minkwe wrote:Good that you agree. Who cares about unmeasured distributions? The only outcomes you can calculate with are the ones that are measured. So your so-called "actual probability distribution" is a fantasy.
But the question is exactly whether such a probability distribution can possibly exist, and explain the measured values. If no Bell inequality is violated, then such a distribution does exist, if there is a violation, then you can't find one. I mean, we want to find whether there could be a theory more fundamental than QM that accounts for all of QM's predictions, while assigning definite values to all observables at all times. Such a theory will have a PD over all possible outcomes in a given experiment. So if there is such a PD possible, then likewise, such a theory is possible; and if not, then no such theory exists.
This is thus not about the PD that you get by making a certain subset of measurements only, but rather, the PD that is actually prepared by nature---the actual ensemble of hidden variable value assignment. That we can do a certain set of measurement in which we simply neglect correlations and hence, obtain a PD that does not include any correlations is completely beside the point. The correlations are what we are interested in---failure to measure them then just means that we did our experiment stupidly, not anything about local realistic completions of QM.
minkwe wrote:The point is that there is a joint PD P(A,B,C,D) of outcomes based on how the experiment was performed, irrespective of whatever mechanism is producing the outcomes, and the corollary is that even if the process producing the outcomes may have a fantastic unmeasurable "actual distribution", you could still obtain measurement outcomes which do not have a joint PD P(A,B,C,D) simply by choosing to measure the outcomes in a certain way, such as is done in EPRB experiments.
No, this isn't possible. If there exists a fundamental joint PD, then no experimental outcomes exist that aren't compatible with the existence of that PD, no matter how you perform the measurements, since all the outcomes are just sampled from this distribution.
minkwe wrote:I take it then you believe that a system producing 3 correlated spin-half particles heading towards Alice, Bob and Cindy, with Cindy simply ignoring her particles, and Alice and Bob measuring theirs like a typical EPRB cannot violate a Bell inequality no matter the setting combination they use, and no matter the nature of the correlation between them? Yes or no?
That depends: if the state is separable wrt both the Alice-Cindy and Bob-Cindy splits, but maximally entangled across the Alice-Bob split, then they will be able to violate the CHSH inequality maximally. If there is some entanglement present between Cindy and Alice-Bob, then there won't be a maximal violation, and the violation will decay in proportion to the amount of this entanglemen.
minikwe wrote:And if you believe the fact that it doesn't violate Bell's inequality can be used to conclude that there is no-disturbance present, and no non-locality present.
The fact that no Bell violation exists does entail that there is a local realistic model for the particular scenario. But the fact that there are scenarios where Bell violation exists means that there is no such model that can be used to explain every quantum prediction.
minkwe wrote:If you believe that then, I'm asking you if you believe the claimed non-locality or disturbance only shows up for specific states, but decides to hide if you have more particles that can actually be measured.
Just like for any other characteristic, you must make the right measurement on the system in order to detect the nonlocality. Making the wrong measurements won't tell you anything.
minkwe wrote:Take for example the CHSH in which 2 spin-half particles in the singlet state are measured at 4 settings
, in the pairs
. If instead of producing just the 2 particles each time, our source produces 4 entangled particles heading towards 4 stations, Alice, Bob, Cindy, and Dave, such that the particles pair going to Alice and Bob are always in a singlet state, those going to Cindy and Dave are also always in a singlet state, and the particles going to Alice and Cindy are identical to each other, just like the particles going to Bob and Dave. Thus all the paired measurements
are by themselves measurements on a pair of spin-half particles in a singlet state.
This characterizes the state fully to be
, i.e. the state is maximally entangled between Alice and Bob, respectively between Cindy and Dave, and completely uncorrelated between the A-B and C-D pairs. Thus, correlations
, while
. Hence,
, and there is no CHSH violation predicted by QM.
minkwe wrote:Would those values be different if Cindy and Dave simply ignored their particle pairs, so that Alice and Bob did all the measurements at different times and different settings on different ensembles?
Since the state is separable along the A-B|C-D split, what Cindy and Dave do or don't do doesn't affect the results that Alice and Bob get from their measurements. Thus, if Alice and Bob add measurements c and d to their repertoire, they're now measuring the full CHSH-correlations on an ensemble of maximally entangled particles, and will obtain
.
minkwe wrote:Nope, you did not understand. I say the presence or absence of a joint PD is based on how you do the measurement, not due to disturbance or non-locality, I've given you examples (tablets) in which even with locality and no-disturbance, you did not not have a joint PD of outcomes based on how you did the measurement.
In this case, there is a joint PD (trivially), but you can't find it because you can't repeat the measurements. From throwing a coin once, you can't know the probability of it coming up heads.
minkwe wrote:I have given examples (non-local state machine pressed in sequence ) in which a joint PD of outcomes was present even with disturbance or non-locality to prove this point.
A joint PD is trivially present if you neglect all correlations, because then you can just use a product distribution. But that distribution won't be able to explain all measurements, i.e. the outcomes of joint measurements. Again, throw two correlated coins, only noting down the outcome of one, and you can write down a joint PD; but according to that PD, the coins will be completely uncorrelated, so it's just not in any sense the PD of those coins.
minkwe wrote:I have also given another example (see above) using 4 spin-1/2 particle particles in which a joint PD is present and the inequalities must be satisfied. I hope you will address that example because I think it shows clearly the problem with your argument.
I don't see any problem; there's clear predictions from quantum mechanics, which will agree with experiments.
minkwe wrote:So let me ask you again the questions I asked you are the beginning. A simple yes/no answer will resolve all the word games
1) Is locality required or necessary in order to have a joint PD? Yes or no.
2) Is pre-determination required or necessary in order to have a joint PD? Yes or no.
3) Is no-disturbance required or necessary in order to have a joint PD? Yes or no.
1) No. There are nonlocal models which nevertheles admit a joint PD; however, whenever a joint PD is absent, then we know that there is no local (realistic) model. This is what Bell is about.
2) Again, no. But again, the question is: "We have this data. Can it be explained by a local realistic model?", and if there is a joint PD, then it can; otherwise, it can't, since any local realistic model admits a joint PD. There are nonlocal, nonrealistic models that nevertheless do, but those are simply besides the issue. We don't want to know whether the data is compatible with non-local antirealism, we want to know whether it is compatible with local realism, which it is if and only if there is no BI violation.
3) No. See above.
If you want to change your answers to no, no, no. Then we can put this issue to bed and proceed to other things.
The problem is, however, that you seem to think that answering no to all of the above would resolve the issue, but you've still simply got the logic backwards: if we find data compatible with a joint PD, then (and only then) can we write down a local realistic model that replicates the data, because any local realistic model will have a joint PD---local realism is sufficient for the existence of a joint PD. So if there is no joint PD, then local realism doesn't hold.
minkwe wrote:The problem is that you continue to argue that the inequality should hold even in the scenario I have shown it does not apply to. You continue to argue that a joint PD must be possible if the model is a local HV one. There is no disturbance in my simulations, and there is no non-locality.
And hence, there is a local realistic model; in fact, your model just is that model. The simulation is intended to argue that local realistic models can violate Bell inequalities, but it misses its mark, in violating a Bell inequality that would not be expected to hold in this scenario anyway, since one needs a higher detection efficiency than you provide in order to perform a conclusive test.
minkwe wrote:The simulations are completely local realistic, and yet they reproduce the QM predictions very well. So it must be false that a joint PD can always be constructed if the model is local realistic and does not have any disturbance. If you disagree, show me the disturbance or non-locality that my simulations are using to produce their outcomes. They are designed to be run on separate unconnected computers.
And one can explicitly write down a joint PD for your model; it's just that some samples from that PD will be rejected, i.e. not lead to a detection.
minkwe wrote:All you have to do is admit that based on how the measurements are done, it is not always possible to reconstruct a joint PD, even if the model is local and realistic, just like is the case in the EPRB experiment. If you admit that, then we can put this issue to bed.
I can't admit it, because it happens to be false. If the model is realistic, then there is always some value assignment prior to measurement. If there is no disturbance, then that value assignment is not influenced by other measurements. Hence the convex combination of value assignments according to their frequency in the ensemble is a joint probability distribution, from which measurement outcomes are sampled.