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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.
Reply
#2
Then, an interesting discussion between Klaus Kassner and me followed:
K. Kassner Wrote:@Schmelzer:
" dBB does not have a collapse at its fundamental, ontological level."
This is true for standard qm as well, as the wave function is not ontological there.
"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."
For standard qm this would roughly read: "It appears as a derived concept, once you distinguish, on a purely pragmatical level, that there are parts of the universe that are considered 'system' and parts that are considered 'the outside universe', containing the 'observer'."
The collapse is, in standard qm, a consequence of the necessity of separating quantum object and observer. Give up that separation and you have no collapse. (E.g. the many-worlds interpretation.)
" 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."
No. Relativity says a preferred frame is not detectable by any experiment. And it says that before any equations. It then takes the view that one should not assign reality to anything that cannot be detected. In fact, the reason to prefer relativity over Lorentzian ether theory does not have anything to do with empirical results, which are the same for both. The reason is essentially Occam's razor: don't invoke entities that are not necessary. And that same reason can of course be brought up against Bohmian mechanics.
Of course, I agree with you that Bohmian mechanics has continuous, even differentiable trajectories, and hence, something must be wrong with Sofia's proof, because we have a working counterexample.

Sofia D. Wechsler Wrote:K. Kassner and Ilja Schmelzer,
There is a total mathematical separation between the macroscopic objects and microscopic objects. The latter are described by a wave-function and admit states which are superposition of several eigenstates of some operator. The former do not admit a wave-function, they follow a trajectory described, at each time, by parameters - for example position and linear momentum - which are incompatible in the quantum theory. Macroscopic object don't admit superposition of states, e.g. |dead cat> + |living cat>.
People speak of entanglement between microscopic systems and macroscopic objects, e.g. |S1>|living cat> + |S2>|dead cat>, where S1 and S2 are states of the microscopic system. Such a superposition is impossible. It remains impossible when we replace the cat by another macroscopic system.
Klaus says "The collapes is, in standard qm, a consequence of the necessity of separating quantum object and observer." Wording does not help!!!!! The mathematics of QM gives us a wave-function which is a superposition of eigenstates, while the result of the macroscopic measurement leaves us with only one of those eigenstates. About "many worlds" I wonder when did Klaus visit those worlds, for relying on their existence? We would be pleased to understand what happens in OUR WORLD.
I repeat, there is no such superposition as |S1>|one world> + |S2>|another world> + |S3>|a third world> + . . . A world is even more macroscopic than a cat.
With kind regards to both of you, and despite the difference of opinions, I am thankful for comments.

Ilja Schmelzer Wrote:Dear K. Kassner,
in standard QM (minimal interpretation) you cannot give up separating quantum object and observer. The split is part of the formalism, measurements (which presuppose observers) are defined by operators-valued measures and the states (which describe quantum objects) are defined by density operators.
I will not comment the value of the many wolds interpretation, given the restrictions by netiquette.
You write "No. Relativity says a preferred frame is not detectable by any experiment. And it says that before any equations. It then takes the view that one should not assign reality to anything that cannot be detected."
I agree with "not detectable". The point is that by "taking the view that" it makes a metaphysical assumption. So far we seem to agree.
"The reason is essentially Occam's razor: don't invoke entities that are not necessary. And that same reason can of course be brought up against Bohmian mechanics."
But, surprisingly, we end up with entities we would like to see if they would exist, but which we cannot see at all - our future. Instead of the common sense 3D world filled with matter which changes we get a whole four-dimensional manifold, which is claimed to exist in the same sense as what I see here before me now exists. A strange application of Occam's razor, there I'm forced to accept fatalism (the future exists already in the same way as the present) without any necessity and any empirical evidence for this.
A 3D world containing entities which change continuously is certainly necessary (it is, last but not least, also contained in the 4D spacetime). But everything beyond it is not necessary, given that there exist interpretations of the accepted theories which do not contain more than this.
I can present a similar proof for the existence of God. There are, clearly, theories which contain, together with humans, also angels and various Gods. If somebody who looks like a human (say, Jesus) is a God or not I cannot measure. So, the theory which distinguishs Gods from humans requires additional information which I cannot measure. So, using Occam's razor, it does not exist, and we should prefer the theory that Gods exist and are indistinguishable by observation from humans.
Ilja Schmelzer Wrote:Dear Sofia D. Wechsler ,
while I agree with most of your reply to K. Kassner, let's note the difference to dBB theory.
|S1>|living cat> + |S2>|dead cat> is possible as a wave function, and unproblematic, because together with this wave function there is also the configuration, which is either a living cat or a dead cat. And the wave function
|S1>|living cat> + |S2>|dead cat> guides, say, the living cat (and together with the living cat also the rest of its universe) in the same way as |S1>|living cat>.

K. Kassner Wrote:@Schmelzer:
"But, surprisingly, we end up with entities we would like to see if they would exist, but which we cannot see at all - our future. Instead of the common sense 3D world filled with matter which changes we get a whole four-dimensional manifold, which is claimed to exist in the same sense as what I see here before me now exists. "
No. That is only an impression implied by inaccurate use of the word "exist". Of course, four-dimensional spacetime "exists" in a mathematical sense. But that is precisely not the same sense of what I see here before me now exists. The number pi definitely exists, one can prove it does -- mathematically. And once you have described to aliens how it is defined and explained our decimal system to them, they can verify its existence by calculating the nth digit of it and finding that it agrees with our nth digit. So pi exists, contrary to, say, ghosts or dream entities but it does not exist in a physical sense. Nor do distant spacetime events exist in a physical sense. They do exist, but this is not the same way of existing as what you see before you now. (In fact, the word "existence" has as many different facets as, or more than, the word "real". And as Bohr taught us, in the light of quantum mechanics, we have to learn anew what the word "real" means -- it is not just a given and most certainly not just a matter of definition. The same goes for the word "existence". A certain level of language analysis à la Wittgenstein would do many of these would-be-philosophers of science good. And this is a point Bell did not really understand well, in spite of his other profound insights.)
Your example with God is far-fetched, even a bit nonsensical. What Occam's razor says about God is that his existence is not provable, so we should not use the entity God in our physical theories (contrary to what Newton did). Occam's razor is useful to distinguish between theories that have precisely the same empirical content, so it cannot be ridiculed by some silly arbitrary examples.
Of course, you may or may not believe in God, depending on your mental constitution, but you should not use God as a hypothesis in physical theories, just as you should not use ether unless you are forced to. The question is not whether an entity looks like a more plausible explanation. The question ist whether it is necessary in an explanation. Neither God nor ether are disproved, nor Bohmian trajectories. But none of these concepts is needed either. Moreover, some of them may impede progress.

Ilja Schmelzer Wrote:Dear K. Kassner ,
First, quantum mechanics does not explain why we don't see such superpositions. (Last but not least, this failure to explain it makes such nonsense like the many worlds interpretation possible.)
Only realistic interpretations, which include some physical reality beyond the wave function, like the Bohmian trajectories, explain in a simple way why we don't see such superpositions: Because what we see are the trajectories, not wave functions.
It is fine that you mention the differences in the notions of existence. Pi exists in a different sense that the cup of tea before me, fine. And that the 4D spacetime exists in the same sense as pi exists, is unproblematic too.
(BTW, the difference between pi and ghosts is much less clear than you think. Mathematics are rules of thinking. They are applicable to human thinking, as well as to alien thinking. We can define, say, real numbers, or groups, or ghosts. We give some axioms, and then one can apply logic to make conclusions. Nothing prevents us from making axioms about ghosts, say, that they can appear only during a ghost hour, and the application of logic to these axioms will lead to a similar agreement between humans and aliens about some theorems about ghosts.)
But about what type of existence Occam's razor is about? It is about the existence which is relevant in physical theories. A realistic theory has to describe what really exists, in the sense of the cup of tea before me. That means, it has to define its ontology. (There are also physical theories which don't give such a definition - like Bohr's version of quantum theory. For such theories, Occam's razor does not make sense, once we cannot even say how many entities exist in this theory. For realistic theories, Occam's razor makes sense, once the ontology is well-defined.)
The ontology of the spacetime interpretation is the 4D block world. With me somewhere inside moving along a predefined trajectory, (seeing it like a film, which also exists completely now). The ontology of the Lorentz ether contains only a 3D world, which changes. The fatalistic 4D world certainly contains much more than necessary. The entity "myself" is multiplied there an infinity of times, including my whole worldline, without necessity.
For you, a little bit Popper would do good, to prevent you from using the word "provable" in connection with theories of physics, SCNR. So, no, Occam's razor does not tell us we should not use things in our theories if their existence is not provable, simply because nothing about the physical world is provable. BTW, this interpretation of Occam's razor would be deadly for relativists, because the existence of the 4D spacetime is obviously not provable.
The point of my example with God was to show the absurdity of the "application" of Occam's razor by the relativists, which implicitly forces us to accept the whole 4D blockworld and then to consider the 3D part which really exists in the Lorentz ether to be defined by some additional entity together with the whole 4D blockworld. But the really existing entities used in the Lorentz ether are not 4D + a preference for some frame, but simply 3D. Which is much less.

K. Kassner Wrote:Hi Ilja,
"First, quantum mechanics does not explain why we don't see such superpositions. "
Of course, it does. See my answer to Sofia.
"It is fine that you mention the differences in the notions of existence. Pi exists in a different sense that the cup of tea before me, fine. And that the 4D spacetime exists in the same sense as pi exists, is unproblematic too. "
It does not exist in the same sense as pi. It just exists in a different sense from "existing now". It exists in a similar sense as the whole past exists. "(Nothing prevents us from making axioms about ghosts, say, that they can appear only during a ghost hour, and the application of logic to these axioms will lead to a similar agreement between humans and aliens about some theorems about ghosts.)"
Not really. The existence of pi is testable by verifiable predictions such as the value of the nth digit. The existence of ghosts isn't. Of course, you cannot consider predictions that turn out to be true whether ghosts exist or not as tests of their existence. "But about what type of existence Occam's razor is about? It is about the existence which is relevant in physical theories."
Occam's razor is not about reality. It is about how to compare theories. So it is not about physical existence. It gives you a condition on when you should assume an entity to be acceptable in a theory and when you should not.
"A realistic theory has to describe what really exists, in the sense of the cup of tea before me."
No, we are well beyond that stage. Kinetic energy certainly does not exist in the sense of the cup of tea before you. It is absent for some observers and present for others, even in Newtonian mechanics. Nevertheless it is real. So physics is not as narrow-minded in its conception of reality.
"That means, it has to define its ontology. "
Definitely not. Ontology is a concept invented before quantum mechanics. By people who believed in a deterministic and objective world. The concept may simply not be applicable to the real world. Note that objective and real are not the same thing. A length is real in special relativity but not objective because it is different for different observers.
"(There are also physical theories which don't give such a definition - like Bohr's version of quantum theory. For such theories, Occam's razor does not make sense, once we cannot even say how many entities exist in this theory. "
Occam's razor makes perfectly sense for theories without an ontology. An entity need not be defined by an ontology. The vector potential in electrodynamics is an entity but it is not ontological.
"The ontology of the spacetime interpretation is the 4D block world."
Well, I would not say it like that but if we accept that statement then we must say that the ontology of any deterministic theory is the 4D world. Because in any deterministic theory, past, future and present coexist in the same way as in relativity. Once you specify the "state of the world" at one time, it is fixed, inevitably, at all times. The only difference in comparison with relativity is that you have substructures of the world -- given by slices of constant time -- that are also absolute, i.e. the same for everyone. So you can define something that looks like a whole world at one time as if it were independent of the rest. But it is not, due to determinism, so the 4D block world is there as a necessary ontological concept as well. In special relativity, the slices are not absolute but conventional. You can also produce substructures such as past, present and future, but they are not absolute. Not that enormous as a difference. General relativity has solutions that do not allow a foliation, so things are a little different there.
"With me somewhere inside moving along a predefined trajectory, (seeing it like a film, which also exists completely now)."
No. It does not exist completely "now". That is the misunderstanding. There is no time in which the existence is simultaneous. It is not even an existence within time. That is just your film picture, but that picture is an analogy and not a perfect one.
"The ontology of the Lorentz ether contains only a 3D world, which changes."
No. As soon as you add determinism, all of the past and the future can be claimed to exist in precisely the same sense in which the spacetime continuum of special relativity exists. Not "now" of course, they do not exist "now" in spacetime. But inevitably.
"The fatalistic 4D world certainly contains much more than necessary. "
Fatalism is present in determinism, too.
"The entity "myself" is multiplied there an infinity of times, including my whole worldline, without necessity. "
I would dispute both the "without necessity" and the multiplicity. "For you, a little bit Popper would do good, to prevent you from using the word "provable" in connection with theories of physics, SCNR."
I guess for you a little more careful reading of Popper would be good, too. Popper's statement about non-verifiability refers to theories, not to predictions of theories. Theories are only falsifiable. Their predictions are verifiable or falsifiable in each single instance. And even erroneously verifiable.
"So, no, Occam's razor does not tell us we should not use things in our theories if their existence is not provable, simply because nothing about the physical world is provable."
That is nonsense. If I do an experiment and the result is a pointer pointing on "4" (which may or may not be what the theory predicted), then I have proven that the pointer in that particular experiment may point on "4". I have disproved an impossibility. I have proved a possibility.
"BTW, this interpretation of Occam's razor would be deadly for relativists, because the existence of the 4D spacetime is obviously not provable. "
You are severely confusing things. I was talking of provable consequences, and maybe I should have said verifiable consequences. But otherwise, Occam's razor is about concepts that are not necessary (if a concept is necessary to explain an observation then it clearly cannot be eliminated by Occam's razor) and all concepts that strictly have no verifiable consequences do not seem absolutely necessary.
Now, I am not a purist in that regard. I do not want to throw out pure gauge quantities from physics just because they have no observable consequences. I would justify their "necessity" by their utility in simplifying the mathematics. On the other hand, Bohmian trajectories or the Lorentzian ether do not really simplify anything.
Even Hiley changed his mind about the true Bohmian trajectories in the ESSW experiment -- and he took decades for it. Now he thinks they agree with the path suggested by the which-way detectors; before, he thought the detectors were triggered by the wave function. If it is so difficult to figure out the true Bohmian trajectories in such a simple experiment and took more than 20 years to find agreement with the ESSW prediction from standard quantum mechanics, then these trajectories do not render quantum mechanics simpler.
Ilja Schmelzer Wrote:"Occam's razor is not about reality."
Occam wrote "don't multiply entities without necessity". I would interpret this as being about the real entities in your theories.
"Fatalism is present in determinism, too."
So what, I'm not a fan of determinism. dBB is deterministic, but most other realistic interpretations are not. Nonethless, they also use continuous configuration space trajectories.
"As soon as you add determinism, all of the past and the future can be claimed to exist in precisely the same sense in which the spacetime continuum of special relativity exists."
This is mathematical existence only, and therefore as irrelevant as the existence of pi. Moreover, if I assume that a deterministic theory is only an approximation of a more fundamental random one, that predefined future disappears immediately into thin air.
"I have disproved an impossibility." Sorry for sloppy formulation, Poppers fallibilism is of course about general theories.
"Even Hiley changed his mind"
Please references to paper before and after, I would like to look at that. Whatever, it would be irrelevant if Hiley has made some error some time, this happens. The equations are simple enough.
"On the other hand, Bohmian trajectories or the Lorentzian ether do not really simplify anything."
They add a lot conceptual simplity. The measurement problem disappears, problems with realism and causality because of Bell's theorem disappear, we have a simple ontology, continuous trajectories, the quantum gravity problems disappear (we know how to quantize condensed matter theories, no topological foam or problem of time), we have no confusion with twin paradoxes and so on.
"Kinetic energy certainly does not exist in the sense of the cup of tea before you. It is absent for some observers and present for others"
Nice try, but in Newtonian mechanics we have absolute space, and in absolute space it is well-defined. It has already the same problems with observability because of Galilean relativity as absolute time in the Lorentz ether, that's all.
"It does not exist completely "now". That is the misunderstanding. There is no time in which the existence is simultaneous. "
That means, there is no difference in the status of existence between the the cup of tea before me now and the cup of tea before me tomorrow. Some guy which exists around now on Andromeda cannot tell which of the two is his "now", so either both exist in the same sense or none.
"The vector potential in electrodynamics is an entity but it is not ontological."
I disagree. You can, of course, use some mystic interpretation without ontology, but nothing prevents you from using the potential as the ontology. It makes sense, given that it is a much simpler ontology than the EM fields. In a theory with such an ontology it makes, of course, sense to have definite physical equations, so that the gauge condition gains the status of a physical equation. But so what? Similar to the Lorentz ether, where there is no candidate beyond harmonic coordinates for the preferred coordinates, there is only one plausible candidate equation for this, the Lorenz gauge.
The ontology should contain everything you need to make all physical predictions, via the equations of the theory. And for this purpose, it should be minimal. Thus, the "now" is sufficient, no need for the whole 4D.
Reply
#3
Schmelzer Wrote:Dear Sofia D. Wechsler
you write "Anyway, an entanglement cannot hold only in one frame of reference. It cannot happen that the wave-function (in particular the wave-function of an entanglement) is true according to one frame of reference, and false according to another frame."
But there is the counterexample of dBB theory - which has all the explicit formulas you need - together with the Lorentz ether (extended to relativistic gravity, see https://ilja-schmelzer.de/ether ) as a background, which shows that a theory where quantum theory holds in one frame is viable.
To clarify the logic behind this: The theory has one preferred frame, essentially the CMBR frame. It has continuous trajectories of the configurations q(t) (which may be particle positions in a particle ontology, may be not in other ontologies) and gives in this frame all the empirical predictions of quantum theory. This is a theorem.
To apply it to other frames is, according to the theory, erroneous, nonsensical, and does not describe reality. Nonetheless, this error does not lead to erroneous empirical predictions, That it does not have such consequences is also a theorem - else, those empirical predictions could be used to identify the preferred frame.
So, we have a theory where entanglement holds only in one frame of reference, it is explicitly constructed, and proven to be viable. So, your claim is wrong, and proven to be wrong.
It is, essentially, the dogma of a fundamentalist interpretation of relativity, which simply ignores or rejects theories with a preferred frame as anathema, even if they are as viable (making the same empirical predictions) as fundamentalist relativity.
You have, of course, any right to prefer, for whatever reasons, the fundamentalist interpretation of relativity. But you cannot claim that the Lorentzian alternative does not exist once it exists.
You can claim that it has some internal contradictions, ok, but this is a hard job, and essentially hopeless. And if you do it, you have to show internal contradictions of the Lorentzian alternative, but not that it is in contradiction with some ideas of the fundamentalist interpretation. Your theorem shows such a contradiction with fundamentalist relativity - the Bohmian trajectories would be different, for "the same" experiment described in different frames. So, if these trajectories would be real trajectories, there would have to be a preferred frame. But this is certainly not an internal contradiction of the Lorentzian approach.
Sofia D. Wechsler Wrote:Ilja, good evening!
"But there is the counterexample of dBB theory - which has all the explicit formulas you need - together with the Lorentz ether (extended to relativistic gravity, see https://ilja-schmelzer.de/ether ) as a background, which shows that a theory where quantum theory holds in one frame is viable."
Ilja, an acquaintence of mine said that "for Bohmians, the Bohmian mechanics is a religion". There is NO THEORY that is SAINT. Any theory has to be checked. Bohm's mechanics introduces assumptions alien to QM, for which reason it was always suspect. It was shown to be incompetent with the relativity by HONEST BOHMIANS, Berndl and Goldstein, in 1992 in base of Hardy's paradox. In 2018 Wechsler D. Sofia showed in
Preprint Are particles possessing rest-mass, STRICTLY waves?
that the Bohmian particle cannot exist, and the proof does not use relativity. It is valid even in the frame of the aether. See the section 5, named
Does a quantum object have a “particle” ?
I repeat, the proof is in one single frame of reference. That frame may be the aether frame you speak of.
One more thing: for proving that a theory is correct, IT IS NECESSARY to show that it explains some experiments. But that IS NOT SUFFICIENT. One has to check, in addition, if there aren't experiments that the theory is unable to explain.
Bottom line, read my section 5.


Schmelzer Wrote:Dear Sofia D. Wechsler
we have discussed this, and I'm surprised about this new line of argument. There was agreement about the fact that the Bohmian trajectories would be different in different frames, which is a conflict with fundamental relativity. But there is no problem if only a single frame is used.
To quote myself: "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."
There are no contradictions if there is only one frame used, because in one frame the trajectories are defined in a well-defined, unique way. The proof constructs a contradiction by implicitly using different frames (or alternatively by ignoring the influence of the first experiment on the other side on the second experiment).
Last but not least, there is no way to prove a theory is correct. But what can be proven is the equivalence of the empirical predictions of two different theories. So, one can prove that an experiment can falsify the first theory (here dBB/Lorentz ether) only if it also falsifies the other theory (here QT, SR).
So, you have no proof that dBB trajectories fail, and I have a proof that they don't fail. And let's note that I'm not a Bohmian, I propose an own interpretation, see https://ilja-schmelzer.de/quantum/ so that even if that rant against Bohmians would be correct (it is bad style anyway even if attributed to "an asquaintance") it would be irrelevant.
Sofia D. Wechsler Wrote:Ilja,
I don't use the terminology "experiment 1" and "experiment 2." So, I don't know what you talk about. Also, in my proof no experiment is done first, all the detectors are at the same distance from the central beam-splitter that produces the wave-packets |u1> and |u2>.
I believe that you speak of another experiment than mine, and of another mathematical treatment than mine. If you want to criticize my conclusions you have to refer to my experiment, and my treatment. Your https://ilja-schmelzer.de/quantum/ does not refer to my experiment. You can't accuse John of a fraud by judging Tom, you have to judge John.
Schmelzer Wrote:I speak about the two measurements on the two sides. So, "experiment 1" means the measurement done to measure C1 and D1 and "experiment 2" is the measurement of C2 and D2.
Ok, this was sloppy language on my side, these are measurements and only the combination of both are a the experiment.
You wrote "Also, in my proof no experiment is done first, all the detectors are at the same distance from the central beam-splitter that produces the wave-packets |u1> and |u2>."
No. The two measurements are done at very different places, and there will always be also some, however minor, difference in absolute time between them. In the relativistic context, both measurements are space-like separated, and it depends on what is the ether frame which one happens first.
The page https://ilja-schmelzer.de/quantum/ refers to my interpretation of quantum theory, just to explain you that I'm not even a Bohmian (even if my interpretation shares a lot of formulas with Bohmian mechanics, it differs in many parts, and, in particular, I propose a field ontology instead of a particle ontology. So, nothing of which you attack here is even part of what I believe, so that an accusation that I defend here some own religious dogma is off.
Sofia D. Wechsler Wrote:Ilja,
The time of measurement is not a parameter in my calculi. All the detectors in the picture are are the same distance from the central beam-splitter BS that produces the wave-packets |u1> and |u2>. The rationale would be the same if a pair of detectors would be more distant than the other pair.
Moreover, I have full right to do the experiment dynamically, i.e. to place the beam splitters BS1 and BS2, with the accompanying detectors, when I want. The particle does not know my intentions.
Thus, the bottom line of my proof is that if we keep the idea of a particle, then, for obtaining a detection of type F1 = F2 = 1, the particle should have gone, compulsorily, to BS1, but, also, it should have gone, compulsorily, to BS2. It's not a personal interpretation of QM - I have no interpretation - it's a PROOF according to the QM formalism.
Schmelzer Wrote:Dear Sofia D. Wechsler
that your experiment does not contain a complete description so that to answer the questions you pose like "there have the particles been if we observe F1=f2=1" means the answer is not completely defined by what is fixed in your description of the experiment.
You have, of course, the full right to do the experiment dynamically. But in this case, the answers to the question "there have the particles been if we observe F1=F2=1" will depend in a complex way on these dynamics.
You write "the bottom line of my proof is that if we keep the idea of a particle, then, for obtaining a detection of type F1 = F2 = 1, the particle should have gone, compulsorily, to BS1, but, also, it should have gone, compulsorily, to BS2." Yes, this is the bottom line. And this bottom line is wrong.
What holds in dBB theory is something different than you claim. If the measuremen 1 is done first, and F1=F2=1, then there was a particle and it was in BS2. If the measurement 2 is done first, and F1=F2=1, then there was a particle and it was in BS1.
So, your claims are simply not correct. (Your claim would be correct, if you would add the fundamental-relativistic hypothesis that the position of the particle could not depend on a preferred frame. But in dBB it depends on it. Thus, dBB allows for different answers for a different order in absolute time of the two measurements.)
Sofia D. Wechsler Wrote:Ilja,
"that your experiment does not contain a complete description so that to answer the questions you pose like "there have the particles been if we observe F1=f2=1" means the answer is not completely defined by what is fixed in your description of the experiment."
Why my experiment does not contain a complete description? Don't I present clearly my calculi? Please place the finger on the wrong point in my calculus.
"You write "the bottom line of my proof is that if we keep the idea of a particle, then, for obtaining a detection of type F1 = F2 = 1, the particle should have gone, compulsorily, to BS1, but, also, it should have gone, compulsorily, to BS2." Yes, this is the bottom line. And this bottom line is wrong."
And why is it wrong? Because Bohmian mechanics says this and that? If my proof is wrong, it is not wrong because of the Bohmian mechanics or any other mechanics, but because it contains a wrong equality. So, can you place the finger on it?
Schmelzer Wrote:Dear Sofia D. Wechsler
In the experiment which measures F1 and F2 the question where the particle was depends on which of the two measurements was done first. Your statement "the probability of obtaining F1=F2=1 with the initial particle going to BS1 is (22)" holds only for F2 measured first. If F1=1 is measured first, it is zero, because the particle goes through BS2. The F1=1 measurement collapsed the wave function, what remains is the particle being in BS2. And this state gives with some probability F2=1 even if the particle is in BS2. A consequence of the collapse which you have somehow ignored.
Sofia D. Wechsler Wrote:Ilja,
The idea of an aether is so precious to you, that you forget what we talk about. (Well, it's understandable.) We question the concept of a particle in the sense similar to that given by Bohm (but without Bohm's formalism). I mean, a "particle" supposed to float inside the wave-packet, and trigger a detector.
The question is whether such a particle may exist. If it does not exist, can we prove that, or it is a NO-GO?
Now, if you invoke the collapse, you don't need that concept of particle. I remind you that the concept was proposed by physicists for avoiding the principle of wave-function collapse, which is not clear how works.
I claim that my proof in the section 5 of
Preprint Are particles possessing rest-mass, STRICTLY waves?
is part of such a proof as I ask. I say that it's just a part, because it needs an additional assumption: that the"particle" doesn't jump from a region of the space to another one.
But this assumption can be justified. Imagine the wave-function of an electron in the form |a> + |b>, and both wave-packets pass through electric fields as in the picture. Imagine that for a short time the "particle" jumps from the wave-packet |a> to |b>. Then, for that short time, in |a> there is no charge s.t. it does not feel the influence of the field. QM does not permit such a thing, each wave-packets should feel the respective field all the time.
Schmelzer Wrote:Dear Sofia D. Wechsler
in dBB theory it is clear how the collapse works. It works always once we have a pure quantum system (which is one where we do not see the trajectories) with a classical system (where we can see the trajectories) and can have a Schroedinger evolution for the combined system Psi(q_q,q_c,t) and the trajectory of the classical (visible) part q_c(t) to define an effective wave function of the quantum part by the straightforward formula psi_eff(q_q,t) = Psi(q_q,q_c(t),t). This effective wave function collapses during the interaction with the measurement device. So, I do not have to invoke any collapse once it is already nicely described in dBB theory (which is, btw, one of its advantages).
Your "without Bohmian formalism" makes no sense, and looks very strange and suspicious. If you want to prove that particles cannot exist, you have, of course, to cross-check what is wrong with the theory which explicitly describes such trajectories. This is the straightforward way to find the error in your "impossibility proof". (And if the ether is precious to me or not is completely irrelevant, because this is a cross-check which you would have to do yourself.)
The solution of this conflict would be either a contradiction in mathematics (highly improbable), an error in your proof (as I claim) or that you make an assumption which does not hold in dBB theory (like von Neumann's proof and all the other well-known and correct impossibility proofs for hidden variables).
The assumption that the particle does not jump holds in dBB theory too (the trajectories are continuous), so that this is not the additional assumption you may have introduced.
Your proof is, from the start, a variant of Hardy's proof, and Hardy's proof is ok. But he proves nothing which is in conflict with dBB. And he uses quantum theory appropriately, and considers also the collapse: After his (8), we read "Now, consider the case in which no photons are detected at detector U2 (so that U2 = 0). When this happens, the state is projected onto the first term in Eq. (8) such that..." So, the claims Hardy is using, which you use too without deriving them somehow independently without using any collapse or so, depend on usual quantum theory which is using a collapse to describe a sequence of different measurements.
My claim is that you simply have not used the full, adequate description of the experiments which measure F1 and F2 instead of U1 or U2, which has to consider the collapse caused by the first of the two F1 resp. F2 measurements.
Hardy's "If F1 =1 then U2=1" is about an experiment where U2 is measured. One can reasonably argue that in this case the particle has to go through BS2. Fine. One can argue that we decide only after F1 is measured if we measure U2 or F2. Also fine. But then F2 is anyway the second measurement, and its result influenced by the first one of F1. We cannot simply apply the result, as it is, to the experiment where F2 is done first. Because in this case we have no base for the consideration which leads to "If F1 =1 then U2=1", because there is no measurement of U2 anyway, and if we do one, its result is clearly distorted by the measurement of F2 before.
Sofia D. Wechsler Wrote:Ilja,
I can't repeat endlessly what about is this thread - read the title.
I claim that I proved that we don't have a NO-GO. I did it in two steps:
1. In my article
Preprint Are particles possessing rest-mass, STRICTLY waves?
, section 5, I proved that if the particle doesn't jump from one region to another, then the answer to the question "in which detector is the particle detected", is contradictory.
2. In my previous post I proved that the particle cannot jump from one wave-packet to another, otherwise the behavior of the wave-packets in fields, won't obey QM.
I didn't invite you to a discussion on Bohm's mechanics (BM) - by the way BM falls due to step 1, because it requires continuous trajectories. Neither do I care what did Hardy in his proof, which has another purpose than mine. Third thing, as I already said, if one accepts the collapse postulate, one doesn't need the "particle" floating in some wave-packet. The present thread poses the problem if we have the choice to accept one of these options, i.e. if we cannot exclude the particle. And my answer is that we should exclude the idea of the particle, i.e. it remains that the collapse wins.
I don't want to repeat again and again about what is the thread.
Schmelzer Wrote:In other words, you don't invite me to present any counter-evidence against the obviously erroneous (because contradicting the well-established mathematics of dBB theory) "proof" of impossibility of dBB theory.
You don't want to hear the simple truth that your proof in section 5 of your paper is false.
Your choice. Ok, good bye. Feel free you have proven whatever you like. Scientists will not care about this, neither the Bohmians, nor their opponents, because even the opponents of dBB theory know that it is not self-contradictory and has continuous trajectories.
Sofia D. Wechsler Wrote:Ilja,
Phraseology doesn't work with me. I am an engineer. One can present me rigorous proofs.
Bohm's mechanics falls if my proof in section 5 is correct. And you didn't present no rigorous argument against my proof, you discussed Hardy's experiment, not mine. I can talk with you if you refer EXCLUSIVELY to my rationale. I claim that you did not understand it. For instance you speak of collapse. This is not a hypothesis in my rationale. If you want to talk with me READ ATTENTIVELY my calculus, and PLACE THE FINGER on the first equation that seems to you wrong.
I was for tens of years a programmer - a debugger. Debugging a program, an electric circuit, a proof is the same thing. You go statement after statement and place the finger on the first statement that is wrong.
This is the way you can talk with me, I won't invest time in another way.
"Feel free you have proven whatever you like. Scientists will not care about this, . . ." Stop here!!!! I don't permit you this style with me. You are not the speaker of the quantum community. You'd better learn how to do debugging. You don't even know the trivial fact that if you want to criticize a rationale, you speak of THAT rationale, not on another one.
I have no obligation to Bohmians or others, not even to Hardy. My obligation is only to the RIGOROUS LOGIC. And if you say GOOD BYE, then GOOD BYE ! I never forced somebody to talk with me.
Schmelzer Wrote:Dear Sofia D. Wechsler
Your proof in section 5 is wrong, and I have given arguments for this. You have ignored them. But, ok, I will give it a last try, referring only to your paper.
The place where your reasoning becomes wrong is here:
"Then, since a particle at the input of BS_j can go to D_j with the probability ½, one infers
1)the probability of obtaining F_1=F_2=1 with the initial particle going to BS_1
is (22)"
There is nothing in quantum theory which justifies this inference. It obviously ignores the possibility of interference effects. The probability of coming from BS_1 to D_1 is 1/2 in the case where there was not yet a measurement on the other side. It may be dependent (and in fact depends) on the result of the measurement of F_2. In this case, only the sum of the probabilities for F_2=1 and F_2=0 will be 1/2, not the two probabilities themselves.
You have simply no base from quantum theory to compute probabilities for F_1=F_2=1 with the initial particle going to BS_1 and the original quantum state being (19).
Sofia D. Wechsler Wrote:Hi, Ilja,
I believe that I understand what is not clear to you. I should have added more explanations. Well, this is the advantage of publishing on RG, I can get notifications on things which are not enough clear.
So, here is my explanation:
As you can see in (19), three 2-particle waves contribute to the result F1 = F2 = 1, and the contributions undergo superposition.
Namely:
1) 1/√2 from the amplitude of the wave |1>_u_1 arrives at D1 , and jointly, 1/√2 from the amplitude of the wave |1>_a_2 arives at D2;
2) 1/√2 from the amplitude of the wave |1>_a_1 and jointly, 1/√2 from the amplitude of the wave |1>_a_2 arrive, respectively, at D1 and D2;
1) 1/√2 from the amplitude of the wave |1>_a_2 arives at D1 , and jointly, 1/√2 from the amplitude of the wave |1>_u_1 arrives at D2 .
In the detectors, the three contributions interfere. Now, you have to look well at what happens when introducing the transformations (20) in (19). See in (22) the signs of the three terms of type |1>_d_1 |0>_c_1 |1>_d_2 |0>_c_1. The term originating from the contribution 1 has the factor -i, the term originating from the contribution 2 has the factor i, and the term originating from the contribution 3 has again the factor -i.
So, you see, we can say that the result F1 = F2 = 1 is due to the contribution 1, because the two other cancel out mutually. That means the original particle appeared in D1. But we can also say that the result F1 = F2 = 1 is due to the contribution 3, because the two other cancel out mutually. That means the original particle appeared in D2.
You see how the things go? This is why I say that I don't need to speak of collapse, of U1 and U2, and of precedency in arrival time. It's not Hardy's rationale here. But I agree that my explanation may be not so clear and should be improved, and thank you for convincing me.
Schmelzer Wrote:Dear Sofia D. Wechsler
the wave function is the whole expression (21), or (19). Once you measure F_1 and F_2, it is (21) which defines the amplitudes and probabilities of this experiment.
That you have computed (21) starting from (19) with using (20) does not mean that you can you can conclude that a particular measurement result can be attributed to a particular part of (19). There is no base for such a conclusion in quantum theory.
Dear Juan Weisz
Sophia has, of course, the right to think that there are no particles (by the way, this is also what I think - in my understanding, particles are quantum effects, like phonons in condensed matter theory, and the ontology should be a field ontology). But Sophia's theorem claims that there cannot be particles in principle, while dBB theory gives explicit formulas for particle trajectories,together with an equivalence proof with quantum theory. and it gives them for the experiment considered in the proof too. There is an obvious conflict, and it is a straightforward but possibly nasty job to identify the point where something is wrong.
So all I had to do was to compute the trajectories of dBB for this particular experiment. The result depends on the question if F_1 or F_2 is measured first, and, thus, disagrees with the Sophia's claim that "the result F1 = F2 = 1 is due to the contribution 1". Then I had to see how this claim is derived, and I see no base for such a derivation. This is where the theorem fails. There is no derivation of this claim based on the principles of quantum theory (in the minimal interpretation).
If Sophia will add now some more details about this derivation, I will follow the same basic idea. I will use the dBB trajectories known for the experiment considered, and see at which place in the extended proof there is the first contradiction with the dBB trajectories. This will be the weak place of the extension of the proof. This is the standard debugging procedure for such proofs.
Sofia D. Wechsler Wrote:Ilja,
You say
"the argument of Sophia may be quasi valid, but tends to prove that the quantum is far more important than relativity in the micro world."
I don't tend to prove such a thing. Where from do you take it?
From the rest of that comment of yours I understood nothing: "location is weighed by probability, it is not some concrete thing with concrete trajectory (obviously not ddB oriented) . . ." I don't care about dBB. I care to prove that the concept of "particle" floating in a wave-packet, is impossible, and that is more general than rulling out the dBB. My proof relies on that a particle - if we admit that it exists - has to have at a given time a given position. It can't be in two places at once, unless it jumps instantaneously between them. Further, such instantaneous jumps are a sick assumption, because of the relativity of the simultaneity: what's simultaneous in one frame is not simultaneous in another one. From this there emerge troubles when we have to do with entanglements. I already explained that. I can explain again but in a separate post.
"But there is some sort of contradiction, you assume a particle, ie. definite trajectory, and you finish off what would give you this trajectory, this is contradictory. So better rethink the whole thing . . ."
Ilja, you talk to me or to yourself? I don't have antenna in other people's mind, please be clear.
Now, to your last post.
"That you have computed (21) starting from (19) with using (20) does not mean that you can you can conclude that a particular measurement result can be attributed to a particular part of (19). There is no base for such a conclusion in quantum theory."
Ah, Ilja! Of course that by QM what you say is true. But for ruling out the idea of a particle, I have to assume that it exists, i.e. add to QM this assumption, and prove that it leads to a contradiction in the logic.
So, I repeat, there are three 2-particle waves that contribute to the result F1 = F2 = 1. One of them is provided by the oscillators only, s.t. our particle is not involved. Since we admit the concept of particle, the particle is present either in the wave-packet |u1> impinging on BS1, or in |u2> impinging on BS2. In the first case, F1 = F2 = 1 is the result of our particle in D1 and an oscillator particle in D2. In the second case, it's vice-versa. But, our particle can't be in both places. I repeat, because you missed this, a particle cannot jump from one region to another. Therefore, in continuation, if the particle impinged on BS1 it will go to D1 (or C1) but not to D2.
Thus, admitting the idea of particle, the result F1 = F2 = 1 emerges either from one part of (19), or from another part - the part that conteined the particle.
The impossibility of jumps I proved elsewhere, not in the section 5. In section 5 I took the "no-jump" as a hypothesis.
Schmelzer Wrote:Dear Sofia D. Wechsler
in the part addressed to me but answering to Juan you wrote " I don't care about dBB. I care to prove that the concept of "particle" floating in a wave-packet, is impossible, and that is more general than rulling out the dBB." But if you prove the impossibility of something which has been already constructed, in a quite explicit way, you would better care about this construction. Either your proof will be wrong or something in the construction. If the construction is quite simple, and in the case of dBB it is, the probability is high that the error is in your construction.
You write "My proof relies on that a particle - if we admit that it exists - has to have at a given time a given position." But this alone will not give any contradiction, because the dBB trajectories which you can easily compute (all you have to do for this is to specify which of the two measurements is the first one - different choices give you different trajectories) are at a given time at a given position, without any jumps.
"Ilja, you talk to me or to yourself?" That was Juan talking to me and you.
Now about the answer to my post.
"Of course that by QM what you say is true. But for ruling out the idea of a particle, I have to assume that it exists, i.e. add to QM this assumption, and prove that it leads to a contradiction in the logic."
But it does not. The continuous dBB trajectories are simple and have no contradictions. (That I construct the counterexample using dBB is, BTW, quite irrelevant - it is simple the straightforward method to construct one. But it is an explicitly constructed counterexample, constructed for your experiment, and it constructs what you claim to have proven does not exist.)
"Since we admit the concept of particle, the particle is present either in the wave-packet |u1> impinging on BS1, or in |u2> impinging on BS2. In the first case, F1 = F2 = 1 is the result of our particle in D1 and an oscillator particle in D2. In the second case, it's vice-versa. But, our particle can't be in both places."
And it is not. In every particular experiment, it is on one well-defined side.
If F1 is measured first, it is the particle going through u2 which gives F1=1, and, then, possibly also F2=1. If the particle in this experiment goes through u1, it gives F1=0.
In the second case, it is vice-versa. But this "second case" reads in the following way:
If F2 is measured first, it is the particle going through u1 which gives F2=1, and, then, possibly also F1=1. If the particle in this experiment goes through u2, it gives F2=0.
That means the other case is about another experiment. An experiment which starts with the same state, but measures things in a different order and can, therefore, obtain different results for the same initial state (the particle being in u1, for example).
I use here the dBB trajectories which are continuous. So, no, I do not miss your requirement that there should be no jumps.
"Therefore, in continuation, if the particle impinged on BS1 it will go to D1 (or C1) "
And, indeed, it is. If the particle is going through u1 it ends either in C1 (if F1 is the first measurement) or in D1 (if F2 is the first measurement). So, your no-jump hypothesis is fine and unproblematic. In the dBB counterexample the particle does not jump.

Some further comments:
Sofia D. Wechsler writes:
"You see how Ilja fights for finding a mistake in my proof and does not succeed."
Except that I see the situation quite differently. The mistake is an obvious one, given that dBB provides the counterexample in a straightforward way, the only difficulty is that you don't understand this point.
Note also that if you don't like dBB, no problem. The counterexample, once constructed, works fine even without naming its origin. Then, if you insist that I should not consider two experiments - one with F1 measured before F2, one with F2 measured before F1 - also no problem. Let's forget about the details. Instead of the single dBB counterexample, we have now even two counterexamples. That the first one is the dBB trajectory for F1 being measured first, and the other one the dBB trajectory for F2 being measured first, can remain hidden. It does not change the fact that both are counterexamples. They are continuous trajectories with give the probabilities predicted by quantum theory for your experiment.
Having two different counterexamples is certainly not a problem for the counterexamples themselves. Each of them is sufficient to show your proof fails.
"Then, why do you need that "token", or "quantum particle" as you call it?"
It is the only way to have, on the one hand, Schroedinger's cat being either alive or dead, and to have the Schroedinger equation as a universal equation which works also for cats. The alternative is a physical collapse of the wave function, something much more artificial, and in need of new physics. (Or many worlds insanity).
Juan Weisz writes:
" Trajectories and such sound to me like going back in time."
This is a type of argument I don't understand at all. What is wrong with reviving old physical principles? I think there should be a simple conservative rule: Don't give up established principles without necessity. If there is an empirical necessity to give up something, o k, such is life. But if there is an interpretation which allows to preserve them, there is no necessity to give them up. Many modern physicists seem to think differently - they support giving up old principles without any necessity.
Essentially this is a good description of an essential part of my research program: To look at good old principles of physics which have been given up and to ask if giving them up was really necessary. Usually it was not necessary at all.
As an additional criterion I look at the mathematics. If there are nice, beautiful mathematics available to describe the classical structures I try to revive, fine, I use them. dBB has such nice additional mathematics which support the continuous trajectories, other realistic interpretations have even more nice mathematics. The Lorentz ether has nice mathematics too (harmonic coordinates are preferred). Artificial constructions usually do not have nice mathematics to support them.
Sofia D. Wechsler Wrote:Ilja,
what you talk about?
". . . two counterexamples. That the first one is the dBB trajectory for F1 being measured first, and the other one the dBB trajectory for F2 being measured first, can remain hidden. It does not change the fact that both are counterexamples. They are continuous trajectories with give the probabilities predicted by quantum theory for your experiment."
I don't understand what you think that happens if F1 or F2 is measured first. And what remains hidden? Please decide if you are interested to talk with me or with yourself.
What is the counter-example? Since you want very much that some measurement be done first, let's say that I change the configuration of my experiment, for you, and F1 = 1 is always obtained first. Which special thing do you believe that would happen? As to probabilities, how can I refer to results you claim, if you don't show me the calculus? It's not serious.
You have to take in consideration that I am busy, one should not tell me uncontrolled things.
Schmelzer Wrote:Dear Sofia D. Wechsler
Fine. So, F1 is measured first. If the particle goes through BS1, it ends in C1 Thus, once F1=1, it goes through BS2. There is no particle at A2, but there is one in A1, which goes to D1. The particle in BS2 goes with some probability either to C2 or D2. No jumps, everything is fine.
The calculus is simple, that the particle has to go through BS2 is something you can copypaste from Hardy replacing "photon" by "electron to get your experiment. Once F1 is measured, and the collapse gives for the remaining state of one particle |u2>|a1>, which is no longer a superpositional state but a simple product state, thus, your (20) gives some probability for C2 and some for D2 for the particle in BS2.
Given the triviality of this (namely a simple copypaste from Hardy and the using your formula) I thought this should be obvious. Moreover, in general this simply follows from the equivalence theorem of dBB in quantum equilibrium with QT, and the fact that my counterexample is the dBB trajectory. You should know, I do not doubt well-known established theorems.
Sofia D. Wechsler Wrote:No, Ilja,
It's probably a difficult thing to understand. You see, the mathematics in my proof is simple, but one has to be very careful about what it means.
When one does a proof, there are three parts: assumptions, processing, and conclusions. One cannot use the conclusions in the processing. This is what you do.
My proof proves that the idea of particle as the item that triggers a detector, is contradictory. What remains is that we have to do with WAVES, and in which-way experiments what triggers a detector leaving other detectors silent is the collapse. I told you repeatedly but probably it's difficult to grasp: I do the assumption that what triggers a detector is a particle - NOT THE COLLAPSE. So, I don't want to hear of collapse in the body of the proof.
Next: I may perform the experiment in a dynamic way, i.e. insert the set 1 (beam splitter BS1 together with the detectors D1 and C1) and the set 2 (beam-splitter BS2 together with the detectors D2 and C2), when I wish. The electron that exits the central beam-splitter BS, has NO IDEA when I intend to place each set. Then, it may go to whichever direction it wishes.
Now, I introduce first the set 1 and Hardy proved that if the detector D1 fires, the electron should have gone toward the region of the set 2. But, later on I introduce the set 2. If the detector D2 fires, Hardy proved that the electron should have gone toward the set 1.
You may claim otherwise only if you can prove that Hardy's proof is wrong.
(P.S. would you kindly leave me in peace with dBB? I am too much busy. dBB is not an issue in my proof. In the same way one can tell me stories about quantum gravity, about the cosmic radiation, but they are not issues in my proof. If you want to discuss my proof you please stick to the assumption of my proof, and nothing else. The assumption is particles which do not jump from one region to another. )
Schmelzer Wrote:Sorry, Sofia D. Wechsler
but standard quantum theory (minimal interpretation) describes a sequence of several measurements using the notion of a collapse. A state with wave function psi = sum_i a_i psi_i where psi_i are the eigenstates of what is measured is after the measurement with probability |a_i|^2 in psi_i. If you reject to hear elements of the minimal interpretation, your choice, but in this case we cannot talk about probabilities. (Not really a problem, once the point of the proof is independent of the probability of F1=F2=1 as long as it is greater 0, but, nonetheless, you have to explain what are, IYO, the allowed mathematical methods to compute the probabilities if in the initial state the wave function is psi, then some operator A1 is measured, and then some operator A1.
But, ok, I can even reformulate all the things without naming the collapse. What collapses is only the wave function of the measured subsystem, the full system wave function which includes the measurement devices does not collapse. But I would not recommend this, we would, in addition to all the particles also have to include all the measurement devices into the consideration, without necessity (except if the aim is obfuscation of a simple issue, which I hope is not the case).
Let's also note that to be a counterexample to your theorem my description does not really have to compute the probabilities. All what is necessary is that there is a description of continuous paths of the particles themselves for this particular experiment and for every outcome of the experiment which is possible (probability > 0). This is what you claim is impossible for the possible outcome F1-F2=1. I have given such a description, that means, it is possible.
Given that you after this start to modify the argument, introducing another type of experiment, a dynamical one, it seems that you understand that without the dynamical element the proof fails, and start to use arguments closer to Hardy's original ones. This would be some progress. So, let's consider now the dynamical variant of the experiment.
"Now, I introduce first the set 1 and Hardy proved that if the detector D1 fires, the electron should have gone toward the region of the set 2."
No, this is not what Hardy proves. He proves that if F1 and U2 is measured, then from F1=1 follows U2=1.
Now you can try to extract from this, together with the hypothesis that there are continuous trajectories, the idea that this information gives more, namely some information about other measurements too. But you cannot, without introducing additional assumptions. Like assumptions about causality: the particle cannot know what experiments you will do in the future. This allows you to conclude: If I measure first F1, and do not yet decide if I measure U2 or F2, and it appears that F1=1, then the particle is at BS2, and we know this before we made the decision what to measure, U2 or F2. So far, fine.
"But, later on I introduce the set 2. If the detector D2 fires, Hardy proved that the electron should have gone toward the set 1."
No, this is, again, not proven by Hardy. He proves that if F2 and U1 is measured, then from F2=1 follows U1=1.
Similarly, by analogy, you can prove now that if F2 is measured first, so that it is not known if U1 or F1 is measured, it follows that the particle goes through BS1. Here you have to use, again, causality, namely that at the time of measurement of F2 it is not known what you will measure, but, once you will obtain, with certainty, U1=1 if you measure U1, you can conclude that the particle is in BS1.
But both causal arguments fail if you don't have the assumption that F1 resp. F2 is measured first. So, if we consider only the experiment where F1 is done first, then we can, following Hardy, and applying the causal argument (essentially EPR, we can predict, with certainty, U2=1, thus, conclude that it is really in BS2) conclude that it is in BS2. But the second part fails. The information about the result of the measurement of U1 and F2 gives you nothing for predicting what happens if F1 was measured and then F2.
Let's also note that my argument remains: "That you have computed (21) starting from (19) with using (20) does not mean that you can you can conclude that a particular measurement result can be attributed to a particular part of (19). There is no base for such a conclusion in quantum theory."
Your additional considerations, following after your "Ah, Ilja! Of course that by QM what you say is true. But for ruling out the idea of a particle, I have to assume that it exists, i.e. add to QM this assumption, and prove that it leads to a contradiction in the logic." did not add any evidence for this conclusion. Thus, your "proof" remains to be a "and then a miracle happens" proof.
PS: Feel free to ignore sentences containing "dBB". I do not write them for you, but to explain to the general public the general strategy how to argue with all those who propose various "dBB is impossible" proofs.
Sofia D. Wechsler Wrote:Ilja,
You cannot argue with people about which assumptions they choose for their proofs. Can you argue with GRW on the assumptions they assume? Could you have argued with Bohm on which assumptions he assumed? No! And Bohm assumed like me that what triggers a detector is a particle floating in the wave-function. The fact that we remain with the collapse is a conclusion in my proof, not an assumption.
The assumptions of my proof are: 1) A detector is triggered by a particle floating in one of the wave-packets. 2) There is no jump between regions.
The conclusion of my proof is: One or both assumptions is /are wrong. The assumption of no-jump is proved in another place s.t. it is not under question mark. Thus, the conclusion is that the assumption of the particle is wrong. Therefore standard QM wins, and what triggers a detector is decided by the collapse, not by a particle.
You are not permitted to add a new assumption to my proof. You can't use the conclusion of the proof as an additional assumption.
Let me stress something that escapes you all the time: The fact that thק particle is on u2 is not due to finding F1 = 1. The particle takes a path before your test of F1 and/or F2, and does not jump between paths. It's BECAUSE the particle is on u2 that you can get F1 = 1. If the particle were not on u2 you couldn't get F1 = 1. So, since the particle is objectively on u2, you can test F1 whenever you want, before or after testing F2, and you still can get F1 = 1.
Similarly, if the particle were not on u1, you couldn't ger F2 = 1. Full stop! From this situation stems the contradiction I found.
On the other hand, if you stick to the collapse hypothesis, then yes, it's the collapse following the detection F1 = 1 that confines the particle on u2. Before the collapse, by the standard QM, we could not even speak of a particle confined to some track. But, I repeat, the fact that the concept of a particle is wrong and we remain with the collapse principle, is the conclusion of my proof, not a hypothesis.
Is the line of the proof clear now to you? Is it clear which are hypotheses and which is conclusion?
Schmelzer Wrote:Dear Sofia D. Wechsler
Of course, I can restrict myself to the point that your proof is invalid because the important claims you use are simply not proven. In your previous answer, you have proposed a variant of your proof containing a "and Hardy proved that if the detector D1 fires, the electron should have gone toward the region of the set 2." which was simply wrong because it was not what Hardy has proven. The same thing I have done with your original proof, I have also found there a statement without a proof.
Sorry for trying to explain you (which I obviously failed) which could be the reason for the big hole in your proof, by suggesting which additional assumption could have saved some parts of your proof (even if not the whole proof, given that the conclusion is wrong).
The line of the proof is clear to me, as well as the big holes in the proof, which make it invalid as a proof. You want to prove that F1=1 means the particle is at BS2 independent of any other additional assumptions, but you cannot. Similarly you want to prove that F2=1 means the particle is at BS1 independent of any other additional assumptions, but you cannot. If you could prove both things, your proof would be fine. So the line is simple and clear, but the theorem fails, because you cannot prove those two claims. You cannot and did not. Hardy has proven some in some sense quite close statements, and his proofs are correct, but they are not what you claim he has proven, and what he has proven does not help you to prove your claims.
Your "proof" is not a proof, it does not prove what it claims to prove, because of the errors - big holes in the argument - which have been identified.
"If the particle were not on u2 you couldn't get F1 = 1." Unfortunately for your proof, one can. All one has to do is to measure immediately F2 and only after this F1.
Sofia D. Wechsler Wrote:Ilja,
Your tone of certainty that my proof is wrong, irritates me. I'll adopt an analogous tone, and no doubt you won't like it.
"your proof is invalid because the important claims you use are simply not proven."
The "important claims I use" have a standard name - ASSUMPTIONS. Assumptions you don't prove, you assume. And I am tired of explaining this to you endlessly.
"You want to prove that F1=1 means the particle is at BS2 independent of any other additional assumptions, but you cannot."
This is Hardy's proof, not mine. I went with you through Hardy's proof only for showing you that you stick to the assumption (of Hardy) that the confinement of particle on one track is the result of collapse. (And of course, the first measurement produces collapse.) But in my proof the collapse is a CONCLUSION not an ASSUMPTION. So, do your criticism to Hardy, not to me. I am tired of explaining you the difference between my assumptions and Hardy's assumptions.
My proof is a series of equations according to the QM formalism. If you disagree with this formalism, write an article and disprove it. My equations prove that F1 = F2 = 1 is totally due to the particle going to D1, but, also, totally due to the particle going to D2. The assumption of NO-JUMP tells us that if the particle is detected at Dj, it was previously at the input of BSj. Thus, F1 = F2 = 1 is totally due to the particle going to BS1, but, also, totally due to the particle going to BS2.That's ALL.
I am not going to waste my time anymore. From now on, you can say whatever you want, I'll ignore.
Schmelzer Wrote:Dear Sofia D. Wechsler
you wrote "The "important claims I use" have a standard name - ASSUMPTIONS. Assumptions you don't prove, you assume. "
So "Now, I introduce first the set 1 and Hardy proved that if the detector D1 fires, the electron should have gone toward the region of the set 2." was an assumption? And "the probability of obtaining F1=F2=1
with the initial particle going to BS1 is (22)" is an assumption? These were the claims I have referred to in "your proof is invalid because the important claims you use are simply not proven."
No problem, in this case you simply make wrong assumptions which contradict each other and the "proof" proves nothing of interest about the possibility of particles.
"My proof is a series of equations according to the QM formalism."
No, it is not, and you have even already acknowledged this before. The QM formalism does not give you anything about the particle being in either BS1 or BS2 if you measure F1 and F2.
"My equations prove that F1 = F2 = 1 is totally due to the particle going to D1, but, also, totally due to the particle going to D2. "
No. You are not even close to a proof of such a thing. As we have seen at the beginning, you name them now "assumptions".
"I am not going to waste my time anymore. From now on, you can say whatever you want, I'll ignore.'
This is what has to be expected from a crank who is unable to defend a completely inconsistent "proof". To be honest, this end is not really unexpected.
Sofia D. Wechsler Wrote:Schmelzer,
Use the word "crank" when describing yourself.
I told you repeatedly that what confines a particle to a track is not the measurement which is done first. If a particle is considered an objective thing, it is on the given track no matter if you measure F1 and/or F2, neither in which order you measure these observables.
The measurement of F1 or of F2 doesn't have the power to change a pre-existing objective reality, as I assume.
But I say all these things in vain. It's in vain that I say that I have the full right to choose my assumptions, and you don't tell me with which assumptions to work. You stick to Hardy's style of rationale, to the order of measurements, and this is why I said that I won't waste more time with you.
You also accuse me of having accepted to assign relevance to the order of measurements. This also you didn't understand, I did it just for showing you that you impose an alien assumption that I don't make.
Now you resorted to insults. Sorry, insults are not a scientific argument. A talk with me can be only polite, and one should read very attentively what I explain. You violate these rules, your posts are aggresive, conceited, and insulting. This is why I won't waste any more time with you.
Display these "qualities" of yours with other people. Full stop!
Schmelzer Wrote:Dear Sofia D. Wechsler
It is up to the readers to apply the criterion I have given. I can only repeat: It is quite typical for cranks if they have no more arguments to stop a discussion claiming victory. If this criterion can be applied to you or not depends on your behavior, it is essentially your decision.
I will answer all your objections against my claim that your proof fails. In this post, you have given the following argument:
"If a particle is considered an objective thing, it is on the given track no matter if you measure F1 and/or F2, neither in which order you measure these observables."
Indeed, and this holds in my counterexample too. If the particle is in BS1, it remains on this side, independent of what will be measured.
What depends on the order of the measurements is the result of the measurements. If F1 is measured first, it will certainly have the result F1=0. If it is only the second measurement, this can no longer be proven, and the result may be as well F1=1. As one can see, the result depends on what is known at the given moment, thus, everything is compatible with causality.
"The measurement of F1 or of F2 doesn't have the power to change a pre-existing objective reality, as I assume."
The measurement of F2 has the power to change the outcome of a later measurement of F1. This is a known property of quantum mechanics. Measurements change the state and influence the results of later measurement.
"You also accuse me of having accepted to assign relevance to the order of measurements."
No. My remark about "you have even already acknowledged this before" refers to your "Ah, Ilja! Of course that by QM what you say is true. But for ruling out the idea of a particle, I have to assume that it exists, i.e. add to QM this assumption".
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