18. The Speed of Light

Having described in the last section how stimulated emission is involved in transparent materials, we will use the theory here in an attempt to derive Fresnel drag. This turns out to be successful.

To have a complete representation of light speed, it will be necessary to determine the absolute velocity of light through a transparent medium with index of refraction n which is itself moving with absolute velocity v. (It is assumed that such a material can now exist in this space, a composite of particulate wave forms (charge fields), the exact geometries, as of yet, undetermined.) The delay in light propagation is not based on a change of real permeability or permittivity in the space between the atoms, but the time-lag between absorption and re-emission of the photons as they traverse the substance. Even though the speed of light is unaffected by the motion of the source, when the light is in the absorbed state, it is transported at the velocity of the material until it re-emits. Thus the absolute velocity of the medium does have a partial effect on the transit time of the photon. This time-lag can be determined by considering the distance traversed such that:

(1)

where t is the total time of flight and t is the total time that the photon is absorbed. The time-lag is then

(2)

The change in the velocity of light is shown by

(3)

Substituting for t yields

(4)

where c₀ is the speed of light in a vacuum. This shows a relation to absolute velocity, but when the phase is observed, the absolute velocity is not detected. Since the re-emission of the light is stimulated, the phase matches the phase of the light that was not absorbed. This can be accounted for by defining a phase shift that just cancels the phase shift expected from the mechanical transport of the photon (while absorbed) thus:

(5)

where f is the phase shift and l is the wave length. To understand what total phase shift would be observed, consider the following experiment.



Fig.6: A flowing liquid in a frame moving at absolute velocity v.

The apparatus of length L moves at absolute velocity v and the liquid (with index of refraction n) flows at a relative (to the apparatus) velocity u. The velocity of light through the liquid is

(6)

The change in phase is

(7)

The time taken for the light to traverse the liquid T₂ is given by:

(8)

The time taken for the light to go the same distance outside the apparatus T₁ is:

(9)

If v is much greater than c, then.

(10)

and

(11)

The total phase shift is then given by:

(12)

where the first term gives the expected phase shift for the difference in flight times alone and the second term gives the phase shift caused by the stimulated emission. Substituting for the times and eliminating second and higher order terms yields

(13)

In an experiment where the velocity of liquid was changed, only the second term would be significant thus,

(14)

Note that the absolute velocity is not revealed (at least to first order) and the phase shift measured is dependent on the relative velocity of the liquid and the square of the index of refraction¹.

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1. This is the same result as obtained by Fizeau⁸ and also Michelson and Morley⁹ from the Fresnel convection coefficient (see for example Ditchburn¹⁰ 440) using

(a)

where v is the velocity of the liquid. Here we have shown that it can be derived from first principles based on the unchanging velocity of light. Many (like Jackson² 506) thought that this was evidence against the ether, but, in fact, it actually supports the concept, not as a physically moveable medium, but as an absolute rest frame. This is true regardless of other aspects of this theory and the success of the calculation adds further support to the existence of an absolute rest frame. We have assumed all along that electromagnetic radiation propagates with regard to an absolute rest frame and is thus independent of the motion of the source. This is demonstrated by many experiments and observations, some examples being Sadeh¹¹ with gamma rays; Alväger et al¹² using very high source velocities; Moon and Spencer¹³ with analysis of light from binary stars; and Bretcher¹⁴ with astronomical X-ray sources. It has also been shown convincingly by the phase shift of light reflected off of moving mirrors by Michelson¹⁵ and Sagnac¹⁶ (described by Post¹⁷). The peculiar velocity of the solar system determined by Smoot, Gorenstein and Muller¹⁸ and possibly corroborated by the terrestrial one-way phase comparisons Silvertooth aand Whitney¹⁹ apparently indicate the actual absolute velocity in respect to the rest frame of the electric and magnetic fields herein discussed. This experiment still needs to be repeated and verified as the results are of some importance.

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