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, R1,3×TD−4. The electromagnetic field is assumed to pervade all compact and non-compact dimensions. In particular, the total radiated power becomes R(T)=σBT4+σD(a)TD, 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⋅10−7m.