Hans-Juergen Treder and the discovery of confinement in Einstein's unified field theory

TL;DR

Treder's 1957 analysis of Einstein's unified field theory revealed that properly defined point charges exhibit Coulomb-like interactions and confinement, foreshadowing later understanding of quark confinement in particle physics.

Contribution

The paper revisits Treder's 1957 work, demonstrating how Einstein's unified field theory inherently accounts for charge confinement, a concept later confirmed in particle physics.

Findings

Properly defined charges interact via Coulomb-like forces

A distance-independent force component implies confinement

Exact solutions support charge confinement in the theory

Abstract

In the year 1957, when interest in Einstein's unified field theory was fading away for lack of understanding of its physical content, Treder performed a momentous critical analysis of the possible definitions of the electric four-current in the theory. As an outcome of this scrutiny he was able to prove by the E.I.H. method that properly defined point charges, appended at the right-hand side of the field equation $R_{[[\mu\nu],\lambda]}=0$, interact mutually with Coulomb-like forces, provided that a mutual force independent of distance is present too. This unwanted, but unavoidable addition, could not but lay further disbelief on the efforts initiated by Einstein and Schroedinger one decade earlier. However in 1980 Treder himself recalled that the potential $\phi=a/r+cr$, found by him in 1957, was the one used by particle physicists to account phenomenologically for the spectrum of bound quark systems like mesons. Exact solutions have later confirmed beyond any doubt that Einstein's unified field theory does account in a simple way, already in classical form, for the confinement of pole charges defined by the four-current first availed of by Treder. In the present paper it is proposed, ad memoriam, a thorough recollection of the article published by Treder in 1957, showing the way kept by him to find what would have been later recognized as confinement in Einstein's unified field theory.