Photon Gas Is the Medium of Electromagnetic Waves

The aim of this paper is to find the carrier or medium of electromagnetic waves that has been searched for many years. The thermal radiation is composed of the shot noise and the wave noise, so the Planck formula can be separated mathematically into two parts. Assume every photon has the same proper magnetic moment and an equal rest mass which has been estimated from the cosmic background temperature in space where the photon gas is at an open state of thermal equilibrium. The magnetic-electric dynamic equation is established that means magnetic curl caused electric change, and the electric-magnetic dynamic equation is established that means electric curl caused magnetic change. After the wave equation is caught, it is clear that the photon gas is the medium of electromagnetic waves in vacuum.


Introduction
Many people have been searching for the carrier or medium of the Maxwell's electromagnetic waves since the last century, and some scientists thought that the photon gas may be the medium, but the dynamic equations hasn't been caught. After the experiment of Michelson and Morley, the searching job was abandoned in the face of the almost universal adherence of physicists to the purely interpretation that the electromagnetic wave is carried by the energy of itself. To prove that the photon gas is the carrier or medium of electromagnetic waves, the magnetic-electric and the electric-magnetic dynamic equations must be established. The origin ideas is based on Planck formula, Einstein Special Relativity, and E. M. Purcell's Electricity and Magnetism, all that is come from textbooks. When dealing with the theoretical derivation, it is necessary that

The Estimation about the Rest Mass of the Photon
In the last century, the cosmic microwave background radiation [1] [2] was discovered and the cosmic background temperature (T CB = 2.725 K) is calculated by the data of COBE satellite [3]. Supposing every photon has the same rest mass m s and the rest frequency ν s , when it is moving with the group velocity c g , the parameters of the photon can be described as In the thermal radiation of a black body, the intensity is composed of two parts: one is the shot noise and the other is the wave noise [4], and the Planck formula can be separated mathematically into two parts:

( ) ( )
If the average velocity of the photons is zero and the photon gas is an isotropic medium in visual system, then the photon gas is moving as an anisotropic medium in the proper system. Since the relativistic transformation of the magnetic moment is complicated as a tensor of second order, so that the magnetic field B should be defined based on the line current, then the interacting magnetic field is a tensor of second order in proper system (Figures S4-S6, Equations (S6)-(S19)) and the magnetic inductivity is a tensor of second order in proper system too, but both the characteristic magnetic field and the characteristic magnetic inductivity are relatively simple in proper system. A photon is traveling in the y 0 direction with the group velocity c g in the visual system ( Figure S7) and the suitable coordinates are selected. To simplify the mathematical analysis, considering one dimension electromagnetic wave E y −B z in the visual system and the curl of the electromagnetic field can be calculated (Equations (S22)-(S25)). The photon's proper magnetic moment can be equivalent to a circle current according to the principle of correspondence, The proper force acted on the photon by the curl of magnetic field has been sin .
The characteristic electric moment of a moving photon is ( Figure S11, Equa- The partial derivatives of the characteristic electric moment of a moving photon with respect to photon's velocity are ( Figure S12, Figure S13, Equations ,ˆ. The partial derivative of the characteristic electric moment with respect to time can be calculated and averaged by the random properties of the photons in the state of thermal equilibrium (Equation (9), Equation (11), Equations (S52)-(S55)), then ( ) The electric field is the integration of the characteristic electric moment of the photons, and then the partial derivative of the electric field is To calculate the integration (Equation (4)) and defined function: Then the magnetic-electric dynamic equation of the photon gas is The change of the electric field is counteractive compared with that in the Maxwell's equation, because the curl of magnetic field is active at the magne-

The Electric-Magnetic Dynamics of Photon Gas
A moving photon has two transverse components of characteristic electric moment and the longitudinal component is zero, since the transverse interaction is enlarged by one factor of relativity, so that the interacting electric moment is a tensor of second order. The first part of the proper force acted on the photon is the cross production of the interacting electric moment and the curl of electric field, and then the first part of the visual force is obtained (Equations (S56)-(S60)).
To transform the visual electric field into the characteristic magnetic field in The characteristic magnetic moment of a moving photon in the visual system is ( Figure S11, Equations (S41)-(S43)) The derivatives of the characteristic magnetic moment of a moving photon with respect to the photon's velocity are ( Figure S14, The partial derivative of the characteristic magnetic moment with respect to The magnetic field is the integration of the characteristic magnetic moment of photons, and then the partial derivative of the magnetic field is To calculate the integration (Equation (4)) and defined function: Then the electric-magnetic dynamic equation of photon gas is The change of the magnetic field is counteractive compared with that in the Maxwell's equation, because the curl of electric field is active at the electro-dynamics of photon gas and is passive in the Maxwell's equation that is the mechanism of Lenz law too. At high temperature and compared with the Maxwell's equation, the magnetic moment of rest photon has the same value as Eq.
16, and the simplified electric-magnetic dynamic equation of the photon gas at general temperature is 1 0 The wave equation can be obtained by the association of Equation (17) and Equation (25), If the speed of electromagnetic wave is just equal to the ultimate velocity c, in a good approximation, the temperature factor of the number density of photon gas is Then the three dimensional wave equation in photon gas is Since the electromagnetic field is discrete at the photon scale in photon gas, so that the two dynamic equations and the wave equation are only valued when the wavelength is far larger than the average interspaces of photons, and then the photon gas can be treated as a continuous medium.

Conclusions and Discussions
After the magnetic-electric and the electric-magnetic dynamic Equation (17) (27) is only a good approximation, so that the speed of electromagnetic wave in photon gas should be a function of temperature too, and there should be a deviation, very small but not zero, between the ultimate speed c and the wave speed at the cosmic background temperature. The photon's velocity will approach the ultimate speed when its visual frequency is very higher and the wave speed might approach the ultimate speed when the temperature of the photon gas is going higher too.
The propagation of electromagnetic wave is influenced by the moving of the photon gas, but the photon's traveling is rather independent to the moving of the photon gas in a short distance when its visual frequency is far higher than the rest one, so the null result had been got in the experiment of Michelson and Morley. When an electron and a photon are very nearby, their magnetic moments will entangle each other and that might be the process of Compton Effect, although the out behavior is like a collision.

Supporting Materials
Method S1: Defined the Force Based on the Acceleration Figure S1. Transformations of acceleration.
Between the visual system S where the observer is rest and the proper system S' where the object is rest, the transformations of acceleration and inertial mass The general transformation of the magnetic (potential) field is  The characteristic magnetic field in the proper system is The characteristic magnetic inductivity in the proper system is To simplify the mathematical analysis, considering one dimension electromagnetic wave E y − B z , in the visual system the curl of magnetic field is, In the visual system the curl of electric field is ( ) 0 0 0ˆĉ url sin cos sin sin cos y y y y y y Using Equation (S18), the transformations of the curls of magnetic field are

Method S4: The Curl of Magnetic Field Interacts with the Magnetic Moment
If every photon has a same proper magnetic moment, then in the visual system the moving photon has three components of characteristic magnetic moment and two transverse components of characteristic electric moment. Figure S8. The curl of magnetic field interacts with the magnetic moment (1).
The transverse curl of magnetic field interacts with the longitudinal magnetic moment. In the proper system the transverse curl is equivalent to an increment of magnetic field which interacted on one edgy of the longitudinal magnetic moment (Equatiom (S16), Equatiom (S24)), The proper force acted on the proper magnetic moment is The transverse curl of magnetic field interacts with the transverse magnetic moment. In the proper system the transverse curl is equivalent to an increment of magnetic field which interacted on one edgy of the transverse magnetic moment (Equation (S16), Equation (S24)), The proper force acted on the proper magnetic moment is Then the acceleration of the photon acted by the curl of magnetic field is