Minimum Interior Temperature for Solid Objects Implied by Collapse Models

TL;DR

This paper investigates the minimum temperature solid objects can reach due to heating effects from wave function collapse noise, providing bounds for metals and insulators based on collapse model parameters.

Contribution

It derives quantitative lower bounds on the temperature of solids caused by collapse-induced heating, connecting collapse models with measurable thermal effects.

Findings

Lower temperature bounds for metals and insulators due to collapse noise

Specific bounds for copper and Torlon 4203 materials

Exact heat transfer solution for spherical objects

Abstract

Heating induced by the noise postulated in wave function collapse models leads to a lower bound to the temperature of solid objects. For the noise parameter values $\lambda ={\rm coupling~strength}\sim 10^{-8} {\rm s}^{-1}$ and $r_C ={\rm correlation~length} \sim 10^{-5} {\rm cm}$, which were suggested \cite{adler1} to make latent image formation an indicator of wave function collapse and which are consistent with the recent experiment of Vinante et al. \cite{vin}, the effect may be observable. For metals, where the heat conductivity is proportional to the temperature at low temperatures, the lower bound (specifically for RRR=30 copper) is $\sim 5\times 10^{-11} (L/r_C) $K, with L the size of the object. For the thermal insulator Torlon 4203, the comparable lower bound is $\sim 3 \times 10^{-6} (L/r_c)^{0.63}$ K. We first give a rough estimate for a cubical metal solid, and then give an exact solution of the heat transfer problem for a sphere.