# Invariant Speed of Light using Binary Stars and Tangential Velocity

So I was in class the other day and my professor mentioned that we can prove that light is invariant using a binary star system. His reasoning:

1. Assume a binary star system 1000-light years away from Earth, with the stars orbiting counterclockwise.

2. Assume stars rotating at 0.003c and stars positions at top and bottom of orbit. The time light takes to get from top star to earth is longer than the bottom star.

My question is how does this show that light is invariant?

• Are both the stars the same distance from Earth at this point? And are we assuming that we have a way to determine how long a light beam took to travel here? (Because that's not always guaranteed.) – probably_someone Jul 24 '17 at 19:31
• Yea they are the same distance, and we're finding the difference between the times we see the stars on earth I believe – Jeffrey Chiu Jul 24 '17 at 19:33
• Wouldn't the invariance of $c$ mean that the light takes the same amount of time to reach us, regardless of the source? – probably_someone Jul 24 '17 at 19:36
• But since the velocity of the top is moving away and the bottom is moving torwards, the distance is longer toa time takes longer according to d=ct – Jeffrey Chiu Jul 24 '17 at 19:39
• You just said the distance from each star to Earth was the same, though. – probably_someone Jul 24 '17 at 19:48

## 2 Answers

Assuming we have a way to determine the time it takes light to reach us, this gives us a way to validate one of two hypotheses. Either:

1. The speed of light is not invariant, which means its speed is dependent on the source velocity, or

2. The speed of light is invariant, which means its speed is independent of the source velocity.

Under hypothesis 1, the light coming from one star is traveling faster than the other (since the two stars have different velocities relative to Earth), and under hypothesis 2, the light coming from each star has the same speed. Since the stars are the same distance away, under hypothesis 1, the faster light should reach us first, and under hypothesis 2, the light from both stars should reach us at the same time.

Experimentally, we have determined that hypothesis 2 is correct.

• Can you explain to me how experimentally? Does this have to do with the De Mite experiment or whatever? – Jeffrey Chiu Jul 24 '17 at 21:28
• @JeffreyChiu Usually the Michelson-Morley experiment is the one quoted for the discovery of the invariance of the speed of light. – probably_someone Jul 25 '17 at 7:41

Binary system are quoted as a way to check the velocity of the star does not affect the speed of propagation of light, but, as far as I know the argument uses the amount of light observed at earth.

If the velocity of the rotating stars does not affect the speed of light we should observe the same amount of light no matter the phase of the orbital motion of the stars.