## Velocity of Light

### introduction

With the publication of Einstein's two axioms in 1905, some within the scientific community could not accept that the velocity of light was the same for all observers. All attempts to disprove Einstein's axiom have failed. All experimental results to date confirm that the velocity of light is a constant for all observers.

One alternative theory called the emitter theory, or ballistic theory, assumed that light only travelled at c relative to the emitter. If the emitter was moving with a velocity v relative to an observer then the observer would see the light emitted with a velocity c+v. Light then followed Newtonian mechanics and behaved like a particle that was always emitted with one velocity relative to the emitter.

In 1910 Daniel Frost Comstock, and three years later Willem de Sitter, both proposed that the emitter theory would result in the apparent peculiar motion of stars in binary systems. De Sitter and other observers of binary star systems had not observed any such peculiar effects. For example, the orbiting stars would be seen not to follow Kepler's Laws of planetary motion. No such deviation had been observed.

### animation

The animation depicts a star in a binary system emitting photons that travel to a distant observatory.

1. In the upper animation the light emitted by the star obeys Einstein's axiom and each photon travels with a velocity of c.
2. The lower animation depicts a possible outcome of the emitter theory. The speed of light is affected by the velocity of the star.

In the emitter theory when the star is approaching the observatory the light travels faster than c. When the star is receding from the observatory the light travels slower than c. In the animation the velocity of the light is c plus the velocity of the star in the direction of the observatory.

Compare the apparent motion of the binary star for different velocities.

• For the slower velocities note how the observed motion of the lower star deviates from upper star.
• For higher velocities note how, given enough time, the faster light overtakes the slower light.

The animation does not depict a realistic configuration. In reality stars in binary systems are generally moving much slower than the velocities available for selection in the animation. Also binary stars are much further away from the Earth than depicted. However as you may have noted in the animation the aberration effect predicted by the emitter theory is distance dependent. The more time the light travels the more the faster light can catch up to the slower light. So even though stars in real binary systems are moving slower than in the animation the fact that they are at a great distance means the effects depicted in the animation are possible if the emitter theory were true.

The 29cm telescope at Sydney Observatory was used to observe double stars from 1874, including the closest binary system called Alpha Centauri. Its observational results are consistent with the speed of light being a constant.