[hamdani yusuf (OP)]

When v=0, sensor receive laser. If v>0,will it still get the laser?

[Janus]

Yes.

[hamdani yusuf (OP)]

Yes.

have you done the experiment?
or is it based on a theory? how is the mechanism?

[Kryptid]

As I understand it, mirrors work by changing an incident electromagnetic wave into a surface current and then that surface current gives rise to a second electromagnetic wave. If that's the case, you'd expect the relative velocity of the surface current to be affected by the velocity of the mirror. Thus, there should be some non-zero distortion in the reflection of such a moving mirror. I suppose that the mirror would have to be moving very, very quickly for this to be noticed by the human eye.

[hamdani yusuf (OP)]

I suppose that the mirror would have to be moving very, very quickly for this to be noticed by the human eye.

alternatively,  the detector could be located very far away from the mirror.

[Halc]

have you done the experiment?
or is it based on a theory? how is the mechanism?

Any other answer would violate the principle of relativity. The absolute motion of the mirror could be measured by a deflection of the beam.

In some frame, the mirror is stationary and the emitter/detector is moving, and if the mirror didn't behave as normal, it would have to be because of the light speed relative to the mirror somehow being dependent on the speed of the device that emitted it, which contradicts light speed not being a function of the motion of the emitting object.

[Bored chemist]

I suppose that the mirror would have to be moving very, very quickly for this to be noticed by the human eye.

alternatively,  the detector could be located very far away from the mirror.

I'm not sure.
I think there would be a change in the path of the beam, but I think it would be a displacement, rather than a deviation.
I think the light would be parallel to the path it would take if the mirror was stationary

[alancalverd]

The ring laser gyroscope works by measuring the change in light path length when a mirror system moves. I can't see why a linear movement would be any different from a small rotation in that respect, so whilst it would be difficult to construct  a detector with a sufficiently narrow acceptance angle to measure it, you should be able to see interference between beams reflected from a fixed and moving mirror. But for a practical application, laser Doppler is a much easier means to measure speed.   

[hamdani yusuf (OP)]

have you done the experiment?
or is it based on a theory? how is the mechanism?

Any other answer would violate the principle of relativity. The absolute motion of the mirror could be measured by a deflection of the beam.

In some frame, the mirror is stationary and the emitter/detector is moving, and if the mirror didn't behave as normal, it would have to be because of the light speed relative to the mirror somehow being dependent on the speed of the device that emitted it, which contradicts light speed not being a function of the motion of the emitting object.

Does stellar aberration violate the principle of relativity too? The situation is similar to the case shown here.
https://en.wikipedia.org/wiki/Aberration_(astronomy)

The apparent position of a star viewed from the Earth depends on the Earth's velocity. The effect is typically much smaller than illustrated.

[hamdani yusuf (OP)]

I suppose that the mirror would have to be moving very, very quickly for this to be noticed by the human eye.

alternatively,  the detector could be located very far away from the mirror.

I'm not sure.
I think there would be a change in the path of the beam, but I think it would be a displacement, rather than a deviation.
I think the light would be parallel to the path it would take if the mirror was stationary

How much the displacement would be? What factors, other than mirror's speed, can affect the magnitude of the displacement?

[Halc]

Does stellar aberration violate the principle of relativity too?

Neither aberration nor a moving mirror violate the principle. Neither can be used to measure absolute motion.

[hamdani yusuf (OP)]

Does stellar aberration violate the principle of relativity too?

Neither aberration nor a moving mirror violate the principle. Neither can be used to measure absolute motion.

Can they be used to measure relative motion, between light source and detector?

[Halc]

Neither aberration nor a moving mirror violate the principle. Neither can be used to measure absolute motion.

Can they be used to measure relative motion, between light source and detector?

Aberration is the result of relative motion, but it can only be used to measure that motion if you know where the (star say) would have appeared had it no relative motion. So the relative motion of that star is more likely measured by its apparent motion against the background rather than a hypothetical device that measures aberration directly. I don't know of one.
As for the mirror, your light source and detector have no relative motion, and the motion of the mirror makes no difference to the scenario for the reasons given in prior posts.

[hamdani yusuf (OP)]

Neither aberration nor a moving mirror violate the principle. Neither can be used to measure absolute motion.

Can they be used to measure relative motion, between light source and detector?

Aberration is the result of relative motion, but it can only be used to measure that motion if you know where the (star say) would have appeared had it no relative motion. So the relative motion of that star is more likely measured by its apparent motion against the background rather than a hypothetical device that measures aberration directly. I don't know of one.
As for the mirror, your light source and detector have no relative motion, and the motion of the mirror makes no difference to the scenario for the reasons given in prior posts.

in the reference frame of a point on the mirror where reflection occurs, the pointer is moving away while the receiver is coming closer. What makes you think that those motions have no effect whatsoever to the directions of the reflected light?

[Halc]

in the reference frame of a point on the mirror where reflection occurs

A moving laser is going to trace a line across a mirror, not a point.  We can consider a single photon if you like, which yes, reflects at a specific point on the mirror.  So I'm assuming you just mean 'in the frame in which the mirror is stationary'.

the pointer is moving away while the receiver is coming closer.

Both come closer at first, and move away after passing a point of closest approach. Between the times when one has passed but the other has not yet, your statement is true, yes.

What makes you think that those motions have no effect whatsoever to the directions of the reflected light?

I don't think that, so question is ill-phrased.

The direction and thus the velocity of light is frame dependent.  For instance, if, in the frame of the detector, the velocity of the emitter/detector is v=-0.7c (approx, based on the OP drawing where positive is to the right as indicated), then a given photon is going to travel straight down in the frame of the mirror and thus reflect straight back up as you'd expect. Each subsequent photon will also travel vertically like that, but further to the left each time. Assuming a finite size mirror, the beam will only hit it for a short time before running off the end.

[hamdani yusuf (OP)]

The direction and thus the velocity of light is frame dependent.  For instance, if, in the frame of the detector, the velocity of the emitter/detector is v=-0.7c (approx, based on the OP drawing where positive is to the right as indicated), then a given photon is going to travel straight down in the frame of the mirror and thus reflect straight back up as you'd expect. Each subsequent photon will also travel vertically like that, but further to the left each time. Assuming a finite size mirror, the beam will only hit it for a short time before running off the end.

No. The diagram shows the positions when v is very low. We can say that vx is close to 0.7c.
What is predicted by theory of relativity when the mirror moves at relativistic speed, say 0.7c?

[Halc]

No. The diagram shows the positions when v is very low. We can say that vx is close to 0.7c.
What is predicted by theory of relativity when the mirror moves at relativistic speed, say 0.7c?

I worded that poorly (wrong), but essentially answered your question above.
The diagram shows the positions of the components regardless of mirror speed since mirror speed makes zero difference. It would make a difference if the mirror was moving in the y direction, but you show motion only in the x direction along which it is aligned.

To reword: if, in the frame of the detector, the velocity of the mirror is v=0.7c (approx, based on the OP drawing where positive is to the right as indicated), then in the frame of the mirror, the emitter/detector is moving at -0.7c and a given photon is going to travel straight down to the stationary mirror and thus reflect straight back up as you'd expect.  A Lorentz transform of that sequence of events to the frame of the devices gives your picture in the OP. To assert otherwise is to assert that light coming in to a stationary mirror is going to reflect at a different angle of reflection than the angle of incidence, which isn't how mirrors work.

[yor_on]

You can exchange it for a set system, parts at rest with each other, consisting of a emitter and receiver. Either accelerating or in a uniform motion, which makes for two different cases. In both cases bouncing a light signal against a predefined 'unmoving' mirror. In which case would you expect the light from the emitter bouncing of the mirror to hit the receiver? At what speed? Different speeds and accelerations, do they matter?


syntax
=

Actually this one becomes very tricky to me. How do you imagine the light? As some bullet? Bouncing at a angle? The reciever will register the light no matter what as I think? Point a laser at at mirror at home, then let a friend walk around, in front of the mirror. As far as I get it that light reflected should be visible no matter at what angles he choose? As long as he stays in front of that mirror. Am I wrong?

seems to me the only time it wouldn't register is when it is outside the recievers lightcone?

[Bored chemist]

Light reflected from a mirror is subject to a phase change.
Classically, that's interpreted as the time it takes for the light to be absorbed and re-emitted.
If the mirror is a piece of gold leaf  (and the wavelength isn't too short) some of the light will go through. The light is definitely "in" the metal.
So, for part of its journey, the light is  converted to energy stored in the distorted electric field of the electrons and nuclei in the metal. That metal is moving. The mirror would have moved by the time the light was re-emitted.
It's hard to see how it wouldn't drag the light along for the duration.

There's no conflict with relativity here.
It's establishing relative motion, not absolute.
If the mirror, laser and detector all move together then the outcome is the same as if they are all stationary.
There's only an effect if the mirror moves WRT the other components.
In the same way that I would expect a different result if I put my finger on a fast moving mirror rather than a stationary one, I can expect a different outcome if I bounce light off it.

[hamdani yusuf (OP)]

When v=0, sensor receive laser. If v>0,will it still get the laser?

If the laser pointer is replaced by a BB gun, while the moving mirror is replaced by a treadmill conveyor, I expect that the bullet will miss the target. What makes the result different in case of light?