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An interesting discussion with SofiaD. Wechsler
#1
The full discussion is from a Researchgate discussion titled Could this be a NO-GO of the quantum mechanics? started by Sofia D. Wechsler:
Could this be a NO-GO of the quantum mechanics? Wrote:There are different proofs that the quantum nechanics (QM), more exactly the quantum formalism (that was NEVER contradicted by experiment), does not admit a substructure of particles following continuous trajectories. As two rigorous proofs I recommend my article
Article Hardy’s paradox made simple – what we infer from it?
and section 5, "Does a quantum objecthave a 'particle' ? ", in my article
Preprint Are particles possessing rest-mass, STRICTLY waves?
However, with all my efforts until now, I didn't succeed to prove a stronger statement: that the quantum object, which travels in our apparatus(es) does not possess a weird 'particle' which jumps accross disjoints regions, separated by a space in which the wave-function is null. This problem arises very strongly when we have to do with a wave-function consisting in two or more wave-packets traveling through isolated regions, e.g. : |ψ> = |a> + |b>.
In my last article mentioned above, I used as assumption the idea that a particle cannot do such a jump. i.e. cannot jump from the wave-packet |a> to the wave-packet |b>. The motivation is that an instant jump between two disjoint regions would mean, in a suitable frame of coordinates in movement with respect to the lab, that the particle disappears for a while from the universe. That would contradict the energy conservation, which has to be respected in any frame of coordinates.
Could there be a NO-GO here? Could it be that it is impossible to prove that there is no such weird particle? Could it be that it though exists?

Given that after a recent interface deconstruction by Researchgate the particular posts in the discussion itself can no longer be linked separately and are hidden now behind a lot of clicks of "show previous answers", to preserve this discussion it seems necessary to copy the interesting parts to make them accessible. So, here some quotes from the discussion:
Ilja Schmelzer Wrote:Dear Sofia,
you wrote in the article "Berndl et al. showed that from Hardy’s article results that Bohmian trajectories are non Lorentz-invariant, therefore, Bohm’s mechanics requires a preferred frame". This answers the question, but has always been well-known.
Ilja Schmelzer Wrote:Dear Sofia D. Wechsler
I disagree, you come not even close to bury de Broglie-Bohm theory.
Let's start with the point that you claim "For photons, even Bohm’s mechanics acknowledged that particles and trajectories cannot exist [26]." What is written in [26] is essentially a Bohmian field theory for bosons. Such a field theory preserves the main points of dBB theory, namely continuous trajectories for the classical objects, namely, in case of the EM field, for the fields, thus, A^m(x,t). So this not at all buries dBB theory for bosonic fields.
Hardy's experiment does not do it too. He discusses this explicitly, pointing out that the contradiction appears only if one ignores non-locality. dBB theory is non-local, thus, no contradiction appears.
You essentially acknowledge that you only reinterpret the same math, using the same experiment except for using the word "electron" instead of "photon". But let's see how the non-locality appears in your variant of interpretation. Essentially, dBB trajectories look quite local as long as what is measured is the position (configuration). But you consider the experiment where on both ends it is not the position which is measured. In this case, the Bohmian trajectories depend on which experiment is done first, and the first non-position experiment modifies the Bohmian trajectory of the measurement devices which defines the result of the second experiment.
"The partial phenomenological answer is that both wave-packets, when passed through an electric field, bend. That would be impossible if one of them would not contain an electron"
This is plainly wrong. The wave function follows the Schroedinger equation independent of the question if it contains an electron or not.
Sofia D. Wechsler Wrote:Dear Ilja Schmelzer,
Thanks for your comment. Although I disagree with it, it's a good comment.
Now, I did not draw by myself the conclusion that the photons don't have particles following trajectories. It's Hiley who claimed that, calling my attention on that in an exchange of letters. Let me ask you straightly: would you send Hiley a letter and tell your claim about their Bohmian field for bosons?
"Such a field theory preserves the main points of dBB theory, namely continuous trajectories for the classical objects, namely, in case of the EM field, for the fields, thus, A^m(x,t)."
Hiley is a kind person, I think he would answer you. You see, the photons cannot obey the Bohmian velocity, which comprises mass, so, it's a problem. But I encourage you to ask Hiley and tell us what he answered you. I won't argue with him because I am not particularly interested in photons, as long as I can show that particles possessing rest-mass do not obey dBB.
You also say
"Hardy's experiment does not do it too. He discusses this explicitly, pointing out that the contradiction appears only if one ignores non-locality. dBB theory is non-local, thus, no contradiction appears."
I did not say that Hardy proved that dBB is false. Regrettably, he drew from his excellent thought-experiment with the proton and electron, the minimal conclusion. As to his article "Nonlocality of a Single Photon Revisited", it was severely criticized. But, immediately after his article about lack of Lorentz invariance of the elements of reality, the Bohmians understood that Hardy's experiment is also an argument against the quantum equilibrium - see " Berndl K., Dürr D., Goldstein S., and Zanghì N., "EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory", sections 2 and 3.3, quant-ph/9510.027 ."
I suppose that my article
Article Hardy’s paradox made simple – what we infer from it?
shows clearly continuous trajectories that the hypothesis of particles following continuous trajectories, is impossible.
Then you say
"But you consider the experiment where on both ends it is not the position which is measured. In this case, the Bohmian trajectories depend on which experiment is done first, and the first non-position experiment modifies the Bohmian trajectory of the measurement devices which defines the result of the second experiment.""
How it is not position what is measured? The detectors Cj and Dj locate the particle. And how the Bohmian trajectories depend on which experiment is done first? Also, how the first non-position experiment modifies the Bohmian trajectory of the measurement devices? It makes no sense to me. To the contrary, the measurement result depends on the Bohmian trajectory, as to measurement devices, they have no Bohmian trajectories, they are fixed in space. You are trying to say something, but it is not clear to me. So, please, make it more clear.
Maybe it would be of help if I'd add that I don't ask in my proof which measurement is done first. No time-order interests me. The detection in a detector behind the beam-splitter BS1 is simultaneous with the detection in a detector behind the beam-splitter BS2. I only assume that a particle doesn't jump from the BS1 to BS2, and vice-versa. That means, a particle detected by the detector D1 (D2) was previously at the input u1 of BS1 (u2 of BS2) - i.e. it has a continuous trajectory. That brings a contradiction: any joint detection in D1 and D2 was produced by the electron that previously was at the input u1 of BS1, however, also, any such joint detection was produced by the electron that was previously at the input u2 of BS2. This is impossible, a particle has a position, it is either at BS1, or at BS2.
Please tell me whether I made myself clear.
Kind regards
Ilja Schmelzer Wrote:Dear Sofia D. Wechsler
"Let me ask you straightly: would you send Hiley a letter and tell your claim about their Bohmian field for bosons?"
There is no need for this, because this is what they have presented in the paper - the field ontology instead of a particle ontology for bosons. See eq. (13) for the "field velocity", which is simply the Bohmian velocity of the field configuration phi(x,t).
What Duerr et al have understood is something I have never questioned, namely that dBB theory needs a preferred frame. You can, of course, choose any frame you like, and prefer it, but for different frames the Bohmian trajectories will be different too. (Or, if you formulate this from the other end, closer to the language of the paper, if you use a particular set of Bohmian trajectories from one such frame, this set will not give in another frame quantum equilibrium.) So, it is not an argument against quantum equilibrium, but against the idea that it could be made Lorentz-invariant.
"And how the Bohmian trajectories depend on which experiment is done first?"
Look at the equation for the Bohmian velocity. The position of the measurement device influences during the interaction the whole configuration, on both sides. The experiment done first influences the whole wave function and the whole trajectory (which becomes surrealistic).
"shows clearly continuous trajectories that the hypothesis of particles following continuous trajectories, is impossible."
No. You exclude the Bohmian solution, which defines such trajectories in the preferred frame, with:
"Admitting “collapse at a distance”, i.e. that the measurement of one particle collapses the description of the other particle to a certain state, is at odds with the relativity theory."
As well in the article itself, you write:
"Berndl et al. showed that from Hardy’s article results that Bohmian trajectories are non Lorentz-invariant, therefore, Bohm’s mechanics requires a preferred frame [2]. Though, not only Bohmian trajectories but any continuous trajectories appear to be impossible."
The first statement is completely correct, but then you slip from "needs a preferred frame" to "impossible".
It is well-known that dBB is at odds with fundamentalist relativity (but not with the Lorentz ether). If this is sufficient for you to reject dBB, so be it. But it has nothing to do with any impossibility.
You assume that somehow the velocity of the labs somehow matters: "assume now that Alice’s and Bob’s labs are in movement". So what? In the Lorentz ether, it does not change anything, what defines the collapse is the absolute preferred frame (thus, plausibly the CMBR frame).
"That means, a particle detected by the detector D1 (D2) was previously at the input u1of BS1 (u2 of BS2) - i.e. it has a continuous trajectory. "
In this case, read the Hardy article again. The outcome he cares about, F_1, is not the one which tells the outcome of U_1. It tells that U_2 = 1, that means, the particle is on the other side. The detector D1 clicks, but the particle is at U2.
In the experiment, you have two particles which possibly reach the detector, one from u direction, the other possibly from some other coherent source. See the formulas below (8). There is a |0>_a|1>_u contribution and also a |1>_a|0>_u contribution, and both interfere: "This means that the two possibilities contributing to the |0>_C|1>_D, term as can be seen from (9) will interfere destructively". So, you see a particle has reached D1, but it may be from U1, but also from A1. You cannot know, given that they interfere. Both trajectories may be continuous - from A1 to D1 as well as from U1 to D1.
So, if the 1 experiment is first, then it is the A1 which arrives at D1 and U1 is not present. And even more is known, U2 is present.
If you measure 2 first, and measure U there, the same happens. Position measurements are harmless in dBB. But if you don't measure U2, but the superposition of |0>_a2|1>_u2 and |1>_a2|0>_u2 then this influences the final measurement at 1. And it may be the particle U1 which arrives at D1.
"How it is not position what is measured?"
D2 as well as C2 measure superpositions of |0>_a2|1>_u2 and |1>_a2|0>_u2. So, they do not measure the Bohmian positions of the particles u and a.
Sofia D. Wechsler Wrote:Dear Ilja,
I appologize for reacting to your comment with such a delay.
1. Please see, I read some papers recommended to me by Hiley, and I was displeased. Bohm's mechanics has imprinted on its flag the removing of the collapse postulate. If it does not do that, it looses any value. If we have to admit the collapse, the standard quantum theory is good enough.
To put it in short, in those articles that Hiley recommended I saw no explanation of how the photon field leaves a single spot on a photographic plate. And, you see, I consider the duty of those who present a theory, to solve its problems. One cannot tell me "read my article" and solve by yourself the problems remained open.
Bottom line, if it is left to me to complete the ellimination of the collapse from the field ontology you talk about, my reply may be only "NO, thank you!"
2. ". . . . for different frames the Bohmian trajectories will be different too. . . . . it is not an argument against quantum equilibrium, but against the idea that it could be made Lorentz-invariant."
Ilja, let's stay focused. Did you see a rocket that passes above Prague, but in fact it passes above Congo? This is exactly what gives us the dBB interpretation, and it's unacceptable. I suppose that you read my article
Article Hardy’s paradox made simple – what we infer from it?
and you saw the proof. Sorry, if the Bohmian particle exists, its trajectory has to be well defined.
"And how the Bohmian trajectories depend on which experiment is done first?"
NO, Ilja, there is no experiment done first. Each experiment is done first, you have only to choose the appropriate frame of coordinates. And, according to the relativity there is no preferred frame. Please tell me, why should I sacrifice the relativity, so well verified, for Bohm? As to the aether, what does it help? Do you want to introduce a violation of the relativity principle through the back door? No, Bohm's mechanics is not so precious to me, it wasn't so widely confirmed as the relativity, s.t. I don't have any reason to sacrifice the latter for the former.
In continuation you discuss my proof against continuous trajectories. I am very glad that you read seriously these articles of mine. In short, I can say that you did not understand properly my statement. But I want, at this step, to make a pause and wait for your reactions to my comments above. My proof based on Hardy's schema in "Nonlocality of a single photon revisited", may be a bit difficult and let's discuss it separately.
With kind regards,
Sofia
Ilja Schmelzer Wrote:Dear Sofia D. Wechsler
You wrote: "Sorry, if the Bohmian particle exists, its trajectory has to be well defined."
It is well-defined, in a theory which has a preferred frame. In dBB theory there is one, as in its particle variants as in its relativistic field theory version. The Dürr group tries to get rid of it, and therefore tries to present it as relativistic as possible. I don't. There exists a preferred frame, it is roughly the one defined by CMBR, with possible local corrections defined by the preferred coordinates being harmonic. The trajectories defined by dBB in this preferred frame are the well-defined trajectories you want.
I have no objections at all against the thesis that dBB theory needs a preferred frame. But once this is clarified (and essentially this has been clarified already by Bell's theorem), further criticism of dBB theory cannot be based on this necessity of a preferred frame. This is already known, and further criticism requires that one accepts, even if only for the sake of the argument, that dBB has a preferred frame. And once it has a preferred frame, it has also well-defined trajectories for the configurations.
"Each experiment is done first, you have only to choose the appropriate frame of coordinates. And, according to the relativity there is no preferred frame. Please tell me, why should I sacrifice the relativity, so well verified, for Bohm?"
Feel free to sacrifice realism, causality (even the logic of plausible reasoning, the Bayesian interpretation of probablity following Jaynes, see
Article EPR-Bell realism as a part of logic
) to preserve the spacetime interpretation of relativity. Even if all this is compatible with another interpretation of relativity, the Lorentz ether.
Relativity does not say that there is no preferred frame. All it says is that it is not defined by the equations of classical relativity. It may exist, it may not exist. This is left to interpretations. It is the spacetime interpretation which adds the metaphysical hypothesis that no preferred frame exists. In the Lorentz ether, it exists.
A dBB theory is useful to show that the alternative exists, and that the alternative theory has a very simple and natural math apparatus. It is already part of the Schroedinger equation.
"Bohm's mechanics has imprinted on its flag the removing of the collapse postulate. If it does not do that, it looses any value. If we have to admit the collapse, the standard quantum theory is good enough."
dBB does not have a collapse at its fundamental, ontological level. It reappears as a derived concept, once you distinguish, on a purely pragmatical level, that there are parts of the universe where you see the trajectory yourself, and other parts, where you cannot see them yourself, but have to rely on the equations of the whole theory to make some conclusions about what happens based on the trajectories you see in the environment of the process.
Sofia D. Wechsler Wrote:Ilja,
I owe you an answer for a couple of days already. I appologize!
Now, if there exists a preferred frame, there means that there exists a preferred wave-function, and the other wave-functions, written according to the other frames, are false. Gisin did many experiments with moving frames. He considered frames attached to beam-splitters, frames attached to detectors, frames attached to a fixed aether around the Earth, with respect to which the Earth moves. For none of these frames he found that the wave-function is violated.
So, if a preferred frames exists, the wave-function should be usually violated, because inall the other frames than the preferred one, the wave-function should be violated. But we did a lot of tests, typically with the polarization singlet of photons, even tests in space (Zeilinger's group). No violation of the wave-function.
Now, I'll refer to the 2nd part of a comment of yours from 4 days ago (the comment begins by quoting my question, "Would you send Hiley a letter . . .?") You also discuss there the proof against continuous trajectories in the section 5 of my
Preprint Are particles possessing rest-mass, STRICTLY waves?
By the way, I am glad that you read the proof. I acknowledge that it is a bit difficult proof. So, you say
"read the Hardy article again. The outcome he cares about, F_1, is not the one which tells the outcome of U_1. It tells that U_2 = 1, that means, the particle is on the other side. The detector D1 clicks, but the particle is at U2."
Yes, Hardy proved that. But, my proof follows another line. So, please follow me. I have suspicion against continuous trajectories. The stategy I use to rule them out, is to prove that assuming continuous trajectories I get a contradiction. Therefore, I do this assumption.
Now, look please at the formula (22). You see that the probability of getting F1 = F2 = 1 (i.e. both D1 and D2 click, while both C1 and C2 remain silent) is
(22) Prob[F1 = F2 = 1] = q2M2 |α|4/4.
I also prove that the probability of the initial electron to impinge on BS1 and an electron from the coherent wave to impinge on BS2, is q2M2 |α|4. Thus, according to the hypothesis of continuous trajectories, the initial electron will cross in continuation BS1 and the electron from the coherent wave will cross BS2. None of them would jump from the lefthand end of the apparatus to the rigthhand end and vice-versa.
Therefore, it's trivial to get from q2M2 |α|4 that the probability of obtaining F1 = F2 = 1 from the initial electron impinging on BS1 and an electron from the coherent wave impinging on BS2, is again (22).
Well, I also prove that the probability of the initial electron and an electron from the coherent wave to impinge vice-versa, i.e. the initial electron on BS2 and an electron from the coherent wave on BS1, is again q2M2 |α|4. Therefore, according to the hypothesis of continuous trajectories, we get that the probability of obtaining F1 = F2 = 1 from the initial electron impinging on BS2 and an electron from the coherent wave impinging on BS1, is again (22).
Bottom line, F1 = F2 = 1 is obtained from the initial electron going to BS1. But, F1 = F2 = 1 is obtained from the initial electron going to BS2. Where goes the initial electron, PLEASE TELL ME!
I stop here again, my reply is very long. I'll let you read it and after that I'll go on.
With kind regards.
Ilja Schmelzer Wrote:Dear Sofia D. Wechsler
I will give you an immediate answer to the first argument and look at the problem with your proof later. You write:
"Now, if there exists a preferred frame, there means that there exists a preferred wave-function, and the other wave-functions, written according to the other frames, are false. Gisin did many experiments with moving frames. He considered frames attached to beam-splitters, frames attached to detectors, frames attached to a fixed aether around the Earth, with respect to which the Earth moves. For none of these frames he found that the wave-function is violated."
How do you know that the wave-function is violated? Do you see it? You don't.
Then, you use here a quite sloppy language: Gisin did not make experiments with moving frames, he did experiments with moving devices. Then, he possibly described them using corresponding moving frames. But experiments with moving devices can be described also using the CMBR frame. The experiments do not have frames.
Then, you know, he cannot measure trajectories. What he can measure are only the predictions of quantum theory. But the empirical predictions of quantum theory do not depend on the decision which frame has been used to define the wave function. This independence of the choice of the frame is a proven result in QFT.
Then, the next use of sloppy language: "For none of these frames he found that the wave-function is violated." This suggests that he measured the wave function. He did not, because he cannot measure it. He has data from the preparation procedure, which allows, assuming the Schroedinger equation holds in this frame, to conclude that the wave function is the one he uses in his computations.
You can argue that this is all a big conspiracy theory: If you use the wrong frame, you start with a wrong initial wave function, use a wrong Schroedinger equation to compute how it evolves, with wrong Bohmian trajectories, and nonetheless the final measurement result is the same - such a conspiracy needs explanation. Fine. But this is the same conspiracy argument which is already present 1905 in the classical situation. If you use the wrong frame, you use wrong time, wrong spatial distances, a wrong ether model, a wrong notion of contemporaneity, but finally obtain the correct result.
But this can be explained and has been explained. It is a mathematical artefact, the equations are mathematically equivalent to equations for some completely different mathematical objects (namely some traces of some operators localized in some four-dimensional space following some operator equation). And these other strange mathematical objects do not depend on a choice of some frame. So, this is nothing but a consequence of the fact that the same math can be applied to very different things. The same math being applicable to very different things starts with the applicability of natural numbers to counting whatever you like. 32 + 42 = 52 holds for every application of natural numbers, like for counting apples, even if they have no relation at all to right-angled triangles.
Ilja Schmelzer Wrote:Dear Sofia D. Wechsler
Now the answer about your proof. We already have an agreement about the fact that the Bohmian trajectories depend on the choice of the preferred frame. The same experiment, described based on different assumptions which frame is the preferred one, gives different trajectories. So, every statement made about Bohmian trajectories makes sense only if one adds information about the particular preferred frame used to compute the trajectory. This information is missed in your proof. So, it cannot be a valid proof about dBB theory in this form.
Let's try to correct this flaw. Say, we assume that the statements hold for the trajectories computed for the CMBR frame. But in this case, we find that one cannot prove the claims without additional information being given.
The necessary additional information is which of the two final measurements is the first one in the CMBR frame.
If experiment 1 is the first one, we can prove that F1 -> U2. But if experiment 2 is the first one, we cannot make this conclusion. In this case, F2->U1. But this cannot be proven if experiment 1 is the first one.
The answer to your question "Where goes the initial electron, PLEASE TELL ME!" is, therefore, quite simple: If the experiment 1 is done first, and F1=F2=1, then there was a particle and it was in BS2. If the experiment 2 is done first, and F1=F2=1, then there was a particle and it was in BS1.
We have here two different experiments (one with measurement 1 before 2, one in the reverse order). So, even if the final outcomes seem identical, it is certainly possible that the initial conditions to reach these final outcomes have to be different.
But in both scenarios all trajectories are continuous.
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An interesting discussion with SofiaD. Wechsler - by Schmelzer - 12-19-2018, 09:45 AM

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