Nonzero photonic mass

From the hypothesis of a nonzero electrical conductivity in the vacuum and the corresponding dispersion relation [20,48, 50-52], the concepts of tired light and the observed cosmical redshift could be interpreted and associated with a nonzero photon mass of about 10 68 kg. The related frequency dependence can also become a measure of the mass. 

A weaker alternative would be to admit Eq = 0 in a preferred frame of reference E, but to allow for a local nonzero rest mass mo 10-34 g as an artifact of the total motion of the earth relative to E [10]. However, this value is too high compared to the limits set to the photon mass, typically in the range mo 10-52-10 43 g [11]. At any rate, there are two implications of a nonzero photonic mass ... 

Again, Fuli [41] established a relation between nonzero photon mass and the Hubble constant H. Using that relation, one obtains... 

In 1992, Vigier [46] surveyed the experimental status of nonzero photon mass. In 1940, de Broglie [46] arrived at an upper limit for the photon mass by estimating the experimental mesaurements of the dispersion of photons and comparing this dispersion with that predicted for a photon with finite mass. Photons with finite rest mass do not all travel at the same velocity, but one, dependent on the ratio of kinetic to rest mass energy. 

Starting from the equation with nonzero photon mass my, one gets dispersion relation k2 = co2c2 — p2. The group and phase velocities can be found to be... 

In 1988, Riis et al. [52] observed a direction-dependent anisotropy of light in the direction of the apex of the 2.7 K microwave background radiation in the universe. These data are consistent with nonzero photon mass. The upper bound on photon mass was estimated as mT 10-65g. A compilation of laboratory data [53] established that the photon mass should not exceed 10-24 eV or even 10 26 eV. 

But now, if there is a ample evidence of nonzero photon mass, the question of absorption or emission amplitudes for longitudinal photon has to be answered in a consistent manner. Goldhaber and Nieto [49] showed that these are suppressed in comparison with their transverse counterparts by a factor The corresponding rates and cross sections are suppressed by the square of this factor. The quantum mechanical matrix element for ordinary transverse photon is given by Tf(x,y) = (f JX)y i) for a photon-induced transition to an arbitrary state/, where i is the initial target state. The corresponding matrix for a longitudinal photon is... 

Here, we shall mainly discuss those solutions that are related to nonzero photon mass only. In this framework, we got three kinds of solutions ... 

Munera and Guzman [56] obtained new explicit noncyclic solutions for the three-dimensional time-dependent wave equation in spherical coordinates. Their solutions constitute a new solution for the classical Maxwell equations. It is shown that the class of Lorenz-invariant inductive phenomena may have longitudinal fields as solution. But here, these solutions correspond to massless particles. Hence, in this framework a photon with zero rest mass may be compatible with a longitudinal field in contrast to that Lehnert, Evans, and Roscoe frameworks. But the extra degrees of freedom associated with this kind of longitudinal solution without nonzero photon mass is not clear, at least at the present state of development of the theory. More efforts are needed to clarify this situation. 

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