"Nobody understands quantum mechanics." Why?

TL;DR

This paper explores the hidden parameters problem in quantum mechanics using a group-theoretic approach, demonstrating that traditional methods violate conservation laws and that a complete set of observables clarifies the probabilistic interpretation.

Contribution

It introduces a group-theoretic framework that includes all necessary observables, resolving conservation law violations and questioning the necessity of a complete set of observables in quantum mechanics.

Findings

Traditional schemes violate conservation laws at potential steps.

Group-theoretic approach preserves all conservation laws.

Complete set of observables makes the probabilistic interpretation excessive.

Abstract

The well known and oft-quoted Feynman's expression, entered the title, leading at a loss and even being objectionable, has not yet a clear explanation. The hidden parameters problem in quantum mechanics is considered here on the base of group-theoretic approach which includes the complete set of observables indispensably. The last ones are the bilinear Hermitian forms constructed from the Schroedinger equation solutions and its first derivatives, they satisfy the algebraic completeness condition. These Hermitian forms, obtained for the simplest standard problem of particle transmission above potential step, had been compared with the Hermitian forms which are usually considered in this problem, and an additional ones, which may be obtained within the framework of an ordinary schemes of quantum mechanics. It is shown that the generally recognised schemes of the problem solution lead to violation of some conservation laws on the step directly. On the contrary, the group-theoretic approach leads to fulfillments of all necessary conservation laws everywhere at the same time. It is also shown that the complete set of observables leads a probabilistic interpretation in quantum mechanics to be excessive.