Jochen wrote:In all the discussions of weak measurements I know, it's simply a measuring device weakly coupled to the system to be interrogated.
I know, that is why I ask you to provide an actual experiment in which weak measurements were done and we can discuss. It is very easy to speak nonsense "theoretically".
Jochen wrote:OK, so how do you justify the existence of a joint PD? If I am allowed nonlocal signalling, then I can always alter the PD of one part of the system due to measurements done on the other, and no joint PD exists.
If you review my response carefully, you will see examples of how to do it. For example, the your state-machine
with non-local disturbance, in which the measurements are always done in sequence A,B,C,D, would produce a joint PD. So long as the 4 numbers are jointly measured, it matters not one iota what physical mechanism is generating them, you will get a joint PD of outcomes and Bell's inequalities will apply.
Jochen wrote:In fact, let me give you another very clear example. The Bell inequalities will apply to 3 spin-half entangled particles measured simultaneously by Alice, Bob and Cindy. This should give you a huge hint that non-locality or disturbance or even any physics is completely irrelevant.
If I read you right, then this is wrong: there are Bell inequalities, such as Mermin's inequality, that are violated by measurements on three partite entangled states
Of course if the original bell inequalities would have been violated by 3 spin-half particles, the goal-posts would not have needed to be shifted. The original Bell inequalities involve 3 simultaneous measurements at settings (a,b,c). That can be done for 3 spin-half particles directly, and the original Bell's inequalities will apply, shouldn't they? And if they are satisfied, as they must be in this case, are you suggesting your "disturbance" or "non-locality" decides to manifest itself only when two particles are being measured at the time, but decides to stays silent when a third is being measured? Otherwise, why would you expect a joint PD (A,B,C) to be present in this case, but absent in the case of only 2 particles, if you refuse to acknowledge that it is the joint measurement that determines whether you have a joint PD, so that when you measure the 3 simultaneously, you get a joint PD P(A,B,C), and when you measure only 2 you do not get a joint PD P(A,B,C). It does not matter what physical mechanism is generating the outcomes.
Jochen wrote:Take three coins,
,
, and
. If you flip the first and second together, they will always agree, giving both H = heads or T = tails with 50% probability. If you flip the second and third together, they will always land oppositely (again with 50% probability). If you flip the second and third together, they will always agree (50 % HH, 50% TT). Clearly, there does not exist a joint PD
. Nevertheless, flipping each coin on its own is a perfectly ordinary stochastic process---for which, however, BIs can't be derived.
But your contrived example does not translate into a general truth. Besides your coins lack many crucial relevant components which is the paired correlation between individual pairs of coins, and the impossibility of re-tossing a specific coin more than once. The point was, that contrary to your claim that pre-determination of values is required, a random number generator which generates the 4 numbers (A,B,C,D) without any pre-determination, must obey the CHSH inequality because the outcomes represent a joint PD P(A,B,C,D). Therefore pre-determination is not required to obtain a joint PD. Do you agree or disagree?
Jochen wrote:Take the machine reproducing the coin throws above: the single coint throw marginals are just those of a fair coin, hence, what you get this way is just a sequence of random heads and tails; but this doesn't suffice to pin down the PD---a product distribution would reproduce this just fine, but fail to account for the correlations.
See above why your coin example misses the mark, and the fact that you use "fair" coins makes the example even worse. If you want, to bring it up to par, you should modify it such 1) that all three coins produced by the machine each time will produce the exact same result when tossed together, and 2) The coins are destroyed by the tossing process as soon as the results are read, and 3) that each triple of the coins contains a specific biasing mechanism not necessarily present in other coins. Once you make those modifications and are convinced that your argument can still proceed (which I don't think it can), then present the new argument and I will address it. You have a bigger burden than me. You are trying to argue that it is ALWAYS possible to reconstruct a joint PD for ALL local HV theories. Using specific contrived examples do not serve your purpose. I'm arguing that in some cases where you have a local HV theory, it is not always possible to reconstruct a joint PD from measured pairs. So I can use simple contrived examples to make my point effectively, you cannot.
Jochen wrote:This is what degrees of freedom can do. Alice and Bob do not have the freedom to test the same tablet more than once. They do not have the freedom to test all tablets at the same time.
What, exactly, do you mean by 'degrees of freedom'? The way you use it here seems at variance with how the term is usually used.
You do not say what you mean by "at variance" so I don't know how to answer a claim that is not substantiated. I use degrees of freedom it in the same way it is usually used. So please explain what you mean by "at variance".
Jochen wrote:Jochen wrote:Finally, regarding your point of whether the correlators
are the same across different trials
minkwe wrote:- Since you can't measure all the terms simultaneously, you make the additional assumption
, that counterfactual averages
, should all have the same value as averages each measured on a separate set of particle pairs
. And you think this assumption is justified because the values you actually measure
are reproducible?
Just because you can measure
repeatedly and reproducibly does not mean
So you misunderstood me. The fact that averages actually measured on separate sets of particles are always reproducible does not and cannot reasonably be taken to mean that those averages are the same ones represented by the terms in the inequality which were not measured on the same set of particles. It is a fact that the measured averages are reproducible. But that has nothing to do with the fact that the actually measured correlations are not the same as the unmeasured counterfactual ones from the same set of particles.
Reproducibility of measured averages does not necessarily translate to equality between measured outcomes and counterfactual outcomes, even for local hidden variable theories. In fact, I have simulations which prove this point (see below).
In the expression
, for the particle pair
, three of the paired terms are counterfactual and one is actual. Once a measurement has been made at
,
then the rest of the results are fixed. This is what crucial factorization
means! The terms are not independent from each other, there are 4 independent values which are free to vary in that expression, and those 4 values are cyclically shared by the paired terms such that they are not independent. Once three of the paired terms are given, the fourth one is determined automatically. That is the origin of the relationship
. The problem is that you are trying to take away the feature that gives you that relationship while at the same time claiming that the relationship continues to hold. For example, the expression
where each term is an actual outcome measured on a different particle pair, completely lacks that the original relationship, because there are 8 independent values which are free to vary. Knowing three of those paired terms, tells you absolutely nothing about the fourth one. As you can see, the factorization is no longer possible, and the relationship here should be
. You haven't presented a convincing argument to support your claim why we should have
rather than
. All you argued is that since
and
are reproducible, therefore
. That argument does not make sense. You have to start from
, and make all the necessary assumptions you need to make to derive
. Once you do that, you will realize that it is impossible, unless you also claim that for every
, there must exist a function
which would permit you to to rearrange the list of outcomes
into
such that
, ie, the number of +1's and -1's are the same, and the patterns are the same. This is the only condition under which
is true. But as I have explained in my previous post, this is impossible. The cyclical nature of the terms in the inequality precludes the general existence of such functions. You did not address that argument at all.
Jochen wrote:I sense there's probably not going to be a real meeting of minds between us, so all I can really do is extend the same invitation to you as I offered to Joy: produce a simulation, such that I can locally enter the measurement directions for party A and party B on separate, noncommunicating computers, then get out a list that gives for each measurement direction the measurement's outcome, which I then use to compute the correlations; and if that then manages to violate a Bell inequality, I will rescind and retract everything I've said so far.
I already have written two local realistic simulations of EPRB experiments, which reproduce the QM correlations without any disturbance, and without non-locality. You can find them
https://github.com/minkwe/epr-simple/, and
https://github.com/minkwe/epr-clocked. But you are not going to understand what is going on there, if you do not understand my arguments. In fact, epr-clocked does exactly what you asked on separate computers. I have written my own analysis program to analyze the results to show you that it closely reproduces the QM results. But actually I would prefer if you take the two output files from my simulation programs, and do your own analysis. It will be very educational as it will reveal quite a few hidden assumptions, even in the phrasing of your request.
The whole point of my simulations and all my arguments here is the following:
1) There is only one assumption required to derive Bell's inequalities (and the CHSH). ie, the existence of a joint probability distribution of outcomes P(A,B,C) for Bell's original, or P(A,B,C,D) for the CHSH. Nothing else. Therefore, the inequalities do not apply to any experiment in which such a joint probability distribution of outcomes does not exist, such as the EPRB experiment, or their simulations such as "epr-simple" or "epr-clocked".
2) The absence of a joint PD, does not necessarily imply non-locality or disturbance, and can easiliy be obtained when sampling in pairs rather than quartets (or triplets, as in the case of Bell's original). This is what the simulations achieve, just like for the experiments and QM, where measurement can only be done in pairs for 2 spin-half particles.
3) Therefore, there is no conflict between QM and local HV theories. Rather, there is a conflict between the assumption of a joint PD P(A,B,C,D) and experiments in which only pairs are measured. It is the assumption that the joint PD can be reconstructed from the separate paired measurements that fails. The simulations show counter-examples for which it is not possible to reconstruct the joint PD from paired measurements. Therefore it is wrong to assume that local HV theories must allow us to reconstruct the joint PD from separate measurements.