Reply To: The Locality of the Modified Quantum Mechanics

AvatarJiri Soucek

Dear Robert

thank You for Your mail

your comments were very inspiring for me

to the locality: I agree with You that QM must be local – in the sense that locality must be among axioms. Then possible derivation of Bell inequalities (BI) gives the inconsistency of QM. Thus for me the problém is how to make local QM consistent. I have red your paper, but I was not able to understand the argumentation – Your interpretation seems to me to be too complicated. For me the most difficult problem in local QM is the local explanation of EPR correlations – how the result of Alice` measurement can be transported immediately to Bob – one possibility is the pre-determination of individual results, but this means the hidden parameters and then BI. In standard QM this is the nonlocality of the Collapse rule. I have proposed the possible solution (in – perhaps You have found the another way how to obtain the local explanation of EPR. In each case I think that to obtain the local QM one must modify standard QM.

to the non-realism: the point is in the concept of the individual state. Following von Neumann, each pure state is individual state (“ensemble in the pure state is homogeneous”). I called this the von Neumann axiom and I think that it is the hidden assumption in standard QM and that it is the main error in QM which must be rejected and substituted by the anti von Neumann axiom: two different individual states must be orthogonal. This then gives the starting point of the modified QM. The main point is the following: the individual state of the measuring system does not imply the individual state of the measured system. There is a fine interplay between collective properties (of ensembles) and individual properties (of individual systems). I have shown that both standard QM and modified QM have the same experimental consequences (quantum predictions are only probabilistic and related to ensembles) – thus the choice between realism and non-realism cannot be experimantally resolved. In modified QM there is nothing classical, only the set of individual states is the small subset of the set of pure states.

to the observation: this concept can be introduced in the non-realistic QM, but not in standard realistic QM. This made possible to solve the measurement problém. I have introduced also the intermediate vetrsion of “minimally non realistic QM” (“”), where only anti von Neumann axiom is introduced without the introduction of the concept of the observation. The concept of the observation serves exactly for the task to cut the von Neumann chain.

In general I believe that QM is the probabilistic theory and in each probabilistic theory the state means the probabilistic distribution (the density operator in QM) and the probabilistic distribution is associated with ensemble but not with the individual system. I agree also with You that the evolution of the individual state is stochastic, but the evolution of the probability distribution is smooth.

Your Jiri Soucek

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