A proof of the constancy of the velocity of light

by Willem de Sitter

In the theory of Ritz light emitted by a source moving with velocity u is propagated through space in the direction of the motion of the source with the velocity c u, c being the velocity of light emitted by a motionless source. In other theories (Lorentz, Einstein ) the velocity of light is always c, independent of the motion of the source. Now it is easily seen that the hypothesis of Ritz leads to results which are absolutely inadmissible.

Consider one of the components of a double star, and an observer situated at a great distance Δ. Let at the time t, the projection of the star's velocity in the direction towards the observer be u. Then from the law of motion of the star we can derive an equation:

$u=f(t-t_{0})\$

(1)

The light emitted by the star at the time t reaches the observer at the time $\tau =t \Delta /c-au$. In Ritz's theory we have, neglecting the second and higher powers of $u/c,\ a=\Delta /c^{2}$. In other theories we have a=0. If now we put $\tau _{0}=t_{0} \Delta /c$, we have

$u=f(\tau -\tau _{0} au)\$ or $u=\varphi (\tau -\tau _{0})$

(2)

The function φ will differ from f, unless au be immeasurably small. Therefore if one of the two equations (1) and (2) is in agreement with the laws of mechanics, the other is not. Now a is far from small. In the case of spectroscopic doubles u is not small, and consequently au can reach considerable amounts. Taking e.g. $u=100{\frac {KM}{sec}}$, and assuming a parallax of 0",1, from which $\Delta /c=33$ years, we find approximately au=4 days., i.e. entirely of the order of magnitude of the periodic time of the best known spectroscopic doubles.

Now the observed velocities of spectroscopic doubles, i. e. the equation (2), are as a matter of fact satisfactorily represented by a Keplerian motion. Moreover in many cases the orbit derived from the radial velocities is confirmed by visual observations (as for δ Equulei, ζ Herculis, etc.) or by eclipse-observations (as in Algol-variables). We can thus not avoid the conclusion that a=0, i.e. the velocity of light is independent of the motion of the source. Ritz's theory would force us to assume that the motion of the double stars is governed not by Newton's law, but by a much more complicated law, depending on the star's distance from the earth, which is evidently absurd.

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