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A note on the possibility of incomplete theory.

Han J.F. Geurdes

Published Dec 3, 2017• 0 citations
Publisher

Abstract

In the paper it is demonstrated that a concrete inconsistency occurs in experimental conclusions concerning quantum foundation. This inconsistency is similar to concrete mathematical incompleteness. We would like to stress that in the derivations there are no physics assumptions. Nevertheless the basic physics requirements of a local model are fulfilled.

DOI
10.31219/osf.io/eyr4w_v1

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In the paper it is demonstrated that a concrete inconsistency occurs in experimental conclusions concerning quantum foundation. This inconsistency is similar to concrete mathematical incompleteness. We would like to stress that in the derivations there are no physics assumptions. Nevertheless the basic physics requirements of a local model are fulfilled.
Different level sources of possible inconsistencies of Quantum Physics are studied. The point of view is defended that inconsistencies may arise due to improper philosophical foundations of Quantum Physics but that there is a way out to each of the up to now suggested purely mathematical inconsistencies of each of the main mathematical formulations of Quantum mechanics. An example is worked out explicitly. The point of view is also supported that even if the above statement may be correct, i.e., that no purely mathematical inconsistencies exist in each of the main mathematical formulations, it is highly worthwhile to study alternatives as those offered by the Lie-Admissible Formulations of Quantum Mechanics.
Based on a thought experiment the Einstein-Podolsky-Rosen paper’s authors concluded that in quantum mechanics the mathematical objects called wave functions fail to describe the physical reality and consequently quantum theory is incomplete. They left open the question of whether or not a complete description of the physical reality exists, but expressed their belief that such a complete theory is possible. In this paper I show that indeed a theory that gives a complete description of the physical reality exists.
The crucial role of counterfactual reasoning in generating inconsistencies between local subquantum theories and quantum mechanics is stressed. It is argued that the physical justification of such reasoning requires the fulfilment of a criterion of actualizability of hypothetical situations. It is demonstrated that in a subquantum framework this criterion is equivalent to the assumption of actual reproducibility of individual subquantum states. Therefore, inconsistencies between local subquantum theories and quantum mechanics disappear if a nonreproducibility property of nature, in full agreement with the empirical fact that past, present and future are basically distinct, is invoked. The proposal also leaves the universal validity of the locality principle untouched, in agreement with all existing empirical evidence.