Energy production in varying {\alpha} theories

TL;DR

This paper investigates how variations in the fine-structure constant {} affect energy exchange processes in matter, using Bekenstein's model, and derives constraints on the theory's parameters from planetary thermal data.

Contribution

It provides a detailed analysis of energy flow modifications due to scalar fields in Bekenstein's {} variation model and sets new upper limits on {} variation based on planetary data.

Findings

Upper limits on {} variation comparable to atomic clock constraints

Fundamental length scale {} cannot exceed Planck length

Energy exchange between matter and scalar fields is significantly constrained

Abstract

Aims. On the basis the theoretical model proposed by Bekenstein for {\alpha}'s variation, we analyze the equations that describe the energy exchange between matter and both the electromagnetic and the scalar fields. Methods. We determine how the energy flow of the material is modified by the presence of a scalar field. We estimate the total magnetic energy of matter from the "sum rules techniques". We compare the results with data obtained from the thermal evolution of the Earth and other planets. Results. We obtain stringent upper limits to the variations in {\alpha} that are comparable with those obtained from atomic clock frequency variations. Conclusions. Our constraints imply that the fundamental length scale of Bekenstein's theory "lB" cannot be larger than Planck's length "lP".