The Fine Structure Constant and Habitable Planets

TL;DR

This paper explores how the existence of habitable planets constrains the fine structure constant, linking fundamental physics with planetary and stellar conditions to understand the universe's habitability.

Contribution

It introduces two anthropic constraints on the fine structure constant based on stellar fusion outcomes and planetary heat, connecting fundamental physics with planetary science.

Findings

The fine structure constant is constrained to be near its observed value.

Stellar fusion end-products influence the allowed range of the constant.

Planetary heat production requirements further narrow the constant's value.

Abstract

We use the existence of habitable planets to impose anthropic requirements on the fine structure constant, $\alpha$. To this effect, we present two considerations that restrict its value to be very near the one observed. The first, that the end product of stellar fusion is iron and not one of its neighboring elements, restricts $\alpha^{-1}$ to be $145\pm 50$. The second, that radiogenic heat in the Earth's interior remains adequately productive for billions of years, restricts it to be $145\pm9$. A connection with the grand unified theory window is discussed, effectively providing a route to probe ultra-high energy physics with upcoming advances in planetary science.