# Results of two equivalent scenarios in SR

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?

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.

• The animation seems to be raising more questions (at least for me). First of all yes, the source is focused light source. As for questions, 1. Why is there redshift and blueshift (in case of diffused light)? There should be similar result in each case since they are equivalent scenarios. If not, the observer can detect his own state of motion. 2. Why the need to tilt the light source? It feels like some sort of momentum cancellation needed to make the photon go is straight line. (Similar to rowing boat in running water?) – Gaurav Goyal Jan 31 '17 at 7:54
• We can imagine an observer who hides behind the second pinhole. If photon goes through the both pinholes, photon approached the observer at right angle in the observer's frame. If the source was in motion in the observer"s fame, it had to be released at oblique angle in the source's frame. That's why laser pointer had to be tilted back. Well, we can admit that system of pinholes was in motion and source was at rest. That means the pinholes were receading from the source and source sent a beam at the same oblique angle. Photon goes through the first pinhole and a bit later through the second – Albert Jan 31 '17 at 8:34
• I agree with the last part of your previous comment where you said 'pinholes were receding.......through the second.' I completely agree with that. – Gaurav Goyal Jan 31 '17 at 8:53
• Do you have any questions towards the first part where the pinholes are at rest and the source moves in their frame? – Albert Jan 31 '17 at 9:09
• As per for the first part, let us say that photon emitted at oblique angle covers $x$ distance parallel and $y$ distance normal to motion in frame of source (moving). In the frame of observer, only value of $x$ will be dilated and hence he will observe a different angle. True. ($y$ will not be dilated because motion is normal to it.) But to observe completely normal angle, $x$ has to 0 in source's frame also i.e. it has to emitted normally in source's frame too. – Gaurav Goyal Jan 31 '17 at 9:10

Gaurav Goyal is right. The result of the experiment depends on which of the reference systems is defined as to be at rest. This can be shown in another similar experiment: Two astronauts being in relative translational motion aim at a target with their laser guns. They hold their guns totally parallel. They each emit a short flash as they are flying by. Both laser flashes are moving in parallel and perpendicular to the relative motion of the astronauts. The target has the same vector of motion as the first astronaut. If the first astronaut and the target is defined to be at rest, both flashes hit the target. In contrast, if the second astronaut is defined to be at rest, both flashes miss the target. Both reference systems are not equivalent, because the propagation of light is regarded to be independent of the motion of the source. Therefore the two postulates of SRT are in conflict and cannot both be true.

The experiment is explained in an youtube-video called Einstein's final prank.

Paul E.

• Then why no one writes academic paper on it to put it before the world? – Gaurav Goyal Feb 4 '17 at 13:19
• It is not easy to succed in publishing such a paper because it is totally against mainstream. Who in physics wants to be blamed for a revolution that kills Einstein's former revolution? On VixrA you can find a paper that is dealing with the crucial aberation problem, titled: Testing Electrodynamics and Verification of the Results of Michelson and Morley by Laser Beam Aberration Measurement. Another paper will follow. – paule Feb 4 '17 at 14:42