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 × 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 ) = σ B T 4 + σ 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 ⋅ 1 0 − 7 m.