Special Relativity Q: Choosing Light as Ref

[Cathr]

Special relativity states that the speed of light is constant for all the references, as long as they are not accelerating. For example, the speed of light would be c for a train moving linearly with a constant speed and would also be c for an observer who's not moving at all (I took the Earth as reference).

I know that it was proved experimentally, but I don't completely understant it. Is it true because of space and time dilation?

But what if we choose a photon as reference? How would the light itself perceive the movement of other objects, of the train and the observer for example? Wouldn't they be perceived as moving with the same speed?

 

[jtbell]

But what if we choose a photon as reference?

We can't. This would mean that there is an inertial reference frame in which the photon (or pulse of light) is at rest. However, there is no such reference frame, because the speed of light is always c, in any inertial reference frame.

 

[Dale]

Is it true because of space and time dilation?

Usually the proof is written the other way. You start with the invariance of c and then you derive time dilation (TD) and length contraction (LC) and the relativity of simultaneity (RS). However, you certainly could write the proof backwards starting with TD, LC, and RS and then proving the invariance of c. I am pretty sure that nobody would find that proof particularly compelling.

But what if we choose a photon as reference?

There is no such thing as the reference frame of a pulse of light. An object's frame is a tetrad where the timelike vector is tangent to the object's worldline. The worldline of a pulse of light has a null tangent, and a null vector cannot be equal to a timelike vector.

 

[Cathr]

Never thought of that, thank you!

 

[Cathr]

Thank you!

What did you mean by the object's worldline? Is this the set of space vectors? And why does it have a null tangent for the pulse of light?

 

[PeroK]

Thank you!

What did you mean by the object's worldline? Is this the set of space vectors? And why does it have a null tangent for the pulse of light?

If you haven't come across the term "worldline" yet, then the answer from @Dale may be a bit advanced. The basic answer is that light follows a special type of path through spacetime (it's called "null", because no proper time passes along its path). Particles with mass, on the other hand, follow "timelike" paths through spacetime, where proper time is experienced.

 

[Cathr]

What if we take, as reference, a particle that moves really fast, with a speed very close to the one of light, will if also perceive the speed of light as being c?

 

[PeroK]

What if we take, as reference, a particle that moves really fast, with a speed very close to the one of light, will if also perceive the speed of light as being c?

Yes. But, more fundamentally, there is no such thing as a particle that moves fast. All velocities are relative. That particle would perceive you as moving near the speed of light.

 

[Mister T]

I know that it was proved experimentally, but I don't completely understant it. Is it true because of space and time dilation?

It's hard to answer a "why" question, because it's not always clear what that means. But it is possible to start with the notions of time dilation, length contraction, and the relativity of simultaneity and use them to show that if something moves with speed $c$ in one inertial reference frame, it moves with speed $c$ in all inertial reference frames. The idea that all inertial reference frames are in this sense equivalent is the called the Principle of Relativity.

Once you grasp the idea that the speed $c$ is the same in all inertial reference frames you conclude that it's the fastest possible speed and that no reference frame can ever have that speed. Thus it's not possible to understand what things would look like from such a non-existent frame.

If you are familiar with space-time graphs you know that, for example, you can make a graph of time versus (one-dimensional) position. If you plot the position and time of a particle on such a graph you create the worldline of that particle.