The Size of Compact Extra Dimensions from Blackbody Radiation Laws

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.