Undergrad Bell violations + perfect correlations via conservative Brownian motion

[iste]

A Perimeter talk https://pirsa.org/11100113
"Does Time Emerge from Timeless Laws, or do Laws of Nature Emerge in Time?"

Thanks for the link! I'll definitely have to take a look and digest.

 

[iste]

I just wanted to update my thoughts on the question by Fredrik about how the "Barandes transition matrices (or lack of) emerge".

It seems to me that if the Barandes non-Markovianity condition is related to correct multi-time correlations due to its interferences, then the amelioration of incorrect Nelsonian/Bohmian multi-time correlations by measurement imply that the non-commutativity of position and momentum are in some way the source of the non-Markovianity, since clearly measurement related disturbance would be what is ameliorating the faulty correlations when explicitly accounting for measurement.

I then saw that the effect of the non-commuting Non-Selective Measurements on temporal behavior are described in the following paper:

https://arxiv.org/abs/quant-ph/0306029

"So the NSM of the position ˆx at time t = 0 not only has changed immediately the probability distribution of the momenta p, as we have analyzed in b1), but it has changed also the probability distribution of x at any time t > 0. Now the reader may wonder why the probability distributions ρP (x|t) and ρM (x|t) were the same at t = 0, see (3.16)-(3.17), but they are different at any time t > 0. The explanation is that during the evolution, which is given by ˙x = p and couples x with p, the distributions in x are influenced by the initial distributions in p which, as shown in (3.18) and (3.19), are different in the two cases in which we perform, case b), or not perform, case a), the NSM of ˆx at t = 0. So the NSM of ˆx influences immediately the distribution of probability of the conjugate variable p. Next, since the momenta p are coupled to x via their equations of motion, the changes in the distribution of p are inherited by the distribution of the positions at any instant of time t > 0."

So the authors observe how the non-commutativity means the measurement is disturbing the behavior at other instances of time. It seems that this kind of disturbance would be what is ameliorating the faulty Nelsonian/Bohmian multi-time correlations. Maybe then the Barandes non-Markovianity and its interferences are linked to the non-commutativity which also exists in the Barandes theory like in QM - measurements at one time disturb the trajectory / transition statistics for other times, violating (total) joint probability consistency conditions for its trajectory's transition matrices.