Exploring the Bohmian Interpretation: Why Study It?

[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

 

[jambaugh]

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.

This mental picture of all past and future as a fixed state is a useless arguing point. I can argue that I can flap my arms and fly. You can't disprove it because I am predetermined to never actualize this ability. It redefines the word "can" and "ability" to be meaningless.

It is the same problem moral philosophers have with ethics and (quasi)deterministic models of human behavior. It is pardoxically used to justify relaxing punishment for criminal behavior rather than more consistently being used to say that the choice of punishment we make is just as predetermined.

In short the use of such argument in context is self contradictory in that choice is a priori assumed in the very foundation of the argument. You can't say the value of the observable you choose to measure is predetermined because everything is predetermined (implicitly including your choice). The "because" here is meaningless because you must change contexts from this hypothesized globally determined states in the very semantics of the language in which you express the physics.

There is in fact a subtle category error built into such arguments. Even asserting metaphysically such a globally deterministic state, one recasts the concept of choosing to execute an experiment in terms of metachoice of circumstances where such an experiment is determined to occur. It then just as certainly leads to questions about whether the metachoice exists which will find in the deterministic clockwork of the universe the appearance of backward in time causality.

The very notion of cause and effect and hence determinism is premised on external free choices in the operational verification of cause and effect. Determinism must always be relative to a system epi-system cut and is meaningless in a universal context (except as "religious" dogma).

Without it all you get semantically is correlation and the ordering of cause and effect is all together meaningless. You can adopt such a world picture but it doesn't fit into quantum theory. The "bras" in quantum theory correspond to an experimenter causing e.g. an electron to be emitted which he knows from past experience will always affect one type of detector (the dual "ket") and never affect specific others (the dual "kets" of orthogonal "bras").

Now your point is well taken that this does appear resolve the objection I have to the Bohm pilot waves propagating back in time, i.e. that it is only partial resolutions of this universal system which appear to have this behavior due to the nature of how the piece of the whole is resolved. But then again this relativizes the "objective reality" one is trying to latch onto.

If it makes you sleep better to imagine this universal wave function is "out there" instead of just an imaginary construct then great. I've no real problem with other people's belief systems be they this or say "intelligent design" just so long as they don't try to call it science.

Regards,
James Baugh

 

[Anonym]

Now your point is well taken that this does appear resolve the objection I have to the Bhom pilot waves propagating back in time

Please write Bohm.

Dany.

 

[jambaugh]

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.

All particles move "in a gravitational field" but ok let's take your premise. How can you tell in terms of operational measurements whether this gravitatonal field is "approximately stationary". Do not forget that there are gauge degrees of freedom in the definition of "the gravitational field". It is exactly those gauge degrees of freedom we are talking about here.

The Friedmann universe is identical to a whole host of "skewed Friedmann universes" in so far as empirical observations are concerned. In solving Einstein's equations for the Friedmann cosmology you must invoke gauge conditions with make this one way speed of light "measurement" ontologically meaningful but not distinct operationally from the distinct "skewed" cases.

In the end you still get the implication that FTL signals (as defined in each case) can be used to send signals back in time due to this gauge symmetry. If you deny this symmetry exists you invalidate GR and must replace it with another theory. Maybe that one better conforms to experiment in which case of course my arguments are no longer valid as they are premised on the correctness of local SR which is implied by regional GR.

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.

One needn't select one of the advance vs retarded solutions to sources field equations to invoke "local causality" in Maxwell theory. One needs only invest the two with the correct interpretation. Take the simple case of a moving charged particle which is given an impulsive boost.
You get advanced and retarded solutions and one is the field resulting from the acceleration while the other is the field necessary to induce the acceleration assuming no external force was utilized. The advanced field is the component of the total EM field which would be absorbed by the sources acceleration. In short they are components of a classical scattering problem where you solve for the IN and OUT EM field uniquely defined by the behavior of the scattering center.

Then when you look at a charged particle in uniform motion you have both advanced and retarded fields present and canceling so that you get the frame boosted Coulomb field which "appears" non-local only because the electron is constantly effecting and being affected by the local field. The Coulomb field presupposes the uniform motion of the particle into the infinite past.

I beg to differ w.r.t. gravitation. de Sitter or no. The same principles apply as in EM but with the difficulty in that all matter is a source term so it is impossible to effect a change in motion of a particle without bringing another source into conjunction with the particle. It relates to the spin-2 nature as well since we can't neutralize the sources to mask them. There is thus no way to independently affect sources of gravitation. Thus even simple seemingly local assertions about a source term, say that a mass receives an impulsive force, are not local in that to effect such an impulse you need to transport momentum to the event and that momentum is also a source.

I can't see where de Sitter makes any difference as you still have the same local Einsteinian field equations and the same regional correspondence to the general case (with cosmological constant if necessary).

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.

The non-local aspects in quantum mechanics are not causal but conceptual.

In the case of Bell's derivation of his inequality he used non-locality as one means to ensure the measured variables are independent.
This needn't be the means of this assumption. We need only assume there exists some pair of commuting variables. You then with Bell's other assumptions get the inequality and you then with QM are able to entangle those variables and violate the inequality. It is those other assumptions which are negated in the reducto ad absurdum argument.

You should know what I think about wave function collapse as well. I use the analogy of lotto ticket expectation value collapse. It is an instantaneous update of our knowledge which we (may) index via spatial coordinates and not of physical entities located at said coordinates.

W.r.t the FTL BIT signals, it doesn't imply signals we cannot measure yet but rather that we fundamentally cannot measure period (assuming the very quantum theory one is "interpreting" by invoking these "signals".).

To measure the objects sending these signals we would then be able to either empirically prove Bell's inequality in contradiction to experience and to the predictions of QM or again require they have the same quantum nature in an extended quantum theory. We would then need "pilot waves" for the pilot waves. Where does it end?
[/QUOTE]

 

[jambaugh]

Please write Bohm.

Dany.

Pardon my transposing, I need to do a few drills so the o key gets hit before the h when I get going fast. I'll be careful in future.
R. J. B.

 

[Careful]

All particles move "in a gravitational field" but ok let's take your premise. How can you tell in terms of operational measurements whether this gravitatonal field is "approximately stationary". Do not forget that there are gauge degrees of freedom in the definition of "the gravitational field". It is exactly those gauge degrees of freedom we are talking about here.

If you want it very strict : - say - the preferred spaces in a static universe; you can carefully relax this condition furthermore. Moreover, in line of my argument it is irrelevant how to determine such frame operationally; but I guess you can retrieve the metric in free space by studying deviations in light paths (and reflection times) between different free falling mirrors (and by defining your units).

In the end you still get the implication that FTL signals (as defined in each case) can be used to send signals back in time due to this gauge symmetry.

Yeh, so what ? Is that against observation ? What if special relativity is only valid for elementary particles with velocity almost up to c (but not quite) in almost empty space ?

One needn't select one of the advance vs retarded solutions to sources field equations to invoke "local causality" in Maxwell theory.

Of course one does.

One needs only invest the two with the correct interpretation. Take the simple case of a moving charged particle which is given an impulsive boost.
You get advanced and retarded solutions and one is the field resulting from the acceleration while the other is the field necessary to induce the acceleration assuming no external force was utilized. The advanced field is the component of the total EM field which would be absorbed by the sources acceleration. In short they are components of a classical scattering problem where you solve for the IN and OUT EM field uniquely defined by the behavior of the scattering center.

Euh that doesn't make any sense to me. The retarded field exists without any acceleration. Moreover, if no external force is used, there is no acceleration at all for a single electron (there is enough discussion on that point in the literature concerning the Lorentz Dirac equation).

Then when you look at a charged particle in uniform motion you have both advanced and retarded fields present and canceling so that you get the frame boosted Coulomb field which "appears" non-local only because the electron is constantly effecting and being affected by the local field. The Coulomb field presupposes the uniform motion of the particle into the infinite past.

Euh, for an electron at rest (or uniform motion), the Coulomb field = Field strength arising from the RETARDED propagator.

I can't see where de Sitter makes any difference as you still have the same local Einsteinian field equations and the same regional correspondence to the general case (with cosmological constant if necessary).

Gravitons are plane wave solutions of the linearized field equations around a flat background metric; hence the local causality principle simply follows from the well known causality theorems for hyperbolic partial differential equations. If I linearize around de Sitter, I get different null geodesics (expanding congruences) and hence different causality properties.

The non-local aspects in quantum mechanics are not causal but conceptual.

That doesn't make any sense to me (and denying the reality of the measurement of Alice, being Bob, doesn't really help in making progress IMO).

For the rest, you basically say : nothing real can correspond to the quantum waves -->> what is the use of BM ? Again, why do you think the first thing is true at all ?? Some people would say particles are not reall at all, but merely localized field exitations, and that it is the wave which is fundamental (Einstein was one of them).