Bohmian Interpretation: Equivalent or not to Standard QM

[Ilja]

I agree with Hurkyl, what you have presented for the "conditional" wavefunction does not make sense, and at the very least is quite ill defined. Based on your comments you seem to be referring to a partial trace.

No trace, but inserting the actual value of q_rest.

Before continuing, please note that what you are calling a conditional wavefunction is not what Demystifier was calling a conditional wavefunction. It is frustrating that measurement in BM is ill defined enough that reading many sources seems to provide many different theories. Bohmists don't seem to even agree what their theory is (this is especially true when looking at "extensions" to achieve relativistic quantum mechanics).

Given that you have not understood my definition of the conditional wave function, I feel free to ignore this. I have never experienced such feelings reading Bohmian theories. (But this rather nicely describes my initial feelings reading about many worlds.)

In particular, you claim that for the conditional wavefunction:
"its evolution is well-defined"
yet you also claim
"Thus, different measurement results correspond to different values of qrest, which are then used to define the conditional (effective) wave function."

You are defining the conditional wavefunction (and hence the supposed collapse) using the results of a measurement, instead of something intrinsic in your theory.

No, I don't use the result of some measurement of q_rest, but the actual value of q_rest(t) at the moment of time t when the observer sees the difference. q_rest(t) exists and is intrinsic to the theory.

That is a major point, you are adding something outside of BM evolution of the system to try to incorporate measurement. And like the "bohmians" before you, you cannot derive a measurement from your postulates but instead insert a measurement to explain another measurement.

I don't. Now, given the fact that positions are observable in pilot wave theory, it is easy to mingle the actual values with some measured values. So some "Bohmians" can mingle them. In particular, such a confusion appears in a natural way if we follows the way we have learned in the CI: To describe the measurement using at first some quantum process, and, then, leaving everything else (the human observing the classical device) to the classical part of the CI. The better and more consistent way is to take the whole universe described in a Bohmian way, with the observer already being part of it, and its state described by some part of q_rest.

So all you've done is transfer the measurement of Demystifier's "obvious" measurement of a classical system, to the brain's consciousness somehow "obviously" knowing the actual position of its particle components in the wavefunction.

Not at all. The brain does not have to know its own state. It simply is this state.

At least Demystifier's a priori dichotomy was non anthropic (micro vs. macro), but you are adding in a dichotomy that consciousness can "obviously" know the positions of its particles.

No. Different states of consciousness have to have different states of _rest. This is a triviality. (It doesn't even matter here if you are a pure materialist or believe into some dualism. All we need is that if the brain states are identical, then the corresponding states of consciousness have to be identical too.

Consider the N particle positions to be a vector in R^3N space. I was hoping it was clear what is meant by unitary here. If not, the point is that the evolution is reversible.

Since the fundamental evolution in your theory is unitary, then no collapse is possible.

If I replace your "unitary" with "reversible", then this is the old objection how one can get thermodynamic equilibrium from reversible Newtonian mechanics. Of course, pilot wave theory uses the same ideas to get, in quantum equilibrium, an equilibrium out of a reversible theory. If you think that what is done in thermodynamics is in some sense inherently wrong, then, ok, quantum equilibrium is inherently wrong in the same sense. But this is nothing I have to care much, and clearly doesn't make BM cranky.

Then please give an explicit example.

Standard QM measurement theory (with decoherence) describes how the initial state

(a_1\psi_1+a_2\psi_2)\phi evolves into a_1\psi_1(q_S)\phi_1(q_{rest})+a_2\psi_2(q_s)\phi_2(q_{rest}). Any description of Schroedingers cat uses this. We need that \phi_1,\phi_2 (the two resulting states of Schroedingers cat) have different support in q_rest. If you see the cat alive or dead, the state of your brain will be different if the cat is alive and if it is dead.

Now, we put the actual state of q_rest into the expression and obtain or a_1\psi_1(q_S)\phi_1(q_{rest}) or a_2\psi_2(q_s)\phi_2(q_{rest}), because \phi_i(q_{rest})=0 for the other i. Above are product states, thus, if we consider only experiments related with the subsystem, it can be handled now as equivalent to one of the \psi_i(q_S).

But there is an evolution between the starting point where \phi_1=\phi_2=\phi(q_{rest}) and the final point where \phi_1\phi_2=0. During this time, the state is not in a product state, and its evolution is not unitary.

There is no tracing over all possible values of q_rest to defined the intermediate state, but one always uses the actual value of q_rest(t).

I've reread his paper "Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem." and I don't see him assuming relativity anywhere. In fact he never even refers to relativity in the entire paper. As should be clear from the title, he quite explicitly allows theories with non-local interactions which violate relativity.

AFAIR the whole game was based on different notions of "before" for measurement devices in relative motion. In a theory with preferred frame, there is no such incompatibility. The relativistic "before" of a moving measurement device is simply irrelevant.

Again, from what I've read, the "equivalence" proofs of Bohmian mechanics merely show that measurements have the same distributions but doesn't prove they have the same correlations. That isn't a true proof of equivalence at all.

How can one have the same distributions on the same global configuration space and not have the same correlations? Explain. One should, of course, consider the distribution of the whole configuration, not only the traces of the distribution for the different subsystems. But of course BM considers the global distribution.

 

[Hurkyl]

Standard QM measurement theory (with decoherence) describes how the initial state
...
Now, we put the actual state of q_rest

In "standard QM measurement theory", q_rest is a dummy variable; there isn't an an "actual state".

The thing I think you're thinking, but haven't really conveyed, is that you are taking the two-variable function \Psi(u, v), and plugging {the positions of the corresponding Bohmian particles} in for v.

(I purposely changed the dummy variables to u and v to reduce the chance that they would be confused with something else)

 

[Ilja]

In "standard QM measurement theory", q_rest is a dummy variable; there isn't an an "actual state".

The thing I think you're thinking, but haven't really conveyed, is that you are taking the two-variable function \Psi(u, v), and plugging {the positions of the corresponding Bohmian particles} in for v.

(I purposely changed the dummy variables to u and v to reduce the chance that they would be confused with something else)

Correct, that's the difference between QM and pilot wave: In pilot wave we have an actual state q_rest(t) which we can put into it.

And, again, correct, I consider the wave function of the whole universe as a function depending on two parameter sets, q_S and q_rest, and put the actual value for q_rest into it, to obtain a function of q_S only. The function of q_S only is the conditional wave function.

 

[JustinLevy]

And, again, correct, I consider the wave function of the whole universe as a function depending on two parameter sets, q_S and q_rest, and put the actual value for q_rest into it, to obtain a function of q_S only. The function of q_S only is the conditional wave function.

Then "collapse" as you describe it can only happen if you already know some of the hidden variables (ie. quantum equilibrium is not fullfilled).

You keep talking as if you've fixed the "measurement problem", but you haven't. Just like Demystifier, you require:
1] entangling the position of what you wish to measure with a larger object
2] determining the position of the larger object

All you have done is transfer the problem of measurement to a problem of a different measurement. Demystifier did step #2 by creating a dichotomy between micro and macroscopic objects and declaring, outside of the theory, that one can "obviously" know the position of macroscopic objects. You indeed take a different approach, but it still does not solve anything. You instead state that a conscious object can obviously know more information that its wavefunction. You make a dichotomy between conscious and non-self aware objects. This is not an improvement. If anything it is worse than Demystifier's dichotomy, since his at least has a clear parameterization based on some variables (size), while yours is incredibly ill defined.

This is the problem of your theory in a nutshell:
A] If the hidden variables where known, the theory would not be equivalent to quantum mechanics for experimental predictions (the theory's postulate of quantum equilibrium would be wrong).
B] However, if the hidden variables are NOT accessible, then the theory cannot describe measurement.

This is a catch 22. Either way your theory is wrong.

Now, given the fact that positions are observable in pilot wave theory, it is easy to mingle the actual values with some measured values.

To do this, you would have to be able to ... using only the postulates of your theory ... have a closed system start in quantum equilibrium and be able to LEARN that it is NOT in quantum equilibrium. Are you saying a closed system can do experiments to learn it is not in quantum equilibrium? And if so, what prevents further experiments distinguishing the theory from standard quantum mechanics?

Not at all. The brain does not have to know its own state. It simply is this state.

But you are assuming the brain can distinguish between these states. That it can enumerate these states. That is what is needed for "knowing" the result. You are stating that the secret to obtaining information about hidden variables is through consciousness in objects.

If I replace your "unitary" with "reversible", then this is the old objection how one can get thermodynamic equilibrium from reversible Newtonian mechanics.

No, yours is the opposite problem. You start with equilibrium, and despite unitary evolution, claim collapse into a non-equilibrium state. Unitary evolution forbids this.

AFAIR the whole game was based on different notions of "before" for measurement devices in relative motion. In a theory with preferred frame, there is no such incompatibility. The relativistic "before" of a moving measurement device is simply irrelevant.

I am getting the strong impression you have never read this paper yourself.
Look, you made a complaint and I looked up the paper again ... it turned out your complaint wasn't valid. In response you make yet another claim without looking at the paper? Come on. I don't remember anything like that in the paper. As a double check I searched for "relativ" and saw no mention of relativity nor relative motion. Please stop arguing with what are effectively guesses. Please read the paper.

How can one have the same distributions on the same global configuration space and not have the same correlations? Explain. One should, of course, consider the distribution of the whole configuration, not only the traces of the distribution for the different subsystems. But of course BM considers the global distribution.

You are trying to replace the randomness in individual measurements, by cloaking it as the distribution of an ensemble of measurements. These concepts are by no means equivalent nor necessarily compatible.

As pointed out by other physicists, in the interaction picture, positions can become non-commuting observables. Bohmian mechanics cannot describe away such situations by an ensemble of measurements, because the positions, while hidden variables, are always definite and single valued.

Look, Newton made mistakes, Einstein made mistakes, we've all made mistakes. I truly hope you are not sweeping away any doubts on the theory due to Bohm's laurels. Bohm truly thought that experiments on Bell's inequality would show that quantum mechanics was incomplete. Instead, he ended up conceding that spin had to be treated, not classically, but quantum mechanically. Sure, BM was extended. Yet even then, several issues with BM have been pointed out by other physicists. What would it take for you to come to an understanding that Bohm's theory is incorrect, is a mistake?

Look how many posts, and papers, and websites, have been suggested and read and yet it is still unclear how BM can even explain measurement without falling into the catch 22 above. These complaints are by no means new ideas, but Bohmists seem to ignore all complaints and trudge on anyway.

 

[Demystifier]

Look how many posts, and papers, and websites, have been suggested and read and yet it is still unclear how BM can even explain measurement without falling into the catch 22 above. These complaints are by no means new ideas, but Bohmists seem to ignore all complaints and trudge on anyway.

You are wrong that your complaints are not new. Other people complain for several reasons, but nobody complains about stuff that you do.
The reason is the following. Maybe you are right that the Bohmian interpretation does not COMPLETELY solve the measurement problem. But at least it solves it partially, by making it completely equivalent to the measurement problem in CLASSICAL mechanics. Namely, in classical mechanics it is also true that one can observe only macroscopic stuff, not microscopic. Not because there is a fundamental boundary between macroscopic and microscopic, but because the observers are macroscopic. Other people see no problems with it, because they do not see any fundamental problems with measurement in classical mechanics. You either do not realize the analogy between the measurement problems in classical and Bohmian mechanics, or consider the measurement problem in classical mechanics to be unsolved as well.

 

[zenith8]

Look how many posts, and papers, and websites, have been suggested and read and yet it is still unclear how BM can even explain measurement without falling into the catch 22 above. These complaints are by no means new ideas, but Bohmists seem to ignore all complaints and trudge on anyway.

Recall that in pilot-wave theory there is nothing special about measurements; they are just experiments of a certain kind designed to respect a formal analogy with classical measurements. In particular, they do not actually 'measure' any pre-existing property (apart from position). They are perfectly ordinary many-body interaction processes which are special only in that they are designed such that the interaction leaves the system in a particular state - an eigenfunction of a Hermitian operator. The apparatus is left in a state whose subsequent behaviour in no way influences the system. Considering for simplicity the case of 'ideal measurements', the two stages are:

(1) State preparation of a certain kind where the system wave function gets correlated with the apparatus wave function and evolves into an eigenfunction of a Hermitian operator.

(2) An irreversible act of amplification which allows one indelibly to register the outcome (generally by coupling to a very large number of degrees of freedom such as in a macroscopic object).

Both of the above steps can be done using completely rigorous mathematics (see any pilot-wave textbook)..

Now note that it stops there - the fantasy that conscious 'observers' are required was a desperate invention of the 1930s when no-one could think of any better ideas (they'd already forgotten about de Broglie's). You just get a mark on a piece of paper or a digital readout or a dead cat or whatever. No-one needs to look at it. Ever. So unless you're the kind of weirdo who thinks that the Moon isn't there unless someone looks at it - that is the end of it.

Now if you want to look at it, then feel free. It is indeed obvious - as Demystifer said - that humans can see macroscopic objects. The outcome of any conceivable experiment may be expressed in terms of the positions of macroscopic objects. This has nothing to with the physical observable being measured - it just relates to how we as humans receive information through our senses. If you want a full description of that information-receiving process, then fine go ahead and try but you'll need a proper theory of consciousness first. A theory which er.. absolutely no-one in the whole world knows - even the supporters of other interpretations or 'standard QM' or whatever you want. Criticizing 'Bohmians' because they don't know this either is a bit rich.

Your criticisms are bizarre to say the least, and also extremely intemperately expressed. Please provide some cited references for all the people you claim agree with you (i.e. people who think pilot-wave theory is wrong for the reasons you state, rather than for some other reason).

If you've managed to convince yourself otherwise, then why don't you write a paper about it? People have been trying to disprove the theory since 1927 and not doing very well; in fact the number of supporters has been growing year on year since at least the early 1990s (before that people had either not heard of it, or had been ordered not to hear of it in order to avoid making all the famous people who had said it was impossible look like idiots). If the Amazing Justin has managed to show the whole thing is obviously incorrect then your paper will be an important contribution, and it will certainly make your reputation. It'll be Physical Review Letters or Nature at least. What have you got to lose?

 

[Ilja]

Then "collapse" as you describe it can only happen if you already know some of the hidden variables (ie. quantum equilibrium is not fullfilled).

No. The collapse happens objectively. What I know is completely irrelevant. I don't know the wave function of the universe, and I don't know the q_rest as well. All I know about them is that they exits.

As a consequence, the effective wave function which I have defined also exists.

You keep talking as if you've fixed the "measurement problem", but you haven't. Just like Demystifier, you require:
1] entangling the position of what you wish to measure with a larger object
2] determining the position of the larger object

No. The "larger object" is me. And I don't have to determine my position or the positions of my neurons to experience what I experience.

You instead state that a conscious object can obviously know more information that its wavefunction. You make a dichotomy between conscious and non-self aware objects.

No, I do not make any assumptions about "knowing more information" or so. The postulate of pilot wave theory is that my state is part of the state of the universe, thus, my state is described by q_rest. If I have different experiences about measurement results which I see (macroscopic or whatever else) my state has to be different, thus, q_rest has to be different too.

This is correct also if I'm completely stupid. Self-awareness is unnecessary: If there is some non-self-aware worm who is experiencing something, this worm has also different possible states, which somehow correspond to the different possible experiences of the worm, and which have to be described, therefore, by different values of q_rest.

A] If the hidden variables where known, the theory would not be equivalent to quantum mechanics for experimental predictions (the theory's postulate of quantum equilibrium would be wrong).
B] However, if the hidden variables are NOT accessible, then the theory cannot describe measurement.

It can. The worm does not have to access the different states of q_rest. The hidden variables should not be accessible to observation at all to solve the measurement problem.

The catch22 is your own: You require that q_rest should be accessible to observation, and end up in a circle. But this is only your problem: Measurements should not be explained in terms of other measurements, but in terms of objective reality (as postulated to exist by the theory). That's what I do: I explain the measurement in terms of objectively existing things - the wave function of the universe and q_rest. I do not even care if they are observable: Some part of q_rest may be observable in principle, but q_rest completely is certainly not observable, and the wave function of the universe is certainly unobservable.

To do this, you would have to be able to ... using only the postulates of your theory ... have a closed system start in quantum equilibrium and be able to LEARN that it is NOT in quantum equilibrium. Are you saying a closed system can do experiments to learn it is not in quantum equilibrium? And if so, what prevents further experiments distinguishing the theory from standard quantum mechanics?

You have a gas in thermodynamic equilibrium. Now assume that the gas molecules are small conscious human beings. Do they observe something beyond equilibrium? I think so. They observe their own positions, their own collisions with other molecules and so on. Does it follow that the gas is no longer in equilibrium? I don't think so.

What prevents further experiments distinguishing the observations of the particular molecule from equilibrium thermodynamics? I would say the simple fact that the pure molecule cannot tell other molecules some nice repeatable experiments which predict derivations from equilibrium.

But you are assuming the brain can distinguish between these states.

No, the brain is in different states.

No, yours is the opposite problem. You start with equilibrium, and despite unitary evolution, claim collapse into a non-equilibrium state. Unitary evolution forbids this.

The non-unitary evolution of the conditional wave function is a simple mathematical consequence of the equations. And, as I have already told you, the configuration does not have any "unitary" evolution.

I am getting the strong impression you have never read this paper yourself.
Look, you made a complaint and I looked up the paper again ... it turned out your complaint wasn't valid. In response you make yet another claim without looking at the paper? Come on. I don't remember anything like that in the paper. As a double check I searched for "relativ" and saw no mention of relativity nor relative motion. Please stop arguing with what are effectively guesses. Please read the paper.

The Leggett paper itself is indeed not accessible to me, because I live in a location without any scientific library. If you have some pdf, it would be nice if you could send it to me.

I have based my answers (ok, guesses) on papers on arxiv which refer to it.

You are trying to replace the randomness in individual measurements, by cloaking it as the distribution of an ensemble of measurements. These concepts are by no means equivalent nor necessarily compatible.

I think you have not answered my question.

As pointed out by other physicists, in the interaction picture, positions can become non-commuting observables. Bohmian mechanics cannot describe away such situations by an ensemble of measurements, because the positions, while hidden variables, are always definite and single valued.

In interacting field theory, I do not endorse pilot wave theories based on particles. I prefer theories with field ontology. So, non-commuting particle positions are not problematic.

Look, Newton made mistakes, Einstein made mistakes, we've all made mistakes. I truly hope you are not sweeping away any doubts on the theory due to Bohm's laurels. Bohm truly thought that experiments on Bell's inequality would show that quantum mechanics was incomplete. Instead, he ended up conceding that spin had to be treated, not classically, but quantum mechanically. Sure, BM was extended. Yet even then, several issues with BM have been pointed out by other physicists. What would it take for you to come to an understanding that Bohm's theory is incorrect, is a mistake?

First, I do not believe that pilot wave theory is the final theory of everything. Second, I'm open to other interpretations, and, in particular, I like Nelson's stochastic variant very much.

What is needed for me to give up pilot wave theory is simply a better theory. I look at other interpretations, and what I have found is that they are much worse than pilot wave theory. In particular, all decoherence-based interpretations, including many worlds, ignore the problem of defining the decomposition into systems one needs to start decoherence. (See my paper http://arxiv.org/abs/0903.4657" )

Look how many posts, and papers, and websites, have been suggested and read and yet it is still unclear how BM can even explain measurement without falling into the catch 22 above.

It is unclear to you, but not to me. That's your particular problem of understanding, and not a problem of pilot wave theory.

These complaints are by no means new ideas, but Bohmists seem to ignore all complaints and trudge on anyway.

Similar things one can read in many versions from cranks who don't understand relativity and claim that it is full of logical contradictions. And the relativists, even if there are much more of them, are already tired answering such crank complaints and usually simply ignore them.

I certainly take reasonable arguments against pilot wave theory serious. In particular, one reasonable objection against the viability of pilot wave theories with field ontology I have considered in http://arxiv.org/abs/0904.0764"

I don't claim at all that your complaint is a trivial one or an unreasonable one. Instead, in the paper I'm writing now (I plan to publish it in May on arxiv) I spend (in the context of another reasonable objection made by Wallace) a whole section discussing essentially this particular point - the confusion between the use of actual values of q_rest and measured values.

So it is also very interesting for me to see if I'm able to explain you the point, to help you to understand it. (And the first lecture I have learned from this is that I have to write this section with even more details.)

 

[Demystifier]

As pointed out by other physicists, in the interaction picture, positions can become non-commuting observables. Bohmian mechanics cannot describe away such situations by an ensemble of measurements, because the positions, while hidden variables, are always definite and single valued.

Bohmian mechanics is formulated in the Schrodinger picture, not in the interaction picture, so this is not a problem.

 

[Demystifier]

This is the problem of your theory in a nutshell:
A] If the hidden variables where known, the theory would not be equivalent to quantum mechanics for experimental predictions (the theory's postulate of quantum equilibrium would be wrong).
B] However, if the hidden variables are NOT accessible, then the theory cannot describe measurement.

This is a catch 22. Either way your theory is wrong.

I still claim that you do not understand the concept of conditional probability. So you are wrong. The correct situation is neither A] nor B] but
C] Before the hidden variables are measured, your knowledge about them is best described by the quantum equilibrium with respect to the wave function. After you measure them, your knowledge is changed, so your knowledge is no longer best described by the quantum equilibrium with respect to the wave function. Nevertheless, the knew knowledge can still be described as a quantum equilibrium with respect to some NEW wave function. This new wave function corresponds to a collapsed wave function, even though no true collapse of the wave function has happened. The only thing that really collapses is your knowledge. And all this is not only specific to quantum mechanics. Just replace "wave function" with "probability distribution" and remove the word "quantum", and the same can be said for any classical system that can be described in statistical terms.

 

[Ilja]

Nonsense. The Legett inequalities are about some strange way to combine non-local realistic theories with relativity, which is not used in BM. The assumptions made in this inequality fail for BM.

I have checked the sources available for me about Leggett, and found the one which has been the base of my initial spontaneous response:

"If one assumes that Bohm’s time-ordered nonlocality belongs to physical reality, one has to cast it into a description using real clocks and accepting the experimental result of the relativity of time. As said above, the essential ingredients of a realistic theory lead naturally to accept that the relevant clocks are those defined by the inertial frames of the beam splitters. In this sense, Bohm’s model [16] is the adequate time-ordered nonlocal description for entanglement experiments with beam splitters at rest. And its natural extension to experiments with beam splitters in motion is the model leading to the prediction that the nonlocal correlations should disappear in the before-before experiment [8, 9, 11, 12]. Therefore, this experiment proves nonlocal determinism in the testable relativistic extension of Bohm’s model [16] wrong.

Models assuming that the “realistic” mechanism happens in a single preferred frame even in relativistic experiments with devices in motion, are not refuted by the before-before experiment ..."

(Antoine Suarez, Nonlocal “Realistic” Leggett Models Can be Considered Refuted by the Before-Before Experiment, Found Phys (2008) 38: 583–589, DOI 10.1007/s10701-008-9228-y)

But you seem to be right that Leggett is not really about this time ordering:

"Both in the original paper [5] and in [6], the model was presented by implicitly assuming a time-ordering of the events. Any model based on such an assumption had already been falsified by the so-called before-before experiment [10, 11], as Suarez emphatically stressed [12]. However, assumptions (3–4) clearly define non-signaling correlations, and Leggett’s model can be defined without any reference to time-ordering."

(Cyril Branciard, Nicolas Brunner, Nicolas Gisin, Christian Kurtsiefer, Antia Lamas-Linares, Alexander Ling, Valerio Scarani, Testing quantum correlations versus single-particle properties within Leggett’s model and beyond, arXiv:0801.2241)

But it is also clear and mentioned that the Leggett model has nothing to do with BM:

"It is a very important trait of this model that there exist subensembles of definite polarizations (independent of measurements) and that the predictions for the subensembles agree with Malus’ law. It is clear that other classes of non-local theories, possibly even fully compliant with all quantum mechanical predictions, might exist that do not have this property when reproducing entangled states. Such theories may, for example, include additional communication [23] or dimensions [24]. A specific case deserving comment is Bohm’s theory [25]. There the non-local correlations are a consequence of the non-local quantum potential, which exerts suitable torque on the particles leading to experimental results compliant with quantum mechanics. In that theory, neither of the two particles in a maximally entangled state carries any angular momentum at all when emerging from the source [26]. In contrast, in the Leggett model, it is the total ensemble emitted by the source that carries no angular momentum, which is a consequence of averaging over the individual particles’ well defined angular momenta (polarization)."

(Simon Groeblacher, Tomasz Paterek, Rainer Kaltenbaek, Caslav Brukner, Marek Zukowski, Markus Aspelmeyer, Anton Zeilinger, An experimental test of non-local realism, arXiv:0704.2529)

 

[JustinLevy]

But it is also clear and mentioned that the Leggett model has nothing to do with BM

In the paper, Leggett uses a toy model to show an example of a theory that, while (as he puts it) it is realistic and "relatively" plausible, it disagrees with QM on the inequality he proposes. Yes, the toy model as the people you quote point out uses definite polarization, but his inequality doesn't require that. It is merely a feature of the toy model he used to demonstrate.

Leggett has been incredibly busy since winning the nobel prize (he hasn't taught much since then), but I was able to talk to some gradstudents that have discussed it with him (and one has even given presentations on foundational issues for students). One said that Leggett refers to the copenhagen interpretation as a "non-interpretation" since even with the measurement postulate, there is nothing to define the contact between experiment and the operators. (I had never heard that particular wording before, but sounds like the usual measurement problem.) As for BM, he said Leggett says it is useless window dressing as it solves nothing but he has never heard him call it experimentally ruled out. (It sounds like Leggett may take what I called route "B" above: the hidden variables are not accessible, so it cannot explain measurment.)

I've attached the paper. But since Leggett doesn't seem to consider it ruling out BM, then I doubt it does. I'd love to discuss it more, as I don't understand the full implications of some of his stated assumptions. I guess BM violates one of them.

Please note that I do not mean to put words into his mouth. I'll still try to sit down and discuss it with him at one point, but regardless, it appears this paper cannot rule out BM (in that part, the important part, you are correct).

-------

This is the problem of your theory in a nutshell:
A] If the hidden variables where known, the theory would not be equivalent to quantum mechanics for experimental predictions (the theory's postulate of quantum equilibrium would be wrong).
B] However, if the hidden variables are NOT accessible, then the theory cannot describe measurement.

This is a catch 22. Either way your theory is wrong.

I still claim that you do not understand the concept of conditional probability. So you are wrong. The correct situation is neither A] nor B] but
C] Before the hidden variables are measured, your knowledge about them is best described by the quantum equilibrium with respect to the wave function. After you measure them, your knowledge is changed, so your knowledge is no longer best described by the quantum equilibrium with respect to the wave function. Nevertheless, the knew knowledge can still be described as a quantum equilibrium with respect to some NEW wave function. This new wave function corresponds to a collapsed wave function, even though no true collapse of the wave function has happened. The only thing that really collapses is your knowledge. And all this is not only specific to quantum mechanics. Just replace "wave function" with "probability distribution" and remove the word "quantum", and the same can be said for any classical system that can be described in statistical terms.

You have not described a different route. All you have done is describe route A: The 'hidden variables' ARE accessible. In which case the theory is trivially experimentally distinguishable.

Also, as zenith8 stated, and Ilja agreed, if the ensemble of positions is not in equilibrium with the TOTAL wavefunction, in time it will evolve to equilibrium with the TOTAL wavefunction. You cannot just neglect the rest of the wavefunction. As you yourself agreed earlier, if we are EVER not in quantum equilibrium, the theory is experimentally distinguishable from QM.

Furthermore, you keep willy-nilly switching between the view of the wavefunction as a potential and as a probability distribution. Imagine that the hidden variables are in principle accessible... then we could update the wavefunction to a "conditional wavefunction" to denote this information if it is a probability distribution. Instead of the goundstate wavefunction for a hydrogen atom, we could truncate the wavefunction about the actual electron position:

\Psi(r) \rightarrow \Psi(r) \Theta(A - |r-r_0|)
Where \Theta(x) is a step function, and A is the radius of a sphere around r_0 which is the actual position of the electron. Yes, this does not change the particle's evolution at the time we do this truncation, however let this evolve for a couple minutes and it wildly disagrees with experiment. So you CANNOT just say that because the wavefunction gives us the probability distribution, that the wavefunction can be updated if we new more about the probability distribution.

As soon as you are no longer in quantum equilibrium you may no longer make arguments about probability and relations to the wavefunction.

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But you are assuming the brain can distinguish between these states.

No, the brain is in different states.

To explain measurment with BM, the hidden variables at some point need to become no longer hidden. You claim not just that the states are different, but implicitly that the brain can distinguish these states ... that it can know the states are different. If the brain in your example doesn't have this "outside the theory" access to the hidden variables, then the states are NOT distinguishable, and therefore a measurement was NOT made (since it in no way determined anything about the particle positions).

You are wrong that your complaints are not new. Other people complain for several reasons, but nobody complains about stuff that you do.
The reason is the following. Maybe you are right that the Bohmian interpretation does not COMPLETELY solve the measurement problem. But at least it solves it partially, by making it completely equivalent to the measurement problem in CLASSICAL mechanics.

My complaints are not new.
This is not an issue in classical mechanics, for in classical mechanics, we don't need to require that some things are "hidden variables" in order to agree with experiment. Here, in order to maintain agreement with quantum mechanics, BM requires the positions to be hidden. Yet you ALSO want to claim that it is accessible to describe measurement ... your theory, which you present as if it solves the "measurement problem", merely just relates the measurement to another measurement outside of the theory... by claiming that macroscopic object positions can be observed directly instead of their wavefunction. You can't have it both ways.


Zenith8 also seems to claim no one ever complained about this before. Nothing here is new. As I've said before, I have not been thinking about this in a vaccuum... I've talked to physicists about this. And if you don't believe me, a quick google search easily found me evidence of other physicists making similar complaints.

Here's a snippet from a rant by R.F.Streater on this topic
"The theory is not consistent in its interpretation. It is set up as a probability theory; but a measurement of the position of the particle does not result in a conditioning of the probability distribution of the position. This is at the insistence of J. S. Bell, who championed the Bohm theory when it was more or less discredited. Bell said "No-one can understand this theory until he is willing to see psi as a real objective field rather than just a probability amplitude" [The Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, page 128, 1987]. This allows believers to claim that there is no measurement problem, as a measurement just reveals what the position is. The usual rules of probability would lead to the replacement of psi by a conditional probability, after a measurement has given us more info as to the whereabouts of the particle. However, this conditioning is exactly the collapse of the wave packet, and this is a dirty word among Bohmists: to allow it here might weaken the case against quantum mechanics.

The failure to condition after measurement leads to peculiar results even for positions. Y. Aharonov and L. Vaidman (pp 141-154) in "About position measurements", give many examples of this, similar to those in Englert, B.-G., Scully, M. O., Sussmann, G., and Walthier, H. : Surrealistic Bohm Trajectories, Zeitsschrift fur Naturforschung, 47a, 1175-1186, 1992. Ahahonov and Vaidman admit: "We worked hard, but in vain, searching for an error in our and Englert et al arguments"[sic]. They conclude "The proponents of the Bohm theory do not see the phenomena we describe here as difficulties of the theory", and quote a riposte of the Bohmists [Durr, D., Fusseder, W., Goldstein, S., Zanghi, N., Comment on Surrealistic Bohm Trajectories, Z. Fur Natur, 48a, 1261-1262, 1993."

Everett has also been known to complain that since the Bohm particles are unobservable entities, their addition provides nothing.


So again, I conclude either:
A] The hidden variables are accessible, thus the theory would not be equivalent to quantum mechanics for experimental predictions.
B] The hidden variables are NOT accessible, thus the theory cannot describe measurement.

 

[zenith8]

Here's a snippet from a rant by R.F.Streater on this topic

Let's not bring Streater into this. His arguments are just farcical. I believe Ilja has a http://www.ilja-schmelzer.de/realism/BMarguments.php" discussing exactly why..

 

[Demystifier]

This is not an issue in classical mechanics, for in classical mechanics, we don't need to require that some things are "hidden variables" in order to agree with experiment.

Yes we do. By definition, hidden variables are properties that exist even when we do not measure them. In classical mechanics we also assume that particles have positions and velocities even when we do not measure them, which, by definition, are hidden variables. If classical mechanics were formulated without hidden variables, then it would take a form similar to that of standard QM:
http://xxx.lanl.gov/abs/quant-ph/0505143 [Found.Phys.Lett. 19 (2006) 553-566]
http://xxx.lanl.gov/abs/0707.2319 [AIPConf.Proc.962:162-167,2007]

 

[Demystifier]

Everett has also been known to complain that since the Bohm particles are unobservable entities, their addition provides nothing.

They are observable, by weak measurements:
http://xxx.lanl.gov/abs/0706.2522 [New J. Phys. 9 165 (2007)]
http://xxx.lanl.gov/abs/0808.3324

 

[JustinLevy]

If you want to avoid Streater, fine.

I just got very annoyed by your method of arguing that no one has ever complained about these things, and therefore stating I believe there is a problem amounts to me claiming I am smarter than all the physicists before me. That is an insulting way to argue against my points. I readily admit that my tone is also not appropriate at times, due to my frustration. I will assume the best and take your tone to be evidence of similar frustration. Either way, please do not continue to use such methods of false debate.

So, which do you believe, are the bohmian positions accessible or not?

Yes we do. By definition, hidden variables are properties that exist even when we do not measure them. In classical mechanics we also assume that particles have positions and velocities even when we do not measure them, which, by definition, are hidden variables. If classical mechanics were formulated without hidden variables, then it would take a form similar to that of standard QM:
http://xxx.lanl.gov/abs/quant-ph/0505143 [Found.Phys.Lett. 19 (2006) 553-566]
http://xxx.lanl.gov/abs/0707.2319 [AIPConf.Proc.962:162-167,2007]

In classical physics, in principle, all variables are knowable to arbitrary precision. This makes none of the variables "hidden variables" as the term is usually used in physics.

I did not claim that classical mechanics assumed particles did NOT have positions and velocities when we do not measure then. You are using a combination of annoying semantical leaps and strawman arguments here.

So let's cut to the chase. You seem to clearly believe that the bohmian particle positions are accessible, if this is true, what prevents us from getting in a situation where the quantum equilibrium postulate is incorrect?

They are observable, by weak measurements:
http://xxx.lanl.gov/abs/0706.2522 [New J. Phys. 9 165 (2007)]
http://xxx.lanl.gov/abs/0808.3324

Okay, let's define bohmian particle velocity as the standard probability current divided by the wavefunction norm at that point.

These predict different root mean square velocities than quantum mechanics. If this is observable, then it is distinguishable.

As one friend mentioned, and I've also noticed on wikipedia, consider the ground state of a proton and muon. In bohmian mechanics, the ground state is a stationary state and the muon does not move, so rms velocity is zero. QM predicts non-zero velocity, and therefore the muon lifetime will be relativistically time dilated. They are distinguishable.

If you want to consider relativistic quantum mechanics, let's do so. Okay, the probability current in the ground state of the muon hydrogen atom now is non-zero (although only due to the "small" 3,4 component of the spinor). The velocity distribution still differs greatly from quantum mechanics, and therefore the lifetime distribution will disagree as well. Again, they are distinguishable.

The point is, if the "hidden variables" are no longer hidden and actually accessible, then the theory is no longer equivalent. You are on 'route A'.

 

[Demystifier]

JustinLevy, please read my post #39 and tell me whether you agree with it, and if not, why.
After that, we can continue the discussion.

 

[Demystifier]

As one friend mentioned, and I've also noticed on wikipedia, consider the ground state of a proton and muon. In bohmian mechanics, the ground state is a stationary state and the muon does not move, so rms velocity is zero. QM predicts non-zero velocity, and therefore the muon lifetime will be relativistically time dilated. They are distinguishable.

If you want to consider relativistic quantum mechanics, let's do so. Okay, the probability current in the ground state of the muon hydrogen atom now is non-zero (although only due to the "small" 3,4 component of the spinor). The velocity distribution still differs greatly from quantum mechanics, and therefore the lifetime distribution will disagree as well. Again, they are distinguishable.

I think we have already discussed that point and I have explained why I disagree.
But the crucial thing to understand is the GENERAL explanation why the predictions of BM are identical to those of standard QM. After that, the example above will be irrelevant.

 

[zenith8]

If you want to avoid Streater, fine.

Directing you to a page where every criticism that Streater makes is precisely and carefully rebutted is not avoiding him. What do you want me to do, type it all out for you?

So let's cut to the chase. You seem to clearly believe that the bohmian particle positions are accessible, if this is true, what prevents us from getting in a situation where the quantum equilibrium postulate is incorrect?

Of course Bohmian particle positions are accessible by ordinary position measurements (though not full trajectories, as the act of measuring generally disturbs the original trajectory).

What prevents you from getting in a situation where the quantum equilibrium postulate is incorrect is a property generally called 'equivariance' - which is carefully explained in just about every general article on BM that you have been referred to. Are you sure you've read them, as you claim?

Basically:

- particles initially not in quantum equilibrium that are 'stirred' by the guiding wave function tend towards quantum equilibrium i.e. they tend to become distributed as psi-squared. This has been shown theoretically and through explicit numerical simulation.

- if at some time t the particles are distributed as psi-squared, then at all later times they will continue to be distributed as psi-squared, provided that the wave function evolves according to Schroedinger's equation between the two times, and the particle configuration evolves according to the usual Bohm guiding equation. This is trivial to prove.

- What is not so simple to prove is that psi-squared is the only distribution with this property. Nevertheless it has been proven - see for example the paper "On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics" by Goldstein and Struyve (available online).

Thus quantum equilibrium is unique, and once established cannot be undone by Schrodinger evolution. Is that what you mean?

 

[Demystifier]

Okay, let's define bohmian particle velocity as the standard probability current divided by the wavefunction norm at that point.

These predict different root mean square velocities than quantum mechanics. If this is observable, then it is distinguishable.

You didn't read the papers above on weak measurements, did you?

 

[Demystifier]

So let's cut to the chase. You seem to clearly believe that the bohmian particle positions are accessible, if this is true, what prevents us from getting in a situation where the quantum equilibrium postulate is incorrect?

Perhaps you should read this:
http://xxx.lanl.gov/abs/quant-ph/0308039 [Journ. of Statistical Phys. 67, 843-907 (1992)]

 

[Demystifier]

Your answer to #1 and #2 lead to the obvious conclusion that Bohmian mechanics is NOT equivalent to standard QM in regards to experimental predictions.

Strictly speaking, that is true. Yet, nobody succeeded in proposing a concrete experiment that could distinguish between the two theories IN PRACTICE. In other words, they seem to have the same measurable predictions FOR ALL PRACTICAL PURPOSES.

This is a sort of the conclusion or summary of this thread.