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The Proper Time of Photons and the Nature of Light

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Revision as of 20:28, 23 December 2006 by George Barouxis (Talk | contribs) (Implications)

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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).

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



See also