# Predictions we can derive if light were corpuscular

1. Jul 25, 2012

### spaghetti3451

I am a third year undergrad in the UK and I have been looking over my first year notes on special relativity. I found this passage talking about predictions we can derive if light is corpuscular.

"If light is corpuscular (emitted like bullets) one expects the speed of light to depend on the speed of the source. Can one infer the speed of the source by measuring the speed of light?
For instance the light emitted in front of a plane travelling at speed u would be travelling at speed c + u and the light emitted from the rear at speed c − u. If this was the case one could have systems of binary stars in which one star could be seen at two places at the same time."

I can understand that we can take the difference between the speed of light c+u from the front of the plane and c-u from the rear and divide by two. That will give us the speed of the source, if the corpuscular nature were true. What I don't understand is how 'if this was the case one could have systems of binary stars in which one star could be seen at two places at the same time'?

Any ideas?

2. Jul 25, 2012

### ghwellsjr

The Double Star Experiment provides the proof that light is not corpuscular. There is an animation in the link that shows how one star could be seen twice.

3. Jul 25, 2012

### bcrowell

Staff Emeritus
Let's pick some unrealistic numbers to make the arithmetic easy. Say that the distance to the binary star is 100 light-years, and the orbital speed is v=0.01c. Then a photon traveling at c+v takes only 99 years to get to us, and one at c-v 101 years. That's a 2-year difference, which could be greater than the orbital period.

IMO your prof's explanation isn't all that great. Light actually *is* a particle, so this prediction can't be generically true. I'd say that the double-star observations are evidence evidence that the speed of light is independent of the motion of the source, not that light isn't a particle.

Another way of putting it is that we can't explain the observations if we model spacetime as Galilean and light as a Newtonian particle. An easier observation that proves the same thing is that when light refracts, it's closer to the normal in the medium in which its speed is slower. The opposite would be true in the Galilean spacetime/Newtonian particle description. (Imagine a putting green split into two levels, with a ramp connecting them. Golf balls would be *farther* from the normal on the upper side.)

4. Jul 26, 2012

### HallsofIvy

Where did you see this? It is certainly untrue. In fact, it is not even true for bullets. If you are on an airplane moving at speed u, relative to the earth, and you fire a bullet, with speed v, relative to the airplane, then the speed of the bullet, relative to the earth, would be
$$\frac{u+ v}{1+ \frac{uv}{c^2}}$$

Bullets, in this sense, obey the same laws at light. If either u or v were equal to
c, the resulting speed relative to the earth would also be c.

This assume that "if light were corpuscular" then relativity would not apply. I can see no reason for that assumption.

5. Jul 26, 2012

### bcrowell

Staff Emeritus
I think what it was intended to demonstrate was that you can't have both of the following: (1) spacetime is Galilean, and (2) light is a Newtonian particle. The statement would be true for bullets if 1 held. But yes, I agree that it can't be used to rule out 2, only to rule out (1 and 2).