This is not a homework question. It may appear as noob to most of you but SR is not my area of expertise and hence it seems very complex to me.
Question: Consider that there are two in-line pin hole separated by some distance. Both the pinholes at rest w.r.t to each other. There is a light source that moves relative to the pinholes. The relative movement is normal to line joining the pinholes.
Case 1: I consider that pinholes is the rest frame and light source as moving. In this configuration when the light source and one of the pinholes are overlapping, a pulse of light can pass through the first pinhole and strike the other pinhole, passing it too.
Case 2: Now I consider pinholes to be moving and light source to be rest frame. From the rest frame of light source, I see that a pulse of light passes through the first pinhole during the overlap. This light pulse will travel to other pinhole but will not be able to pass the second pinhole because the pinhole has already moved. (For this to happen, I will assume suitable relative velocity and separation between the pinholes so that the second pinhole has moved enough to avoid avoid the light ray)
So, you see that although these two are equivalent scenarios, their result is not same. Now I believe that I might be wrong because the relative motion and light are normal to each other and hence it does not qualify to be equivalent scenarios and so their results are not bound to be same. Is my thinking correct? Or is there any other explanation or am I missing something important here?
Answer
It is important to consider whether the source emits dispersed light or directed ray.
These examples can be considered either as the Transverse Doppler Effect or the or longitudinal Relativistic Doppler Effect (to be exact - a mix of longitudinal and transverse components).
The first example is the Transverse Doppler effect.
If the source emits diffused light, photon will pass through both holes in both cases. It's not a problem, and the photon will be red shifted after passing through second pinhole. Please note that if a photon approached observer at right angle it was released at oblique angle in source's frame.
If the source is laser pointer, the laser pointer has to be tilted backward to direction of motion. The angle depends on relative velocity of the source and can be calculated employing relativistic aberration formula. Otherwise a photon will not go through the both pinholes. Neither in first nor in the second example. For example, if a laser pointer is directed at right angle to direction of it's motion, photon will not go through the holes. But, if laser pointer is tilted backward, the photon will pass through the both pinholes and it will be red shifted.
You can imagine a tube that connects pinholes.
Very simple animation in youtube. Maybe it helps to visualize.
https://www.youtube.com/watch?v=hnphFr2Iai4
https://www.youtube.com/watch?v=5-AAC4pemDI
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