into the equations of classical mechanics.

Are there some bohmian programs to grand unification? I think that's what we need.

I've dropped the semiclassical manipulations for myself, and I decided to start from scratch.

I think we need a mechanism that links the apparent non-unitary evolution as a dynamic driver of expansion/modification of configuration space. Static event spaces is too restrictive. Also assuming a crapload of unobservable dimensions that we need to hide when not needed is also very ad hoc and also unnecessarily complex. I think the solution is that the missing part is a dynamics of hte eventspaces themselves.

Non-unitary observations doesn't mean the world collapses, rather in any general learning model non-unitary behaviour is natural. The question is, what is the dynamic model response to non-unitary evidence? I think zero probability does not mean it will never happen, it means it never _happened_. But what about when it happens for the first time? I expect a model that can handle that and let data take charge. I am not suggesting a model that allows everything arbitrary, but I an suggesting a model that should be very careful to forbid things. It should however provide probabilities for things, but the probabilities are only inferences based on a relative, and in practice always incomplete data.

/Fredrik

 

[Demystifier]

Are there some bohmian programs to grand unification?

Not really. Although, some results indicate that consistency of the Bohmian interpretation with particle creation and destruction requires particles to be extended objects, that is - strings. Other independent results indicate that if we assume strings, then Bohmian mechanics emerges rather naturally, more naturally than in the case of pointlike particles.

 

[Fra]

Not really. Although, some results indicate that consistency of the Bohmian interpretation with particle creation and destruction requires particles to be extended objects, that is - strings. Other independent results indicate that if we assume strings, then Bohmian mechanics emerges rather naturally, more naturally than in the case of pointlike particles.

I've always considered string theory to smell a lot like a hidden variable approach, so while I don't know the details of your conjecture, or have any specific opinion on it, it would not surprise me.

As for extended objects, I can see that logic emerging out of non-unitary observations but I'd expect think the non-unitary observations should infere the nature of these extension, not the other way around. From my past thinking of this I think the particle -> string -> branes, has some similarities to a constrainted generic quantization procedure. If you consider the probability of a particle, you get a field defined over the configuration space. A space field can maybe be thought of as an (infinitely, or at least covering the event space) extended n-brane (n-beeing configuration space dimension), and an evolving field might be an evolving n-brane. But IMO I would interpret such a "n-brane" as representing information rather than physical matter, which OTOH doesn't bother me one bit, because what the heck is the difference :) I think information doesn't just refer to human brains, even a particle has to inform itself about the world. So for most practical purposes I'd equal information structure with physical structure, with the difference that the former notion renders some things that lack sensible interpretation in a mechanistic interpretation. But I guess that's where we disagree. But of course, the future may show what approach is more efficient.

I do not rule out string (or more likely membrane like) structures appearing, but if they do they will evolve into such in response to data, there should not need to put them in manually.

Until I have an answer myself I leave anyone the benefit of doubt, and even though I have my own preferences there are elements of other approaches I can appreciate too.

/Fredrik

 

[Demystifier]

I've always considered string theory to smell a lot like a hidden variable approach

I am glad that you also think so. Unfortunately, I cannot convince the traditional string theorists that it is so.

 

[Demystifier]

Why Bohm? In my opinion, that's why:
http://xxx.lanl.gov/abs/0705.3542
As a byproduct, it also answers the question "Why strings?".

 

[Fra]

I only quickly skimmed it. (Some quick comments better than none I hope) I think many approaches share similarities, therefore it gets a bit ambigous to decide from what reference to make comments... you are somehow comparing your bohmian ideas with strings... my reference is neither of those... so freely interpret my comments

1) I share some of your taken issues with the standard theories of QFT regadring unitarity etc.

2) Second, needles to say, I never liked string theory, but if I was forced to defend it's foundations, smearing of particles into extended "objects" is a reasonable way to preserve unitarity, which is sort of what the quantization procedures do in the first place - so it's not unique to strings. One can consider "excitations" of expectations, which is very intuitive.

Doesn't sound that bad to start with. However I've sense a few problems with this approach. One is that smearing stuff on a general basis leads to a lot of new degress of freedom, also what stops us from smearing the string into a membrane and apply induction we soon get "inf-branes"? We quickly get infinitely many degrees of freedom and which one do we pick? and howto get rid of the freedom we don't need in an non-ambigous manner? I think this scientific method (unless adding something more!) is divergent. Each attempt to resolve a problem leads to not only a solution, but several ones. So the method is divergent. these are hunches, I'm not into prooving it, but I think it can be done. It's just not anything I give priority to.

The solution I favour is that the transformation of dimensionality should be done dynamically. Not on the theorists desktop. We need to understand how this works in reality.

I think I am trying to solve the same things like you, but we have different philosophies on howto do it.

In the information theoretic approach I work on, non-conservation of "probabilities" isn't really weird when you realize that probabilities are just expectations on expectations. Violation of probabilities means our expectations were off, which is a non-trivial interaction, but so what? it happens in my brain every day, and there is a response to it! But this thinking is I suspect highly non-pleasing to bohmians.

The question is if one method can be expected to more successful than the other? A method that leads to more solutions that you want, seems to evaporate away the problem but offer no preferred solution? :)

/Fredrik

 

[Fra]

At any rate I appreciate your philosophical (though I'm another flavour) attitude :)

/Fredrik

 

[Fra]

Reminds me an embarrasing story when there has been weird unknown stain on a plastic surface beloning to a customer and ethanol wouldn't dissolve it. And a brilliant colleague come up with the ultmate solvent that he guaranteed would remove the stain.

The stain went away alright, but so did a few other things

/Fredrik

 

[jambaugh]

Why Bohm? In my opinion, that's why:
http://xxx.lanl.gov/abs/0705.3542
As a byproduct, it also answers the question "Why strings?".

I've deleted my earlier post as I did not "skim" the article quite thoroughly enough. More later...
Regards,
JB
... time passes...

OK, I've read through the article more thoroughly. I see it as an apology for the Bhomian "interpretation" without addressing the lack of operational interpretation for the Bhomian pilot wave/string objects.

Point 1: The author argues that since in QFT and Relativistic QM, position is reduced to a parametric status instead of being an observable he fails to realize that this still gives a perfectly meaningful interpretation to the wave function \psi(x,t).
It is still interpreted as the probability amplitude of observing the particle at position x and time t. (Or limiting amplitude as you rescale and consider space-time interval centered at x and t). This does not promote x to observable status if you carefully understand the distinction between the boolean observable P_x which indicates "1=Yes the particle is at x and no it is not at x+c or 0-No the particle is not at x and yes it is elsewhere" vs the actual observable X in non-rel. QM. The status of x in relativistic QM and QFT is no different than the status of the Euler angles (which are not observables) as parameters indicating the orientation of the momentum measuring devises (momentum being an observable!).

Point 2: The author (as do many other Bohmian apologists) describes the fact that Bohmian interpretation avoids the "problem" of wave-function collapse, said problem only being a problem when one is in fact investing the wave functions with ontological meaning, e.g. a Bohmian interpretation. In short the virtue of the Bohmian interpetation is that it is consistent with the Bohmian interpetation.

Point 3: The author (as do most other Bohmian apologists) accepts glibly the trans-luminal nature of these causally deterministic effects which by virtue of SR undermine their very objective nature. If a future "pilot wave" can propagate back in time and revise the reality of the past then how can we say a past "state" has any objective meaning?

Point 4: There are many straw-men in his paper which have been well dissected. The non-positivity of the time component (for a given inertial frame) of the Klein-Gordon currernt j_\mu is no different from the non-positivity of a possible classical relativistic velocity vector u_\mu. It corresponds to either a non-physical system in the direct interpretation or a possible extension it distinguishes a "negative energy" or equivalently "anti-partner" to the usual particle. The choice depends on the operational implementation of the experimental devices associated with the observables. E.g. can said device distinguish particle fluxes through a surface from anti-particle fluxes in the opposite spatial direction. Projecting out non-physical modes e.g. "ghosts" is no different from classically restricting 4-velocities to time-like unit 4-vectors. The other e.g. space-like elements of the vector space are understood as representing components only i.e. differences in velocities and not properly physical velocities themselves.

Point 5: It is not clear to me exactly what his distinct predictions are. I'll have to hunt down copies of the references to fully understand it. (Or at least spend a great deal of time parsing and reconstructing). I'm not inclined to put that much effort into it.

If he indeed has a predictable deviation from standard interpretation then I'll be quite happy to see it experimentally tested. But I'm still not clear on how he is dealing with gauge conditions and thus whether:

...the particle cannot be found at some positions at which the wave-function does not vanish.

is a physically meaningful distinction or just an incorrect understanding of the interpretation of the wave-function in the relativistic case. It is a question of whether one can integrate a non-zero probability over a region and not just point values. I'll have to study this some more.

I see his arguments as stemming from issues he thinks need resolution because they are problems stemming from (i.m.n.s.h.o incorrect) insistence on an ontological interpretation. The arguments simply show that the Bhomian interpretation is not self-inconsistent and doesn't per se argue it is necessary from any context outside its presumption. In short I believe it is a cyclic argument.

Regards,
J. Baugh

 

[jostpuur]

I have now got rid of my spring courses, and can use the summer to study things on my own pace. Can you recommend some sources on the internet for studying the idea of Bohmian mechanics? I mean, not a debate, but an introduction.

(btw. I found http://arxiv.org/abs/quant-ph/0408113 right away, but any recommendations appreciated anyway)

 

[Demystifier]

I have now got rid of my spring courses, and can use the summer to study things on my own pace. Can you recommend some sources on the internet for studying the idea of Bohmian mechanics? I mean, not a debate, but an introduction.

(btw. I found http://arxiv.org/abs/quant-ph/0408113 right away, but any recommendations appreciated anyway)

Sorry for not being able to answer earlier. Thank you also for your interest and comments. The introduction above is a good one, see also the references therein.

 

[Demystifier]

I
Point 1: The author argues that since in QFT and Relativistic QM, position is reduced to a parametric status instead of being an observable he fails to realize that this still gives a perfectly meaningful interpretation to the wave function \psi(x,t).
It is still interpreted as the probability amplitude of observing the particle at position x and time t. (Or limiting amplitude as you rescale and consider space-time interval centered at x and t). This does not promote x to observable status if you carefully understand the distinction between the boolean observable P_x which indicates "1=Yes the particle is at x and no it is not at x+c or 0-No the particle is not at x and yes it is elsewhere" vs the actual observable X in non-rel. QM. The status of x in relativistic QM and QFT is no different than the status of the Euler angles (which are not observables) as parameters indicating the orientation of the momentum measuring devises (momentum being an observable!).

Point 2: The author (as do many other Bohmian apologists) describes the fact that Bohmian interpretation avoids the "problem" of wave-function collapse, said problem only being a problem when one is in fact investing the wave functions with ontological meaning, e.g. a Bohmian interpretation. In short the virtue of the Bohmian interpetation is that it is consistent with the Bohmian interpetation.

Point 3: The author (as do most other Bohmian apologists) accepts glibly the trans-luminal nature of these causally deterministic effects which by virtue of SR undermine their very objective nature. If a future "pilot wave" can propagate back in time and revise the reality of the past then how can we say a past "state" has any objective meaning?

Point 4: There are many straw-men in his paper which have been well dissected. The non-positivity of the time component (for a given inertial frame) of the Klein-Gordon currernt j_\mu is no different from the non-positivity of a possible classical relativistic velocity vector u_\mu. It corresponds to either a non-physical system in the direct interpretation or a possible extension it distinguishes a "negative energy" or equivalently "anti-partner" to the usual particle. The choice depends on the operational implementation of the experimental devices associated with the observables. E.g. can said device distinguish particle fluxes through a surface from anti-particle fluxes in the opposite spatial direction. Projecting out non-physical modes e.g. "ghosts" is no different from classically restricting 4-velocities to time-like unit 4-vectors. The other e.g. space-like elements of the vector space are understood as representing components only i.e. differences in velocities and not properly physical velocities themselves.

Point 5: It is not clear to me exactly what his distinct predictions are. I'll have to hunt down copies of the references to fully understand it. (Or at least spend a great deal of time parsing and reconstructing). I'm not inclined to put that much effort into it.

1. If I understood you correctly, you claim that the relativistic wave function, say the one satisfying the Klein-Gordon equation, still can be interpreted in terms of a probability density in the position space. Can you specify how exactly one can do that? In particular, is such probability conserved? If not, why is it not a problem?

2. A solution of the collapse problem is one of the main motivations in the traditional motivation for the Bohmian interpretation, but is not the motivation in the present paper.

3. The pilot-wave cannot propagate backwards in time. It is the particle that can. Nevertheless, it does not lead to inconsistencies, as discussed in Ref. [3].

4. Note that negative j_0 appears even for superpositions of POSITIVE frequencies.

5. See Ref. [10] for more details.

 

[jambaugh]

1. If I understood you correctly, you claim that the relativistic wave function, say the one satisfying the Klein-Gordon equation, still can be interpreted in terms of a probability density in the position space. Can you specify how exactly one can do that? In particular, is such probability conserved? If not, why is it not a problem?

No I didn't claim that the relativistic wave function can be interpreted in terms of a probability density. I claimed it has a probability interpretation.

The various wave functions are elements of either a Hilbert space or (more usually in relativistic QM) a pseudo-Hilbert (pHilbert) space. These in turn represent modes of system preparation and dually selective system detection. In the Hilbert space case the interpretation is that the inner product of two mode vectors (sometimes expressed as integral of conjugate product of wave functions) is the transition probability amplitude. In the indefinite case of a pHilbert space then there is a frame dependent projection operator which you use to project out non-physical modes (effectively applying a gauge constraint) and this projects all vectors onto a nice positive definite Hilbert sub-space. The probability interpretation is then as before.

In this latter case the transition probabilities will be conserved under transition group actions which are unitary within the pseudo-unitary representation of the whole group. Those which are not unitarily represented will in general not conserve probabilities.

All that this means is that the system definition itself is not fully invariant under the whole of the transformation group. In particular you will find that Lorentz boosts do not conserve particle number and hence when working in a "one particle" system you will not get conservation of probabilities for observations made in distinct inertial frames.

This is one way of understanding Hawking-Unruh radiation, an accelerating observer (detector) is constantly having "particle number" redefined as it changes inertial frames and thus "vacuum" at one instant becomes "superposition of vacuum and non-vacuum" at a later instant, et vis versa so that an inertial observer will also see the accelerating detector emit particles.

2. A solution of the collapse problem is one of the main motivations in the traditional motivation for the Bohmian interpretation, but is not the motivation in the present paper.

W.r.t. motivation, that's fine. However the collapse "problem" is only a problem which you adopt an ontological "interpretation" (e.g. Bohm's) beyond the given operational interpretation. There can be no virtue beyond self consistency for an "interpretation" which solves the very problem it creates.

3. The pilot-wave cannot propagate backwards in time. It is the particle that can. Nevertheless, it does not lead to inconsistencies, as discussed in Ref. [3].

Pardon my confusion but as I understood the original Bohm pilot-wave model the pilot waves of necessity must causally propagate information (hidden variables) FTL which is equivalent to backwards in time for suitable choice of inertial frames. Are you saying your version does not propagate FTL?

4. Note that negative j_0 appears even for superpositions of POSITIVE frequencies.

Fine, it depends on your convention (whether you allow negative m vs negative P_0 i.e. anti-particles as "holes" vs. "negative velocity" versions of particles). But if you read the basic texts this is well explained. j_0 is not meaningful by-itself except as we integrate over a hyper-surface:
A= \int_S j_\mu ds^\mu
is the expectation value for the particle prepared in the mode corresponding to the given wave-function crossing the specified hyper-surface over which the integral is taken. If you want to incorporate anti-particles in your theory then you interpret this flux as a net flux of particle - anti-particle. Or equivalently allow negative energy and let the flux be the difference in flux relative to the ground-state "sea of negative energy particles". But if you wish to stick to a single particle interpretation then simply project out those negative modes.

As I stated before this projection is not invariant and reflects the frame dependence of your system definition. Remember that operationally in QM one doesn't speak of probabilities for a particle existing in a state other than where one is speaking of probabilities for specific acts of measurement or detection. Transition probabilities define all the correlations between acts of measurement and thus it is in the definition of whole transition probabilities and not probability densities where the interpretation lies. If you are having problems understanding/interpreting a probability density then first try to define the corresponding transition probability and respective modes. E.g. can in the given theory a delta-function type wave function be given meaning? If not then you can't give a direct interpretation to the amplitude densities or probability densities.

In the relativistic examples we've hinted at, one must take that delta-wave-function and resolve it in positive components only before you go a. normalizing it and b. calculating a probability. In so doing you may find that it is better to forget about treating coordinate position as an observable and rather stick to averaging particle detection-counts within finite volumes over finite intervals of time. (Noting also that these are not "sharp" measurements and thus do not define unique wave-functions but rather must be associated with a specific density co-operators.)

Regards,
James Baugh

 

[Demystifier]

1. All that this means is that the system definition itself is not fully invariant under the whole of the transformation group. In particular you will find that Lorentz boosts do not conserve particle number and hence when working in a "one particle" system you will not get conservation of probabilities for observations made in distinct inertial frames.

This is one way of understanding Hawking-Unruh radiation, an accelerating observer (detector) is constantly having "particle number" redefined as it changes inertial frames and thus "vacuum" at one instant becomes "superposition of vacuum and non-vacuum" at a later instant, et vis versa so that an inertial observer will also see the accelerating detector emit particles.

2. Pardon my confusion but as I understood the original Bohm pilot-wave model the pilot waves of necessity must causally propagate information (hidden variables) FTL which is equivalent to backwards in time for suitable choice of inertial frames. Are you saying your version does not propagate FTL?

3. Fine, it depends on your convention (whether you allow negative m vs negative P_0 i.e. anti-particles as "holes" vs. "negative velocity" versions of particles). But if you read the basic texts this is well explained. j_0 is not meaningful by-itself except as we integrate over a hyper-surface:
A= \int_S j_\mu ds^\mu
is the expectation value for the particle prepared in the mode corresponding to the given wave-function crossing the specified hyper-surface over which the integral is taken. If you want to incorporate anti-particles in your theory then you interpret this flux as a net flux of particle - anti-particle. Or equivalently allow negative energy and let the flux be the difference in flux relative to the ground-state "sea of negative energy particles". But if you wish to stick to a single particle interpretation then simply project out those negative modes.

1. But a free non-interacting particle seen by an inertial observer should not lead to particle creation. A single-particle interpretation should work at least in this case. Yet, a negative j_0 appears even for this case.

2. I am saying that the WAVE FUNCTION does not propagate FTL. Of course, the information between TWO particles in the Bohmian interpretation propagates FTL.

3. It seems to me that you misunderstood my point. If I project out the negative modes (it does not matter if I call them negative energies, negative frequencies, antiparticles, or modes propagating backwards in time), I STILL obtain negative j_0. See e.g. Eq. (53) in hep-th/0202204.

 

[jambaugh]

1. But a free non-interacting particle seen by an inertial observer should not lead to particle creation. A single-particle interpretation should work at least in this case. Yet, a negative j_0 appears even for this case.

Yes. But that same free non-interacting particle as defined and seen by a distinct inertial observer will not appear as a single particle. It will appear as a superposition of single particle and other-than one-particle modes. The negative j_0 expresses the fact that if the distinct observer tries to "catch" single particle modes as he defines them from modes prepared by the first observer which are single particle as he defines them then the probabilities are necessarily not conserved. Each observer is projecting out different "ghost" components, said components being what lead to the negative probabilities.

2. I am saying that the WAVE FUNCTION does not propagate FTL. Of course, the information between TWO particles in the Bohmian interpretation propagates FTL.

You do understand that FTL causality is equivalent to backwards in time causality? The only way to resolve paradox is to universally prevent causal interaction between these FTL phenomena and actual measuring devices. In essence this FTL causality universally requires that the Bhomian pilot waves be operationally meaningless, (empirically invisible). [Or SR is wrong].

In short it proves they do not "exist" in the empirical framework of science. Again I assert these ontological "interpretations" are attempts to hold onto pre-quantum notions of classical objective states. Accept what QM says..."forget what you think is look at what happens!".

3. It seems to me that you misunderstood my point. If I project out the negative modes (it does not matter if I call them negative energies, negative frequencies, antiparticles, or modes propagating backwards in time), I STILL obtain negative j_0. See e.g. Eq. (53) in hep-th/0202204.

It seems to me that you misunderstood my point. So what if j_0 is negative? The probability interpretation begins and ends with the inner product on the Hilbert space or frame dependent Hilbert sub-space. NOT with a probability density over some parameter manifold. You may in some cases define a set of parameterized probabilities or probability densities as in particular when you look at expectation values for boolean observables where said observables are parameterized. If you are getting "negative probabilities" look again more closely at your assumptions about what is an observable and at how you are calculating the expectation values.

Regards,
James Baugh

 

[Demystifier]

You do understand that FTL causality is equivalent to backwards in time causality? The only way to resolve paradox is to universally prevent causal interaction between these FTL phenomena and actual measuring devices. In essence this FTL causality universally requires that the Bhomian pilot waves be operationally meaningless, (empirically invisible). [Or SR is wrong].

I prefer the option that SR is wrong, or more precisely, not so universally valid.

 

[Demystifier]

Yes. But that same free non-interacting particle as defined and seen by a distinct inertial observer will not appear as a single particle. It will appear as a superposition of single particle and other-than one-particle modes. The negative j_0 expresses the fact that if the distinct observer tries to "catch" single particle modes as he defines them from modes prepared by the first observer which are single particle as he defines them then the probabilities are necessarily not conserved. Each observer is projecting out different "ghost" components, said components being what lead to the negative probabilities.

I never heard for such an interpretation in the mainstream literature. Is it your own interpretation? Is there a reference where such an interpretation is advocated?

 

[jambaugh]

I prefer the option that SR is wrong, or more precisely, not so universally valid.

Fine, go your own way. But then why worry about relativistic theory at all?

 

[jambaugh]

I never heard for such an interpretation in the mainstream literature. Is it your own interpretation? Is there a reference where such an interpretation is advocated?

It is usually condensed down to "...and so we must abandon the single particle interpretation..." and thenceforth the topic is QFT. In that context usually the analysis is handled for uniformly accelerating observers or particles hence the Fulling-Davies-Unruh effect. I have simply taken the natural special case of a particle accelerated for some finite interval. My exposition here is mainly to point out the need for extending to the many-particle theory even when you are talking about simple transition experiments or equivalently the accepting of non-conservation of probability when you restrict to single particle theory.

In the many particle theory j_0 is interpreted as a particle number density which can be negative at points expressing virtual anti-particle modes in the expansion of a physical particle into this (by my assertion inappropriate) coordinate representation.

The point is not that your original mode isn't a pure one, physical +particle mode. The point is that when you try to expand it in a position representation you necessarily extend outside the one particle domain and even in the many-body theory you are extending outside the physical domain.

Integrating over space cancels out these virtual modes and everything (usually) works fine. But you can't give a physical interpretation to j_0(x) by itself. This I believe is also pointed out in the last reference you gave though the philosophical analysis differed...especially on the virtue/necessity of a position observable.

If I haven't mentioned it before I'll add that if you consider Wigner's work on quasi-distributions over phase-space you'll see again in the non-relativistic theories the emergence of negative probabilities. The essential reason is the same. Quantum probabilities are not expressible by integrating a probability measure over a configuration/state space. This is the essence of Bell's inequality and its violation by QM. I see it as the inappropriateness of a universal ontological model of quantum phenomena and thus the impossibility of ontological "interpretations" of QM to ever provide any insight to the empirical phenomena. They serve only to cloud understanding in the same way as does e.g. aether induced contraction and clock slowing in SR.

Listen, I don't think we are going to get any further on this topic. I am not going to do the necessary work to give a detailed exposition tailored specifically to the questions you present. I am working on a detailed exposition of relativistic QM in general and if I get it to a point where I think it addresses your arguments, I'll send you a link or copy.

Enjoy your summer,
Regards,
J.E.B.

 

[ueit]

2. I am saying that the WAVE FUNCTION does not propagate FTL. Of course, the information between TWO particles in the Bohmian interpretation propagates FTL.

I have two question about the interpretation of Bohmian interpretation

1. BM is deterministic so the trajectory of particle A was "set" at the big-bang. The same is true for B. Is it not possible to see the BM formalism as revealing the preexisting correlation between the two trajectories rather than a causal connection between the two? In other words, B moves as it moves not because of how A moves but because the initial conditions (containing the "ancestors" of A and B) as they were at the big-bang.

2. Is it possible that the non-locality in BM is based on a local mechanism in the same way as Coulombian force or Newtonian gravitational force?

 

[Careful]

Fine, go your own way. But then why worry about relativistic theory at all?

Euh, the statement that SR does not hold up to all energy scales is perfectly plausible from the viewpoint of GR. At very high velocities with respect to the Friedmann Robertson Walker ``restframe'', the particle will generate gravitational shockwaves which -I believe- become singular if the velocity approaches c.

 

[Demystifier]

I have two question about the interpretation of Bohmian interpretation

1. BM is deterministic so the trajectory of particle A was "set" at the big-bang. The same is true for B. Is it not possible to see the BM formalism as revealing the preexisting correlation between the two trajectories rather than a causal connection between the two? In other words, B moves as it moves not because of how A moves but because the initial conditions (containing the "ancestors" of A and B) as they were at the big-bang.

2. Is it possible that the non-locality in BM is based on a local mechanism in the same way as Coulombian force or Newtonian gravitational force?

1. BM is a very specific theory. In this theory, the cause of nonlocal connections is simply not what you suggest. Perhaps a different theory with a property you suggest could be constructed, but that would not be BM as we know it.

2. No. In fact, the Bell theorem says that no local hidden-variable theory can reproduce the predictions of QM.

 

[Demystifier]

Fine, go your own way. But then why worry about relativistic theory at all?

Well, a relativistic wave equation is here, we know that it describes some physical particles, so an interpretation of it is needed. The interpretation should be relativistic as much as possible, but not at the expense of principles that seem even more fundamental to me (such as the assumption of physical reality existing even if we do not measure it).

 

[ueit]

1. BM is a very specific theory. In this theory, the cause of nonlocal connections is simply not what you suggest. Perhaps a different theory with a property you suggest could be constructed, but that would not be BM as we know it.

As far as I understand BM, the velocity of a particle is related to the wave function and the position of all other particles in the system. I see no need to interpret this relationship in a causal way (A moves because of B or B moves because of A) more than I see a causal connection between the display of two distant clocks. You may interpret it this way but you are not forced to.

2. No. In fact, the Bell theorem says that no local hidden-variable theory can reproduce the predictions of QM.

This is true only if the settings of the two detectors are free parameters. In BM this is certainly false as one can consider the whole system (source+detectors+physicists-choosing-detector-orientation).

 

[Demystifier]

1. As far as I understand BM, the velocity of a particle is related to the wave function and the position of all other particles in the system. I see no need to interpret this relationship in a causal way (A moves because of B or B moves because of A) more than I see a causal connection between the display of two distant clocks. You may interpret it this way but you are not forced to.

2. This is true only if the settings of the two detectors are free parameters. In BM this is certainly false as one can consider the whole system (source+detectors+physicists-choosing-detector-orientation).

1. Now I understand your point. In that sense you are right, it can be said that all the correlations are determined at the "big bang".

2. True. Still, BM as a specific theory IS nonlocal. In fact, in
http://xxx.lanl.gov/abs/quant-ph/0703071
I argue that ANY formulation of QM (with or without hidden variables) must be nonlocal in some sense. Essentially, this is because you cannot avoid use of a wave function (or some substitute for it), which is a nonlocal object.

 

[Careful]

Demystifier, Bohmian mechanics simply cannot be the end (nor the beginning) of the story: the reason being that there is no particle - wave interaction. You pick your wave - freely - choose randomly (using |psi|^2) the particle position, and then you let the wave guide your particle. Not only do you have a gross violation of energy-momentum conservation (notice: as a realist you cannot rely upon something coming out of nothing); but it is a complete mystery in your approach how the wave knows about the mass of the particle, that is: (a) how does the wave know about the particle if there is no particle - wave coupling at all and (b) by what mechanism does inertia of a pointlike object provide an imaginary diffusion constant in the wave equation (non- relativistically) ? Normally, the diffusion constant tells me something about the interaction medium-substance in which the latter is diffusing (but here you have neither medium, nor substance).

 

[Demystifier]

Demystifier, Bohmian mechanics simply cannot be the end (nor the beginning) of the story: the reason being that there is no particle - wave interaction. You pick your wave - freely - choose randomly (using |psi|^2) the particle position, and then you let the wave guide your particle. Not only do you have a gross violation of energy-momentum conservation (notice: as a realist you cannot rely upon something coming out of nothing); but it is a complete mystery in your approach how the wave knows about the mass of the particle, that is: (a) how does the wave know about the particle if there is no particle - wave coupling at all and (b) by what mechanism does inertia of a pointlike object provide an imaginary diffusion constant in the wave equation (non- relativistically) ? Normally, the diffusion constant tells me something about the interaction medium-substance in which the latter is diffusing (but here you have neither medium, nor substance).

This is like saying that classical Hamilton-Jacobi (HJ) mechanics cannot be the end (nor the beginning) of the story. HJ equation, similar to the Schrodinger equation, has a functions S as a solution. This function guides a classical particle in the same way as the wave function guides a Bohmian particle. There is no interaction between particle and S. The (initial) particle position is chosen arbitrarily. And so on, and so on ...

Bohmian mechanics is a self-consistent set of equations, so even if it does not comply with some common prejudices on physics, your arguments above do not prove that it cannot be correct. Still, I agree that it is possible that it is only an approximation to some more fundamental laws. It is a possibility, but not a necessity.

 

[Careful]

This is like saying that classical Hamilton-Jacobi (HJ) mechanics cannot be the end (nor the beginning) of the story. HJ equation, similar to the Schrodinger equation, has a functions S as a solution. This function guides a classical particle in the same way as the wave function guides a Bohmian particle. There is no interaction between particle and S. The (initial) particle position is chosen arbitrarily. And so on, and so on ...

Come on: GR can also be written into Hamiltonian form and does not suffer from any of the above problems, so you are mistaken here. The point I made is that QM should be part (as a flat space approximation) of a closed field theory, in either it should be part of a theory of inertia.

Bohmian mechanics is a self-consistent set of equations, so even if it does not comply with some common prejudices on physics, your arguments above do not prove that it cannot be correct. Still, I agree that it is possible that it is only an approximation to some more fundamental laws. It is a possibility, but not a necessity.

If it were not self consistent, one would not even talk about it since when is consistency an argument pro?? I think the above provides a serious case against it's status as a theory and my arguments have btw nothing to do with common prejudices : the only requirement being that wave and particle are interconnected and that some conservation laws exist (since when are these demands prejudices ?).

 

[Fra]

(such as the assumption of physical reality existing even if we do not measure it).

Can you elaborate why this is so important to you? Does it not seem like a paradox to you that you one one hand require that everything is in a definite state, wether it can be verified or not? Then, how would you know what this definite state is, in the first place? If you don't what's the value of this trick? You seems to postulate something, and then say that this is true wether you can prove it or not?

Or perhaps I'm not understanding your thinking. I'm curious to understand your philosophy. Why the "obsession" with realism, whatever that exactly is in the first place? :)

What if I'd suggest that the information about something we lack complete understanding about is real? As a way to recover a higher order "realism". What if we can argue that information is associated with energy and mass as well? Could this possibly in some remote way satisfy a Bohmian mind?

/Fredrik

 

[Demystifier]

Can you elaborate why this is so important to you? Does it not seem like a paradox to you that you one one hand require that everything is in a definite state, wether it can be verified or not? Then, how would you know what this definite state is, in the first place? If you don't what's the value of this trick? You seems to postulate something, and then say that this is true wether you can prove it or not?

Or perhaps I'm not understanding your thinking. I'm curious to understand your philosophy. Why the "obsession" with realism, whatever that exactly is in the first place? :)

What if I'd suggest that the information about something we lack complete understanding about is real? As a way to recover a higher order "realism". What if we can argue that information is associated with energy and mass as well? Could this possibly in some remote way satisfy a Bohmian mind?

/Fredrik

All the questions can be answered by the same answer: analogy with classical mechanics.
But even more: analogy with ALL other sciences (even psychology), except QM.

By the way, have you been reading George Orwell's "1984"? The usual non-realistic thinking about QM, including yours, strongly resembles the dogmatic thinking in the political regime of "1984".

But let me ask you a question:
What would you think about an alternative interpretation of CLASSICAL mechanics that claims that particle trajectories and objective reality do not exist even in classical mechanics?
That such an interpretation is possible see:
http://xxx.lanl.gov/abs/quant-ph/0505143

 

[Fra]

All the questions can be answered by the same answer: analogy with classical mechanics.
But even more: analogy with ALL other sciences (even psychology), except QM.

Ok, I see.

This was a sincere question btw. It's clear that I have another philosophy, but it's nevertheless interesting to try to understand your logic (from your point of view that is). I was thinking that if you had some particular reasoning behing it beyond classical mechanics I'd be interested to see your reasoning.

By the way, have you been reading George Orwell's "1984"? The usual non-realistic thinking about QM, including yours, strongly resembles the dogmatic thinking in the political regime of "1984".

No I haven't so I can't comment on a possible analogy. In either case I'm the first to admitt that I could be wrong, or I'll violate my own ideals :) In my mind beeing right is not the question, I consider the proper question is to make the best guess. One may think that a guess needs no qualifyer, but I disagree.

My own motivation and inspiration does not come from classical mechanics. But 15 years ago I would have given you another answer It comes a lot from human brain, and learning analogies, as well as consistency in reasoning, not just consistency of formalism. I used to think classical mechanics was excellent. But after studying quantum mechanics and some biology, and doing a lot of thinking, I now see what's wrong. Classical mechanics is a static, reductionist model. Reality is alive, and creative. During my study of biology I learned something that was left untouched during my basic physics education. It was very healthy to me. And I thank beer yeasts for that, and guiding me back to physics.

/Fredrik

 

[jambaugh]

Euh, the statement that SR does not hold up to all energy scales is perfectly plausible from the viewpoint of GR. At very high velocities with respect to the Friedmann Robertson Walker ``restframe'', the particle will generate gravitational shockwaves which -I believe- become singular if the velocity approaches c.

With regard to frame relativity equivocating FTL causality with Time reversed causality generalizing to GR makes no difference.

Your point about "gravitational shockwaves" is peculiar since an object "approaching c" is stationary in its own rest frame. So am I generating "gravitational shockwaves" as I sit here? . . . but then let's not digress too far from the current topic and leave this for another thread in another section.

W.r.t. the point I made SR vs GR makes no difference. Any procedure which can send an FTL signal can be boosted and coupled with another such procedure to produce a signal originating from a future time and arriving at the past time of a given observer's frame of reference and spatial origin. I would be able to send my yesterday self today's stock market quotes. More importantly I would be able to alter the outcome of yesterdays observations and so the ontological reality of yesterdays system states is no longer valid.
An ontological model which allows tomorrow to affect today cannot be still considered valid as an ontological model.

Regards,
James Baugh

 

[Demystifier]

I was thinking that if you had some particular reasoning behing it beyond classical mechanics I'd be interested to see your reasoning.

I do have additional reasoning beyond classical mechanics, but I am not able to put it in a clear form. The reasoning is as follows: All concrete non-realistic interpretations of QM (e.g., the relational interpretation) seem rather vague to me.
For example, no such interpretation clearly says in physical terms what an observation/measurement is. Of course, it may mean that some of them is still right, but we only need to further refine it. Nevertheless, as I have never seen a non-realistic interpretation that does not seem vague to me, it is hard to me to believe that some of them is the correct way to go. (As I said, such an argument against non-realistic interpretations is far from being clear.)

To further clarify my point, I am not really so much against the possibility that objective reality does not really exist at the most fundamental level that, perhaps, includes a theory of consciousness. I only do not find convincing that a mathematical model of physics based on a deterministic Schrodinger equation must be interpreted in this way. A solution of this equation looks too objective in a mathematical sense. This equation is too similar to classical equations of motion to accept such a radically non-classical interpretation.

 

[jambaugh]

Well, a relativistic wave equation is here, we know that it describes some physical particles, so an interpretation of it is needed. The interpretation should be relativistic as much as possible, but not at the expense of principles that seem even more fundamental to me (such as the assumption of physical reality existing even if we do not measure it).

There is your problem you are holding on dogmatically to principles (such as the assumption of a physical reality...in the sense of an objective state of reality independent of the mode of empirical determination of that reality) which do not have operational meaning in the empirical epistemology of science.

It helped me greatly to get over this bias to distinguish the terms "reality" and "actuality" as being "what is" vs "what happens". I believe phenomena are "out there" and not just in my head. When a particle detector "goes click" it is not a dream or an illusion. But the belief that those phenomena can be made to conform to a mathematical construct of one element of a set of possible states of reality is not valid at the quantum scale. It is a bias of idealization of the actual. We do not observe continua. We observe discrete outcomes (even at the classical scale). We can rescale these observations and we define equivalence classes of discrete measurements over a range of scales. This is a good thing it helps us generalize knowledge we gain. However the assumption that such scalable discrete measurements are valid all the way down to the continuum limit is a big jump and not an obvious fundamental principle.

This is the nature of quantum mechanics. When we try to resolve observations past a certain level we find the descriptions in terms of a limiting continuum of objective states of reality breaks down. We must back off of such a description and be more carefully pragmatic and operational in our interpretation.

The only truly fundamental principle of science is operationalism: What we define in the theory must be linkable to what we do in a laboratory/observatory, or it must only be considered mathematics.

Hence the fundamental semantic objects of a physical theory are the actions: acts of observation and acts of transformation of physical systems.

One may ask if the observed system of actions can be modeled in terms of acts on manifold of states of a physical object. The answer is, "sometimes yes", indeed "usually yes" when the scale of these actions is large enough. But once you attempt to push it to the limit it would seem that the more predictive theories (quantum theories) back away from such an ontological model and indeed invalidate the assumption that any single such model will be consistent with all possible experimental actions/outcomes.

But your insistence on a "fundamental reality" is no different from the pre-Einsteinian" insistence on a "fundamental universal time". Just because time was relativized doesn't make the concept of dynamic evolution meaningless. Just because we "relativize reality" doesn't make us nihilists. To the contrary.

And if you want to adopt a philosophical interpretation of the physics of quantum phenomena which incorporates pilot waves or other non-observable objects then that's all well and good as long as your physical interpretation sticks to the observable phenomena. I would prefer you call it a "Bohmian model" and I would prefer you recognize the extra-scientific nature of such a model. You exceed the domain of physics\subset science. As long as that is made clear I've no problem with your belief system.

I agree there are problems with the operational interpretation of relativistic quantum mechanics and a need for a clearer exposition of the same. However The current operational interpretation is valid and well defined. If you can glean such within your reality model then great! If someone else thinks their deity gives them a gnostic revelation then great for them too. But neither you nor they should attempt to justify the validity nor express such interpretation in any language other than the operational elements i.e. what goes on in the lab vs what goes on in the mind or on paper.

Regards
J.E.B.

 

[Demystifier]

I agree there are problems with the operational interpretation of relativistic quantum mechanics and a need for a clearer exposition of the same. However The current operational interpretation is valid and well defined.

Sorry, but it seems a bit self-contradictory to me. Can you explain it in more detail, in a manner that does not look self-contradictory?

BTW, I like very much how you distinguish the philosophical issues from the operational ones.

 

[Careful]

Jambaugh : of course a test particle at rest with respect to a Friedmann frame gives rise to a physically distinct solution than one moving with respect to it (obviously one should correctly calculate the back reaction on the geometry). In your argument, you implicitely boost the gravitational degrees of freedom too (moreover, your speed is by far not close enough to the speed of light with respect to an average cosmic frame in order to generate measurable gravitational waves for a Friedmann observer ``at rest''). Regarding your FTL issue... GR itself is such a non-local theory, providing for non-local correlations between field configurations which have spacelike separations; although of course no signals can travel faster than light (in the dynamical metric): but nevertheless these correlations may be thought of in terms of ``action at a distance''.

 

[jambaugh]

Sorry, but it seems a bit self-contradictory to me. Can you explain it in more detail, in a manner that does not look self-contradictory?

BTW, I like very much how you distinguish the philosophical issues from the operational ones.

The "problems" I see are with regard to how well it is presented and how understandable it is not what is actually said. The problem is that relativistic QM is seldom used except in the context of relativistic QFT.

In short the problems of which I speak are ones of presentation and not content. More discussion and research is also needed in making clear the nature of the gauge constraints one may and must impose in a more general context than QFT. I think the operational interpretation can be further "relativized" i.e. expressed in terms of relative frequency of events rather than absolute probabilities of specific outcomes. But as yet this opinion is unsubstantiated.

Regards,
James
P.S. I'm off to my sister's for the weekend and there is no broadband internet so I won't have a chance to read-reply until Monday.
Later All!
JEB

 

[ueit]

2. True. Still, BM as a specific theory IS nonlocal. In fact, in
http://xxx.lanl.gov/abs/quant-ph/0703071
I argue that ANY formulation of QM (with or without hidden variables) must be nonlocal in some sense. Essentially, this is because you cannot avoid use of a wave function (or some substitute for it), which is a nonlocal object.

In the paper "Bohmian Mechanics and the Meaning of the Wave Function", chapter 9, Durr argues that the universal wave function given by a solution of the Wheeler-de Witt equation is stationary, therefore it is not non-local in the sense that, by virtue of being changeless, it cannot transfer any information whatsoever, faster than light or not. The conditional wave function is non-local, but this is an artifact of dropping the constraints the universal wave function imposes on the whole system. In other words, non-locality is the price to pay for introducing free-choice in an otherwise deterministic theory. This step might be necessary for extracting useful predictions from the theory but need not be seen as a characteristic of the theory itself.

Regarding to your paper I see no reason one cannot describe a particle trajectory based only on the universal wave function (which is a constant) and the initial particle configuration at big-bang (which is supposedly known to the particle) disregarding what other particles are presently doing. Even if not elegant, this is an example of local algorithm for QM.

 

[Fra]

But let me ask you a question:
What would you think about an alternative interpretation of CLASSICAL mechanics that claims that particle trajectories and objective reality do not exist even in classical mechanics?
That such an interpretation is possible see:
http://xxx.lanl.gov/abs/quant-ph/0505143

IMO, classical mechanics as a theory has a more idealized view of reality than QM. In many cases this makes perfect effective sense. But the same philosophical issues are still there of course from a realistic point of view. Just as there are issues in improved theories. Because when we speak of "in classical mechanics" and "in quantum mechanics" we are really just talking about models. The reality is and was the same.

From my point of view - it's seems again your ontological perspective that seems to lead to this questions (at least that's how I see it). I do not ask what is X. I ask, what knowledge do I have about X. And it's hard to not ask the next question: What do I know about the validity of my supposed "information of X".

If I am for a second to take on a more obsessive philosophical attitude, even in Newtons days I'd say that strictly speaking things are not completely definite between "measurements". But in the classical case, that attitude would suggest a cure more costly than, what ignoring the tiny issue does. The investment in a more complex model, should be "payed for" by the benefit in increasing fitness.

It's due to our different philosophies, but in my opinion I can only guess what a possible trajectory might be. In cases where I have massive confidence in things, this guess will be more or less dead on to any test mesurement. Like in the classical mechanics domain, and thus for effiency reasons there is not need to talk about "guessing" (even though that, strictly speaking is what we are doing) when our experience repeatadly shows that our guesses are more or less dead on each time. So we say we can "predict the trajectory", when it really means that we are guessing, but the guess is so qualified that it becomes only a silly formality to insist on calling it a guess.

I'm not sure if I got your point by this comment, if not let me know.

/Fredrik

 

[Fra]

But you highlight an important issue! Of course quantum mechanics as it stands, doesn't make sense either. For several reasons. One is that quantum mechanics axioms expects a definite answer to the question, what do we know about X. It ignores the next question : What do we know, about the validity of what we know. That next question loosely speaking is what leads to second quantization. Of course, why should't be ask the same question again, and get the third quantization?

There seem to be an induction step here, triggered by something. I think this triggering point can be formalized, and put into the theory. This is more radical that QM as it stands, but I think it will resolve part of your issue? But probably not in the way you want.

/Fredrik

 

[Fra]

what do we know about X. It ignores the next question : What do we know, about the validity of what we know. That next question loosely speaking is what leads to second quantization. Of course, why should't be ask the same question again, and get the third quantization?

There seem to be an induction step here, triggered by something. I think this triggering point can be formalized, and put into the theory. This is more radical that QM as it stands, but I think it will resolve part of your issue? But probably not in the way you want.

Just to expand on the ideas, this might have seemed cryptical.

One question that spontaneously should appear when seeing this, is ones of general convergent properties, and when do we know when to goto the next step. Ie it seems a bit ad hoc at first. But that is just because it's a special case, in the general case it all makes more sense.

In the abstracted generalisation of this, what I argue in favour of is one gets into modelling the models. And one can talk about "exciting the model" to the next level. And the beauty is that there might be a way to define this evolution of models in terms of natural data processing. Ie. it may turn out this is not as ad hoc as one might first suspect. One would be able to have probabilistic qualifyers between models, that clearly explains why certain models are preferred over others. One sees that this seems to have no end (except in special cases) and thus is some kind of ongoing evolution. And this can provide unification on a very fundamental level.

While this is possibly more strange than ordinary QM, it may solve some of the issues with it and where I think we agree. Still I see no problem so picture these abstractions as real. It's just that I find the abstractions much easier to handle than specific cases.

/Fredrik

 

[Fra]

IMO, classical mechanics as a theory has a more idealized view of reality than QM. In many cases this makes perfect effective sense. But the same philosophical issues are still there of course from a realistic point of view.

In the light of the above comments, one major reason I personally don't like the classical mechanistic realism philosophy is that it suggests static models, that if right, gives a very nice description, but when it's wrong it makes the task to evolve the model very complicated.

So main main issue with many of the classical models is that they lack flexbility. As it also seen in nature, the animals that are survivors aren't necessarily the ones that have the biggest teeth, it's the one that are masters in adaption.

My estimate from the beginning is that everything in my experience suggest that understanding changes, and models change, as new data arrives. Thus, an important property of any model or strategy is an element of efficient evolution. Thus it leads me to suggest model the model.

In this respect the classical modelling, are not impossible or wrong as such, they just seem to me inefficient.

/Fredrik

 

[jambaugh]

Jambaugh : of course a test particle at rest with respect to a Friedmann frame gives rise to a physically distinct solution than one moving with respect to it (obviously one should correctly calculate the back reaction on the geometry). In your argument, you implicitely boost the gravitational degrees of freedom too (moreover, your speed is by far not close enough to the speed of light with respect to an average cosmic frame in order to generate measurable gravitational waves for a Friedmann observer ``at rest'').

I beg your pardon, I wasn't paying close enough attention to your premise, the Friedmann model. But even so, the assertion of uniform distribution of matter on the cosmological scale needn't preclude large regions of near vacuum on the intergalactic scale. In said regions near asymptotically flat GR and local SR is implied by the GR behind the Friedmann model.

Regarding your FTL issue... GR itself is such a non-local theory, providing for non-local correlations between field configurations which have spacelike separations; although of course no signals can travel faster than light (in the dynamical metric): but nevertheless these correlations may be thought of in terms of ``action at a distance''.

Careful about calling GR a "non-local theory" in light of the qualification you are correctly making about casual signals vs non-local correlations. Maxwell's theory is just as much a "non-local theory" as you get the same type of "non-local" correlations. They are implied by the boundary conditions of the exemplar thought experiments. It just gets more difficult to see the local causal nature of such in GR since all interactions imply conditions on the gravitational source term T_{\mu\nu} and so it is far more difficult to see a propagating change in the gravitational field. (Hence gravity waves are very hard to observe as compared to EM waves).

You may at best bring up the "absence of impossibility" in GR for e.g. large scale topological defects (wormholes et al) from allowing global causality violations.

But I am here making the distinction that Bhom's pilot waves necessarily causally propagate back in time within SR. (On the scale where SR is valid even given a larger scale Friedmann cosmology) Note that even with your Friedmann hypothesis, given local SR still applies you can still (assuming you can effect and be affected by Bhomian pilot waves) build a sequence of backward in time Bhomian signals which will then be back in time in all frames. Ultimately this shows that these pilot waves are necessarily non-observable (which is usually already assumed by those positing them).

The critical point is that they are removable from the physics without affecting any predictions of empirical experiments. They are not part of the physical theory but rather elements of a model or "mystical" speculations depending on how seriously their ontological status is taken.

And another more subtle point, once you allow local causality violation even if you give the objects special status as unobservable to allow no practical "time telephones" you run into difficulty giving their objective physical state any meaning since it can be revised by future events. It was this objective physical state of reality for which they are introduced in the first place.

The very purpose for which they are posited is then denied them. The only way then to reconcile their objective status is to introduce an additional meta-time, then you get oscillating causal loops and finally you end up with something on the order of Everett's many-worlds. I admit that Everett's ontology is self consistent but so is the postulate that we are dreams in the mind of God. Neither of these nor Bhom's pilot wave "model" say anything useful within in the epistemological discipline of science.

Regards,
James

 

[ueit]

And another more subtle point, once you allow local causality violation even if you give the objects special status as unobservable to allow no practical "time telephones" you run into difficulty giving their objective physical state any meaning since it can be revised by future events. It was this objective physical state of reality for which they are introduced in the first place.

BM is a deterministic theory, meaning the future is uniquely determined by the past. All events, past or future, were fixed by the initial conditions at the big-bang. So I don't see how future events can "revise" anything.

 

[Careful]

Jambough: the only thing I was saying is that the physics in the limit of v -> c of a particle moving in a gravitational field (one could measure the speed of the particle with respect to a notion of time which makes the gravitational field approximately stationary) is not well represented by imagining the particle to move in Minkowski spacetime, that is all.

Maxwell's theory with nontrivial currents becomes only ``locally causal'' through selection of the retarded Green's function (and by eventually adding positive energy waves); however it does not provide a locally causal model for localized carriers of the EM field. It is important here to realize that the notion of local causality originated from observing electromagnetic disturbances to propagate at the speed of light in vacuum, but nowhere has it been observed that the gravitational field to which these disturbances couple need to obey locally causal physics (as this is enforced by choosing boundary conditions) and actually it won't in a de Sitter universe.

Anyway, there is a non-local aspect about the current formulation of quantum mechanics, and unless we believe in photons reading minds of distant apparati (which I don't) - or hinge upon shortcomings in experiments - we have to believe in nonlocality (you are willing to give up realism). Of course this implies that there exist signals which we cannot measure yet, but nevertheless go faster than light, but I would hardly call that ``something useless'': people only started ``measuring atoms'' less than a century ago, but the concept has been around for more than 2000 years.


Careful