# What information can there be in black body radiation?

It seems to be part of the theory of Hawking radiation that the spectrum is black body and that it therefore cannot carry any information...thus creating a conflict with the conservation of information in QM. But Shannon's information is maximized by a random sequence. And any highly compressed signal looks random. So it seems that a given spectrum doesn't constrain information transmitted, whether the spectrum or is black body or something else. The power spectrum only determines the two-time correlation function. So why is it asserted that radiation with a black body spectrum cannot transmit information?

• Doesn’t black-body radiation contain one piece of information, the temperature? A Planck distribution is completely specified by that one parameter. Aug 24 '20 at 18:56
• Indeed, my digital thermometer serves to obtain this information from black body radiation. Aug 24 '20 at 21:30
• @G.Smith Don't forget $\hat k$. Blackbody radiation also contains a direction.
– JEB
Aug 25 '20 at 0:58

Yes, but two different signals, when (losslessly) compressed, result in two different outputs. The semiclassical theory of Hawking radiation says that two input states which form a black hole of the same mass will evolve into the same output state, which is $$\rho_\beta = e^{-\beta H}/\text{ Tr } e^{-\beta H}$$ where $$\beta = 1/$$temperature.