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An interesting discussion with SofiaD. Wechsler
#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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RE: An interesting discussion with SofiaD. Wechsler - by Schmelzer - 01-19-2019, 04:03 AM

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