Quantum theory as a description of robust experiments: application to Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments

Abstract

We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are separated as much as possible. Application to the Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments are shown to support this thesis. General principles of logical inference which have been shown to lead to the Schrödinger and Pauli equation and the probabilistic descriptions of the Stern-Gerlach and Einstein-Podolsky-Rosen-Bohm experiments, are used to demonstrate that the condition for the separation procedure to yield the quantum theoretical description is intimately related to the assumptions that the observed events are independent and that the data generated by these experiments is robust with respect to small changes of the conditions under which the experiment is carried out.

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

“…We have shown how the Klein-Gordon equation for massive, charged particles derives from logical inference applied to experiments for which the observed events are independent and for which the frequency distribution of these events is robust with respect to small changes of the conditions under which experiments are carried out. The present derivation is a logical generalization of earlier work [24][25][26][27] to the relativistic domain, the fundamental difference being that the measured time is subject to uncertainty.…”

“…(28) Obviously, the weighting factor λ = 4m 2 / 2 cannot be determined on the basis of logic only but has to follow from a comparison of the outcome of calculations based on Eq. (27) with experimental data. It is of interest to enquire to what extent Eq.…”

“…Instead of starting from a set of postulates, the current work presents an alternative derivation of the relativistic wave equation based on the principles of logical inference (LI) [20][21][22][23]. Specifically, we demonstrate how the Klein-Gordon equation for a massive, charged and spinless particle follows from LI based on the analysis of data recorded by a detector, thereby extending earlier work [24][25][26][27] to the relativistic domain.…”

“…But if the experimental data is to be reproducible, the experiment must be robust (to be quantified later) with respect to small changes in the conditions under which the experiment is being performed. Earlier work has shown that the equations of non-relativistic quantum theory can be obtained by analyzing such robust experiments [24][25][26][27]; most notable are the Schrödinger [25] and the Pauli equation [26]. Importantly, the requirement that the experiment is to be robust implies that the plausibility must be viewed as an objective assignment (i.e.…”

Separation of conditions as a prerequisite for quantum theory

“…(12) and (13) does not seem to bring anything new. However, as we now show, by arranging numbers in matrices instead of vectors, it becomes possible to perform the desired separation in terms of a description of the source and the SG magnet [55,59]. The key idea is to note that any pair of matrices F and K satisfying k p a = Tr FK p , p = 0, 1, 2,…”