The quantity of c is a very specific velocity. The only things that can move at the speed of c are photons, hence it is called the "speed of light." What we should really be investigating is whether there is a unit equal to velocity squared, and if so, what is its meaning?
Just as velocity times mass is no longer velocity, but becomes the unit of momentum, velocity squared is no longer velocity, but becomes a different unit. The question is, what is this unit?
One clue is that the unit of v^2 is commonly referred to the Sievert, or unit of radiation. There are no dimensions of mass or charge involved in the Sievert, so it cannot specifically apply to electromagnetic radiation, but must apply to anything that radiates. Another clue is the perfect gas law which states that pressure divided by mass density is equal to temperature. From this law, we can determine that the unit of temperature should be expressed in units of velocity squared.
So it would appear that velocity squared is the unit of temperature. Energy is then equal to mass times temperature. And temperature itself is nothing more than the velocity of particles bouncing off surrounding particles in all directions. The greater the velocity of the particles, the greater the temperature of the total medium.
The quantity of c^2 is merely the fastest velocity a thing can move. Thus, the energy of a single photon (the only object capable of moving at the speed of light) represents absolute hottest temperature. The cosmic microwave backgroud radiation would then be due to the number of photons passing through space at any given time.  |