Speed of Light Reflection: Einstein's Train & Mirrors

[DrGreg]

And there is no difference if mirrors moves away or not? Did you ever play billiards? Do you imagine that ball that bonces back from another ball does not care if it is stationary or moves away with almost maximum speed?

When light reflects from a mirror that is moving relative to an observer, then its energy, frequency and magnitude of momentum (relative to the observer) do all change, but its speed does not.

As has been previously mentioned, when you switch from one observer to another, velocity changes according to formula$$
\frac {u + v} {1 + \frac{uv}{c^2} }
$$ and when you put $v=c$ you get the answer $c$ for all values of $u$ (and $v=-c$ gives $-c$).

 

[malawi_glenn]

And there is no difference if mirrors moves away or not? Did you ever play billiards? Do you imagine that ball that bonces back from another ball does not care if it is stationary or moves away with almost maximum speed?

Have you played billiards with photons or another massless particle?

 

[pinball1970]

Have you played billiards with photons or another massless particle?

I was tempted but knowing how difficult this subject is for me, I thought people in glass houses and all that!

 

[A.T.]

And there is no difference if mirrors moves away or not?

Already answered:

The reflection at a moving mirror can change the frequency and thus momentum of the light, but not its speed in inertial frames of reference.

 

[Drakkith]

So where is it?

If you're referring to the red lines drawn where there is no more jet, there's two reasons. For the lower right line, the jet simply stops being ionized and thus stops being visible, as it emits no more light once the matter is neutral.

The jet that would be where the top left line is located is not visible because of relativistic beaming, which redshifts the light and reduces the luminosity of the emitted light to such an extent that it is buried in the background noise and isn't visible.

If we were nearly side on the jets would look similar to these jets from NGC 383:

 

[C4m]

Maybe this is way too primitive. But doesn't most of these variables affect the different end results how far the light travels and how much time it takes accordingly?

-PoV
-Angle
-Distance

This might be a 0.000000000001-ish difference, yet its a difference.

 

[Drakkith]

Maybe this is way too primitive. But doesn't most of these variables affect the different end results how far the light travels and how much time it takes accordingly?

-PoV
-Angle
-Distance

This might be a 0.000000000001-ish difference, yet its a difference.

If you measure the distance the light travels over some time interval, it is ALWAYS c in a vacuum. The only things that change how long it takes to reach some point is the distance to that point and the path the light takes to reach it.

In the context of astrophysical jets, the light is traveling in very nearly a straight line to get to us, so the only other variable left is the actual distance between the jet and ourselves.

 

[Sagittarius A-Star]

And there is no difference if mirrors moves away or not?

No. The speed $c$ is invariant. It this the same in the mirror's rest frame and in each other frame.

Did you ever play billiards?

There is a difference.
As others mentioned, billiard balls have a non-zero invariant mass

$m=\frac{E}{c^2}\sqrt{1-u^2/c^2}$.

Light has $m=0$ and therefore moves at $u=c$.

 

[Vanadium 50]

This might be a 0.000000000001-ish difference, yet its a difference.

I'm not sure how this can be sensibly discussed. It's effectively saying you don't believe relativity and you guess the correct answer is something different. OK, so now what?