# Page:TolmanEmission.djvu/7

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RICHARD C. TOLMAN.

To show in detail the divergence between the two theories consider the diagrammatic representation of a Michelson-Morley apparatus as shown in Fig. 3.

Light from the sun which is supposed to be moving relative to the apparatus in the direction AB with the velocity v is thrown with the help of suitable reflectors on to the half silvered mirror at A. The divided beams of light travel to the mirrors B and C and after reflection reunite at D to produce a system of interference fringes.

According to the Einstein theory of relativity the velocity of light is the same in all directions with respect to all observers, and hence the velocity along the paths AB and CD would be independent of the orientation of the apparatus and on the basis of this theory no change in the position of the interference fringes would be expected on rotation of the apparatus.

According to the Ritz theory, however, the velocity of light in the directions AB and AC would be different and a change in the position of the fringes would be expected on rotating the apparatus through an angle of ninety degrees. It is easy to see that the Ritz theory would lead us to expect c+v or the velocity of light in the direction AB, c - v for the velocity in the opposite direction, and ${\displaystyle {\sqrt {c^{2}-v^{2}}}}$ for the velocity in either direction along AC.

Assuming for simplicity that ${\displaystyle AB=AC=l}$ we see that the time required for light to travel along the path ABBAD will be longer than that along the path ACCD by the amount

${\displaystyle {\frac {l}{c+v}}+{\frac {l}{c-v}}-{\frac {2l}{\sqrt {c^{2}-v^{2}}}},}$

which neglecting terms of higher orders reduces to ${\displaystyle lv^{2}/c^{2}}$.

If the apparatus should be rotated through ninety degrees, it is evident that the longer time would now be required for the light to pass over the path ACCD and we should expect a shift in the position of the fringes corresponding to the time interval

${\displaystyle {\frac {2lv^{2}}{c^{3}}}}$