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# The Proper Time of Photons and the Nature of Light

## Intro

The equations of motion derived in Proper Time Adjusted Special Relativity show that the proper time of photons is always zero. Let us see what are the implications of this.

## Derivation

Starting from the equations of the Lorentz transformation, we get the equations of motion for the spacetime by setting x' = 0. This gives us the position of the Moving Body itself.

 x' = (x-upsilon T)/sqrt(1-upsilon^2/c^2) t' = (T-x upsilon/c^2)/sqrt(1-upsilon^2/c^2) 0= (x-upsilon T)/sqrt(1-upsilon^2/c^2) t' = (T-x upsilon/c^2)/sqrt(1-upsilon^2/c^2) x=upsilon T t' = (T-x upsilon/c^2)/sqrt(1-upsilon^2/c^2) x=upsilon T t' = (T-upsilon T upsilon/c^2)/sqrt(1-upsilon^2/c^2) x=upsilon T t' = (T-T upsilon^2/c^2)/sqrt(1-upsilon^2/c^2) x=upsilon T t' = (T (1- upsilon^2/c^2))/sqrt(1-upsilon^2/c^2) x=upsilon T t' = (Tsqrt(1-upsilon^2/c^2)sqrt(1-upsilon^2/c^2))/sqrt(1-upsilon^2/c^2) x=upsilon T t' = Tsqrt(1-upsilon^2/c^2)

So, for the specific cases of the Stationary Body, the Moving Body, and the Photon, the equations of motion are:

 x=0*T=0 t' = Tsqrt(1-0^2/c^2)=T x=upsilon T t' = Tsqrt(1-upsilon^2/c^2) x=c T t' = Tsqrt(1-c^2/c^2)=0 Stationary Body Moving Body Photon

## Implications

We see that the proper time of the photon is always 0, irrespective of the value of time T. So, if we have a photon emitted at the start of time, T = 0, it will remain at this time moment while the rest of the spacetime advances in time.

If we have a photon emitted at a later time moment T > 0, its proper time again will be 0, since the expression sqrt(1-c^2//c^2) always equals 0.

It would be interesting to see the implications of this if we assume that it means exactly what it says: Photons are always situated at time moment t = 0, that is just a moment before the space dimension started expanding, just a moment before the start of time (the time moment of the "Big Bang" itself should be considered the first moment that was actually greater than 0).

In Electrostatic Acceleration as the Result of Spacetime Curvature, we introduce the posibbility of the existence of a second time dimension. If this proves correct, it may mean that light remains at time moment t = 0 of the "first" time dimension, but moves along the "second" time dimension. Remember that light is emitted when a charged particle accelerates. Acceleration means also a change in the "rate" of the flow of time for the particle. So essentially light is emitted when we have a change in the rate of time flow of a charged particle. The change of velocity (acceleration) and the change of the rate of time flow may be phenomena that take place in the second time dimension.

We shall explore further this topic in the treatment of EM waves.