# Question on SR

## Main Question or Discussion Point

I have a very basic question about Special Relativity. I am very limited on my knowledge of physics and math and even more so on SR so please keep that in mind when answering.

I have read the basic example many times of two spaceships traveling towards each other with a constant velocity. The observer on ship A could say that his ship is moving while ship B is at rest and he could also say that his ship is at rest while ship B is moving. The observer in ship B could also say the same things. That was all fine until I thought about one of the ships changing into a beam of light. If a beam of light is used the observer on the ship could still say that he is at rest and the light is moving but it doesn't seem that he can say that the light is at rest and he is moving. This would cause his ship to be moving at c which is impossible since it has mass.

Someone pointed out that the observer couldn't see the light until it reached him but you could easily fix that by saying the light has already hit the observer on the ship and continues to pass him. In other words, the beam of light is arbitrarily long and continues to pass by the ship. Thus the observer should be able to say he is moving or the light is moving.

If even that won't work, what if it were a beam of light as one reference frame, and then another beam of light and the rest of the cosmos as another? Then the light and cosmos could say the other light beam is moving and they are all at rest, or that they are moving and the other beam of light is at rest - which again causes the matter in the cosmos to be moving at c. I just don't see how a beam of light can be a frame of reference. The only thing I can think of is that maybe when taking the frame of the light time for the other frame (the ship) stops. But that seems to just enforce the idea that the light must be moving and no other reference can be taken. And you still couldn't take the reference frame of the ship and say the light is at rest because you would have to be moving at c. I don't see how any affect on time would change this for the ship. I'm sure I'm looking over something obvious but I just don't understand. I'd appreciate some help.

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Doc Al
Mentor
I just don't see how a beam of light can be a frame of reference.
You are correct--It can't! You've just deduced some of the nonsense that would ensue if you attempt to attach a reference frame to a beam of light.

Mentz114
Gold Member
Rapt0rzzz:

Welcome to PF. You have got yourself in a tangle because in your thought-experiment you've transgressed one of the axioms of special relativity here

That was all fine until I thought about one of the ships changing into a beam of light. If a beam of light is used the observer on the ship could still say that he is at rest and the light is moving but it doesn't seem that he can say that the light is at rest and he is moving.
It is only possible to define regular motion of matter with respect to other matter, and all matter travels at less than the speed of light. If one of your spaceships 'turned into light', the other spaceship could no longer define motion wrt to the (now gone) other ship. The essential thing is that one cannot define a frame of reference using light.

If you stick to two spaceships, with a constant ( steady) relative velocity, then everything is fine, they will see time dialtion and length contraction when the look into each others frames.

tiny-tim
Homework Helper
Welcome to PF!

{snip} I just don't see how a beam of light can be a frame of reference. {snip}
Hi Rapt0rzzz! Yes … welcome to PF!

I don't see any tangle … you're basically asking about the symmetry of different parts of the "space of velocities".

As you point out, the STL region has symmetry, in the sense that, for any pair of STL observers, either can regard himself as at rest … one is the same as the other in that sense.

But, you point out, for a pair comprising one STL and one SOL observer, there is no symmetry … their two velocities are fundamentally different.

Then you pose the interesting question of a pair of SOL observers … can either regard itself as at rest, with the other moving at c?

I think the answer is that the SOL region of the "space of velocities" has a topological structure, but has no metric (no distance) … so, while there is a concept of "between-ness", no sensible concept of size can be applied to it.

In particular, no SOL observer could say that the speed of another SOL observer is c (whatever "c" might be), because there is no metric by which it could measure a speed.

You are correct--It can't! You've just deduced some of the nonsense that would ensue if you attempt to attach a reference frame to a beam of light.
Well I pretty much figured it can't be taken as a reference frame as soon as I thought of the above example. I'm interested to know exactly why it can't. I know there must be a reason other than the fact that nonsense would ensue. That would only mean it proves SR contradictory which we all know full well it is not. So could anyone explain the reason why light cannot be taken as a reference frame? I don't see any condition that says "any two inertial frames can be used except light" Or that all frames must contain mass. Is there a simple way to explain this?

robphy