# Invariance of speed of light

1. Jan 8, 2010

### Sidnv

Hi, I have a question which to many may seem quite stupid but it honestly has been perplexing me for a while now. I'm actually not sure if this is the correct place to post this but the question does seem to be based on the theory of relativity so here goes.

I think I'm correct in supposing that a photon i.e light moves at a constant speed in vacuum (approx 3 x 10^8 m/s) relative to all frames of reference. That is the speed of light will be measured to be the same by all observers in uniform motion regardless of their velocities.

Now 2 thoughts seem to arise in my mind from this.
First, if we consider the frame of reference of a photon. Now this photon moves at the speed of light relative to all reference frames. So, from the reference frame of the photon, all other frames of reference will seem to be moving relatively at the speed of light since it should be impossible for the photon itself to determine whether it is in moving or whether the other frame of reference is in motion.
So my question mainly is that from the point of view (or frame of reference, if you prefer) of the photon, do all other particles (in any arbitrary frame of reference) seem to be massless? The theory of relativity prevents any object with non zero rest mass from moving at the speed of light from any reference frame so if all other particles move at the speed of light relative to the photon, then to the photon they should appear to have zero rest mass.

The second question which may be an even sillier one is that in the frame of reference of one photon, what would the speed of other photons appear to be?

I really don't know if what I have proposed is correct or not? Could someone please tell me if there is an inconsistency in my logic? And please forgive me if there is something really fundamental which I am unaware of. I am new to relativity so it is very likely that I have missed out something. Thanks.

2. Jan 8, 2010

### Ich

Your logic is fine, but there is no such thing as the reference frame of a photon. Starting from a wrong premise allows you to prove everything (and it opposite too).

3. Jan 8, 2010

### Sidnv

Oh wow! So my initial premise itself was wrong.

Could you however explain your statement a little because I don't really understand why light would have no frame of reference. Is it to do with light being essentially zero dimensional. I always associated frame of reference with anything that carried energy which may be a wrong view.

Thanks

4. Jan 8, 2010

5. Jan 8, 2010

### Ich

Energy is a frame dependent concept, not inherently defined for any object.
Personally, I prefer to have as a minimum requirement for a "thing" to have a reference frame that it is at least in principle possible for that "thing" to define one. A photon does not experience time, it cannot change on it own, so it can't define a reference frame.
But that's armchair philosophy.
You see, every possible reference frame is connected with every other via a Lorentz transformation. these are not defined for v=c, and any combination of v<c transformations won't bring you there.
Maybe it's easier to grasp if you use rapidity instead of velocity. Light has infinite rapidity, and you can't build a reference frame on infinitiy.

6. Jan 8, 2010

### Sidnv

Thanks for the link. As a complete novice in the realm of relativity I guess I get confused easily.