How Many People Actually Understand QM?

[christianjb]

I tried posting details here in QP at one time in a separate thread and got shut down precisely because it's not on the arXive yet. If I post on IR, that almost guarantees no audience. But I'm tired of hearing people complain that QM is not logical, when I clearly have a possible answer to that. So I see no harm in posting a link for those who are interested.

I'm not sure I could get this posted on the arXive anyway since I'm not affiliated with any university, nor do I have a PhD in physics. I have to doubt that any PhD could have derived this theory because it is an implication of consistency and not an equality. I had to start with a premise that QM does not imply. Instead consistency implies QM and not the other way around. Do you believe that's a fair premise to start with?

If it is possible to publish on the arXive, I would certainly want some comment from those more skilled in the art before posting there. And this is the next best thing to the arXive that I know of. It is precisely because I don't what to appear as a "crank" that I'm asking people here to look at it. I would think that if it is you intent to save me from embarrassment, that you would take a look at it and find the obvious flaw. Come on! It should only be a 10 minute read for someone with your skills. None of the experts on sci.physics.foundations has shot it down yet. Who knows, maybe you're wiser than they are.

We're talking about the article at:

https://www.physicsforums.com/showpost.php?p=1308908&postcount=1

I had a quick look- and I estimate your probability of being a crank at >95%.

1) Only scientist mentioned is Feynman. (Though + points for spelling Feynman with the right number of n's.)

2) No references.

3) Attempt at TOE.

4) This theory doesn't predict anything we don't already know, or am I missing something? Does it make any predictions of anything?

5) Your woefully inept attempt at flattery (see above).

6) No university affiliation. No PhD in physics. Hey, who said life was fair?

On the plus side:

1) I don't understand anything you have written, so you might be the next Einstein for all I know.

2) You worked out how to use latex, which requires some brains.

3) Your mathematics is not obviously wrong, i.e.- your equations look like actual equations that you might see in a paper.

4) I can't find fault with it- which doesn't mean much given point 1) above.

 

[Hurkyl]

If it's independent research, then it doesn't really belong in the main forums, and certainly not in someone else's thread.

Your submission has already been placed in the IR queue -- if and when it has been approved, it will be available there for discussion.

 

[vanesch]

The only problem is that, according to QM, classical systems do not exist. :tongue:

Well, that's a sloganesque view on things - although I see what you want to say. Now, as far as Bohmian mechanics goes, it is IMO a DIFFERENT theory from quantum theory, although empirically equivalent, though conceptually and formally totally different. So, the question "How many people actually understand QM ?" doesn't apply to Bohmian mechanics here. If one understands Bohmian mechanics, that wouldn't mean that one has progressed in one's understanding of quantum mechanics (one would probably simply dismiss it as a conceptually erroneous framework).

So, I will limit myself to quantum mechanics proper. As people pointed out, the formal machinery of quantum mechanics is, although somewhat sophisticated, quite understandable ; one can even devellop quite some intuition for it. This is probably sufficient to say that one "understands" quantum theory: one has a certain intuition for the behaviour of the formal solutions, one has a feeling for what part is physically relevant, and what part can be neglected etc... With sufficient practice, this is very similar to the intuition one can have concerning, say, classical electromagnetism.

Concerning the conceptual understanding, things are less clear, but it is not sure that it is quantum theory that is giving difficulties, or our pre-conceived ideas of what nature *should* look like!
I find personally, relativity (with its static block-spacetime) just as intuitively and conceptually difficult as quantum theory: both formalisms do not correspond to what we intuitively expect nature to be like ; and especially, indicate that there is a difference between what we subjectively experience, and what nature "really is like". Once we've realized that there is a non-evident link between the natural picture presented by a formalism, and our intuitive understanding of what we take as an ontological hypothesis, it is not sure that the meaning of "understanding" is relevant on this level, as it is more a matter of philosophy than of physics proper.

 

[Anonym]

QM is strange because Nature is strange. Most of us do very nicely without axioms or postulates and so forth, if we know the physics. If you know QM axioms, but not the physics, then you have no chance to understand QM.

You have no idea what you are talking about. You can’t know QM or Physics axioms (postulates) if you do not know and understand the physics.

Measurement: Are you so sure that the classical measuring process can be fully explained? It cannot.

You consistently repeat that and similar statements in your posts. If so, I do not understand why you choose scientific research to be your profession during last 40 years and what you did during this 40 years.

You confuse the physics with the religion (I am aware that the religion have much deeper historical ruts than the empirical science). I may reconcile your faith with the physics. God worked hard 5 days to define laws of Nature. Then He invented the man and the woman. What was the purpose? He needed something that will be able to appreciate his work, to understand it and to invent the wheel and GPS as a consequence of his/her knowledge and understanding. By the way, it is impossible to construct and operate GPS without math. of SR.

You cannot predict(for the most part) any measurement of anything; you might win occasionally, but your measurements in total will have a nonzero variance. QED

On Russian we say: bred sivoy kobili (“even not wrong”).

There is no way that the consistent and adequate theory of measurements will not be formulated soon.

Regards, Dany.

 

[christianjb]

Anonym (Dany),

There's no need for writing things like

'You have no idea what you're talking about.'

It just causes resentment and bad feelings. Also- your post isn't adding anything useful (that I can see) to the thread.

 

[Anonym]

The OP wasn't really interested in knowing how many people understand the physics, they were asking how many can understand the math. I'm pretty sure they meant the math in an introductory text. When Feynman said no one understands QM, he didn't mean to imply that the authors couldn't do the math in their own books. In my opinion, anyone who is not mentally handicapped can understand an introductory QM text like Shankar's by the simple act of applying themselves to the task. However, lack of interest will prevent most people from commiting themselves for the amount of time it would take.

My POV is identical to that.

There's no need for writing things like
'You have no idea what you're talking about.'
It just causes resentment and bad feelings. Also- your post isn't adding anything useful (that I can see) to the thread.

Provided that Jimmysnyder and mine interpretation is correct, it intended to help OP to be confident that the effort will be fruitful. To study physics is not picnic, it is spit blood.

Your statements like “There is no collapse of the wavefunction! Ever!” only amuse me since you don’t know that they are in contradiction with A.Einstein, E. Schrödinger, W. Heisenberg, P.A.M. Dirac, J. von Neumann, etc. attitude. I exclude the possibility that you consider yourself understand physics better then them.

However, Reilly is completely different story. Reilly has deep and extensive knowledge of CED, QED, Classical and Quantum Optics. In addition, he knows the history of physics. His POV is the expression of ideology or philosophy: agnosticism. I have nothing against that, but 1) not here in PF in front of inexperienced beginners; 2) without falsifications, since it is in contradiction with the experimental evidence provided by 350 years development of physics.

Regards, Dany.

 

[lalbatros]

reilly,

*1* Too bad, I strongly believe that an intro to QM must, repeat must, deal with the phenomena that drove the development of the subject.

Well, don't worry too much.
The professor was really first class and before introducing the postulates he gave us a background to understand them mathematically as well as physically. And of course, most of the lectures thereafter gave a more complete view of the physics. I don't like the postulates very much. But I think they really do catch somehow the physics: every lab experiment can finally be analysed in the terms of the postulates.

I probably don't like them because they go too far in the interpretation of QM and lead to irrealistic questions and useless debates. This is related to the well known question "can the SE represent the measurement process". As a huge majority of people, I am convinced the SE can do this job. Presenting things otherwise with the postulates makes no practical problem, but it is not very satisfactory and not totally convincing.

Michel

 

[Demystifier]

Well, that's a sloganesque view on things - although I see what you want to say. Now, as far as Bohmian mechanics goes, it is IMO a DIFFERENT theory from quantum theory, although empirically equivalent, though conceptually and formally totally different. So, the question "How many people actually understand QM ?" doesn't apply to Bohmian mechanics here. If one understands Bohmian mechanics, that wouldn't mean that one has progressed in one's understanding of quantum mechanics (one would probably simply dismiss it as a conceptually erroneous framework).

The above was your response to my assertion that, according to QM, classical systems do not exist. I cannot understand why do you think that such an assertion necessarily implies Bohmian mechanics? Are you saying that, in all other interpretations of QM, classical systems do exist? What about MWI? In my opinion, the existence of classical systems is assumed ONLY in the Copenhagen interpretation. ALL other interpretations attempt to interpret QM without introducing such a vague assumption.

 

[vanesch]

The above was your response to my assertion that, according to QM, classical systems do not exist. I cannot understand why do you think that such an assertion necessarily implies Bohmian mechanics? Are you saying that, in all other interpretations of QM, classical systems do exist? What about MWI? In my opinion, the existence of classical systems is assumed ONLY in the Copenhagen interpretation. ALL other interpretations attempt to interpret QM without introducing such a vague assumption.

You are right, I went too fast and was presuming that your statement was a critique on quantum theory and an endorsement of Bohmian mechanics (which has a Newtonian ontology as part of its metaphysical structure).

I am with you that quantum theory as it is known today implies somehow that classical systems "do not exist" although -as I said - that's a bit sloganesque.

First of all, one could (as do the Copenhagen adherents) say, that not everything is describable by quantum mechanics. This could be because there is a dichotomy in nature (some things obey quantum mechanics, others obey classical mechanics), or because quantum theory is an approximate theory, which only works well for certain systems, and works worse and worse for others. In other words, we start from the premise that quantum theory is not a universal theory, and that its principles and formalism are approximative.
Quantum theory (as a kind of approximate formalism) can hence only make sense when "bathed" within classical (or other) theories, and clearly, this classical theory isn't then a part of quantum theory. This implies somehow that we don't know the correct theory, unless we accept a dichotomy in nature (which was, if I understand well, Bohr's viewpoint).

One could also say that nature is classical, or contains at least a classical (Newtonian) metaphysics, and quantum theory is just a (correct) statistical description of that Newtonian world. This is Bohmian mechanics. It is the only view I'm aware off in which "quantum theory" can be universal, and in which there is an objective, unique classical world included. The problem (in as far as this is a problem) is that one needs to have an ether-view on relativity (and not a spacetime view).

Or one could take the current unitary quantum formalism as a suggestion for an ontological metaphysical picture (this is the MWI viewpoint, in the broad sense). Now, in order for this to make sense, there needs to be a difference between the metaphysical ontology, and the subjectively experienced "reality". The last one is, by postulate, "classical". So in as much as this last subjectively experienced "reality" is "real", there is some form of classical reality even in MWI, but it doesn't appear in the formalism per se. So in this view, quantum theory can be universal, and in as much as there are postulated to be observers that observe classical worlds, the formalism can tell you what they will see. But you need to bring in that part of "classicity" by hand, as a purely subjective phenomenon. That doesn't mean that the part of classicity is not *suggested* by the quantum formalism. Indeed, decoherence, and the splitting of the wavefunction in "independent" parts which correspond to classical systems is highly suggestive. But saying that a subjective observation will correspond to JUST ONE of them is a statement that must be brought in by hand. I suppose that this is what you wanted to point out with your remark that classical systems do not exist in QM: the quantum state doesn't evolve naturally to a single classically-looking state.

 

[Demystifier]

Or one could take the current unitary quantum formalism as a suggestion for an ontological metaphysical picture (this is the MWI viewpoint, in the broad sense). Now, in order for this to make sense, there needs to be a difference between the metaphysical ontology, and the subjectively experienced "reality". The last one is, by postulate, "classical". So in as much as this last subjectively experienced "reality" is "real", there is some form of classical reality even in MWI, but it doesn't appear in the formalism per se. So in this view, quantum theory can be universal, and in as much as there are postulated to be observers that observe classical worlds, the formalism can tell you what they will see. But you need to bring in that part of "classicity" by hand, as a purely subjective phenomenon.

So, would you agree with the following?
To make the DYNAMICAL equations of QM (which do not include the wave-function collapse) universally valid, both MWI and Bohmian mechanics (BM) introduce something ADDITIONAL that is not already present in the basic formalism of QM. Moreover, in both cases it is something ontologically CLASSICAL. In the case of BM, these are kinematically classical particle trajectories, while in MWI these are classically real subjective experiences. The main difference between MWI and BM is that the additional thing in BM is objective and formal, while in MWI the additional thing is subjective and not formal. In this sense, BM seems to be more in accordance with the usual practice in theoretical physics, which, of course, is by no means a proof that it is more likely to be correct. (Theoretical physicists may be wrong with their common belief that nature must be completely mathematical.)

 

[Anonym]

For myself, the strange questions came right from the beginning.Why would the SE not be able to describe the measurement process? Well, still I would like to present QM in another way and show why and how the measurement postulate in useless.

This is related to the well known question "can the SE represent the measurement process". As a huge majority of people, I am convinced the SE can do this job.

I will integrate your statements here with what was discussed in Is the QM postulate for measurements misleading?:

I don't want to convince, but to learn and to test my opinion.

So, do it!

That the SE governs quantum systems is not an interpretation.The probability amplitude is not either, it is the root definition in QM.

That last sentence is an interpretation.
But this one's not a matter of interpretation; it's a matter of the mathematics. Time evolution in QM is unitary. Wavefunction collapse is not unitary. Therefore, a wavefunction collapse cannot occur through ordinary time evolution.

You not only missed the right page, you don’t want to learn and to test your opinion.

The probability treatment of the single particle state (wave packet) is the M.Born statistical interpretation by definition (for a huge majority of people).

Amazingly, 95% of your statements are correct but in crucial point you miss again the right page:

Each statement in physics should be supported by the experiment. During 80 years it was not suggested and it was not performed the experimental verification of that “root definition in QM”. Today we have ability to do that. My unambiguous prediction of the result is that the M.Born statistical interpretation is wrong.

The M.Born statistical interpretation is the corner-stone of all interpretations. However, I have no doubt that it will remain in the QM dictionary for ever.

Regards, Dany.

 

[vanesch]

So, would you agree with the following?
To make the DYNAMICAL equations of QM (which do not include the wave-function collapse) universally valid, both MWI and Bohmian mechanics (BM) introduce something ADDITIONAL that is not already present in the basic formalism of QM. Moreover, in both cases it is something ontologically CLASSICAL. In the case of BM, these are kinematically classical particle trajectories, while in MWI these are classically real subjective experiences. The main difference between MWI and BM is that the additional thing in BM is objective and formal, while in MWI the additional thing is subjective and not formal. In this sense, BM seems to be more in accordance with the usual practice in theoretical physics, which, of course, is by no means a proof that it is more likely to be correct. (Theoretical physicists may be wrong with their common belief that nature must be completely mathematical.)

Essentially, yes, I agree with what you write. I would, however, like to make two observations. The first one is, that even a classical formal theory, such as Bohmian mechanics, or Newtonian mechanics, is still not giving any explanation of any subjective phenomena. That is, a theory/metaphysics/worldview/philosophy that wants to be universal, must account for the fact that certain parts of the formal ontology must be connected to what I'd call "the subjective experience". It is the mind/brain problem in a way, or the hard problem of consciousness in philosophy ; and also, related to this, the philosophical problem of heaceity (http://en.wikipedia.org/wiki/Haecceity although it is not a very good article).

I mean by the above that, given a Newtonian (or Newtonian-like theory, such as Bohmian mechanics), you still cannot deduce what *I* will experience subjectively, unless you explicitly define that *I* corresponds to a certain body, which is a subset (which one ?) of all the particles in your theory. You have to state explicitly, and outside of your formal theory, that *I* will correspond to this set of (brain) particles, and that these configurations will correspond to these sensations.
However, it is true that in Newtonian-like theories, this step seems so intuitively clear that one doesn't even think about it. Nevertheless, it is part of any "theory of observation", even in Newtonian(-like) theories.

Now, in MWI, this step is also present, but becomes much less intuitively clear (and that's why many people don't like it, simply because they think that the problem *appears* in MWI, although it was also present in Newtonian(-like) theories, but could be overlooked). Here, the designation of what part of the "physical ontology" is going to correspond to the "I-experience" is a non-trivial and essential element in the "observational link" between formalism and perception. But it is based upon the same principle as in Newtonian-like theories: some part of the formalism must be postulated (outside of the theory itself) as to correspond to subjective experience. Now, the difference with Newtonian-like theories is that the part that corresponds to the "Ich-Erlebniss" is not a "material" part (a certain subset of particles), but rather a "state" part. This is counter-intuitive. We seem to be able to accept without problem that our "body" (= the part of the postulated ontology that generates our subjective perceptions) is a particular *material* part of the universe, but we seem to have intuitive difficulties accepting that it is a "state" part. Now, what is so terribly disturbing in MWI is that this definition of the "Ich-Erlebniss" - which is usually relegated to obscure philosophical discussions without any interest for practical people such as physicists - is now a crucial part of the entire phenomenon of observation. Because of its intuitively clear character in Newtonian-like theories, one can pretend to neglect this philosophical aspect, while one is pushed with one's nose into it when looking at something like MWI.

In other words, there is a philosophical problem hiding in *any* interpretation of a physical theory, which must ultimately link a formalism to actual (and hence subjective) perceptions, and which we could call the observational postulate. This problem is, deep down, just as present in a Newtonian-like theory as in MWI or relativity or whatever formal/mathematical physical theory. Only, we can "use our intuition" in these theories, and pretend somehow that the problem doesn't exist there.

As such, what is "attached" as a vague, subjective and informal element (namely, the observer-states which are subjectively perceived) in MWI is exactly that same philosophical problem, but now explicitly put forward, given that it is not intuitive anymore.

The second observation I would like to make is that the "gain" in formality in Bohmian mechanics (which I think is only apparent, because one substitutes the explicitly subjective part of MWI by a non-spoken part as in all Newtonian-like theories) is done away with by its non-compatibility with a spacetime manifold formulation. I agree that this is an observation of another order, as the spacetime manifold formulation of relativity could also be totally misguided, once we are doing all this.

 

[Demystifier]

Vanesch, given what you said above, would you say that MWI is more ambitious than BM, in the sense that MWI attempts to say also something about the origin of subjective experiences, while BM does not even attempt to say something about that (certainly deep, fundamental, and difficult) problem?
By being more ambitious, would you also say that MWI is more speculative as well? BM is only a modification of classical mechanics (in this sense it is not so speculative), while MWI is attempted to be much more than this.

Another question:
If there was an INDEPENDENT (i.e., not based on the assumption of the Bohmian interpretation) theoretical or experimental evidence that the usual spacetime interpretation of relativity is not really correct at a more fundamental level, would BM become more acceptable to you than it is now? (If yes, I can give you links to some of my papers that present some theoretical arguments in that direction.)

 

[reilly]

[/B]:


Each statement in physics should be supported by the experiment. During 80 years it was not suggested and it was not performed the experimental verification of that “root definition in QM”. Today we have ability to do that. My unambiguous prediction of the result is that the M.Born statistical interpretation is wrong.

The M.Born statistical interpretation is the corner-stone of all interpretations. However, I have no doubt that it will remain in the QM dictionary for ever.

Regards, Dany.

How would you show that Born is not right?

What to do if Born is wrong?

Regards,
Reilly Atkinson

 

[vanesch]

Vanesch, given what you said above, would you say that MWI is more ambitious than BM, in the sense that MWI attempts to say also something about the origin of subjective experiences, while BM does not even attempt to say something about that (certainly deep, fundamental, and difficult) problem?

Not really. BM takes on the hypothetical "solution" to that problem by copying the intuitive notion we have about it ; in other words, it *ignores* the issue, but it can get away with it, based upon the intuitive notion we have which fills in the gap.

As MWI needs to propose a non-intuitive "solution" to the problem at hand, it is obliged to state it explicitly. So MWI doesn't attempt to say MORE than BM, but is obliged to state it explicitly, while BM can "leave it to the philosophers", given that our intuitive notion of the problem is good enough.

But I don't see that as a kind of objection. It is not because, say, natural numbers have a (slightly) more intuitive notion to them than integers, with those "counter-intuitive" negative values, that the foundations of integer arithmetic (using sets and stuff like that) is to be seen as "more ambitious and hence more speculative" than the arithmetic of natural numbers, if you see what I mean (maybe a poor example, but I hope you get the gist of it).

No, MWI is not "a theory attempting to explain subjective experiences" or anything of the kind. It just contains a less intuitively evident relationship between "subjective experience" and "ontology" than we are used to, and hence has to state things slightly more explicit, than what we are used to in classical theories. It is just the "explicitness" of the subjective/objective link which is a bit stronger in MWI than in classical theories.

By being more ambitious, would you also say that MWI is more speculative as well? BM is only a modification of classical mechanics (in this sense it is not so speculative)

It is not such an innocent "modification of classical mechanics" as the whole wavefunction ontology (living, remember, in Hilbert space, not in real space) needs to be added onto it. It's not just "changing the force laws" if you see what I mean.

Another question:
If there was an INDEPENDENT (i.e., not based on the assumption of the Bohmian interpretation) theoretical or experimental evidence that the usual spacetime interpretation of relativity is not really correct at a more fundamental level, would BM become more acceptable to you than it is now? (If yes, I can give you links to some of my papers that present some theoretical arguments in that direction.)

If there is another view, that has just as much formal "predictive power" than the usual "spacetime manifold" view of relativity, yes, I guess so. Are you hinting at Ashtekar variables (I am only vaguely aware of what it is about, honestly) ?

 

[Anonym]

How would you show that Born is not right?
What to do if Born is wrong?

“Well, don't worry too much” (Michel).

Consider single electron/photon set up. According to the Born’s statistical interpretation, after beam splitter one obtains the statistical distribution which represents the potential reality carried by the single particle due to interaction with itself. Alternatively, you may treat it as the same particle propagating in the different waveform after interaction with the beam splitter. The difference is that according to the laws of the statistical mechanics, it is impossible to assemble back the initial wave packet. According to deterministic “interpretation” it is enough to include into the measurement assembly a device that will perform the inverse transformation in order to obtain the initial wave packet. If it is correct, then it is clear that the Mach-Zehnder interferometer will do a job. We (I and my son) discussed that as a proposal and turned to the literature to see what A.Tonomura et al. (in particular) are doing last time. We were not surprised to find that they are doing something very similar (“Double-biprism electron interferometry”, App. Phys. Lett., 84(17), 3229 (2004); “Triple-biprism electron interferometry”, JAP, 99, 113502 (2006)). Moreover, it seems that the presented results confirm our expectation. We still do not understand all necessary details of the experiment to be sure that that it (Triple-biprism is expected to present the pattern obtained after the first biprism as in the original 1989 experiment).

From the theoretical side, it was pointed out by Y. Aharonov and L.Vaidman, Phys.Rev.A, 41,11,(1990) that in case of two component wave packet the expansion coefficients are the eigenvalues of two self-adjoint mutually commuting operators (observables) which provide the necessary information about the system and have nothing to do with statistics. Now I work to extend that statement for the n-component case. In principle, I have no problems, but the description is not elegant enough so far and also I would like to see how it works when I consider n-level system. We intend to submit the paper with the detailed discussion for publication when it will be cooked enough.

What to do if Born is wrong? Nothing. You may continue if you wish to consider the deterministic evolution of the probability amplitudes (which describe the potential reality) and the interference effects between them. It is just English or psychology and we both agree that the physics is not there.

To be more serious, I expect to obtain the criterions how the “reading” devices should be constructed in order to extract the information stored in the quantum system without spoiling it (indeed using the collapse phenomenon which Michel consider useless).

With all my sincere respect, Dany.

 

[Demystifier]

If there is another view, that has just as much formal "predictive power" than the usual "spacetime manifold" view of relativity, yes, I guess so. Are you hinting at Ashtekar variables (I am only vaguely aware of what it is about, honestly) ?

Well, not really.
In
http://arxiv.org/abs/hep-th/0407228
http://arxiv.org/abs/hep-th/0601027
I object that standard canonical quantization of fields is not covariant with respect to general coordinate transformations. Instead, canonical method of quantization requires a special choice of time. To fix this problem I propose a new method of quantization which, at the same time, is both canonical and covariant. In this method a "special time", or more precisely a "special" foliation of spacetime, emerges dynamically.
More surprisingly, in order to this new covariant method of quantization be consistent with the standard one, I must assume one additional covariant equation. This additional equation turnes out to contain the Bohmian equation of motion.
In this way, at the same time, from the requirement of covariance of quantum theory I obtain a dynamical preferred time and derive (not simply postulate) the Bohmian equation of motion. All this, however, refers to BM of fields, not of particles.

In
http://arxiv.org/abs/hep-th/0702060
I do something quite different, even more surprising. From the assumption of boson-fermion unification, which is suggested by superstring theory, I conclude that boson and fermion particle currents must have more similar forms. However, in the fermionic case, such a current does not transform as a vector, unless a preferred foliation of spacetime exists. In this approach I do not really derive the Bohmian equation of motion, but I argue that a Bohmian equation of motion is the most natural interpretation of these (otherwise physically obscure) currents.

To conclude, in the first approach I have derived the existence of a preferred foliation of spacetime from the assumption of general-relativistic covariance, while in the second approach I have derived the same from the assumption of boson-fermion unification. In these derivations the Bohmian equation of motion has not been assumed, but turned out to fit well with the proposed theory.

 

[vanesch]

Well, not really.
In
http://arxiv.org/abs/hep-th/0407228
http://arxiv.org/abs/hep-th/0601027

Just a very quick note (this needs much more time to be read seriously): aren't you taking psi as some kind of scalar, frame-independent quantity here ?
Normally, psi is transforming when looked upon from a different frame, and only psi psi^* is conserved under transformations. This is probably a very naive remark, after just a 10 minute skim through the articles...

 

[Demystifier]

Just a very quick note (this needs much more time to be read seriously): aren't you taking psi as some kind of scalar, frame-independent quantity here ?
Normally, psi is transforming when looked upon from a different frame, and only psi psi^* is conserved under transformations. This is probably a very naive remark, after just a 10 minute skim through the articles...

Psi is a scalar.
For a comparison, a wave function of a spinless particle is also a scalar.
When I say scalar, I mean scalar with respect to spacetime coordinate transformations. With respect to rotations in the Hilbert space, it is, of course, a vector.

 

[Tim09]

I barely understand the basics :)

 

[vanesch]

Psi is a scalar.
For a comparison, a wave function of a spinless particle is also a scalar.

Under a galilean boost, in non-relativistic QM, psi is not a scalar...

 

[Demystifier]

Under a galilean boost, in non-relativistic QM, psi is not a scalar...

In relativistic QM, psi of a spinless particle is a scalar under arbitrary coordinate transformations, including a galilean boost.

 

[vanesch]

In relativistic QM, psi of a spinless particle is a scalar under arbitrary coordinate transformations, including a galilean boost.

You mean "psi" as in KG equation ? But that's not a wavefunction, but a classical field...
If you consider Fock space, then, to a boost corresponds a unitary transformation of the Fock space, such that the momenta after transformation are the transformed momenta before transformation. For me, psi is an element of Fock space in (free) QFT.
I would intuitively understand that if you want to limit yourself to trivial transformations in Fock space (those that leave the projective space invariant) that you've then indeed fixed a foliation of spacetime, which is probably what you do in your paper, no ?

 

[Demystifier]

1. You mean "psi" as in KG equation ? But that's not a wavefunction, but a classical field...

2. If you consider Fock space, then, to a boost corresponds a unitary transformation of the Fock space, such that the momenta after transformation are the transformed momenta before transformation. For me, psi is an element of Fock space in (free) QFT.
I would intuitively understand that if you want to limit yourself to trivial transformations in Fock space (those that leave the projective space invariant) that you've then indeed fixed a foliation of spacetime, which is probably what you do in your paper, no ?

1. And what is the nonrelativistic limit of psi in KG equation? It is psi in the Schrodinger equation. So, are you claiming that psi in the Schrodinger equation is also a classical field and not a wave function?

2. No! Think about QFT Fock-space states in the functional Schrodinger picture. That psi is a scalar.

In fact, you will understand much better what I am talking about if you take a look at Sec. 8 of my quant-ph/0609163.