Simple violation of Bell inequalities
Posted: Thu Aug 03, 2017 2:23 am
Here is a simple derivation of (some) Bell inequality (top) - for any probability distribution among these 8 possibilities for 3 binary variables ABC, the inequality is fulfilled.
Bottom: example of its violation assuming just Born rule: probabilities being normalized squares of amplitudes:
Hence we just need to explain Born rule to understand violation of Bell inequalities - and its natural understanding brings MERW diffusion: https://en.wikipedia.org/wiki/Maximal_E ... andom_Walk
So MERW shows why standard diffusion has failed (e.g. wrongly predicting that semiconductor is a conductor) - because it has used only an approximation of the (Jaynes) principle of maximum entropy (required by statistical physics), and if using the real entropy maximum (MERW), there is no longer discrepancy - e.g. its stationary probability distribution is exactly as in the quantum ground state.
In fact MERW turns out just assuming uniform or Boltzmann distribution among possible paths - exactly like in Feynman's Eulclidean path integrals (there are some differences), hence the agreement with quantum predictions is not a surprise (while still MERW being just a (repaired) diffusion).
Including the Born rule: probabilities being (normalized) squares of amplitudes - amplitude describes probability distribution at the end of half-paths toward past or future in Boltzmann ensemble among paths, to randomly get some value in a given moment we need to "draw it" from both time directions - hence probability is square of amplitude:
Here is my just rewritten paper about connection between QM and MERW, also e.g. the Shor's algorithm I would gladly discuss:
https://arxiv.org/pdf/0910.2724v2.pdf
Bottom: example of its violation assuming just Born rule: probabilities being normalized squares of amplitudes:
Hence we just need to explain Born rule to understand violation of Bell inequalities - and its natural understanding brings MERW diffusion: https://en.wikipedia.org/wiki/Maximal_E ... andom_Walk
So MERW shows why standard diffusion has failed (e.g. wrongly predicting that semiconductor is a conductor) - because it has used only an approximation of the (Jaynes) principle of maximum entropy (required by statistical physics), and if using the real entropy maximum (MERW), there is no longer discrepancy - e.g. its stationary probability distribution is exactly as in the quantum ground state.
In fact MERW turns out just assuming uniform or Boltzmann distribution among possible paths - exactly like in Feynman's Eulclidean path integrals (there are some differences), hence the agreement with quantum predictions is not a surprise (while still MERW being just a (repaired) diffusion).
Including the Born rule: probabilities being (normalized) squares of amplitudes - amplitude describes probability distribution at the end of half-paths toward past or future in Boltzmann ensemble among paths, to randomly get some value in a given moment we need to "draw it" from both time directions - hence probability is square of amplitude:
Here is my just rewritten paper about connection between QM and MERW, also e.g. the Shor's algorithm I would gladly discuss:
https://arxiv.org/pdf/0910.2724v2.pdf