Jarek wrote:So let's take the simplest of such inequalities - drawing three coins, at least two give the same value:
P(A=B) + P(B=C) + P(A=C) >=1
Jarek wrote:Not to satisfy it in QM or MERW, it becomes essential that we measure only 2 out of 3 - the not measured coin has literally no value, otherwise the inequality has to be satisfied.
So one question is how to realize it that we measure exactly 2 out of 3 - such that the third one doesn't just have unknown value or is not flipped, but literally has no value? ... like coin hanging and rotating in the air ..
This is the mystery of quantum mechanics.
Jarek wrote:Could you maybe comment this simple realization (page 9 of https://arxiv.org/pdf/0910.2724 ) - of violation of
Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1
inequality from uniform distribution among paths (MERW)?
So the considered space is the graph on the left with all 8 values of ABC: in 000 and 111 we have to stay, in the remaining vertices we can jump to a neighbor.
The presented measurement in time=0 ignores C - we have 4 possible outcomes (red squares) determining exactly AB.
Assuming uniform probability distribution among paths (from -infinity to +infinity in time), we get Pr(A=B) = (1^2 + 1^2) / (1^2 + 2^2 + 2^2 + 1^2) = 2/10.
Analogously for the remaining pairs, we finally get
Pr(A=B) + Pr(A=C) + Pr(B=C) = 6/10
It is able not to satisfy the inequality thanks to:
- maintaining not measured third value,
- by using ensemble of complete paths, what leads to Born rule: probability of alternative of disjoint events is proportional to sum of squares of their amplitudes.
Considering path ensemble toward only one direction (past or future), we would have first power instead of square.
What other models violating such inequality are considered?
Jarek wrote:Sure I can discuss on the Google group if getting invitation (dudajar@gmail.com), but it will be similar like here.
gill1109 wrote:Jarek wrote:Sure I can discuss on the Google group if getting invitation (dudajar@gmail.com), but it will be similar like here.
New thread has been started there.
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy
Jarek wrote:Manfried Faber has just written paper with analogous Bell violation construction, but using only paths up to a given moment:
https://arxiv.org/pdf/1907.00175
Jarek wrote:Richard, while I can analogously violate original Bell or CHSH, the main reason we use "P(A=B) + P(B=C) + P(A=C) >=1" inequality: "tossing 3 coins, at least 2 are equal" is that it is absolutely obvious - it leaves no place for hiding in some sophisticated mathematics, even Fourier analysis.
This is just trivial combinatorics, which QM formalism allows to violate.
While you can try to argue other inequalities, this one does not leave a place for that - you can practically only use combinatorics to explain how physics can violate it ... and the simplest option: uniform path ensemble, allows for such explanation.
It is nonlocal in standard sense, but is "4D local": in space-time.
Please comment - do you agree with such Born rule/Bell violation, or explain why not? ... and suggest an alternative explanation how physics can violate such obvious inequality?
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