Exploring the Bohmian Interpretation: Why Study It?

[Fra]

Then the principles of optimal inference implies that our "dice" is autoadjusting so that while our dice keeps changing, we always have an optimum dice. And optimum here is defined relative to priors and information storage etc. "Human dices" are simply ungraspable for subatomic particles, but they might be said ot have their own dices.

So we make progress with absolute minimal assumptions. The dice notation is just to symbolise that we construct a dice out of the uncertainty and say that at some point we have a range of options and we have no reason to buy one over the other, that defines and forms our dice.

/Fredrik

 

[jostpuur]

There was some confusion about the concept "objective physical reality". Perhaps "classical reality" gives a better intuitive idea of what this terminology was after for? To me complex amplitudes of standard QM and measurements processes themselves could as well be objective physical reality, so it wasn't really my point to try to say that we shouldn't know about reality. Instead my point was, that we should be ready to accept the fact that reality can be confusing (temporarily at least).

Talking about scientifical way, demanding that the nature is of a some specific kind doesn't seem very scientifical either.

 

[Fra]

Hmm... I would like to say what I suspect is a common misconception about "probabilistic techniques". To state a probability distribution, is not by far the same thing as to say that there can never be found further mechanisms. This need not be so.

Like jambaugh also touched, instead I think the proper way to think of these approaches, is as higher order extension to basic boolean(true/dalse) logic, bayesian logic, where the support for each statement is quantified. This allows for development of a scientific theory of "revision updates". Where the update is made on basis of current support with minimal ad hoc guesswork included. Data will guide us.

But current QM doesn't explore this full beauty. It has some old classical probability basis that deserves critics. I of course suspect we will see how this change as a consistent QG gravity is developed

Unlike those people who are more guided by "mathematical beauty" alone, I consider myself pretty philosophically inclined person and I put high emphasis on logical and philosophical consistency of theories and I have come to conclude for myself that this is the best way. I claim that these relational information models are not just "mathematical theories", they are rather IMO more deeply satisfactory on the philosophical level as well and far less speculative, and no ad hoc approach - thus IMO rendering it very scientific. Some of the weirdness is in fact not that weird after all. It's only weird if you try to understand it with a old style realistic mindset.

/Fredrik

 

[Demystifier]

In the past 50 years, Bohm's approach has led to no progress in physics, while the conventional QM approach has led to extraordinary progress in atomic, nuclear, solid state, and particle physics. (Most if not all of this progress involves what might be called a modified Copenhagen interpretation, which boils down to Born's idea that the square of the wave function is a probability density. None involves Bohm's interpretation.)

This is like saying that the undeniable progress in applied nuclear physics, which does not involve the hypothesis that protons and neutrons consist of quarks, while no applied science so far involved quarks, implies that the theory of quarks is a waste of time.
Nobody denies the phenomenological success of the conventional QM. Nevertheless, the Bohmian interpretation is compatible with it. The main goal of the Bohmian interpretation is not to provide an alternative to the conventional QM, but to understand the origin of QM at a deeper, more fundamental level. Just like the main goal of the theory of quarks is not to provide an alternative to conventional nuclear physics, but to understand the origin of nuclear physics at a deeper, more fundamental level.
Even if one day we find evidence that the Bohmian interpretation is correct, one does not expect that it will influence the practical phenomenological use of QM in conventional branches of physics such as atomic, nuclear, and solid state physics. Just as now existing evidence that quarks do exist did not influence the conventional nuclear physics.

 

[Demystifier]

And in all fairness to QM, I think that Bohmians should own up to a simple admission of their own: if there are non-local interactions, why is it that c is so fundamental in the propagation of information and all other cause/effect relationships? This has not been "unambiguously" answered (except maybe in their own minds) ...

That is true. The Bohmian interpretation has not unambiguously answered this question. However, the conventional interpretation has not unambiguously answered some other fundamental questions, which the Bohmian interpretation has. An example closely related to your question above is:
If physics is local, why is it that wave function is a nonlocal object that cannot be replaced by a local one?

Both interpretations have some advantages and some disadvantages.

 

[DrChinese]

That is true. The Bohmian interpretation has not unambiguously answered this question. However, the conventional interpretation has not unambiguously answered some other fundamental questions, which the Bohmian interpretation has. Both interpretations have some advantages and some disadvantages.

I think this is very accurate. I don't think we'd have these "feisty" discussions if one of the interpretations answered everything. Each gives us a somewhat uncomformtable piece of baggage to deal with.

Yet we all appreciate the underlying science, regardless of the correct interpretation.

 

[ueit]

Some points.

I.) A "statistical description" i.e. a probabilistic language is better, not worse than the alternative. We can still indicate certain knowledge of an outcome e.g. [X will occur with 100% probability, Y will occur with 0% probability.] But we can also express those intermediate degrees of knowledge in between. Thus utilizing a statistical language is an expansion of possible physical statements about what we may know about nature rather than a limit.

OK.

II.) Science has no duty per se.

Sure, I meant something like “in the sphere of science” as opposed to “in the sphere of philosophy”. I’ve seen quite often the argument that asking for a reason why a certain particle was detected in a certain place is not a scientific question, but a philosophical one.

Science is an epistemological discipline (that of belief based on repeatable empirical test) and it is the duty of the scientist qua scientist to abide by that discipline. The canard about the Moon ceasing to exist when not observed is a total misconception of this principle. The statement about the non-reality of the moon is just as invalid as the statement of its existence. Baring an empirically verified means of prediction the duty-bound scientist would simply state his ignorance of the moon's state of existence between observations.

With this in mind the duty-bound scientist should formulate theories in an operational language and avoid expressing opinions about what cannot be observed. This can be most difficult when those opinions are implicitly integrated into the formal language he uses. One such case is the use of the language of classical states when the effect of observing said states is an open question. (Another is the use of implicit absolute time in discussing relativistic phenomena such as traveling twins.)

OK.

II.a) Point (I.) then brings up the question as to whether an accurate physical theory, expressed within a probabilistic language, is possible in which all statements about the empirical behavior of a system can be simultaneously predicted with probabilities of the 100% vs 0% variety. Call this classical determinism or classical completeness. It comes to the same thing when one is attempting to extrapolate future phenomena from past experience (the main purpose of science).

OK

If so then Bell's inequality cannot possibly be violated.

False.

Bell's inequality begins by asserting that a physical system has a physical state representable by the selection of one point in a set of possible states.
…
Since empirically we have observed Bell inequality violation then Classical determinism is disproved and QM is still a viable theory.

It also begins by asserting that the particle source and the two detectors must be independent of each other. A theory in which the spin of the entangled particles is a function of detector’s state could violate Bell’s inequality while still not denying classical determinism.

It is not per se a question of locality.

I agree. Any mechanism that denies the assumption of statistical independence between the experimental parts of an EPR experiment could violate Bell. The mechanism can be either local (the source extrapolates future detectors’ state from their past state arrived at the speed of light) or non-local (function collapse).

Note that by allowing FTL causal effect in QM you also allow future-to-past effects (assuming Einstein's theory is close to correct) which in turn allows any past observation to be changed in the future. You loose classical determinism anyway and also loose any sense of reality as it is.

I’m not so sure about this. I think it is possible to simulate relativity on an absolute frame of reference and still retain classical determinism. However, I think that the non-locality of QM is rather an illusion produced by an underlying local mechanism, somehow similar with the non-local gravity of Newton being based on the local GR mechanism.

III.) Quantum mechanics is causally deterministic: When you ask the question: Can any specific outcome be positively determined? The answer is yes in QM. Set up a specific observable and there is a prior measurement which will tell you with certainty which value will be observed. Even in classical mechanics one implicitly assumes a prior measurement must be made before one can know with certainty the outcome of a later observation. This is true for any choice of outcome provided one understands that the choice of prior measurement must depend on the choice of outcome to be predicted. However QM does not assume that intermediate measurements fail to invalidate this predictability e.g. QM recognizes that observation = interaction.

I agree.

IV.) It is the concept of the classical "state of the system" which implicitly assumes that all possible measurements may be made simultaneously. Quantum Mechanics relaxes this a priori assumption and allows that the non-commutativity of observables be determined empirically instead of dictated by "religious tradition".

Yes, but this is because QM works with statistical entities that may not exist per se. In thermodynamics we also see such concepts like temperature, pressure specific heat and so on.

One must at the same time reject the concept of state based reality as a non-contingent absolute. Our construction of an ontological reality is that of building a model in our heads wherein phenomena there correspond to empirical phenomena. In transcending the classical description we must put aside the use of ontological models and stick to a wholly phenomenological language of observables and events.

I strongly disagree. “Putting aside the use of ontological models” does not allow one to get pass statistics and relate experimental observations (the spot produced by an electron on a screen) with the prior state without appealing to chance. “it just happens” is not science.

This is as hard and counter-intuitive as letting go of absolute time in Special Relativity, if not more difficult. But it is necessary to understanding QM whether you agree with it or not.

I disagree that such a sacrifice is necessary. See above.

V.) The indeterminism of quantum mechanics comes from the logical incompatibility of the sequences of assertions in the relevant experiment.
E.g. that a photon is polarized vertically is logically incompatible with it being left-hand circular polarized.

It is not necessary to see a logical incompatibility here. It depends on how one understands spin. In BM, for example, spin is not in intrinsic property of a particle. The indeterminism is probably related with incomplete knowledge of the state.

It is the very deterministic nature of quantum mechanics which equates (e.g. for a free photon) that an earlier plane polarization measurement is equivalent to a later one and thus an earlier assertion about plane of polarization is incompatible with a deterministic assertion about a later circular polarization measurement. The only way to reconcile the incompatibility in what we assert must happen with what we may observe in some cases, is to expand our logical language to include probabilities.

I think that logic works just fine as it is.

Regards,
Andrei Bocan

 

[jambaugh]

OK.
It also begins by asserting that the particle source and the two detectors must be independent of each other. A theory in which the spin of the entangled particles is a function of detector’s state could violate Bell’s inequality while still not denying classical determinism.

I hope you didn't mean "theory" but rather circumstance. If such dependence is necessary "in theory" for all such cases then you again violate classical determinism. The initial preparation of the detectors is forced to depend causally on the later interaction of the particles with the detector. They thus cannot be considered to have been in an "initial state".

Once you assert than you can establish the independence of the source and detectors then any Bell inequality violation in this circumstance denies classical determinism. This is the experiment which has been performed.

If you construct a combined state manifold for all the equipment involved then you again get Bell's inequality on any distributions of outcomes. Classical determinism dictates that probabilities of outcomes form measures on the state manifold of the large system in question. Bell's inequality is just a convoluted way to say that the probabilities form a measure on sets of states. Given a measure you have a metric on set differences and this satisfies the triangle inequality aka Bell's inequality.

 

[jambaugh]

OK.
I strongly disagree. “Putting aside the use of ontological models” does not allow one to get pass statistics and relate experimental observations (the spot produced by an electron on a screen) with the prior state without appealing to chance. “it just happens” is not science.

Not "it just happens" but "if this happens" then "that is likely to happen with probability p". That is all science can ever say and it doesn't need an ontological model to say it. It does take models to say it succinctly but those models need not be fundamentally ontological. We can use nouns to describe electrons as long as we understand that at the foundational level:
"and electron is a process of quantized charge and mass transport" or some other phenomenological description.

What's more ontological models are the most natural conceptually, we evolved using them. In doing chemistry we don't need to get into philosophical debates about the "reality of the proton" it is contingently real and objective. This contingency is on our staying in the domain of chemistry.

Where I see the issue as important is in the attempts to build a fundamental theory of everything by starting with an ontological construct e.g. strings. One should begin elsewhere... out of time... more later.
Regards,
JB

 

[jambaugh]

OK.
I think that logic works just fine as it is.

But one must be careful not to commit category errors and confuse the logic of statements about a physical system (which presupposes an act of measurement) and logical statements about what we know about a system (e.g. statements about what measurements have been or will be made.)

We can assert that we have both determined the z-component of spin of an electron and (later) determined the z'-component of spin. This is a statement about what we have done in a lab. But the statements about an electron; that the z component is +1/2 and that the z'-component is +1/2, are incompatible (in QM) as both cannot be asserted simultaneously (said simultaneity implicit in the objective language).

This incompatibility is apparent at the previously used higher level of abstraction. In a physical theory it is implied by a statement about the system that the determination of that statement has also been made, (or at list can be made). Since both determinations cannot be made simultaneously or in such a way that each doesn't preclude the other then the two statements themselves are incompatible since the meta-statement that both statements have been tested is "anti-tautological" or always false.

The logic is fine when used correctly. But for example parsing the EPR experiment without playing close attention to the levels of abstraction and the use of counterfactual assumptions leads one to headaches and insanity.

The specific confusion in this case is the improper identification of the two statements:
"We can predetermine the outcome of any measurement of one half of an EPR pair" (by making the corresponding measurement of the other half)
with
"We can predetermine the outcome of every measurement of one half of an EPR pair".

Once you choose to make one such measurement then any assumption which is inconsistent with having made that choice, is either meaningless or must presuppose we have jumped into a different instance of the system and thereby making the original assumption invalid.

Regards,
J. Baugh

 

[ueit]

I hope you didn't mean "theory" but rather circumstance. If such dependence is necessary "in theory" for all such cases then you again violate classical determinism. The initial preparation of the detectors is forced to depend causally on the later interaction of the particles with the detector. They thus cannot be considered to have been in an "initial state".

By "theory" I mean a hypothetical local hidden variable theory of the type you claim it has been proven impossible to exist.

I claim that it is possible that the source (a calcium atom in a PDC) generates a pair of entangled photons with the spin being a function of the future detector orientation, which is extrapolated from the data available at the present moment (this is possible in principle if the detectors are deterministic systems)

Let me give you an example. If NASA wants to launch a ship to Mars it will not launch towards the present position of Mars but towards its extrapolated position at the time the ship is expected to arrive there. In this case would you say that this space mission violates classical determinism because "the initial preparation" of the rocket "depends causally on the later" encounter with the planet?

Once you assert than you can establish the independence of the source and detectors then any Bell inequality violation in this circumstance denies classical determinism.

I wouldn't assert such a thing in a fully deterministic system. It is an assumption that may or may not be true. I tend to think it is not true.

This is the experiment which has been performed.

I disagree.

 

[Demystifier]

So far, we have been discussing arguments for the Bohm deterministic interpretation within the nonrelativistic QM. These can be viewed as traditional arguments. However, in the case of relativistic QM, there is an even stronger reason to introduce a deterministic interpretation. This is because the conventional probabilistic interpretation in the case relativistic QM is simply inconsistent. See e.g. Secs. 7. and 8. of
http://arxiv.org/abs/quant-ph/0609163
as well as
http://arxiv.org/abs/quant-ph/0307179
http://arxiv.org/abs/quant-ph/0406173
For a "non-philosophical" formal derivation of the field/string Bohmian equation of motion from the requirement of relativistic covariance see also
http://arxiv.org/abs/hep-th/0407228
http://arxiv.org/abs/hep-th/0601027
http://arxiv.org/abs/hep-th/0512186

 

[Demystifier]

It is interesting that, whenever I use a non-philosophical argument supporting the Bohmian interpretation as in my last post above, the opponents of the Bohmian interpretation suddenly get silent.

 

[Fra]

Perhaps not everyone knows all the math, but i also think it takes more effort to read x number of papers and then response in detail :)

That's why I didn't read and reply.

Actually parts of the bohmian formalism, and deal with amplitude and phase separately has appealed to me as well. I fiddled with that some time ago. I am reevaluating the formalism myself, and I am not sure that the final ultuimate formalism will be the complex amplitude approach. Maybe there are others that have merits.

The complex phase i actually interesting, although I may not like the bohmian notion and his philosophy. For the same reason I choose not to spend very much time analysing alternatives, givne limited time. but of course if the predictions are the same, it no more right or wrong than anything else. But I tihnk for bohmian notion to get more attention the approache needs to take things further and solve things the ortodox approach doesn't.

I've realized the same thing for myself, I'm not going to convince anyone with fuzzy arguments, the remaining choice is to try and work out a proof that solves problems not yet solved. That alone takes a decent amount of time.

/Fredrik

 

[Mentz114]

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

 

[Demystifier]

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

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

 

[Fra]

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

/Fredrik

 

[Mentz114]

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

 

[Cane_Toad]

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

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

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

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

 

[Mentz114]

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

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

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

 

[Fra]

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

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

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

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

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

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

/Fredrik

 

[Demystifier]

Are there some bohmian programs to grand unification?

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

 

[Fra]

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

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

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

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

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

/Fredrik

 

[Demystifier]

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

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

 

[Demystifier]

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

 

[Fra]

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

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

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

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

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

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

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

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

/Fredrik

 

[Fra]

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

/Fredrik

 

[Fra]

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

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

/Fredrik

 

[jambaugh]

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

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

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

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

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

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

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

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

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

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

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

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

Regards,
J. Baugh

 

[jostpuur]

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

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

 

[Demystifier]

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

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

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

 

[Demystifier]

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

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

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

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

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

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

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

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

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

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

 

[jambaugh]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Regards,
James Baugh

 

[Demystifier]

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

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

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

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

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

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

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

 

[jambaugh]

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

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

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

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

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

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

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

Regards,
James Baugh