# I Time Dilation and photodetectors

1. Nov 17, 2017

### Samson4

In the image below, we will be accelerating the entire apparatus. It won't ever reach a frame of inertia. Would someone in a different frame of reference be able to detect this acceleration from the output of the photo-detector?

As time slows and the distance the laser travels contracts; would the photodetector display this energy input to a stationary observer?

If we replace the photodetector with a perfect mirror and create a laser cavity, would we find an interference pattern in the middle of the cavity as we accelerate the apparatus?

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2. Nov 17, 2017

### jbriggs444

If one adopts an accelerating frame of reference in which the assembly is at rest then the photodetector will see red-shifted light due to gravitational time dilation. This is a frame-independent fact that can be read from the photodetector's output.

If one stays with an inertial frame then the detector is always moving faster away from the light at the reception event than the source was moving toward the light when it was emitted. Doppler then says that a red shift will result.

3. Nov 17, 2017

### Samson4

So as the apparatus accelerates the photo detector output signal will decrease in voltage. Will it also decrease in amperage?

4. Nov 17, 2017

### jbriggs444

It will remain constant in voltage. Why would you expect it to change?

5. Nov 17, 2017

### Samson4

I guess I misunderstood redshift. What if the photodetector is replaced with a material that is only transparent to light slightly below the laser's frequency. If the laser light is redshifted enough, would it transmit through the material during acceleration?

6. Nov 17, 2017

### jbriggs444

The light is emitted with no red shift. It is received at the photodetector with a red shift. To a first approximation, the red shift is proportional to distance traveled in the accelerating frame. Yes, a chromatic filter attached at the detector could pass the red-shifted light.

For a fixed ongoing proper acceleration and a Born-rigid structure the redshift at the detector is fixed and unchanging. [Born-rigid means that the proper length of the structure is constant]

7. Nov 17, 2017

### ZapperZ

Staff Emeritus
There is a flaw in the arguments given so far.

How are you sure that the band structure of the photocathode that make up the photodetector does not change due to the relativistic effects? It seems that the nature of the detector itself has been neglected.

Zz.

8. Nov 17, 2017

### Samson4

Would a material's transmission spectrum be expected to change as well?

9. Nov 17, 2017

### Staff: Mentor

Can we avoid this concern by analyzing the behavior of the detector using the momentarily comoving inertial frame in which the detector is momentarily at rest? In that frame the only relativistic effect will be the red shift of the incident laser light.

10. Nov 17, 2017

### ZapperZ

Staff Emeritus
But if you do that, then why should the detector see a red-shifted light, since it is in the same reference frame as the light source?

Zz.

11. Nov 17, 2017

### jbriggs444

It's not though. Classic rocket paradox.

12. Nov 17, 2017

### ZapperZ

Staff Emeritus
"It's not" what? That they are not in the same frame?

Remove the acceleration. If they are in some inertial frame, will the detector see a red-shifted light? If it does, how come I don't see a red-shifted light from the UV source that I'm using to emit photoelectrons?

Zz.

13. Nov 17, 2017

### jbriggs444

Correct. In an accelerating Born-rigid structure, the front and back ends are not at rest in a single inertial frame.

[In particular, the tangent inertial frame in which the source is at rest at the time of emission and the tangent inertial frame in which the detector is at rest at the time of reception do not coincide]
Now they are both at rest in a single inertial frame and there is no red shift.

14. Nov 17, 2017

### ZapperZ

Staff Emeritus
Then Nugatory can't get rid of the problem of the band structure of the material also being affected and thus, can't be ignore, which was my original point.

Zz.

15. Nov 17, 2017

### jbriggs444

Nonsense. The material is at rest in its tangent inertial rest frame in which the arriving light is red shifted.

16. Nov 17, 2017

### ZapperZ

Staff Emeritus
Huh?

The band structure along the direction of motion has to change (unless you want to turn off electromagnetic interaction in that direction as well). Is this in dispute?

Zz.

17. Nov 17, 2017

### jbriggs444

Perhaps I am not understanding you. There is no motion in an object's rest frame.

18. Nov 17, 2017

### ZapperZ

Staff Emeritus
Both the detector AND the laser are moving together with the same acceleration in the OP's post. The question isn't about the rest frame.

If I am in an inertial frame looking at both the laser and the photodetector, and I see the laser being red-shifted, then the photodetector must also be affected by the relativistic effects, resulting in a different band structure based on MY perspective.

Zz.

19. Nov 17, 2017

### Staff: Mentor

If we could remotely observe the instruments measuring clock rate on a spaceship traveling at speed near c relative to us, would we see dilated time? Alternatively, if we could ask a passenger on the spaceship to communicate how fast time passes for him, what would he say?

The answer in both cases, is that we would see or hear that time passes normally on that ship.

I think its a clever question. The spaceship passenger speaks into his microphone, "normal" We hear the message as nnnnnooooorrrrrrmmmmmaaaaalllll because of the red shift, but it does not morph to ssssslllllooooowwww.

20. Nov 17, 2017

### ZapperZ

Staff Emeritus
This is what the OP wrote, and the bold is mine:

So here is what I gather:

1. The frame the laser+detector is the same
2. This frame is accelerating and never an inertial frame
3. The OP wants to know if we simply look at the output of the detector, can we detect that it is accelerating?

So is the above correct or not?

Zz.