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Spin: Newton, Maxwell, Einstein, Dirac, Bell

Edwin Eugene Klingman

Published Nov 1, 2014• 0 citations
OpenAlex

Abstract

In Quantum Spin and Local Reality (QSLR) I show that Bell suppressed key physical phenomena to arrive at his inequality. As a result Bell's conclusions are incorrect — his model fails to match reality. Bell's defense is based on quantum mechanical eigenvalue equations with reference to Dirac. I briefly review some issues in the history of spin, and analyze the non-relativistic Stern-Gerlach eigenvalue equation and the relativistic Dirac equation, and show their relevance to Bell.

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In Quantum Spin and Local Reality (QSLR) I show that Bell suppressed key physical phenomena to arrive at his inequality. As a result Bell's conclusions are incorrect — his model fails to match reality. Bell's defense is based on quantum mechanical eigenvalue equations with reference to Dirac. I briefly review some issues in the history of spin, and analyze the non-relativistic Stern-Gerlach eigenvalue equation and the relativistic Dirac equation, and show their relevance to Bell.
Almost a century ago Stern-Gerlach laid important foundations for quantum mechanics. Based on these, Bell formulated a model of local hidden variables, which is supposed to describe "all possible ways " in which classical systems can generate results, but Bell did not consider one possibility in which classical behavior leads to quantum results. Bell buried the key fact needed to challenge his logic: the θ-dependence of two energy modes: rotation and deflection. An Energy-Exchange theorem is presented and proved: if 0≠dtdθ the implied time-evolution will affect expectation values and the essentially classical mechanism yields quantum correlations ba ⋅ −. Analysis of the spin-component measurement brings Bell’s counterfactual logic into question. I show that Watson’s formal linking of time-evolution operator to measurement operation addresses Bell's stated concerns about measurement in quantum mechanics and produces the ba ⋅ − correlation. Our results, restricted to particle spin, have wider implications, including relevance to the ontic versus epistemic issues currently debated in the literature. The suggested formalism extends
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality – locality – completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality – locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier argument of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell's inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
This paper aims at reproducing quantum mechanical (QM) spin and spin entanglement results using a realist, stochastic, and local approach, without the standard QM mathematical formulation. The concrete model proposed includes the description of Stern–Gerlach apparatuses and of Bell test experiments. Single particle trajectories are explicitly evaluated as a function of a few stochastic variables that they assumedly carry on. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. Notably, it is shown that the proposed model, despite being both local and realist, is able to violate the Bell–CHSH inequalities by exploiting the coincidence loophole and thus intrinsically renouncing to one of the Bell’s assumptions.
Despite the success of the Dirac equation, the incorporation of the special theory of relativity into quantum mechanics predicts some paradoxes, like that the spin prediction from Dirac equation can be only identified with non- relativistic approximations (Pauli and Foldy-Wouthysen), as well as the spin predication is a relativistic quantum phenomena because the spin prediction is a necessary requirement of the relativistic quantum mechanics only. In this paper we show that the derivation of the spin and its magnetic moment can be done with a pure classical treatment. Since we start from the classical physical laws and the classical relativity principle to get the linear Schrödinger equation as a result the derivation of the spin and its magnetic moment can be done with a pure classical treatment. This approach result a Schrödinger equation, in which we show that the spin of the electron is a non relativistic quantum phenomenon too.