Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories

TL;DR

This paper explores how classical and quantum field theories exhibit various forms of empirical equivalence and underdetermination, especially regarding mass parameters in electromagnetic, gravitational, and gauge theories, highlighting implications for theory choice.

Contribution

It analyzes the phenomenon of permanent underdetermination in field theories, emphasizing approximate empirical equivalence and its implications for understanding mass and gravity in modern physics.

Findings

Electromagnetic theories show permanent underdetermination between Maxwell and Proca's theories.

Quantization often breaks classical equivalence in Yang-Mills theories.

Underdetermination in gravity remains a subject of contemporary debate.

Abstract

Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang-Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy.