Why Explore the Bohmian Interpretation of Quantum Mechanics?

[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.