Light Clock query

harrylin

Right.

mananvpanchal

Ok, If there are two intensity detector at front of light source and end of light source in light source's frame. And same two detector in observer's frame.



Will the source's detectors measure equal intensity? And observer's detectors measure unequal intensity?

yuiop

Yes.

mananvpanchal

Thanks harrylin. Thanks yuiop.

A.T.

I don't understand the time dilation part:
http://en.wikipedia.org/wiki/Relativ...#Time_dilation

The picture with the caption "Time Dilation" seems to have nothing to do with time dilation.


http://en.wikipedia.org/wiki/File:AGN_Jet_Dilation.png

In fact it is called "Jet Dilation" and described as follows:
So the picture explains why a resting detector in front of the moving source will encounter more photons/time than a resting detector behind it. But what does this have to do with time dilation?

Time dilation of the moving source would mean that the source is emitting photons less frequently in the rest frame of the detectors, than in its own frame. But that factor alone would affect both detectors equally.

harrylin

Yes I agree, it looks as if there the Doppler frequency effect is confounded with time dilation. Moreover, I would say that the headlight or beaming effect and the forward frequency increase effect are two different aspects of the Doppler effect. While with "Doppler" we usuallly mean something to do with frequencies, the headlight effect is not even frequency dependent.

I gave a link to it as it shows that the OP refers to what is known as the headlight effect, and the intro gives a clear explanation - but as you noticed, that article needs important correction further on.

A.T.

Okay, but what about those points:

- Aside from the increased frequency, is the number of received photons/time also increased for an approaching source? This wouldn't make sense to me. The "higher frequency, with same amplitude" is the wave-model. While "same number of more energetic photons" is the particle-model.

- What effect does the time dilation of the moving source have on the light detected by stationary detectors? If the light source emits 1kW in its own frame, does it emit less than that in the frame where it moves?

harrylin

This is somewhat new to me as well, but my guess is that the same number of more energetic photons corresponds to what I earlier distinguished as the Doppler frequency effect; I would add to that the headlight effect, which, I think, distributes more of the photons forward, so that also slightly more photons/time should arrive at a certain surface in front of it. (But see next about time dilation).
ADDENDUM: also the number of photons/time increases, see post 29.
Yes I think so. The simplest example is radioactive particles that give off heat: at high speed their half life is much increased, so in the same time they should give off less heat.

PS: it looks to me that time dilation implies less emitted photons/time as well as lower frequency. I haven't worked that out. The Wikipedia article seems to suggests that the forward beaming effect is stronger than the time dilation effect, so that still more photons/time are beamed forward. Perhaps someone else knows this stuff?

A.T.

I don't want to conflate it with aberration, so lets say it is a laser beam pointing exactly forward on a moving source. Will a co-moving detector detect a different number of photons/time than a stationary one?

harrylin

Supposing that you mean from a moving source, then I can repeat my basic answer: Yes I think so.
The simplest example is radioactive particles: at high speed their half life is much increased, so in the same time less particles decay and for example less beta photons are emitted.

A.T.

Okay, that is the effect of time dilation, which would reduce the number of photons emitted in both directions by the same factor. So this should not contribute to the headlight effect.

But given two identical (in the source frame) laser beams from a moving source, pointing back and forward. Would stationary detectors at the back and front record different numbers of photons/time?

harrylin

In fact yes, and this can easily be seen. This is classical Doppler. Take two consecutive 10Hz wave trains of 1 s with 1 s interval:

S -_-_-_-_-_-_-_-_-_-_____________________-_-_-_-_-_-_-_-_-_-_____________________ D

As each following wave crest is formed closer to the detector in front, that detector receives each wave crest less than 1/10 of a second after the preceding one. But that is also true for the time interval to the next wave train: the first wave crest of the next wave train is formed much closer to the detector so that it will be received much less than 1 s after that of the preceding one. And the opposite is true for a detector at the back.