Microscopic Fields and Macroscopic Averages in Einstein's Unified Field Theory

TL;DR

This paper explores how microscopic fluctuations in Einstein's unified field theory influence macroscopic electromagnetic and gravitational phenomena, highlighting the importance of microscopic structures and resonance effects.

Contribution

It introduces a method to define spacetime averages in Einstein's theory and demonstrates how microscopic metric fluctuations can affect macroscopic physics through resonance processes.

Findings

Microscopic metric fluctuations can influence macroscopic electromagnetic relations.

Resonance phenomena involving three waves can generate force densities in the continuum.

Wavy microscopic structures are crucial for resonance effects in the theory.

Abstract

The relation between microscopic and macroscopic entities in the generally covariant theories is considered, and it is argued that a sensible definition of the macroscopic averages requires a restriction of the allowed transformations of coordinates. Spacetime averages of the geometric objects of Einstein's unified field theory are then defined, and the reconstruction of some features of macroscopic reality from hypothetic microscopic structures is attempted. It is shown how a fluctuating microscopic behaviour of the metric field can rule the constitutive relation for electromagnetism both in vacuo and in nondispersive material media. Moreover, if both the metric and the skew tensor density that represents the electric displacement and the magnetic field are assumed to possess a wavy microscopic structure, nonvanishing generalized force densities can appear in the continuum. They originate from a resonance process, in which at least three waves need to be involved. This process only occurs if the wavevectors fulfil the three-wave resonance condition, so ubiquitous in quantum physics. The wavy behaviour of the metric is essential for the occurrence of this resonance phenomenon.