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Abstract:

Revisit Jordan’s derivation of Einstein’s formula for energy fluctuations in the black body in ther- mal equilibrium. This formula is usually taken to represent the unification of the wave and the particle aspects of the electromagnetic field since the fluctu- ations can be shown to be the sum of wave-like and particle-like contributions. However, in Jordan’s treat- ment there is no mention of the Planck distribution and all averages are performed with respect to pure number states of radiation (mixed states had not yet been discovered!). The chief reason why Jordan does reproduce Einstein’s result despite not using thermal states of radiation is that he focuses on fluctuations in a small (compared to the whole) volume of the black body. The state of radiation in a small volume is highly entangled to the rest of the black body which leads to the correct fluctuations even though the overall state might, in fact, be assumed to be pure (i.e. at zero temperature). I present a simple derivation of the fluc- tuations formula as an instance of mixed states being reductions of higher level pure states, a representation that is affectionately known as ªChurch of the Higher Hilbert Spaceº. According to this view of mixed states, temperature is nothing but the amount of entanglement between the system and its environment.