Retarded Interaction of Radiation Field and Symmetry Violation of Time Reversal in Light’s Stimulated Radiation and Absorption Processes

The stimulated radiation and absorption processes of light are thought unchanged under time reversal at present. This conclusion is based on dipole approximations without considering the retarded effect of radiation fields. It is proved that after the retarded effect of radiation field is taken into account, the time reversal symmetry of stimulated radiation and absorption processes would be violated, though the interaction Hamiltonian is still unchanged. Speaking strictly, the symmetry violation of time reversal is caused by the connection of two factors, i.e., the retarded effect of radiation field and the difference of initial states before and after time reversals. Some nonlinear optical phenomena obviously violating time reversal symmetry are enumerated and analyzed in the paper. In this way, a more reliable foundation can be established for laser physics and nonlinear optics. PACS numbers: 42.55.A, 42.65, 05.45.T, 11.30.Q Einstein put forward light’s stimulated radiation and absorption theory to explain Planck blackbody radiation formula in 1917 based on equilibrium theory. According to the Einstein’s theory, the parameters of stimulated radiation and absorption are equal to each other with Bik = Bki. The same result can also be obtained by means of the calculation of quantum mechanics for the first order process under dipole approximation without considering the retarded interaction of radiation fields . Because light’s stimulated radiation process can be regarded as the time reversal of stimulated absorption process, the result means that light’s stimulated radiation and absorption processes are with time reversal symmetry. Nonlinear optics was advanced in the 1960s. Also by dipole approximation without considering retarded interaction, nonlinear susceptibilities are proved invariable under time reversal . Because the Hamiltonian of electromagnetic interaction is unchanged under time reversal, it is a common and wide accepted idea at present that the processes of light’s radiation and observation as well as nonlinear optics are with time reversal symmetry. However, it should be pointed out that most processes relative to laser and nonlinear optics are none-equilibrium ones, in which time reversal symmetry is violated generally. It will be proved below that after the retarded effect of radiation field is taken into account, time reversal symmetry would be violated generally in light’s stimulated radiation and absorption processes with Bik 6= Bki. This kind of asymmetry has nothing to do with the invariability of the electromagnetic interaction Hamiltonian, but relative to the difference of initial states before and after time reversal. Or speaking strictly, the symmetry violation of time reversal is caused by the connection of two factors, i.e., the retarded effect of radiation field and the difference of initial states before and after time reversals. In this way, nonequilibrium and nonlinear phenomena in optics can be explained more rationally and a more reliable foundation can be provided for laser physics and nonlinear optics. For simplification, we consider an atom only with an electron in its external layer. Electron’s mass is μ, charge is q. When there is no external interaction, the Hamiltonian and wave function of electron