B Speed of Light Reflection: Einstein's Train & Mirrors

[zasvitim]

TL;DR Summary

What will be the speed of reflected light?

Hello

Let's suppose we have 2 observers. One is in Einstein's train and one is outside. There are 2 mirrors: one inside the train and one outside. Speed of train is v

Both observers emit light which reflects from both mirrors.

What will be the speed of reflected light for both observers from both mirrors? Will speeds be equal? Will there be 2 speeds? 4 speeds?

Thanks.

 

[Ibix]

What does the second postulate of special relativity say?

 

[zasvitim]

It says something strange, which I'm trying to understand. So what will happen according to the second postulate? will there be 2 speeds of reflected photons for each mirror or 1? Will photons somehow split to have speed C for each observer? Does speed of mirror cause any effect on the reflection process and result?

 

[Ibix]

It says the speed of light in vacuum is always $c$. So the light is doing $c$ in either direction (if we assume the train is in vacuum, anyway).

The Lorentz transforms follow from this, and they tell you how the measurements made in one frame relate to those in another.

 

[Nugatory]

It says something strange, which I'm trying to understand. So what will happen according to the second postulate? will there be 2 speeds of reflected photons for each mirror or 1? Will photons somehow split to have speed C for each observer? Does speed of mirror cause any effect on the reflection process and result?

One speed, $c$. What is misleading you here is that you are making a common sense assumption about how speeds add: if B is moving at speed $u$ relative to A, and C is moving at speed $v$ relative to B, then C's speed relative to A ought to be $u+v$ when C is moving in the same direction as B, $u-v$ when C us moving in the opposite direction.
Here A is the ground, B is the train, C is the flash of light, and this common-sense expectation cannot be reconciled with the second postulate.

However it turns out the common-sense assumption is not right. The correct rule for adding the speeds is not $u+v$, it is $(u+v)/(1+uv/c^2)$ - this looks a bit simpler if we choose to measure time in seconds and distances in light-seconds so that $c=1$: we have $(u+v)/(1+uv)$.

Use this formula and you will find that the flash of light is moving at speed $c$ relative to both the train and the ground.

You may be wondering how it could be that in all the millenia before Einstein discovered relativity no one ever noticed that the common-sense rule was wrong. As an exercise, consider a jet fighter flying at 1000 km/hr firing a 1000 km/hr missile... How fast is the missile going relative to the ground, and how different is that from the 2000 km/hr that the common-sense rule predicts? Do that calculation and you'll see why no one noticed.
(Although around 1850 the physicist Fizeau was working with light passing through moving water and didn't get quite exactly the expected $u+v$ result. At the time this was generally considered to be either a mystery or an experimental error, and it remained that way until it was explained by relativity a half-century later).

 

[A.T.]

Does speed of mirror cause any effect on the reflection process and result?

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.

 

[zasvitim]

You may be wondering how it could be that in all the millenia before Einstein discovered relativity no one ever noticed that the common-sense rule was wrong. As an exercise, consider a jet fighter flying at 1000 km/hr firing a 1000 km/hr missile... How fast is the missile going relative to the ground, and how different is that from the 2000 km/hr that the common-sense rule predicts? Do that calculation and you'll see why no one noticed

I don’t have any problems with fighter and rocket that is fired forward. Fighter’s internal time flow slows down and therefor it seems to him that rocket is faster than it is. I have a problem with a rocket that is fired back. If we apply the same rule “it seems to pilot inside that it’s faster that it is”, then it should appear to be even slower then what common sense says.
Imagine a ball that is bouncing back from a wall. It will have the same speed after it bounces back, but with opposite direction. Now imagine that wall moves away. Speed of ball after bouncing back will be slower. The faster the wall is moving away the slower will be the speed of the ball. And at some moment it does not bonce back, but follows the wall instead. Now imagine that ball moves almost with speed of light and bounces back from a wall that moves away. It will be slower again.
But light does not care on wether wall moves away? How so? What if light will have different speed after being reflected by a mirror that moves away with almost speed of light?

And that is why we don't see astrophysical jets of our galaxy for example.

 

[Ibix]

Fighter’s internal time flow slows down

No it doesn't - that's a popsci explanation of what's going on. As you have seen yourself, it is impossible to explain fairly simple scenarios using it.

An observer at rest with respect to the earth will see two things about clocks travelling with the fighter. First, that they tick slowly, and second (and this is the bit that gets missed out), they are not correctly synchronised. Clocks travelling in a fighter in front are set to a time behind clocks in the original fighter, and clocks in fighters following it are set ahead. When you account for this effect too, you see how the fighter measures the missiles (or light pulses) to have the same speed.

But light does not care on wether wall moves away? How so?

Depends what you mean. Fundamentally, we justify that claim post hoc: if you work out the implications of the idea it turns out to match the behaviour of things in our universe. Notably, it resolves a lot of issues with electromagnetism that plagued physics in the late nineteenth century. The intuition you are attempting to use is based in the laws of physics as they were known at the time, which we now know are a low speed approximation still taught and used today, but completely wrong if one tries to understand the workings of light.

On the other hand, if you want to know what are the measurements the pilot makes you can just apply the Lorentz transforms to the measurements that a ground-based observer makes.

 

[zasvitim]

The intuition you are attempting to use is based in the laws of physics as they were known at the time, which we now know are a low speed approximation still taught and used today, but completely wrong if one tries to understand the workings of light.

Can you explain me, how directional light can exist in a world where light is emitted with the same speed in all directions?
Imagine a plane that passes you. You always hear it.
Now imagine an astrophysical jet that passes you. It should emit light in your direction just as plane produces sound waves in your direction.
So why we see only very small part of astrophysical jets? why night sky is not full of lines from every jet that exists?
My explanation would be that Einstein's special relativity works only for the light emitted forward. All other light has the same speed comparing to the source as the light that is emitted forward.
Something like this:

 

[malawi_glenn]

Can you explain me, how directional light can exist in a world where light is emitted with the same speed in all directions?

Huh?
You mean if I shine a light beam to the east, it will have speed c in the north-west direction too?

 

[zasvitim]

Huh?
You mean if I shine a light beam to the east, it will have speed c in the north-west direction too?

You don't have beam of light, you have ball of light. And yes, if we claim that the speed of light does not depend on the speed of observer, it should be the same in all directions whatever you are doing.
If jets were beams of light, we would not see astrophysical jets at all - other than those that point exactly into us.

But we have a mixture: We see astrophysical jet, but only small part of if. Just as we would happen if we were in this cone:

 

[zasvitim]

In other words.. What if light reflected back by a mirror that is moving away has rest mass and therefor moves slower?

 

[Ibix]

In other words.. What if light reflected back by a mirror that is moving away has rest mass and therefor moves slower?

Moving away from what? Moving in what frame? All mirrors are moving in some frames and not others at all times, so light in your "theory" would be at all times travelling at all different speeds.

If you want to learn relativity I recommend Taylor and Wheeler's Spacetime Physics, free for download from Taylor's website these days. We can help if you get stuck. If you prefer to make up incoherent nonsense I recommend that you reread the site guidelines, which you agreed to abide by when you signed up, and then take it elsewhere.

 

[zasvitim]

Moving away from what? Moving in what frame? All mirrors are moving in some frames and not others at all times, so light in your "theory" would be at all times travelling at all different speeds.

If you want to learn relativity I recommend Taylor and Wheeler's Spacetime Physics, free for download from Taylor's website these days. We can help if you get stuck. If you prefer to make up incoherent nonsense I recommend that you reread the site guidelines, which you agreed to abide by when you signed up, and then take it elsewhere.

In the fame of "axis of evil".

One last question on special relativity:
What angle of synchrotron emission does special relativity predict directly from it's postulates depending on the speed of the source (electrons)?

 

[Nugatory]

Fighter’s internal time flow slows down and therefor it seems to him that rocket is faster than it is.

As @Ibix says above, that is not right. One way of seeing this is to think about the problem while considering the aircraft to be at rest: the missile is moving at 1000 km/hr forwards relative to the aircraft and the earth is moving in the opposite direction, also at 1000 km/hr relative to the aircraft (the aircraft is of course not moving relative to itself). Now it’s the ground that is moving, so time should be flowing more slowly for it and we see two problems: first, there’s an obvious contradiction because they can’t both be slower than the other; and second, if that were happening a person on the ground would find that the missile was moving at more than 2000 km/hr, inconsistent with both the $(u+v)/(1+uv)$ rule and actual experimental observations.

Time dilation is real thing, but there’s more to it than the “time slows down” oversimplification that we hear so often. That oversimplification is seriously misleading and is one of those things that you will have to unlearn as part of learning relativity.

In other words.. What if light reflected back by a mirror is moving away has rest mass and therefor moves slower?

It doesn’t. There is an overwhelming mass of experimental evidence (take a look at the sticky thread at the top of this subforum on experimental evidence!) that shows that’s not how light works. It’s not how the equally well confirmed laws of electromagnetism (Google for “Maxwell light waves”) say light should work. And on a more practical level…. If light worked that way then the GPS system wouldn’t work.

 

[Drakkith]

So why we see only very small part of astrophysical jets? why night sky is not full of lines from every jet that exists?

I don't really know what you mean by saying that we only see a small part of these jets, but the night sky isn't full of them for the simple fact that they aren't particularly common as far as light sources go. The overwhelming majority of light sources are main sequence stars.

If jets were beams of light, we would not see astrophysical jets at all - other than those that point exactly into us.

But we have a mixture: We see astrophysical jet, but only small part of if.

Jets are outflows of ionized matter that emit light in all directions, with some directionality depending on how relativistic they are and some other conditions.

Now imagine an astrophysical jet that passes you. It should emit light in your direction just as plane produces sound waves in your direction.

It would emit light in your direction.

 

[Nugatory]

Can you explain me, how directional light can exist in a world where light is emitted with the same speed in all directions?
….
You don't have beam of light, you have ball of light

You are right that we can always think of electromagnetic radiation spreading out in an expanding sphere from the source. However, any realistic configuration will include multiple frequencies and phases so can be mathematically treated as the sum of multiple such spheres; there will be constructive and destructive interference at various places and times, and this can lead to directed beams and flashes. You might try googling for “Huygens wavelets” or for a good practical example look at how phased array radars steer their beams.

 

[zasvitim]

It would emit light in your direction.

So where is it?

 

[zasvitim]

It doesn’t. There is an overwhelming mass of experimental evidence (take a look at the sticky thread at the top of this subforum on experimental evidence!) that shows that’s not how light works. It’s not how the equally well confirmed laws of electromagnetism (Google for “Maxwell light waves”) say light should work. And on a more practical level…. If light worked that way then the GPS system wouldn’t work.

How rest mass in photon can contradict Maxwell's equations if there is no any rest mass in Maxwell's equations?
Shouldn't you reject existence of rest mass as some separate entity if you accept Maxwell's equations and mass and energy equivalence principle (E=mC^2)?
Shouldn't there be some cyclic motion with speed of light instead of rest mass? Something like attached. Moves in cycle but it still follows Maxwells equations?

 

[Nugatory]

Shouldn't you reject existence of rest mass as some separate entity if you accept Maxwell's equations and mass and energy equivalence principle (E=mC^2)?

That’s the wrong energy/mass relationship. Although it gets all the attention, $E=mc^2$ is the $p=0$ special case of the more general $E^2=(m_0c^2)^2+(pc)^2$ where $p$ is the momentum and is never zero for light.

 

[zasvitim]

That’s the wrong energy/mass relationship. Even though it gets all the attention, $E=mc^2$ is a special case of the more general $E^2=(m_0c^2)^2+(pc)^2$ where $p$ is the momentum and is never zero for light.

This equation literally shows what was displayed in my picture. That there are 2 "parts" in particle and that both of them are "connected" with speed of light..

And we also know that there are such entities as de Broglie wave length and Compton wave length that represent movement and rest. So maybe they represent direct motion and cyclic motion? And all matter follows Maxwell's equations?

 

[malawi_glenn]

You don't have beam of light, you have ball of light

Get a laser pointer.

 

[zasvitim]

Get a laser pointer.

Yes, I should get laser pointer, not "Sword of the Jedi" - as we observe jets.

 

[malawi_glenn]

I think you are also confusing speed with velocity components.

 

[zasvitim]

I think you are also confusing speed with velocity components.

You mean that rest mass is internal velocity component?

 

[malawi_glenn]

You mean that rest mass is internal velocity component?

no...

 

[Sagittarius A-Star]

Will photons somehow split to have speed C for each observer?

No, they don't split. Instead, the rest-frame of the train and the rest-frame of the ground have each their own time, $t'$ and $t$. An absolute time does not exist.

$c= \frac{dx}{dt} = \frac{dx'}{dt'}$.

 

[zasvitim]

No, they don't split. Instead, the rest-frame of the train and the rest-frame of the ground have each their own time, $t'$ and $t$. An absolute time does not exist.

$c= \frac{dx}{dt} = \frac{dx'}{dt'}$.

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?

 

[pinball1970]

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?

I just checked on line, £100 for a hard back Taylor and Wheeler, £35 for paper back and free for download.

https://www.eftaylor.com/spacetimephysics/

 

[Nugatory]

@zasvitim: Posting misconceptions to be corrected as you are doing over and over again in this thread is an ineffective way of learning the physics. You started with a question about the constant speed of light and received several good answers which you have pretty much ignored.

You are temporarily banned from posting in this thread to give you some time to digest what has already been said. If you want to start any new threads, be careful that you are asking how current physics explains something, not advancing your own ideas about how they might be explained.

 

[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?