Einstein on measurement theory: A heuristic point of view

Abstract

Einstein did not contribute significantly to the quantum mechanics we are familiar with, but he did contribute to its theoretical foundations. In a seminal theory on black body radiation, he used two physically distinct sets of coordinates, a classical set to describe the continuity of heat energy with Maxwell Boltzmann statistics and an atomic set to describe discrete energy states required by the Planck radiation law. His methods are extended here to reveal that matrix mechanics is an incomplete description of atomic structure. In addition to the discrete energy states of the diagonal matrix elements, classically derived components of kinetic energy are necessary. We conclude that the diagonalized matrix elements and eigenvalues of the Schrödinger equation both describe characteristics of the steady states, but the physical variables they describe are different, because they are measured with respect to different coordinate systems. Einstein’s assumptions lead to a resolution of the measurement problem by introducing statistical laws at the microscopic level.

The Conservation Laws in Quantum Mechanics

“…To compare Einstein's statistically defined measurements of energy fluctuation with the methods of matrix mechanics we refer to the energy matrix [5]. The diagonal elements of the matrix m= n refer to all possible energy states of a quantum system.…”

“…In the path integral approach to quantum mechanics we can see violations of the conservation laws even more clearly. In the following passage Feynman considers absorption and emission by using the field approach of quantum field theory, but then rejects it in favor of a particle model of only emission [5]. "In empty space an atom emits light and yet there is no potential to perturb the systems and so for it to make a transition.…”

The Conservation Laws in Quantum Mechanics

“…Although p in the above equation refers to momentum it is not the momentum of a molecule in K used by Einstein, rather it is the momentum due to photon emission in K'. To compare 1) more closely with Einstein's statistically defined measurements of energy fluctuation we refer to the energy matrix [5]. The diagonal elements of the matrix m=n refer to all possible energy states of a quantum system.…”

The Conservation Laws in Quantum Mechanics

“…Although p in the above equation refers to momentum it is not the momentum of a molecule in K used by Einstein, rather it is the momentum due to photon emission in K'. To compare 1) more closely with Einstein's statistically defined measurements of energy fluctuation we refer to the energy matrix [5]. The diagonal elements of the matrix m refer to all possible energy states of a quantum system.…”