The Size of Compact Extra Dimensions from Blackbody Radiation Laws

TL;DR

This paper extends blackbody radiation laws to higher-dimensional spaces with compact extra dimensions, deriving new formulas that relate the size of these dimensions to observable radiation properties, and compares predictions with experimental data.

Contribution

It generalizes Stefan-Boltzmann and Wien's laws for D-dimensional manifolds including compact dimensions, providing a way to estimate the size of extra dimensions from radiation data.

Findings

Predicted total radiated power includes additional terms for extra dimensions.

Results agree with experimental data for compact dimensions up to 2 x 10^{-7} meters.

Applicable to string and M-theory dimensional frameworks.

Abstract

In this work we generalize the Stefan-Boltzmann and Wien's displacement laws for a $D$-dimensional manifold composed by 4 non-compact dimensions and $D-4$ compact dimensions, $ R^{1,3}$ x $T^{D-4} $. The electromagnetic field is assumed to pervade all compact and non-compact dimensions. In particular, the total radiated power becomes $ R(T) = \sigma_B T^4 + \sigma_D (a) \, T^D $, where $a$ is the size of the compact extra dimensions. For $D=10$, predicted from String Theory, and $D=11$, from M-Theory, the outcomes agree with available experimental data for $a$ as high as 2 x $10^{-7}$m.