Matter, Radiation and Zero Chemical Potential

When we consider interconversion of particles and radiation, as in the case of particle-antiparticle pair creation and annihilation, the chemical potential of thermal photons becomes more significant (Fig. 11.4). Consider thermal photons in equilibrium with electron-positron pairs  

For reasons of symmetry we may assert that (ie+ = Pg-. Since = 0 we must conclude that for particle-antiparticle pairs that can be created by thermal photons Pe = Pe- = 0. 

It is interesting to consider the state of matter for which i = 0. For simplicity, let us consider p. = 0 in an ideal gas mixture for which 

The physical meaning of these equations can be understood as follows. Just as photons of energy hv are excitations of the electromagnetic field, in modem field theory particles of energy E — y/rri c are also excitations of a quantum 

At ordinary temperatures, this thermal particle density is extremely small. But quantum field theory has now revealed the thermod5mamic importance of the state p = 0. It is a state of thermal equilibrium that matter could reach indeed matter was in such a state during the early part of the universe. Had matter stayed in thermal equilibrium with radiation, at the current temperature of the universe the density of protons and electrons, given by (11.6.5) or its modifications, would be virtually zero. The existence of particles at their present temperatures has to be viewed as a nonequilibrium state. As a result of the particular way in which the universe has evolved, matter was not able to convert to radiation and stay in thermal equilibrium with it. 

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