Undergrad Why the speed of light is constant for every observer?

[Arman777]

Why the speed of light is constant for every observer ? Is it a special thing for photons cause I guess there's no other elementry particle that can move with c ?

Also I want to investigate the constant of c for every observer, in the perspective of particle relationship.

For example, can I say "If a particle has zero mass, then all observers will see its speed as c"

(Of course this will be true for, If there's other particles that has zero mass. If not can we assume ?)

Or this statement is only true for photons.
And why such number $(c=299,792,458 \frac {m} {s})$ ? How would be the physics laws worked if c was so small or very large ?

 

[Dale]

For example, can I say "If a particle has zero mass, then all observers will see its speed as c"

Yes. There are several massless particles and they all travel at c in the same way as photons.

And why such number (c=299,792,458ms)(c=299,792,458ms)(c=299,792,458 \frac {m} {s}) ?

Because the SI committee got together and voted on that number. It was chosen because it matched previous definitions of the meter to within the available precision.

 

[Ibix]

You have to be a bit careful with what you mean by "the speed of light". There is a speed that is invariant for all inertial observers. This is a consequence of spacetime having a Lorentzian signature, but why that should be so we don't know.

Light and anything else massless (like gravitational waves) travels at the invariant speed as far as we know. However, it is at least possible that photons have a tiny mass (I believe the current upper bound is around 10^-50kg), in which case light would have a variable speed and would travel slower than c, just like everything else with mass. We presume the mass of the photon is zero, but we can't, strictly speaking, be sure of that.

So we tend to use "the speed of light" interchangeably with "the invariant speed", but that's technically not absolutely certain.

As to the exact value of c, it's fairly meaningless. You get a different number if you use different units. I gather that any careful analysis of the question leads to it actually meaning "why is the value of the dimensionless fine structure constant what it is". To which the answer is that we don't know.

So, in short:

Why the speed of light is constant for every observer ?

We don't know.

Is it a special thing for photons cause I guess there's no other elementry particle that can move with c ?

No. Everything massless moves at c.

And why such number

Because of the value of the fine structure constant. But we don't know why the fine structure constant has the value it does.

How would be the physics laws worked if c was so small or very large ?

Doesn't make sense - it's the fine structure constant you need to adjust.

 

[Arman777]

There are several massless particles and they all travel at c in the same way as photons.

So Let's suppose we have a massless particle and an observer which his speed is non-zero.Then, Is this observer will see the speed of object as c ?
My answer is yes but I want to be sure.

We don't know.

It's interesting. I thought maybe QED can explain it or some other Quantum Field Theory.

No. Everything massless moves at c.

Is this an axiom or proven by math ? Since I guess it would be awkward If we see a massless particle moves with a speed of non $c$.

Because of the value of the fine structure constant. But we don't know why the fine structure constant has the value it does.

So FSC (Fine Structure Constant) adjusts the speed of light, Is that means, FSC is more important then the concept of c in the sense of the SR or GR ?

Doesn't make sense - it's the fine structure constant you need to adjust.

FSC probably would change also other physical systems, but If we adjusted such that c will give us as a low value then how the world would be ?

 

[Ibix]

So Let's suppose we have a massless particle and an observer which his speed is non-zero.Then, Is this observer will see the speed of object as c ?

In Newtonian physics, if I see two cars heading towards each other at 30mph, I can deduce that each car will see the other approaching it at 60mph. So there's no difference in the closing rate of the car measured in any frame. This is not true in relativity; in fact in the rest frame of one of the cars the speed of the other will be slightly lower than 60mph.

So in a frame where the observer is at rest, light will approach him at c. In a frame where the observer is moving, the light is still doing c but the observer has a non-zero velocity and their closing rate will not be c. You are always free to transform into a frame where the observer is not moving.

It's interesting. I thought maybe QED can explain it or some other Quantum Field Theory.

All scientific theories have assumptions that are not justified except that the predictions deduced from them match reality. The existence of an invariant speed is one of the assumptions of modern physics.

Is this an axiom or proven by math ? Since I guess it would be awkward If we see a massless particle moves with a speed of non $c$.

It turns out that what we call the mass of a particle is the modulus of its energy-momentum vector. Things moving at c have a null energy-momentum vector, which is to say that its length is zero. So saying a particle has zero mass is equivalent to saying that it moves at light speed.

So FSC (Fine Structure Constant) adjusts the speed of light, Is that means, FSC is more important then the concept of c in the sense of the SR or GR

It isn't that it adjusts the speed of light; it adjusts the strength of the electromagnetic interaction, which has different effects on things we measure to determine light speed.

FSC probably would change also other physical systems, but If we adjusted such that c will give us as a low value then how the world would be ?

Beyond my level of knowledge, I'm afraid.

 

[Arman777]

It was very enlightening thanks.

Beyond my level of knowledge, I'm afraid.

Maybe there's some articles about it for different level of FSC.there's some things about cosmology and FSC relationship

 

[Nugatory]

So Let's suppose we have a massless particle and an observer which his speed is non-zero.Then, Is this observer will see the speed of object as c ?

In fact, the question as you've asked it is not as clear as you're thinking it is. When you say your observer's speed is non-zero, what exactly do you mean? How would you know whether his speed was non-zero or not?

To see the problem, consider the situation that we find ourselves in when we perform experiments of this sort. I observe a flash of light moving away me at speed $c$. I also observe that you are moving in the same direction as the flash at some non-zero speed, say 100 km/hr just to be definite. You observe the same flash of light moving away from you at speed $c$, and you also observe that I am moving in the opposite direction at 100 km/hr. Which one of us is the one with non-zero speed?

The only useful facts we have are that you have observed me moving in one direction at 100 km/hr and you've observed me moving in the opposite direction at 100 km/hr, and these facts are consistent with either or both of us having non-zero speed. Follow through on this line of thought and you will see that any statement about something having any speed, whether zero or non-zero, will be meaningless unless you also say what that speed is relative. A corollary is that any statements or questions about which of us is "really moving" or "really at rest" are meaningless.

My answer is yes but I want to be sure.

Phrased properly, your question would be "Will two observers moving relative to one another both see the speed of the object as $c$?", and then you are correct. The answer is "yes".

 

[Arman777]

Well, in that case observer's speed is non-zero relative to me and in this case I guess its yes, they will both see the speed of light as c.

 

[Arman777]

there's massless particles but I guess photon is the only particle that moves with a speed of c.

I was doing research and found this,

"So it is a general rule that massless particles travel at the velocity of light, but only when in external lines in Feynman diagrams. This is true for photons, and we thought it was true for neutrinos but were proven wrong with neutrino oscillations.

Gluons on the other hand we only find within a nucleus and these are by definition internal lines in Feynman diagrams and therefore are not constrained to have a mass of 0, even though in the theory they are supposed to. In the asymptotically free case, at very high energies they should display a mass of zero."

"So Let's suppose we have a massless particle and an observer which his speed is non-zero.Then, Is this observer will see the speed of object as c ?"

Actually I was asking this question for other massless particle (gluon), but in the general sense It wasn't make much diffefence but now It might make a difference after this information?

 

[Dale]

My answer is yes but I want to be sure

Yes. With the caveats mentioned by @Nugatory