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== Updated Transverse Doppler effect diagram ==

[[File:Transverse Doppler Effect complete.jpg|thumb|Transverse Doppler Effect diagrams in different frames]]

While I work on animation, I did my best to improve the static picture. 

1)	I have added “bulbs” with arrows. These arrows demonstrate direction of emission or perception of light pulse. Due to aberration moving source emits “transverse” light pulse backward, moving observer sees transverse light pulse coming from the front,

2)	I have added “apparent” positions of the source for all cases.

3)	I tried to vividly demonstrate the identity of rotating and inertial observers, the same interpretation of frequency shifts, the same amounts of frequency shift.

Sure, the diagram must be followed by proper explanation in the article.

This analysis is solidly backed by the primary and secondary sources: A. Einstein 1905 article (&7), Kevin S. Brown (Doppler effect at Mathpages) and a number of papers considering Mossbauer rotor experiments, papers and articles on relativistic aberration.
Animated will look like that: Observer with laser pointer in the origin emits green light pulse straight up, mirror movies parallel to the x axis, light pulse hits mirror, mirror measures blueshift (blue flash), light pulse comes back to origin (redshifts) and appears to the observer at the same green color.

I believe that diagram makes clear, that:

1)	Angle of emission always has corresponding angle of reception; these angles cannot be arbitrary. So, a reference frame is not a private property of observer but mutual. If one is “at rest”, the other will definitely be “moving”.

2)	Reciprocal time dilation is two mixed "by force" special cases, when each observer is “at rest” (looks at right angle and one - way speed of light in “his” frame is isotropic).  Sure, it is nonsense.

If there is will be no objection, in several days I will replace the diagram.[[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 08:01, 4 October 2018 (UTC)

: I object. You continue to illustrate the distinction between scenarios (a) and (b) as between moving observer versus moving source. The distinction rather is between the receiver and source at their closest points to each other, versus the receiver seeing the source as closest. In addition, you continue to mix elements of multiple frames in a single diagram. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 12:56, 4 October 2018 (UTC)
:: Of course, we are in no hurry. I think your arguments are clear in the text. Before starting any dispute resolutions, could you please clarify exactly which diagram you think is appropriate? That which is now or do you have some kind of improved version? What do you think of the animation scenario that I have proposed?[[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 13:58, 4 October 2018 (UTC)
::: The principle of relativity dictates that for a given physical scenario, it makes absolutely no difference whether one considers the scenario from the frame of the source or the frame of the receiver. Your diagram misleads the viewer into thinking that choice of frame (moving observer versus moving source) makes a difference in the outcome of otherwise identical physical scenarios. Choice of frame cannot make any such difference. The reason why (a) results in the receiver observing a blueshift, while (b) results in the receiver observing a redshift, is that the physical scenarios are different in the two diagrams. Your illustration is therefore misleading and unacceptable. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 16:45, 4 October 2018 (UTC)
:::: Dear Sir,

::::You have already expressed several different versions why my diagram “misleads the viewer”. In my opinion, it is your    diagram misleads the viewer, so we have some sort of conflict. I am ready to go far, far, far away to defend my diagram. I will be most thankful for reducing our dialogue to discussing exact features of the diagram instead of exchange of philosophical interpretations. Yes, it is clear, that these diagrams describe different physical scenarios (light emitted at closest approach redshifts, light received of closest approach blueshifts), different angles of perception. In regard of the case a - you mentioned yourself that it is “best analyzed from the frame of receiver”, so I feel completely lost and confused. I have already mentioned that I wish to start dispute resolution procedures and to involve as many people as possible inside or outside Wikipedia. If you think, that this diagram is misleading, could you please to provide yours. I haven’t got any answer yet, which diagram according to you is “acceptable“, so will you please:

::::1)	To make clear, whether you wish to leave existing diagram and explanation “as it is” and to reject mine;

::::2)	Should you wish to provide your improved “acceptable” design instead of mine, 

::::3)	What is your opinion towards my scenario of dynamic presentation?

::::Looking forward to your reply, [[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 18:04, 4 October 2018 (UTC)

::::: {{rto|Albert Gartinger}}
:::::#regarding your statement "''I am ready to go far, far, far away to defend my diagram''": note that without a [[wp:reliable sources|reliable]] [[wp:secondary source]] in which the diagram appears, together with the text of the article, there is no way that it will be taken on board in Wikipedia. The farther you go—without such a source—the more time you will waste, mostly your time, but as soon as editors see that you are wasting ''their'' time, someone will take action to stop you. As you already are on final warning level for talk page abuse, not much is needed to get you blocked.
:::::#regarding your statement "''...to involve as many people as possible inside '''or outside''' Wikipedia...''": be aware of [[wp:canvassing]] with people inside Wikipedia, and, lacking internal consensus, new people from outside Wikipedia are likely to be regarded as [[wp:meat puppets]].
::::: - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 18:56, 4 October 2018 (UTC)
:::::: [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]), thank you very much for you note, I will take it into account. I mentioned [[wp:reliable sources|reliable]] [[wp:secondary source]] behind my analysis. they may seem unreliable to you, but they may seem reliable to others. I am looking for exact answer from another Wikipedia editor towards design of my diagram to start dispute resolutions [[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 19:08, 4 October 2018 (UTC)
::::::: Before you start that, it would be a good idea to have a source that clearly, directly ''and visually'' supports the diagram itself. Good luck. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 19:18, 4 October 2018 (UTC)
:::::::: Dear [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]), thank you very much for your kind words!!! Sadly, my interlocutor only complains that something wrong is with the diagram, but doesn't want to give exact answer exactly what. I don't even understand what exactly scenario is wrong and why and how this scenario should look like.  [[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 19:27, 4 October 2018 (UTC)
::::::::: Your interlocutor is under no obligation to explain anything here. On the contrary, such explanations are off-topic, as you should know by now. The responsibility ''for providing citations'' is entirely yours—see [[wp:BURDEN]]. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 19:33, 4 October 2018 (UTC)
== Citations in support of my diagram ==

Should someone wishes I  to provide quotes, in support of scenario (a) I would like to quote celebrated A. Einstein’s work “On the Electrodynamic of Moving Bodies”, &7, Theory of Doppler Principle and Aberration:

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

''From the equation for  <math>\omega</math> it follows that if an observer is moving with velocity <math>v</math> relatively to an infinitely distant source of light of frequency <math>\nu</math>, in such a way that the connecting line “source-observer” makes the angle <math>\phi</math> with the velocity of the observer referred to a system of co-ordinates which is at rest relatively to the source of light, the frequency <math>\nu'</math> of the light perceived by the observer is given by the equation''

<math>\nu'=\nu \frac {1-cos \phi \cdot v/c}{\sqrt {1-v^2/c^2}}</math>

Mr. Einstein clearly speaks that "'''an observer is moving''' with velocity <math>v</math>" and that "with the velocity of the observer referred '''to a system of co-ordinates which is at rest''' relatively to the source of light"

That exactly what my diagram case a demonstrates. It is clear, that at the moment when "the connecting line “source-observer” makes the angle <math>\pi/2</math> with the velocity of the observer" makes angle that formula reduces to:

<math>\nu'=\frac {\nu}{\sqrt {1-v^2/c^2}}</math>

That exactly what my diagram demonstrates. 
Sure, I have plenty of sources in support of any other scenario. [[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 20:29, 4 October 2018 (UTC)

I believe that it would be very fair to perpetuate the great teachings of Mr. Einstein in my diagram [[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 20:41, 4 October 2018 (UTC)

: Since there doesn't seem to be any means of getting a permalink to the '''current''' version of any figure, I am temporarily using [https://drive.google.com/file/d/1RcV2BgBAoseqLhVlUgVjhBceEXIoxLyI/view a copy of your figure] from my drive account. I will switch the link to an permanent archive link on Commons when/if one becomes available.
: The question is not whether Albert Einstein understood the theory of relativity. The question is whether [https://drive.google.com/file/d/1RcV2BgBAoseqLhVlUgVjhBceEXIoxLyI/view your figure as of 7:54, 4 October 2018] provides a clear and understandable interpretation of the scenarios discussed in the text.
: Unfortunately, as I have '''repeatedly pointed out''', the figures that you have presented to date are totally baffling because
# They mix up elements of multiple frames in a single image
# They imply that shifting frames from moving observer to moving source makes all the difference as to whether the observer sees blueshift or redshift.
: Consider [https://drive.google.com/file/d/1RcV2BgBAoseqLhVlUgVjhBceEXIoxLyI/view scenario (a) of your figure.] 
:* In this one figure, you show the observer as moving in the frame of the source. With a bubble arrow around the source, you show light being emitted from the source perpendicular to the path of the observer. Likewise, with the squiggly green arrow, you show light being emitted from the source perpendicular to the path of the observer. 
:* On the other hand, you illustrate the apparent position of the source from the viewpoint of the observer, and you have a bubble arrow pointing ''to'' the apparent position of the source.
:* In other words, you have mixed up elements from multiple frames into a single diagram.
:* Your legend indicates that "the arrow indicates direction of the light pulse". In some situations, you use bubble arrows to indicate the direction ''of the light,'' in other situations, you use bubble arrows to indicate directions ''to the light.'' You are inconsistent in your use of the bubble arrows.
: Consider [https://drive.google.com/file/d/1RcV2BgBAoseqLhVlUgVjhBceEXIoxLyI/view scenario (b) of your figure.] 
:* You label this scenario as "Moving source" to distinguish it from scenario (a), "Moving observer". As I have indicated above, whether an observer sees the light as blueshifted or redshifted ''cannot depend on the frame in which the scenario is analyzed.'' Your figure is therefore ''totally misleading.''
:* You use bubble arrows inconsistently. From the apparent position of the source as seen by the observer, you have a bubble arrow shooting off to the left, heading off to nowhere. From the observer, you have a bubble arrow pointing ''to the apparent position of the source.''
: The figures that you have presented to date are all completely unacceptable because of these confusing elements. Until you learn how to present things clearly, you are wasting everybody's time here. Any attempt by you to replace the existing figure in the article with your version will be immediately reverted. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 09:33, 5 October 2018 (UTC)
:: Dear [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]), thank you very much for your message and your valuable opinion. I will post on your talk page some other secondary sources in regard of the diagram. Surely I do not intend to go into edit wars, I wish to seek consensus. I can recommend you to learn a little bit more about the aberration of light.  Light emitted in the frame of the source (Case a) at right angle will approach receiver at oblique angle  <math>\sin \alpha = v/c </math>. Yes, this theory is quite difficult and diagrams my appear confusing, they require some mental efforts indeed. Let's postpone our further talks until dynamic animation is ready. Again, could you please to make it clear, do you wish to leave the current figure with moving sources? [[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 10:47, 5 October 2018 (UTC)
:: I have offered compromise to my interlocutor on his page - adjust this figure according to his understanding, just to draw two TRANSVERSE effects - in the rest frame of the observer and in the rest frame of the source.[[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 12:05, 5 October 2018 (UTC)
== Would this be acceptable to you? ==

{{ping|Albert Gartinger}} I have incorporated various design elements that you favor into a new version of Figure 3-7, while omitting the confusing mixed-frame elements that I have strongly objected to. I have also added an extensive note and supplementary figure to discuss how the ease of analyzing a relativistic scenario often depends on the choice of frame. Figures should have a minimum of wording, since English wording tends to discourage a figure's use in non-English Wikis. 
<hr/> 
{{ping|Albert Gartinger}} In your last contribution, you accidentally wrote '''&lt;math>\sin \alpha = v/c &lt;\math>''' with an incorrectly oriented slash in the "\math". This resulted in a parsing error that required 15 minutes for me to diagnose and fix. Please be more careful next time. 
<hr/>
[[File:Transverse Doppler effect scenarios 2.svg|thumb|300px|Figure 3-7. Transverse Doppler effect scenarios]]
Suppose that a source and a receiver, both approaching each other in uniform inertial motion along non-intersecting lines, are at their closest approach to each other. It would appear that the classical analysis predicts that the receiver detects no Doppler shift. Due to subtleties in the analysis, that expectation is not necessarily true. Nevertheless, when appropriately defined, transverse Doppler shift is a relativistic effect that has no classical analog. The subtleties are these:<ref name="Morin2008">{{cite book |last1=Morin |first1=David |title=Introduction to Classical Mechanics: With Problems and Solutions |date=2008 |publisher=Cambridge University Press |isbn=978-0-521-87622-3}}</ref>{{rp|541–543}}
{{plainlist|
* Fig. 3-7a. What is the frequency measurement when the receiver is geometrically at its closest approach to the source? This scenario is most easily analyzed from the frame S' of the source.<ref group=note>
The ease of analyzing a relativistic scenario often depends on the frame in which one chooses to perform the analysis. '''[[:File:Transverse Doppler effect scenarios 3.svg|In this linked image]],''' we present alternative views of the transverse Doppler shift scenario where source and receiver are at their closest approach to each other. 

(left) If we analyze the scenario in the frame of the receiver, we find that the analysis is more complicated than it should be. The apparent position of a celestial object is displaced from its true position (or geometric position) because of the object's motion during the time it takes its light to reach an observer. The source would be time-dilated relative to the receiver, but the redshift implied by this time dilation would be offset by a blueshift due to the longitudinal component of the relative motion between the receiver and the apparent position of the source.

(right) It is much easier if, instead, we analyze the scenario from the frame of the source. An observer situated at the source knows, from the problem statement, that the receiver is at its closest point to him. That means that the receiver has no longitudinal component of motion to complicate the analysis. Since the receiver's clocks are time-dilated relative to the source, the light that the receiver receives is therefore blue-shifted by a factor of ''gamma.''</ref>
* Fig. 3-7b. What is the frequency measurement when the receiver ''sees'' the source as being closest to it? This scenario is most easily analyzed from the frame S of the receiver.

Two other scenarios are commonly examined in discussions of transverse Doppler shift:
* Fig. 3-7c. If the receiver is moving in a circle around the source, what frequency does the receiver measure?
* Fig. 3-7d. If the source is moving in a circle around the receiver, what frequency does the receiver measure?
}}<!--end plainlist-->
In scenario (a), the point of closest approach is frame-independent and represents the moment where there is no change in distance versus time  (i.e. dr/dt&nbsp;=&nbsp;0 where r is the distance between receiver and source) and hence no longitudinal Doppler shift. The source observes the receiver as being illuminated by light of frequency ''f{{'}}'', but also observes the receiver as having a time-dilated clock. In frame&nbsp;S, the receiver is therefore illuminated by [[blueshifted]] light of frequency
:<math>f = f' \gamma = f' / \sqrt {  1 - \beta ^2  }</math>

In scenario (b) the illustration shows the receiver being illuminated by light from when the source was closest to the receiver, even though the source has moved on. Because the source's clocks are time dilated as measured in frame S, and since dr/dt was equal to zero at this point, the light from the source, emitted from this closest point, is [[redshifted]] with frequency
:<math>f = f' / \gamma = f' \sqrt { 1 - \beta ^2  }</math>

Scenarios (c) and (d) can be analyzed by simple time dilation arguments. In (c), the receiver observes light from the source as being blueshifted by a factor of <math>\gamma</math>, and in (d), the light is redshifted. The only seeming complication is that the orbiting objects are in accelerated motion. However, if an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation. (The converse, however, is not true.)<ref name="Morin2008"/>{{rp|541–543}} Most reports of transverse Doppler shift refer to the effect as a redshift and analyze the effect in terms of scenarios (b) or (d).<ref group=note>Not all experiments characterize the effect in terms of a redshift. For example, the [[Ives–Stilwell experiment#Relativistic Doppler effect|Kündig experiment]] was set up to measure transverse blueshift using a Mössbauer source setup at the center of a centrifuge rotor and an absorber at the rim.</ref>
{{reflist-talk|group=note|title=Notes}}
{{reflist-talk}}


In the future I will try to be more careful writing formulas. As far as I know, you have created many beautiful pictures for Wikipeda readers. They must be very grateful to you for your time and your contributions! Yes, your figure is simple, not too crowded. Very nice, I highly appreciate it!
[[User:Albert Gartinger|Albert Gartinger]] ([[User talk:Albert Gartinger|talk]]) 08:22, 6 October 2018 (UTC)

:Thanks! There is a bug in the SVG rendering of the squiggly ray in (c). I do not know if the bug is from the WikiMedia rendering engine, or from Inkscape. I will need to spend time fixing this bug. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 11:15, 6 October 2018 (UTC)
: I worked out a solution to the rendering bug, then removed an element that the [https://validator.w3.org W3C Validator] found objectionable. [[:File:Transverse Doppler effect scenarios 3.svg|The image at this link]] passed W3C validation without any additional changes. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 13:05, 6 October 2018 (UTC)
: I replaced the image and text in main article space with the revised version discussed above. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 13:14, 6 October 2018 (UTC)
: Additional figure tweaks, adopted more of AG's suggestions. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 01:17, 7 October 2018 (UTC)

: Both rendering bugs which exasperated me (misoriented arrowheads and incorrect proportions of rotated bitmap images) are known issue with '''[[librsvg]],''' the SVG rendering library used by WikiMedia. [[User:Prokaryotic Caspase Homolog|Prokaryotic Caspase Homolog]] ([[User talk:Prokaryotic Caspase Homolog|talk]]) 20:36, 8 October 2018 (UTC)