# Page:TolmanEmission.djvu/6

141
THEORIES OF LIGHT.

more nearly parallel than the motion of ${\displaystyle I_{2}}$ and the ray CD. Hence from the principle of Stewart the component ${\displaystyle v_{3}}$ is greater than ${\displaystyle v_{4}}$. Referring once more to equation (4), since ${\displaystyle L_{3}}$ and ${\displaystyle L_{4}}$ are equal and ${\displaystyle v_{3}}$ is greater than ${\displaystyle v_{4}}$ we see that the negative term ${\displaystyle L_{4}/\left(c+v_{4}\right)}$ is numerically greater than ${\displaystyle L_{3}/\left(c+v_{3}\right)}$ and we may write the inequality

${\displaystyle \Delta t'<{\frac {L_{1}+L_{2}+v\Delta t}{c+v}}.}$

Neglecting second order terms this becomes

${\displaystyle \Delta t'\left(1-{\frac {v}{c}}\right)<{\frac {L_{1}-L_{2}}{c}}-{\frac {L_{1}-L_{2}}{c}}{\frac {v}{c}}}$

and substituting from equation (3),

${\displaystyle \Delta t'\left(1-{\frac {v}{c}}\right)<\Delta t\left(1-{\frac {v}{c}}\right),}$
${\displaystyle \Delta t'<\Delta t,}$
${\displaystyle \tau '<\tau .}$

Thus on the basis of the Stewart theory, with an approaching source, a shorter period would produce a bright line at the point D than with a stationary source. In other words the actual bright lines would shift towards the red end of the spectrum when the source is set in motion towards the slit, in contradiction to the actually observed shift towards the violet end of the spectrum.

We see that experimental facts do not agree with the Stewart theory.

## The Ritz Theory.

According to the Ritz theory of relativity, throughout its whole path, light retains the component of velocity v which it obtained from the original moving source. Thus all the phenomena of optics would occur as though light were propagated by an ether which is stationary with respect to the original source. Light coming from a terrestial source would behave as though propagated by an ether stationary with respect to the earth and light coming from the sun would behave as though propagated by an ether stationary with respect to the sun. Now the Michelson-Morley experiment was devised for detecting the motion of the earth through the ether, and hence if this experiment should be reperformed using light from the sun instead of from a terrestrial source, a positive effect would be expected if the Ritz theory were true. On the other hand if the Einstein theory were true, no effect would be obtained, since according to this theory, all optical phenomena occur as though light were propagated by an ether stationary with respect to the observer.