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The statistical ensemble interpretation (SEI) is supposed to be a minimal interpretation of QM with the smallest amount of philosophy, vagueness and controversy. Yet it turns out not to be the case. For instance Ballentine, the inventor of SEI, interprets Bell theorem as a strong evidence of non-locality. By contrast, @vanhees71 , the strongest supporter of SEI on this forum, disagrees. Even though vanhees71 explained his position many times, many share the feeling that he never explained it sufficiently clearly.

In a more recent thread (which is now closed) it crystallized that one of the the most problematic issues in SEI is the concept of

For that purpose let me start with a sharp question addressed to @vanhees71 .

Here are some possible answers:

From previous explanations by vanhees71 I suspect that he will choose answer 4). For that case I have additional questions. Predicted by who? What if one observer can predict it and the other can't? Does it mean that the existence of value is subjective? As a response to those questions, I expect that he would agree with the following refined version of 4):

So far so good, but now I claim that 4) and 4-refined) contradict locality. Let the state initially at time ##t_0## be prepared in the EPR state

$$|A1\rangle|B1\rangle+|A2\rangle|B2\rangle$$

Then 4) implies that values of ##A## and ##B## do not exist at ##t_0##. Next let Alice measure ##A## at time ##t_1## and let she obtain the value ##A1##. Then, according to 4) and 4-refined), she can tell not only that ##A## has value ##A1##, but also that ##B## has value ##B1##. But when did ##B## started to has it's value? Since it did not have a value at ##t_0##, it must have started to have the value at ##t_1##. Since this value is objective by 4-refined), there must have been some objective change with the ##B##-system at time ##t_1##. But the only possible cause of that change can be the measurement of system ##A##, which is spatially separated from system ##B##. Therefore locality must be violated. Q.E.D.

Yet vanhees71 denies violation of locality in this case. I hope he can explain why exactly does he think that locality is not violated. He explained it many times before, but apparently he has never done it sufficiently clearly. If he doesn't agree with 4), the he should pick some other answer on the list 1)-6). If we agrees with 4) and 4-refined), the he should explain what exactly is wrong with my argument above that it violates locality. If he agrees with 4) but not with 4-refined), then he should refine 4) in his own terms.

vanhees71 likes to say that correlations between the observables existed even before the measurement. But that's not the issue here. The issue are the

Finally, let me mention that Einstein et al in the original EPR argument assumed something similar to 4) and locality, and from those assumptions they derived a contradiction. From the contradiction they concluded that QM was incomplete.

In a more recent thread (which is now closed) it crystallized that one of the the most problematic issues in SEI is the concept of

**value**of an observable. Since values of observables are numbers that are obtained in experiments, it's very important to have a clear interpretation of those values. In this thread I hope we can clarify them.For that purpose let me start with a sharp question addressed to @vanhees71 .

**According to SEI, when does the value of an observable exist?**Here are some possible answers:

*1) Value of an observable never exists.*

2) Value of an observable always exists.

3) Value of an observable exists when and only when it is measured.

4) Value of an observable exists when and only when it can be predicted with certainty.

5) The question doesn't make sense.

6) Something else (what?).2) Value of an observable always exists.

3) Value of an observable exists when and only when it is measured.

4) Value of an observable exists when and only when it can be predicted with certainty.

5) The question doesn't make sense.

6) Something else (what?).

From previous explanations by vanhees71 I suspect that he will choose answer 4). For that case I have additional questions. Predicted by who? What if one observer can predict it and the other can't? Does it mean that the existence of value is subjective? As a response to those questions, I expect that he would agree with the following refined version of 4):

*4-refined) If there is at least one observer (say Alice) who can predict the value with certainty, then she has a right to tell that the value exists in an objective sense.*So far so good, but now I claim that 4) and 4-refined) contradict locality. Let the state initially at time ##t_0## be prepared in the EPR state

$$|A1\rangle|B1\rangle+|A2\rangle|B2\rangle$$

Then 4) implies that values of ##A## and ##B## do not exist at ##t_0##. Next let Alice measure ##A## at time ##t_1## and let she obtain the value ##A1##. Then, according to 4) and 4-refined), she can tell not only that ##A## has value ##A1##, but also that ##B## has value ##B1##. But when did ##B## started to has it's value? Since it did not have a value at ##t_0##, it must have started to have the value at ##t_1##. Since this value is objective by 4-refined), there must have been some objective change with the ##B##-system at time ##t_1##. But the only possible cause of that change can be the measurement of system ##A##, which is spatially separated from system ##B##. Therefore locality must be violated. Q.E.D.

Yet vanhees71 denies violation of locality in this case. I hope he can explain why exactly does he think that locality is not violated. He explained it many times before, but apparently he has never done it sufficiently clearly. If he doesn't agree with 4), the he should pick some other answer on the list 1)-6). If we agrees with 4) and 4-refined), the he should explain what exactly is wrong with my argument above that it violates locality. If he agrees with 4) but not with 4-refined), then he should refine 4) in his own terms.

vanhees71 likes to say that correlations between the observables existed even before the measurement. But that's not the issue here. The issue are the

**values**of the observables, not their correlations.Finally, let me mention that Einstein et al in the original EPR argument assumed something similar to 4) and locality, and from those assumptions they derived a contradiction. From the contradiction they concluded that QM was incomplete.

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