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In figure 3-7, I added little icons illustrating what the observer "sees" in terms of redshift or blueshift. Are these little icons helpful, or do they make the diagram too busy? Prokaryotic Caspase Homolog ( talk) 08:21, 28 September 2018 (UTC)
Yes, they are very helpful because they have been stolen from my diagram. I know how to make diagrams clear and simple. However, the icons are too small. Could you please to make it a bit larger? I am going to use your diagram against spacetime concept and relativity in Einstein's incarnation, so that would be fine for my readers to make it easy to understand visually. That will be not a problem to explain them, that observer should move himself and displacement of the source is due to aberration, exactly as in the case of rotation. Could you also please to add the diagram into the section Transverse Doppler Effect in the article Relativistic Doppler effect? It lacks one. Yours most sincerely, Albert Gartinger ( talk) 08:49, 28 September 2018 (UTC)
I think we can also place a question at https://physics.stackexchange.com/ which diagram is better, yours or mine. It has hundreds, if not thousands readers. They can also have a look at this polemics. Sadly, I am too busy today and must leave Albert Gartinger ( talk) 09:38, 28 September 2018 (UTC) SVG! That's good idea, thank you. I have missed it. Albert Gartinger ( talk) 09:45, 28 September 2018 (UTC)
Your interpretation of Case 1 is incorrect. If we think in terms of transverse doppler effect, aberration or light time correction cannot have any effect on frequency shift. Only dilation of observer's or source's clock contribute into the frequency shift, if we think in terms of that frame, in which the effect is transverse.
Theoretically, the observer can always know the actual direction to the source, because there is no aberration of forces. http://www.mathpages.com/home/kmath562/kmath562.htm
It's hard for me to understand if you are serious. This is an elementary problem! The result of the measuremen depends on how you conduct it, that is, on what you think about your movement. Let's think within the framework of the transverse effect, it means that YOU move in the frame of the source and at the moment of reception the source is at closest approach to you. If you consider yourself moving, then at this moment you keep your head or telescope forward in the direction of movement. The angle of inclination corresponds to the speed that you attributed to youself (the angle of relativistic aberration). The frequency of the source becomes gamma times more blue. You treat this phenomenon as slowing down your own clock, so the clock at rest is ticking faster. It is the same explanation for the both rotational and inertial motion. This is a purely Transverse effect.
I have already written, that this is a question of interpretation. Of course, the same effect can be attributed to the presence of the longitudinal component, should you think that you are at rest. But we are talking about the transverse effect and the chapter is about transverse effect. https://www.researchgate.net/publication/304792446_The_Problem_of_Slow-witted_Aliens_or_The_Transverse_Doppler_Effect_Simply_Explained Albert Gartinger ( talk) 12:35, 29 September 2018 (UTC)
B, as the light source, has a trivially simple view of the system compared with A, considered as the receiver.
Prokaryotic Caspase Homolog ( talk) 03:46, 30 September 2018 (UTC)
This is exactly what I have pictured on my diagram. This is a purely transverse effect, as it should be. My diagram shows a transverse effect for both cases, frames of the receiver and frame of the source. Your diagram depicts transverse effect in the frame of the receiver and longitudinal in the frame of the receiver. It is not good, to say the least.
The existing in the article explanation in frame B is nowhere suitable. One might think that the change in frequency measured by the spectroscope is due to what B observes. It is very confusing, that the source highlights the receiver by green monochromatic light and in the meantime by violet radiation . It's unclear how an electric light bulb can observe something. It simply shines. Well, and if the source went to sleep?
Everything is simple. Detector's clock slows down, so processes around him run faster, radiation turns violet. Albert Gartinger ( talk) 06:28, 30 September 2018 (UTC)
According to the receiver, there is no longitudinal component either, if the receiver considers himself moving. The co-moving with the receiver observer understands, that actually path of the photon is perpendicular to his path. He understands, that displacement of the source is apparent effect, a.k.a aberration of light. Albert Gartinger ( talk) 08:01, 30 September 2018 (UTC)
Think about transversely moving mirror. The mirror is a moving observer. A source (laser pointer) in the origin emits green monochromatic light straight up. The light approaches the mirror at relativistic aberration angle. At the reception, when the source crosses Y axis, the light blueshifts, since mirror’s clock runs slower. The mirror reflects the light backward at the same angle as It had once arrived, it travels back into the origin.
Now the mirror turns into is moving source. Since it move in the frame of the laser pointer, its clock dilates, so the light redshifts again and comes back into the origin at the same green color.
There is no even smell of "A is slower than B, B is slower than A" Albert Gartinger ( talk) 08:11, 30 September 2018 (UTC)
Another important point about your diagram A. Why did you draw a slanted beam? The ray, as constructed from individual photons, does not undergo aberration. It remains perpendicular in any frame, either "moving" or "stationary". The moving detector crosses the ray and a single light pulse appears coming from the front. But the whole RAY remains at right angle direction of motion of the receiver or the source.
Albert Gartinger ( talk) 13:23, 30 September 2018 (UTC)