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Talk:Relativistic Doppler effect

Untitled
This article makes no sense. Just to start, it could be better explained in what way speed is a "rotation". Nickptar 21:07, 16 Apr 2005 (UTC)

Moreover, the discussion here doesn't really belong in this page. It should probably be in special relativity if anywhere. 67.165.197.242 06:58, 23 Apr 2005 (UTC)

The basic equation seems to be mis-labled. As the velocity approaches c, the observed wavelength goes to infinity, *not* the frequency, or the convention that recession is positive velocity is mis-stated.

 * I agree that this presentation is weird; it seems to have been made up by someone with a particular background. The standard way of presenting Doppler equations presents the ratio between measured frequencies, as can also be found in the 1905 paper of Einstein -- html link in Special relativity.

Harald88 22:08, 9 January 2006 (UTC)

Hi guys, I agree with your comments, and I revised the article. Hope you like it. Yevgeny Kats 05:46, 23 January 2006 (UTC)

 * IMO it looks better although you made several new unwarrented claims. Anyway, thanks for cleaning up the mess, it now has a much better look. Harald88 20:43, 23 January 2006 (UTC)

 * PS Your simple derivation to illustrate the connection to true Doppler is just what I had in mind to do myself. Thanks again! Harald88 12:14, 24 January 2006 (UTC)

 * Thanks, Harald, but why did you revert my correction of the centrifugal force article? What they have there now is a complete nonsense (based on someone's misunderstanding of the Principia or something). (Sorry, I don't feel like contributing to their 100-page talk page :) Yevgeny Kats 04:09, 25 January 2006 (UTC)

 * Sorry, I had not noticed that the intro had already been messed up; I had not reverted far enough (problem with my watchlist). Harald88 11:13, 26 January 2006 (UTC)

Formulas
Comparison of the formulas on this page with those on Doppler effect is very confusing. On this page, fo (letter o) stands for the frequency observed, but on the other page, f0 (number 0) stands for the actual frequency (i.e. frequency of the source). These should be clarified/reconciled.

 * No, it doesn't. The formulas are consistent. Moroder 02:31, 8 December 2006 (UTC)

Incorrect Plots
--TxAlien 21:45, 10 December 2006 (UTC)--TxAlien 21:45, 10 December 2006 (UTC)

The plots are incorrect because the follow the first set of formulas instead of the second. The error is easy to tell since the plots show an INCORRECT redshift at 90 degrees instead of the correct blueshift. Note to the authors: could you please redo the plots for the correct formulas:

 * $$f_\mathrm{detected} = f_\mathrm{rest}{\left(1 - \frac{v}{c}\ cos\phi\right)/\sqrt{1 - \frac{v^2}{c^2}} }$$
 * as deduced by Einstein (1905).

Thank you Moroder 16:36, 6 December 2006 (UTC)

 * I just added a note explaining that the two plots represent the wrong formula, the plots need to be regenerated in order to represent the right formula:

 * $$f_\mathrm{detected} = f_\mathrm{rest}{\left(1 - \frac{v}{c}\ cos\phi\right)/\sqrt{1 - \frac{v^2}{c^2}} }$$

Moroder 16:05, 7 December 2006 (UTC)
 * Well, according to your formulas, unstable particles in cyclotron should live shorter then the same particles at rest. But it is wrong.. so, I will restore the old version of the article.--TxAlien 18:10, 7 December 2006 (UTC)

 * These are not my formulas, they belong to Einstein. See here . And your plots, pretty as they are are still dead wrong. Please read the Einstein paper (paragraph 7), perhaps you will understand why. Moroder 19:38, 7 December 2006 (UTC)

 * In it says:
 * $$\nu ' = \nu \frac{1-\cos \phi \cdot v/c}{\sqrt{1 - v^2/c^2}}. $$
 * $$\cos \phi '= \frac{\cos \phi - v/c}{1 - \cos \phi \cdot v/c} $$
 * or
 * $$\nu ' = \nu \frac{\sqrt{1 - v^2/c^2}}{1 + \cos \phi ' \cdot v/c} $$
 * We talk about that angle $$\phi ' \, $$ in this article . And it was used in the images.--TxAlien 22:57, 7 December 2006 (UTC)
 * $$\cos \phi '= \frac{\cos \phi - v/c}{1 - \cos \phi \cdot v/c} $$
 * or
 * $$\nu ' = \nu \frac{\sqrt{1 - v^2/c^2}}{1 + \cos \phi ' \cdot v/c} $$
 * We talk about that angle $$\phi ' \, $$ in this article . And it was used in the images.--TxAlien 22:57, 7 December 2006 (UTC)

 * This is what I've been trying to tell you for the last 3 posts. Only the first formula for the Doppler effect shows up in the Einstein paper, the second one (the one that you deduce from the first one using the aberration transformation) does not. Wonder why? If you look at the RHS you can see that it mixes variables from the source and the observer frame (the frequency from one frame and the angle from the other one). This is a "no-no" in relativity. Frankly, the formula that you deduced has no place in wiki. It simply confuses things. So now, would you please regenerate the plots for the original Einstein formula? :-) —The preceding unsigned comment was added by Moroder (talk • contribs) 00:50, 8 December 2006 (UTC).

 * Dear Moroder, your claim that the formula
 * $$f_o = \frac{f_s}{\gamma\left(1+\frac{v\cos\theta_o}{c}\right)}$$
 * is problematic because the RHS "mixes variables from the source and the observer frame" doesn't make any sense. The whole purpose of this formula is to convert quantities from one frame to the other. Would you be happier, for example, if I rearranged the formula as
 * $$\gamma\left(1+\frac{v\cos\theta_o}{c}\right) f_o = f_s$$
 * Now it doesn't mix quantities from different frames in the same side of the equation, but it's still exactly the same formula!! Yevgeny Kats 01:25, 8 December 2006 (UTC)

 * Yes Yevgeny, I would be happy, this is the formula that I kept suggesting for my last 3 posts. Now, can you convince User:TxAlien to regenerate his colored plots? They show an incorrect red shift at 90 degrees, when in reality the Ives-Stilwell experiment shows a blue shift. We have come full circle to my original complaint, the colored plots are WRONG. Moroder 01:59, 8 December 2006 (UTC)

 * Dear Moroder, please read the article and my response above more carefully. The formula that makes you happy (that I wrote above, which is equivalent to the first formula in the article) is very different from the second formula in the article, which is
 * :$$f_o = \gamma\left(1-\frac{v\cos\theta_s}{c}\right)f_s$$
 * Both formulas are correct, and there is no reason to change anything in the text of the article. Yevgeny Kats 05:51, 8 December 2006 (UTC)

Dang, I missed what you wrote. One more time, the correct formula is :

 * $$f_\mathrm{observed} = f_\mathrm{source}{\left(1 - \frac{v}{c}\ cos\phi\right)/\sqrt{1 - \frac{v^2}{c^2}} }$$
 * as deduced by Einstein (1905). This is what Einstein wrote, this is what is used in the Ives-Stilwell experiment. This is exactly what Einstein wrote:
 * $$\nu ' = \nu \frac{1-\cos \phi \cdot v/c}{\sqrt{1 - v^2/c^2}}. $$

Why not use his exact formula? This is also the formula that should drive the correct(ed) plots.Moroder 06:45, 8 December 2006 (UTC)

 * Both formulas that appear in the article are correct. You can use either of them to convert between the emitted frequency and the received frequency and vice versa. Actually, the analogs of both of them appear at the bottom of p. 6 of your reference . Which formula to use depends on what angle you know: whether you know the direction of the velocity in the frame of the observer ($$\theta\,$$ in that reference, our $$\theta_o\,$$) or the direction of the velocity in the frame of the source ($$\phi\,$$ in that reference, our $$\theta_s\,$$). If you're an astronomer, it would be more natural to you to know the angle $$\theta\,$$, i.e. $$\theta_o\,$$, and so use the first formula in our article. In the Ives-Stilwell experiment, it's also more natural to use the angle $$\theta\,$$, and it is indeed what is used there in the same reference of yours - see top of p. 7. (The signs are different here and there because we define angle = 0 when the two are moving away from each other, while they define in the opposite way in the case of $$\theta\,$$ - see picture on p. 6). Yevgeny Kats 16:56, 8 December 2006 (UTC)

 * On the other hand, I agree with Moroder that the plots are incorrect. The article uses the convention that v is positive when the source is moving away from the observer (angle 0), and then there should be a redshift, while the plots show a blueshift. Another problem with the plots is that they don't say whether the angle is measured in the frame of the observer or in the frame of the source. Therefore, I remove the plots from the article for now. Yevgeny Kats 05:51, 8 December 2006 (UTC)
 * If this new plot is good enough to the article what should I change then? --TxAlien 20:49, 10 December 2006 (UTC)

 * Something is still not quite right. The way I know it is that at 90 degrees you should get a blueshift that increases as v/c ->1. In the diagram, the 90 degree line is imbedded in a yellow domain, coresponding to f_o/f_s=1. This cannot be right. Moroder 07:53, 11 December 2006 (UTC)

 * I see the error, you insist on not plotting the formula $$\nu ' = \nu \frac{1-\cos \phi \cdot v/c}{\sqrt{1 - v^2/c^2}}. $$ . Why? Moroder 16:18, 11 December 2006 (UTC)

 * What do these diagrams represent? I guess Diagram 1 corresponds to the first formula in the article, and then it looks fine. But I don't understand what Diagram 2 represents: the frequency is independent of the velocity when the angle is 90; the frequency approaches $$f_s/2$$ for large velocities when the angle is 0 - what is this? Yevgeny Kats 21:16, 10 December 2006 (UTC)
 * Yes, the first diagram represents the first formula. And second plot represents the same formula without $$\gamma \;$$. Actually it is classic case. So, I thought that it will be useful to see the difference. You are welcome to add any comments, and I can change the plots if it is necessarily. Or, we can forget about those plots if you think so.--TxAlien 21:45, 10 December 2006 (UTC)
 * The "classical" case isn't something universal because the classical result also depends on the assumption of whether the medium in which the light propagates is moving with the observer, with the source, or at a completely different velocity. I don't think that simply ingnoring the factor of $$\gamma$$ has any universal "classical" meaning. So I would suggest not including the classical case. On the other hand, I would suggest including a second plot in terms of the angle $$\theta_s$$ (i.e., the second formula in the article). Yevgeny Kats 16:29, 11 December 2006 (UTC)
 * Agreed Moroder 16:39, 11 December 2006 (UTC)
 * Outrageous. Lorentz contraction is not reflected in diagram 2, which is totally misleading. SJGooch (talk) 15:11, 11 December 2010 (UTC)

Well, it is not universal classic case, of course, but the simplest one. On the other hand the second formula describes not easy case. It should have a better explanatory. It might be a short way to show how these formulas were found. Something like this:
 * assume the source of waves moves along the trajectory $$(ct(s),\vec{r}(s)) \;$$, where $$s \;$$ is the proper time of that object and
 * $$\dfrac{d}{ds}(ct(s),\vec{r}(s)) =

\left( c\dfrac{dt}{ds},\dfrac{d \vec{r}}{ds}\right) = \gamma \left( c,\vec{v}\right) $$
 * where $$\left( c\dfrac{dt}{ds},\dfrac{d \vec{r}}{ds}\right) $$ is velocity four-vector. Due to the finite velocity of light, the frequency at the point of observation $$(T,0) \;$$ is determined by state of source at the earlier time $$t(s) = T-r(s)/c \;$$.
 * Differentiating this relation with respect to $$s \;$$, we get
 * $$\dfrac{\omega _{s}}{\omega _{o}} = \dfrac{dT}{ds} =

\dfrac{dt}{ds} + \dfrac{1}{cr} \left( \vec{r}\cdot \dfrac{d \vec{r}}{ds}\right) = \gamma \left( 1 + \dfrac{1}{cr}\left( \vec{r}\cdot \vec{v}\right) \right) = \gamma \left( 1 + \dfrac{v}{c}\cos \varphi_{o}\right) $$
 * or
 * $$\omega _{o} = \omega _{s}\dfrac{1}{\gamma \left( 1+\dfrac{v}{c}\cos \varphi_{o}\right) }$$
 * where $$\varphi _{o}$$ is angle, relative to the direction from the observer to the source at the time when the light is emitted.
 * Differentiating relation $$t = T(s_{o})-r(s_{o})/c \;$$ (as it seen from the reference of the source) with respect to the proper time $$s_{o} \;$$ of the observer, we get
 * $$\omega _{o} = \omega _{s}\gamma \left( 1-\dfrac{v}{c}\cos \varphi_{s}\right) $$
 * where angle $$\varphi _{s}$$ is measured in the reference frame of the source at the time when the light is received by the observer. It is not the easiest way, but it helps to find out how moving objects looks like in theory of relativity.
 * Anyway, the new image will be ready in a few minutes.--TxAlien 03:55, 12 December 2006 (UTC)

 * The images are clearly still wrong.Is this because you insist in plotting the first formula instead of the second one? Moroder 07:44, 12 December 2006 (UTC)
 * Diagram 1 is the first formula and Diagram 2 is the second one. Can you tell me exactly what you think is wrong whith these images?--TxAlien 01:29, 13 December 2006 (UTC)

 * I've been telling you the same thing over and over: at 90 degrees you should see a clear blue shift in formula 2 because of $$\omega _{o} = \omega _{s}\gamma \, $$. Your picture no 2 shows yellow, which is incorrect. Moroder 01:49, 13 December 2006 (UTC)
 * I did not expect this kind of misunderstanding. This image might help
 * http://img242.imageshack.us/img242/3837/dopplerextk9.jpg --TxAlien 02:53, 13 December 2006 (UTC)

 * Yes, it is a surface F(x,y)=F(v/c, cos(phi)). Somehow your plot misses the fact that at cos(phi)=0 you need to get a blue curve embedded in the surface, actually a narrow blue band on both sides of the curve. I don't know how you are getting the yellow but I do know it is wrong.I think that there is a clear error in your second surface plot, for example, at 90 degrees all the surface points should be above 1 (at altitude $$ \gamma\,$$). Your plot shows the points in the 0.25 altitude range which is clearly wrong. I think that you are continuing to plot ::$$\omega _{o} = \omega _{s}\dfrac{1}{\gamma \left( 1+\dfrac{v}{c}\cos \varphi_{o}\right) }$$ instead of $$\omega _{o} = \omega _{s}\gamma \left( 1-\dfrac{v}{c}\cos \varphi_{s}\right) $$ Moroder 04:24, 13 December 2006 (UTC)
 * As you can see on Diagram 2 all values at the angle = $$ 90^\circ $$ are greater then 1 and ->  $$ \infty $$. 3d surface was scaled (to make a nice colors, it was just one of many simple ways), I did not care about its true values. I've made this image for fun, but after this discussion it is not a fun anymore.--TxAlien 16:20, 13 December 2006 (UTC)

 * Not really, in the surface representation you can see z coordinate looming around 0.25. This explains the incorrect yellow coloring as well (it should be greenish/blue). Moroder 16:29, 13 December 2006 (UTC)

 * If you scaled your surface plot, did you scale the color bar accordingly? This may be a partial explanation for the color representation error Moroder 16:59, 13 December 2006 (UTC)
 * It is my last try to explain this to you --TxAlien 18:12, 13 December 2006 (UTC)

 * This looks correct as opposed to all your previous ones  that were incorrect. So, it looks like my criticism turned into something positive, you fixed your plots. They are very nice and correct now, I suggest that you reinsert them in the main aricle. The 3D representation is also much better than the previous 2D ones in terms of clarity. Moroder 19:43, 13 December 2006 (UTC)
 * Yevgeny Kats made big contribution to this article. So, let him decide the fate of these images. (3D is too fancy)--TxAlien 04:10, 14 December 2006 (UTC)

 * I think the 3D plots are great. So what was the error in your previous plots? How did you correct it? Moroder 04:27, 14 December 2006 (UTC)

 * I don't think past contributions give the person extra rights in future decisions :) However, I agree with TxAlien that the two-dimensional plots are better. Yevgeny Kats 05:29, 14 December 2006 (UTC)

 * Difference between old and new images: . It is only scale, but I did not intend to put 3d images in this article. So, there were all correct from my point of view.--TxAlien 05:10, 14 December 2006 (UTC)

 * The old plots (left column) are clearly wrong. The new plots (right column) are correct. Moroder 07:14, 14 December 2006 (UTC)

Did anyone can derive relativistic Dopper effect not from "time dilation" or "Lorentz transformation"? Because these two lack asysmetry. Especially "time dilation", it did not have direction. — Preceding unsigned comment added by Fsshl (talk • contribs) 01:20, 23 April 2012 (UTC)

Hey, not to go back to this whole deal, but are you sure the formulas are correct? Methinks the positive/negative on :$$f_o = \frac{1}{t_o} = \gamma (1-\beta) f_s = \sqrt{\frac{1-\beta}{1+\beta}}\,f_s.$$ is switched, since this expands to
 * $$f_o = \frac{1}{t_o} = \gamma (1-\beta) f_s = \sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}}\,f_s.$$. That, or the 7th edition of Physics for Scientists and Engineers by Serway and Jewett, page 1129 is wrong, which is very much a possibility.  Can anyone confirm this?  I put in a dubious just in case  — Preceding unsigned comment added by 173.240.228.167 (talk) 11:17, 5 December 2012 (UTC)

 * No, it's correct. In this article, beta is negative if moving towards the observer, positive if moving away. Your textbook might be using the opposite sign convention. I'll remove the dubious.--BerFinelli (talk) 11:05, 26 December 2012 (UTC)

Excuse me
Three formulas in the third "Motion in an arbitrary direction" section seem not to agree in all. namely,
 * $$f_o = \frac{f_s}{\gamma\left(1+\frac{v\cos\theta_o}{c}\right)}~.$$ (1)

 * $$\cos \theta_o=\frac{\cos \theta_s-\frac{v}{c}}{1-\frac{v}{c} \cos \theta_s} \,.$$

and
 * $$f_o = \gamma\left(1-\frac{v\cos\theta_s}{c}\right)f_s.$$ (2)

The first and second seem to yield the third but gamma to the power of 3.Like sushi (talk) 10:14, 7 May 2009 (UTC)

I'm sorry. It was a mistake
The post just before was a simple mistake. Sorry. Gamma is simple gamma.Like sushi (talk) 13:47, 7 May 2009 (UTC)

Visualization
I just edited the wording in the visualization section. I do not have a background in relativistic physics, I just reorganized the information already written. Please proofread my writing for technical accuracy. Also, as I was rewriting, I realized that I would like to see two different animations. The one that already exists shows an observer's velocity increasing against a stationary background. Another could show an emitter's velocity increasing relative to a stationary observer located somewhere on the grid (like the plot at the top of the article). Can someone please generate this plot? Also, the aberation of light doesn't appear anywhere in the article and has no context. Please provide a brief description of what causes the aberation of light. (I think it has to do with the time differnce between emitting and receiving the light, but I'm not sure.) David.hillshafer 21:31, 9 June 2009 (UTC)

I moved the visualization to the top, because a visual improves understanding and anticipates a formula. Also, it allows for direct comparison for the case of the observer and the emitter moving. David.hillshafer 17:22, 19 June 2009 (UTC)

Analogy
I added an analogy to explain my understanding of the abberation of light. Again, I do not have a background in relativistic physics. Please check my analogy for technical accuracy. (My background is in engineering mechanics, so I'm comfortable with complicated classical physics equations.) I made this analogy in an attempt make the equations personal and within the scope of normal human experience. I intend to extend the analogy to compare the spin of the ball and the doppler shift, but I'm working on the most intuitive way to describe this. Also, I would like to make a few simple diagrams.David.hillshafer 17:36, 19 June 2009 (UTC)

 * Devising Conceptual and Mathematical Analogies are difficult chores. For example when discussing the second degree of freedom that makes an incompressible fluid (water) behave as a compressible one (a gas) in an open channel, the author of a text book that I studied "back in the day" compared the bow waves of a canal boat in a calm canal to the sonic booms generated by aircraft. I don't know how this works out I never did see the math.

 * However, the acoustic doppler effect has helped me to finally grasp the concept of the constant speed(limit) of mass and energy as being that of the speed of light - I think. Regardless of the speed of the train (horn) -(and it usually is a train which travels at 1/10 to 1/3 the speed of sound and sends long blasts approaching crossings and turns)- the speed of sound is determined soley by the mechanical and thermodynamic (pv^k etc.) properties of air. Simple. The only thing the speed of the source (relative to the observer) does is increase the frequency of the sound.

 * Therefore any analogy that uses projectiles to illustrate a concept has to be clear that the speed of the source does not add to nor subtract from the speed of the projectile. My tentative analogy would be a trolley about roll down a hill with a constant slope. The trolly can trigger the release of soccer balls from the trolley but because the balls quickly reach terminal velocity (determined but the slope and the aerodynamics of the balls) they travel at virtually the same speed.

 * So when the trolley is stationary it triggers the release of one ball every five seconds. The ball quickly reached terminal velocity limited by the slope of the hill - the speed of the trolley is limited to 1/3 of that of the balls. At the bottom of the hill a receiving gutter catches balls at a rate of 12/min. Once the trolley moves down the slope it continues to drop a ball every five seconds. Depending on the speed of the trolley the catcher receives more balls/min - BUT the balls still roll down the hill at the same speed.

 * Still an awkward analogy but I am working on it.

 * Great article. However this suggests more questions about analogies with the acoustical doppler phenomena and light transmission. For example since light does not travel through a medium (as once thought - "the ether") so what happens as the vehicle approaches the speed of light - not the same as sound(??) - Mach 1,2,3 vs, warp 1,2,3!! Further if the (apparent) frequency of light reaching the observer increases - does the spectrum go beyond visible and the source appears to disappear?? What about spectral analysis of starlight - does it have to adjusted to compensate for the speed that the star approaches us ["redshift", "blueshift" etc.]?

 * IMHO, That is is the bad and good of scientific analogies...... they don't always hold water, but they do a great job of stimulating questions in the minds of students until they better understand the precise mathematics of the phenomena.

 * Pete318 (talk) 17:05, 10 October 2012 (UTC)

Discussion on Diagrams
I am curious about *Diagram 1* from the article page. This diagram depicts the redshift and blueshift of waves being emitted by a moving source. To my untrained eye, it looks like this picture does a good job of showing the relative shift in frequencies/wavelengths that would occur and in illustrating the Doppler effect in general terms. The note says that the source is moving at 0.7c. At this speed, I am thinking that the relativistic components of the Doppler effect would show up starkly in the picture. If this is the case, shouldn't waves emitted transverse (and even waves emitted up to some forward angle) appear redshifted in the "stationary" reference frame? When generating this image, was relativistic time dilation accounted for? If not, it would seem appropriate to regenerate this image taking all relativistic effects into account (considering that the wave emitter is moving at relativistic speeds and this article is about relativistic effects). Jsnydr (talk) 22:04, 23 October 2009 (UTC)

Experimental confirmation of transverse Doppler effect
The following reference is mentioned in the Mossbauer spectroscopy article.

Y.-L. Chen, D.-P. Yang (2007). "Recoilless Fraction and Second-Order Doppler Effect". Mössbauer Effect in Lattice Dynamics. John Wiley & Sons. doi:10.1002/9783527611423.ch5. ISBN 9783527611423.

This may report another experimental confirmation of the transverse Doppler effect. Perhaps someone with access to the article could confirm this and determine whether the article also has references to other experiments confirming the effect. —Preceding unsigned comment added by 68.145.187.67 (talk) 21:44, 22 March 2010 (UTC)

Wrong expression
Hallo, I am totally new to article editing, so I will only post here and not in the article. Please feel free to correct it yourself.

The expression of time dilation (second equation) is wrong, as the time between two clock ticks measured in the reference frame moving with respect to the clock is t_o = t * gamma, and not t_o = t / gamma. See for example the article on time dilation. Therefore the relation between observed and emitted frequency (fourth equation ) is wrong as well, since gamma should go on denominator and not on numerator. I believe the problem has to do with one wanting the (1 + beta) to simplify correctly in those formulas. This comes automatically as follows. Start the article by referring to the very first equation in the classic Doppler Effect article, setting v_r (observer's velocity) equal to zero, v_s (source velocity) equal to v, and v (wave velocity) equal to c. One then reads:

f_o (observed) = f_s (emitted) / (1 + beta), with beta= v/c.

Special relativity adds the time dilation effect gamma to times, so 1/gamma to frequencies, so that overall

f_o = (1 + beta) / gamma

The rest follows without problems. If you seek confirmation, see Rindler, Relativity, 2nd edition, page 79; and Weinberg, eq. (2.2.2) pag. 30. Bepibl (talk) 18:52, 8 November 2010 (UTC)

 * Moved new section to bottom per wp:TPG
 * I think you make a mistake. The two wave crest arrival events happen at the same place according to the observer, so per standard time dilation setup they appear longer in some frame in which the observer appears to be moving, in this case the frame of the source. So Δt = γ (Δt0 - v/c2 Δx0) and therefore (with Δx0 = 0), we have Δt = γ Δt0 and thus indeed Δt0 = Δt / γ.
 * DVdm (talk) 19:30, 8 November 2010 (UTC)

Hi DVdm, let me put it differently. The velocity appearing in the classic Doppler effect is the component of the relative velocity of source and observer in the direction of the line connecting them. The link between f_o and f_s in the section "Transverse Doppler effect" (eq. 2 of that section) states exactly this. So eq. 2 of transverse doppler section should reduce to eq. 4 from top if you take theta = pi/2. But it does not, as eq.3 of transverse doppler section states f_0 = f_s / gamma, not *times* gamma. As it is now, equation 4 from top and equation 3 of transverse doppler are inconsistent between them. Do you agree? Bepibl (talk) 20:43, 8 November 2010 (UTC)

 * Note that eq. 2 of transverse doppler section reduces to eq. 3 of same section (i.e. transverse) with θ=π/2, and should reduce to eq. 4 from top (i.e. longitudinal) if you take θ=0, (not π/2), which as you can verify, it does. In both cases we have fo< fs, giving redshift (since β>0), as it should, since in the longitudinal case the observer is moving away from the source. DVdm (talk) 21:09, 8 November 2010 (UTC)

Hi there, sorry, I meant of course theta = 0...! Eq.4 from top agrees with the general form (eq.2 of transverse doppler section) for theta=0 because gamma*(1-beta) = 1/(gamma*(1+beta)). However expressing eq.4 from top as it is now and not as eq. 2 of transverse doppler for theta=0 hides this equivalence. I think all would be much easier to understand if eq.4 from top were expressed as I stated above, i.e. in the reference frame of the observer. As is now, I find rather tortuous to follow, because in the first section the effect is "observed" by the source, whereas in the transverse section it is observed by the observer (in its own reference frame).Bepibl (talk) 22:31, 8 November 2010 (UTC)

 * Ah yes, I see what you mean. I have made a little change, replacing "the time observed between crests" with "the time (as measured in the reference frame of the source) between crest arrivals at the observer", so that should make it somewhat less tortuous. With this amendment, I wouldn't agree that in the first section the effect is "observed" by the source. As I read it now, it is observed by the observer, who can straightforwardly apply the standard Lorentz transformation to calculate the time between the two events (colocal from himself) of wave front reception in the frame of the source. Anyway, i.m.o. eq. 4 from top is indeed expressed in the reference frame of the observer, so to speak. And of course I don't think that it really makes sense to talk about such an equation as "expressed in the reference frame of the observer" or "expressed in the reference frame of the source". It is a an equation relating two quantities on equal footing, and the text explains (--a little bit better now--) where it comes from. DVdm (talk) 23:16, 8 November 2010 (UTC)

I'm confused also about the equations. In Eq.1, the relativistic factor causes the detected frequency to INCREASE rather than DECREASE as it should for time dilation.2405:9800:B640:AB0F:D409:CC54:3DDE:E3BB (talk) 15:25, 28 March 2023 (UTC)

 * The context of Eq. 1 is stated as "... assume the receiver and the source are moving away from each other...", in which case the frequency decreases.

What is this supposed to say?
In the section on Transverse Doppler Effect, it says, "If the predictions of special relativity are compared to those of a simple flat nonrelativistic light medium that is STATIONARY in the observer’s frame (“classical theory”), SR’s physical predictions of what an observer sees are always "redder", by the Lorentz factor..." Really? Stationary??? The Lorentz factor has no effect if the source is not moving relative to the observer. What is this supposed to say??? Thank you. — Preceding unsigned comment added by 98.212.132.146 (talk • contribs)

 * Please put new messages at the bottom, provide a header and edit summary, and sign with four tildes ( ~ )? Thanks.
 * It means that in SR the transverse Doppler effect predicts a redshift for a source that is instantanously moving transversally w.r.t. the observer. I.o.w. light from a source that is not approaching or receding from the observer, but that is moving w.r.t. the observer, is redshifted. In this case the source is moving w.r.t. to observer, but not approachin or receding: it could be moving in a circle with the observer at the centre, or it could be moving along a straigh line with the observer sitting at the point of shortest distance to the line — that's what "transverse (i.e. lateral)" means. (note: I have removed the unhelpful wikilink to Transversality). DVdm (talk) 11:45, 12 December 2010 (UTC)

Accelerated motion
The article says:

"For general accelerated motion, or when the motions of the source and receiver are analyzed in an arbitrary inertial frame, the distinction between source and emitter motion must again be taken into account.

The Doppler shift when observed from an arbitrary inertial frame:
 * $ f_o = \frac { c + v_o \! \cdot \! cos( \theta_o ) }{ c - v_s \! \cdot \! cos( \theta_s ) } \cdot \frac{ \gamma_o }{ \gamma_s } \cdot f_s $

where:
 * $ v_s $ is the speed of the source at the time of emission
 * $ v_o $ is the speed of the receiver at the time of reception
 * $ \gamma_s $ is the Lorentz factor of the source at the time of emission
 * $ \gamma_o $ is the Lorentz factor of the receiver at the time of reception
 * $ \theta_s $ is the angle between the light path and the velocity of the source
 * $ \theta_o $ is the angle between the light path and the velocity of the receiver"

Consider the situation where the observer and the source are moving in opposite directions at the same speed such that $$v_o=v_s$$ (where $$v$$ is the symbol for speed). In this case $$\frac{ \gamma_o }{ \gamma_s }=\frac{\sqrt{1-v_s^2/c^2}}{\sqrt{1-v_o^2/c^2}}=1$$, while $$cos( \theta_o ) = - cos( \theta_s )$$, and thus $$\frac { c + v_o \! \cdot \! cos( \theta_o ) }{ c - v_s \! \cdot \! cos( \theta_s ) }=1$$. The result would be that $$f_o=f_s$$. Why is that? Kmarinas86 (Expert Sectioneer of Wikipedia) 19+9+14 + karma = 19+9+14 + talk = 86 16:11, 30 December 2010 (UTC)
 * Okay. I see:

The transverse Doppler effect can be analyzed from a reference frame where the source and receiver have equal and opposite velocities. In such a frame the ratio of the Lorentz factors is always 1, and all Doppler shifts appear to be classical in origin. In general, the observed frequency shift is an invariant, but the relative contributions of time dilation and the Doppler effect are frame dependent.
 * Per above, if $$cos( \theta_o ) = - cos( \theta_s )$$ when the velocities are equal and opposite of each other, then $$f_s=f_o$$ apparently resulting in no frequency shift. For the equation to work, $$cos( \theta_o )$$ would have to equal $$cos( \theta_s )$$ in this case. Yet this point is not clear, and in fact, made less clear with the following passage:

Due to possibility of refraction, the angles of emission and reception are relative to the light path, not to any "connecting line" between the points of emission and reception.
 * It appears that the angles $$\theta_s$$ and $$\theta_o$$ only make sense in connection with scalar products $$\mathbf{c}_s\cdot\mathbf{v}_s$$ and $$\mathbf{c}_o\cdot\mathbf{v}_o$$, such that if the velocities of $$s$$ and $$o$$ go in opposite directions, then the angular directions would be opposite with respect to the arbitrary inertial frame and also opposite with respect to the light path. This would make the ratio $$\frac{c - v_o cos(\theta_o)}{c - v_s cos(\theta_s)}$$, which can be represented as $$\frac{c - \frac{1}{c}\mathbf{c}_o\cdot\mathbf{v}_o}{c - \frac{1}{c}\mathbf{c}_s\cdot\mathbf{v}_s}$$ or $$\frac{\mathbf{c}\cdot\mathbf{c} - \mathbf{c}_o\cdot\mathbf{v}_o}{\mathbf{c}\cdot\mathbf{c} - \mathbf{c}_s\cdot\mathbf{v}_s}$$.
 * Kmarinas86 (Expert Sectioneer of Wikipedia) 19+9+14 + karma = 19+9+14 + talk = 86 17:55, 30 December 2010 (UTC)

In the previous section, we have the following:

If, in the reference frame of the observer, the source is moving away with velocity $v\,$ at an angle $\theta_o\,$ relative to the direction from the observer to the source (at the time when the light is emitted), the frequency changes as

 * $ f_o = \frac{f_s}{\gamma\left(1+\frac{v\cos\theta_o}{c}\right)}.$

As you can see, the denominator here has a factor $$\left(1+\frac{v\cos\theta_o}{c}\right)$$, whereas in the formula I quoted has the equivalent of $$\left(1-\frac{v\cos\theta_s}{c}\right)$$ if you factor out $$c$$ from both the numerator and the denominator. There would appear to me no justification for assuming that, in the general case, $$cos( \theta_o ) = - cos( \theta_s)$$.Kmarinas86 (Expert Sectioneer of Wikipedia) 19+9+14 + karma = 19+9+14 + talk = 86 16:45, 30 December 2010 (UTC)

 * I have removed both new sections added by, since one was added without a source and the other was not to be found in the cited source. When we have proper sources some of it can be restored. DVdm (talk) 19:58, 30 December 2010 (UTC)

Note. I have left a second level wp:NOR warning on talk page of. DVdm (talk) 17:14, 7 January 2011 (UTC)

Note. We have worked this out on (User NOrbeck's talk page). The equation is now taken over from the source. DVdm (talk) 12:43, 10 January 2011 (UTC)

 * Large portions of this section got carried over into Motion in arbitrary inertial frames, which I have temporarily deleted for a major reworking. It should never have gotten in. Original research backed up by misinterpreted reliable secondary source references. Prokaryotic Caspase Homolog (talk) 11:36, 14 October 2018 (UTC)
 * thx! - DVdm (talk) 15:12, 14 October 2018 (UTC)

Refraction Outside Domain of Special Relativity?
The article says refraction is outside the domain of special relativity, and cites a web FAQ by Tom Roberts, but the cited page does not make any such claim, and as a matter of fact the claim is false. Special relativity has no trouble with refraction. Of course, one can't use vacuum equations when dealing with something other than vacuum, but this doesn't mean special relativity is inapplicable. As long as no gravitational fields are significant, special relativity applies. But the point is, the cited reference doesn't support the claim, so I'm boldly deleting it. Also, the statement in the article about the Doppler shift being being purely classical when viewed from the median reference frame between two objects is simply wrong, and there is no reference supporting that claim, so I'm boldly deleting it. To be helpful, I though I'd mention why it is false. The velocities appearing in the relativistic equation cannot be mapped to the classical velocities, so the whole statement is misleading. If people think this is too difficult to understand, I'd be happy to simply delete it. But definitely we shouldn't retain the false and unsourced claim.Cattlecall1 (talk) 21:24, 25 February 2011 (UTC)

 * Without a source for your claim, it is entirely useless. Replacing sourced content "because you think it is wrong" with unsourced content is one of the most definite no-no's of Wikipedia. I have reverted your edit and left a second level warning on your talk page. DVdm (talk) 22:43, 25 February 2011 (UTC)

No, you misunderstand. The content on the page was not sourced. It claimed that refraction is outside the domain of special relativity, and it referenced a web FAQ, but a review of the referenced page shows that it does not make any such statement. So it is not a well-sourced claim, and needs to be removed, per Wikipedia policy. Since there are multiple issues here, I'll just focus on this one specific point, and we can discuss the other unsourced claims in the article later. The most important and blatent one to fix is the "refraction outside the domain of special relativity" claim, which is completely unsourced. If you can provide a valid source for that claim, please do so. Thanks.Cattlecall1 (talk) 23:16, 25 February 2011 (UTC)

 * In support of Cattlecall1: The claim "Refractive media are explicitly outside the domain of Special Relativity, which applies only to light propagation in gravity-free vacuums" makes no sense here for several reasons:
 * it's only gravity that lies outside the domain of SR, refractive media are certainly within it
 * the cited source makes no mention of refraction so it's original research to claim that it does
 * the section in which this sentence appears makes no mention of gravity, so why is it being brought up here?
 * However it is true to say that an equation derived for an inertial frame need not be true in a non-inertial frame, and I guess that is the point that is attempting to be made here. The cited source expresses the opinion that non-inertial frames (in the absence of gravity) are still within the domain of SR. --  Dr Greg   talk  23:22, 25 February 2011 (UTC)

 * In further support of Cattlecall1 (or perhaps non-support of the statement that SR only applies to vacuum): has everybody forgotten the Fizeau experiment? The derivation of its odd result from Einstein's SR treatment of additive velocities at relativistic speeds (in this case, the 3/4 c speed of light in moving water, complete with use of water's refractive index of 4/3) was one of the first experimental tests of SR (albeit a "retrodictive one"). Lorentz had already come close to using Einstein's methods, but did not realize that he was onto a completely general principle of time and coordinate transformations that applied to all physics.  S  B Harris 02:05, 26 February 2011 (UTC)

Cattlecall1, sorry for my previous reverts. I hadn't looked closely and assumed that you just reverted, so my reverts were mistaken and my edit summaries and warnings inappropriate. My apologies. DVdm (talk) 15:21, 26 February 2011 (UTC)

Inconsistent definitions of theta?
The formula for a 2D doppler shift appears twice on the page, once under "Transverse Doppler Effect" and once under "Motion in an arbitrary direction" but their definitions of $$\theta_o$$ are not consistent. The first definition has $$\theta_o$$ defined as, when seen from receiver's frame, the angle between the direction the emitter is traveling and the "observed direction of the light at reception" which to me translates as the vector from the emitter to the receiver. The second definition is the angle between the velocity and the direction from the receiver to the emitter. Assuming $$v$$ has the same definition in both equations (I didn't see anything to indicate otherwise), these definitions cannot both be true and using one or the other will change the sign of the $$ v \cos \theta_o $$. I think the second definition is the correct one and the first definition should be changed. — Preceding unsigned comment added by 198.129.105.67 (talk) 19:17, 22 December 2011 (UTC)

undefined 02:19, 23 December 2011 (UTC)
 * "The first definition has $$\theta_o$$ defined as, when seen from receiver's frame, the angle between the direction the emitter is traveling and the ' observed direction of the light at reception' which to me translates as the vector from the emitter to the receiver."
 * The direction the emitter is traveling is not the "vector from the emitter to the receiver", that would be the "observed direction of the light at reception".
 * "The second definition is the angle between the velocity and the direction from the receiver to the emitter."
 * That's the same thing as the first definition.siNkarma86—Expert Sectioneer of Wikipedia

 * I think there is just a simple misunderstanding here, we agree that that the "observed direction of the light at reception" is the vector from the emitter to the receiver. The first definition has $$\theta_o$$ as the angle between the velocity and this vector, whereas the second definition has $$\theta_o$$ as the angle between the velocity and a vector from receiver to the emitter (different than vector from emitter to receiver).  These two definitions are not consistent.  — Preceding unsigned comment added by 198.129.105.67 (talk) 01:53, 30 December 2011 (UTC)

Sources? Original Research?
The majority of this article doesn't list any sources at all. Here's a summary" by section:

 * 1 Visualization                                NO SOURCES
 * 2 Analogy                                      NO SOURCES
 * 3 Motion along the line of sight               NO SOURCES
 * 4 Systematic derivation for inertial observers 1 ref at very end, not clear what it refers to
 * 5 Transverse Doppler effect                    NO SOURCES
 * 5.1 Reciprocity                                NO SOURCES
 * 5.2 Experimental verification                  2 sources
 * 6 Motion in an arbitrary direction             NO SOURCES
 * 7 Accelerated motion                           2 sources (but mostly original research?)

I think it would be better to base the article more firmly on sources. At present it just seems to be a collection of essays written by various editors describing their personal (and in some cases non-standard) views of the subject.Flau98bert (talk) 14:39, 14 September 2012 (UTC)

In addition to the classical Doppler effect...
Re Jordgette's edit and my amendment: actually, the original wording was, if properly interpreted, correct after all. The classical Doppler effect is given by
 * $$f_o = \frac{f_s}{1+\frac{v\cos\theta_o}{c}}.$$

The relativistic effect is
 * $$f_o = \frac{f_s}{\gamma\left(1+\frac{v\cos\theta_o}{c}\right)},$$

and thus, for the transversal case —which is the subject of the section— this reduces to, classically
 * $$f_o=f_s, \,$$

versus relativistic
 * $$f_o=\frac {f_s} {\gamma}. \,$$

So, indeed, in addition to the classical Doppler effect —being null (aka factor 1) in the transversal case—, the received frequency is reduced by the Lorentz factor. Since we're dealing with factors here, the word "addition" was a bit awkward, so I propose we leave it out, specially since the section is about the transverse effect, which is really non-existent classically. Subtle. - DVdm (talk) 13:26, 10 January 2013 (UTC)

C' or V'
Full disclaimer, I am not a physicist, but, under "Motion along the line of sight", shouldn't the last equation (the approximation) be v', not c'? How can there even be a c'? — Preceding unsigned comment added by 174.98.234.239 (talk) 16:35, 9 September 2013 (UTC)

Deriving Lorentz factor from the Doppler effect
The text of the article says that we use Lorentz factor to correct the classical Doppler because it comes from the coordinate transformation. However, Lorentz factor itself can be derived from the classical Doppler effect, which differently distorts the observed frequency, depending on whether receiver or transmitter is in motion. This violates the principle of relativity and attempt to correct gives a birth to the Lorentz factor, like here but I am sure that I have also seen some serious Einstein 2006 anniversary article, which does the same thing - derives the Lorentz factor reconciling the frequency shifts. I mean that it is insightful. Can we add this treatment into the article? --Javalenok (talk) 14:21, 22 March 2014 (UTC)

 * Not a wp:reliable source, this. - DVdm (talk) 15:49, 22 March 2014 (UTC)

 * really? The question is not whether this source is reliable or not. It is just an illustration. The question is whether should I dig deeper for this approach or we should forget about inferring the Lorentz factor as simple byproduct of reconciling the Doppler effect with relativity principle? --Javalenok (talk) 10:33, 23 March 2014 (UTC)

Replace $$f_s$$ with $$\nu_s$$?
Just that. The use of the Greek $$\nu$$ is standard in the physics literature for frequency. — Preceding unsigned comment added by 68.146.90.105 (talk) 16:31, 29 March 2015 (UTC)

Wrong Formula for relativistic Doppler Effects
In this section in the article:

"Replacing $$\tau$$ with $$1/f$$ and simplifying, we get the required result that gives the relativistic Doppler shift of any moving wave in terms of the stationary frequency, $$f^\prime$$:
 * $$f = \gamma \left( 1 - \frac{v}{u^\prime} \right) f^\prime.$$

Ignoring the relativistic effects by taking $$v \ll c$$ or $$c \rightarrow \infty$$ (equivalent to $$\gamma \rightarrow 1$$) gives the classical Doppler formula:
 * $$f = \left( 1 - \frac{v}{u^\prime} \right) f^\prime.$$

For electromagnetic radiation where $$u^\prime = c$$ the formula becomes
 * $$f = \gamma \left( 1 - \frac{v}{c} \right) f^\prime = \gamma \left( 1 - \beta \right) f^\prime = f^\prime \sqrt{\frac{1-\beta}{1+\beta}}$$

or in terms of wavelength:
 * $$\lambda = \lambda^\prime \sqrt{\frac{1+\beta}{1-\beta}},$$

where $$\lambda^\prime$$ is the wavelength of the source at the origin $$O^\prime$$ as the observer in $$S^\prime$$  sees it."

If $$\lambda$$ is the observed wavelength, then the equation should read $$\lambda = \lambda^\prime \sqrt{\frac{1-\beta}{1+\beta}},$$. The equation in terms of frequency should similarly reverse signs.

Sources: 1)http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/reldop2.html Hyperphysics clearly lists that $$f = f^\prime \sqrt{\frac{1+\beta}{1-\beta}}$$, which of course means $$\lambda = \lambda^\prime \sqrt{\frac{1-\beta}{1+\beta}},$$.

2) http://spiff.rit.edu/classes/phys314/lectures/doppler/doppler.html This university website states the equation similarly. Just note that the author of that webpage put the $$ \lambda^\prime $$ on the LHS of the equation rather than the right.

Unless someone sees some problem in what I am saying, we should correct teh equations. — Preceding unsigned comment added by 130.212.214.227 (talk • contribs) 01:19, 6 August 2015 (UTC)

 * Please sign all your talk page messages with four tildes ( ~ ). Thanks.
 * Note that it depends on how v is defined. In the article v is assumed positive when the source is receding from the observer, and negative when approaching—see opening line of section Relativistic Doppler effect. How ever the variables are defined must result in the fact that observed wavelength should be larger than emitted wavelength when the source is receding from the observer—red shift.
 * This is how Spiff does it, but there obviously is a typo in that "Likewise, one can express the shifted wavelength λ as...". That should probably be "Likewise, one can express the shifted wavelength λ' as..." Earlier in that section they say "perceived frequency f' is higher than the emitted frequency, and the perceived wavelength λ' is shorter than the emitted wavelength." Bad source.
 * Hyperphysics defines v the other way around. By the way, see how unreliable that site is—they don't understand the bug rivet paradox. More silliness from the same site: "Accelerations are outside the realm of special relativity and require general relativity." Bad Source. To be avoided at all cost.But see Special:LinkSearch/*.hyperphysics.phy-astr.gsu.edu.
 * See for instance this source: https://books.google.com/books?id=-uMRwLaNbC8C&pg=PA87.
 * I have explicitly repeated the assumption at the end of the section. Hope this helps. DVdm (talk) 07:19, 6 August 2015 (UTC)

The article seems to hide what it should point out and is wrong in many ways
The article rather seems to hide than to show things. Wikipedia is not the right place to hide things.

In the beginning even the first sentence is most cryptic:

"The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity."

The sentence is meaningless. Actually it should point out:

The classical Doppler effect is the change in frequency of light.

The relativistic Doppler effect is the change in both frequency and wavelength of light.

The next sentence adds even more confusion:

"The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point."

Both the relativistic and the classical Doppler effect give results for the case when no medium of propagation is involved. Time dilation as well as length contraction result from the postulate of the constancy of the speed of light. You cannot just include the one and ignore the other, both are inseparably connected.

Let's have a closer look at the section "Motion along the line of sight":

(Note: In contrast to the article I have marked the results of the Lorentz transformation with an apostrophe (') and the results of the Galilean transfomation with a superscript o ($$^o$$).)

The first paragraph describes the problem in the reference frame of the source. Put into a diagram it looks like this:

In the next paragraph the period $$T^o$$ in the observers's frame is calculated from a classical point of view (Galilean transformation):

$$T^o=T/(1-v/c)$$

The other well known results of the classical Doppler effect are

$$c^o=c-v$$ (relative speed of light c-v)

$$f^o=1/T^o=(1-v/c)f$$

$$\lambda^o=\lambda$$ (the wavelength $$\lambda$$ is the same in both the source's and the observer's frame)

The results of the Galilean transformation, based on the scenario given in Diagram 1, are shown in Diagram 2.

In the following paragraph ("Due to the relativistic time dilation, the observer will measure this time to be ...") relativity comes in. Firstly, in the article the Lorentz transformation is applied to results of the Galilean transformation. That's the wrong way, the Lorentz transformations "supersede the Galilean transformations" (see Lorentz transformation). A transformation on top of the results of the Galilean transformation leading to the results of the Lorentz transformation, if any, should be derived or well sourced. Secondly, the observer will not "measure this time to be ...". Following special relativity the observer's clocks run slower such that he will not notice the change of the time rate (see here). Thirdly, the factor for length contraction and time dilation in not $$\gamma$$. Einstein showed in his popular book here that the correct length contraction and time dilation factor for a single light front ($$x=ct$$) evaluates to $$\gamma(1-v/c)$$ in his equations (here slightly rewritten)

$$x'=\gamma(1-v/c)x$$

$$t'=\gamma(1-v/c)t$$

although he failed to notice it. A simple animation (Diagram 3) shows a visualization of the equations. The observer's frame is travelling through space and time of the source's frame.

Finally, the results of the Lorentz transformations should not be missing, here summarized

$$c'=c$$ (constant speed of light)

$$T'=T/\gamma(1-v/c)$$

$$f'=1/T'=\gamma(1-v/c)f$$

$$\lambda'=\lambda/\gamma(1-v/c)$$

and shown Diagram 4.

There is one point to notice:

In the last sentence of the section it says: "In the non-relativistic limit (when $$v \ll c$$) this redshift can be approximated by $$z \simeq \beta = \frac{v}{c},$$ corresponding to the classical Doppler effect." This is not true for the redshift defined some lines above. The classical Doppler effect results in $$\lambda'=\lambda$$, $$\lambda'$$ does not change with $$v/c$$.

GHT153 (talk) 23:02, 12 June 2016 (UTC)

 * The lead sentence of the article seems very clear and correct to me, and is backed by the article, which in turn seems to be very properly sourced. Please note that (1) we don't allow original research in Wikipedia—see wp:NOR—and (2) that article talk pages are places to discuss the article, not the subject or your views on it—see wp:TPG, for which you were warned on your user talk page more than once before. - DVdm (talk) 10:42, 13 June 2016 (UTC)

 * Are you kidding? The first source given in the article is far behind the section I have been referring to. In contrast to the article my remarks are very well sourced. Just in case Einstein's publications recently have been removed from the reliable sources list for relativity, please let me know.

 * And please stop bothering me with thrown around warnings before have read anything.

 * GHT153 (talk) 23:29, 14 June 2016 (UTC)

 * Re your "remarks are very well sourced": taking wp:SYNTH and wp:CIRCULAR into account, I see no reliable sources (in the Wikipedia sense!) here for your analysis, drawings and remarks, so per wp:TPG they are off-topic. Not kidding. - DVdm (talk) 07:52, 15 June 2016 (UTC)

 * Regarding reliable sources for the article I don't want to repeat what already has been said on this page, please see Talk:Relativistic_Doppler_effect. The criticism is still up-to-date.

 * My contribution here is solely based on Einstein's own publications, and the diagrams are a visualization of his own equations.

 * GHT153 (talk) 23:04, 16 June 2016 (UTC)

 * Yes, exacly, based on Einstein's own publications, and visualizations of his own equations, and therefore a schoolbook example of wp:SYNTH, which means not for Wikipedia, because without explicit reliable sources, lacking wp:VERIFIABILITY and possibly completely wrong. It's just Wikipedia policy. - DVdm (talk) 07:16, 17 June 2016 (UTC)

 * Einstein's relativity it not a game, it's a billion dollar business. By whom are you paid for your work at Wikipedia? I cannnot find anything about it on your user page.
 * The results of the Lorentz transformation (e.g. length contraction and time dilation by a factor of $$\gamma(1-v/c)$$ just because a light front is passing by) show by means of simple algebra that Einstein's relativity is merely a product of erroneous mathematics and nothing else. It's nonsense.
 * Wikipedia should stop spreading nonsense and assisting in committing fraud.
 * GHT153 (talk) 23:02, 29 June 2016 (UTC)

 * These comments are highly inappropriate here—see wp:talk page guidelines. Here we can and must only discuss the article and changes to it, not the subject and changes to it, not contributors and who pays them, and not Wikipedia itself. You were warned about this before at User talk:GHT153, so I have left a final warning on your talk page. Given the policies, it's not likely that Wikipedia will stop doing whatever it is doing, so if you are indeed convinced that it is spreading nonsense and assisting in committing fraud, perhaps it's best for you to stay away from it. In any case this is not the place to discuss that. You can continue on your user talk page if you like, but this discussion must be closed here. - DVdm (talk) 07:04, 30 June 2016 (UTC)

No point to the Analogy section
A person reading up on the Relativistic Doppler Effect would presumably be familiar with the "conventional" Doppler effect and should not need such a back-to-basics explanation. Furthermore, this section is unsourced, and is almost certainly original research.

If you disagree, feel free to restore the section, which I have preserved below if you believe it needs to go back in. Prokaryotic Caspase Homolog (talk) 05:39, 10 October 2018 (UTC)

==Analogy== Understanding relativistic Doppler effect requires understanding the Doppler effect, time dilation, and the aberration of light. As a simple analogy of the Doppler effect, consider two people playing catch. Imagine that a stationary pitcher tosses one ball each second (1 Hz) at one meter per second to a catcher who is standing still. The stationary catcher will receive one ball per second (1 Hz). Then the catcher walks away from the pitcher at 0.5 meters per second and catches a ball every 2 seconds (0.5 Hz). Finally, the catcher walks towards the pitcher at 0.5 meters per second and catches three balls every two seconds (1.5 Hz). The same would be true if the pitcher moved toward or away from the catcher. By analogy, the relativistic Doppler effect shifts the frequency of light as the emitter or observer moves toward or away from the other.

To understand the aberration effect, again imagine two people playing catch on two parallel conveyor belts (moving sidewalks) moving in opposite direction. The pitcher must aim differently depending on the speed and the spacing of the belts, and where the catcher is. The catcher will see the balls coming at a different angle than the pitcher chose to throw them. These angle changes depend on: 1) the instantaneous angle between the pitcher-catcher line and the relative velocity vector, and 2) the pitcher-catcher velocity relative to the speed of the ball. By analogy, the aberration of light depends on: 1) the instantaneous angle between the emitter-observer line and the relative velocity vector, and 2) the emitter-observer velocity relative to the speed of light.

The various derivations are unsourced
The various derivations for longitudinal Doppler effect, transverse Doppler effect, effect with source and receiver traveling at arbitrary angles, etc. are unsourced. I am doing a literature search to find appropriate sources for these various derivations. All of the ones that I have found so far use different approaches and different nomenclature than employed here.

Until I find appropriate sourced derivations that fit in with pedagogical approach adopted in this article, I am going to go ahead and make clarifying improvements to the current unsourced derivations. Prokaryotic Caspase Homolog (talk) 13:57, 10 October 2018 (UTC)
 * https://www.mathpages.com/home/kmath587/kmath587.htm Mathpages covers this issue perfectly well. Very good treatment. I have also seen other good sources in books, but it is more difficult to reach these sources and to dig them up. Kevin S. Brown mentions cases of rotation, I believe it is important to mention these cases in this article. Albert Gartinger (talk) 16:14, 10 October 2018 (UTC)
 * Feynman is also plain and simple. He works it out in the frame of the observer first and in the frame of the source then, reducing the both derivations to the one "universal" form as we know it. Albert Gartinger (talk) 16:16, 10 October 2018 (UTC)
 * Kevin Brown is the rare author, who understands and describes null - shifted relativistic Doppler effect, when observer and source move within a reference frame with equal and opposite velocities, i.e. they share full amount of time dilation fifty - fifty. Thus relativistic contributions cancel each other and relativistic Doppler effect turns into classical one. If they move head - on, sure they would see the same violet shift, but just it is no different from the classic one. Exactly the same Brown explains null - shifted phase of the Transverse Doppler Effect. (Champeney and Moon experiment). Brown's treatment is beautiful! Albert Gartinger (talk) 16:40, 10 October 2018 (UTC)

 * Yes, I am familiar with all of the sources that you cite, but the derivations used in this article use different variable names, differ in whether v approaching means it has a positive or negative value, differ whether you use a vector approach or not, etc. etc.
 * The pedagogical approach used in this article more or less goes: (1) We first start with the simple case of longitudinal Doppler effect, beginning with the conventional analysis and then applying gamma. This is similar to the approach used by Feynman, except Feynman uses different nomenclature. (2) Then we derive longitudinal Doppler effect starting with the Lorentz transformation. (3) Then we analyze transverse Doppler effect. The section here on TDE is confusing and unsatisfactory, by the way. (4) Then with source and receiver moving in arbitrary directions, etc. etc.
 * So none of the sources that you refer to above can be cited as reliable secondary sources for any section, unless I entirely throw out the contents of each section and replace with a treatment that is consistent with its source in nomenclature, sign convention, etc.
 * I am normally reluctant to do such drastic housecleaning.
 * Re Champeney & Moon. Are you familiar with Group Motions in Space-time and Doppler Effects, by J. L. Synge. Nature volume 198, page 679 (18 May 1963)? He analyzes rotating Mossbauer emitter and absorber for the general case of R1 not equal to R2. It's quite an elegant treatment.
 * Another defect of the article is that it doesn't go enough into experiment and observation. The relativistic Doppler effect is extremely important in astrophysics, etc. Prokaryotic Caspase Homolog (talk) 17:48, 10 October 2018 (UTC)

I did some cleanup on the first derivation of the longitudinal Doppler effect, and provided two reliable secondary source references to the approach that was used in the derivation, even though the variables employed and even the sign conventions differed from one reference to the other. I changed "source and observer" to "source and receiver", because in the original version of this section, I got all mixed up about the observer being observed from the frame of the source, etc. Please scrutinize for stupid errors. Thanks! Prokaryotic Caspase Homolog (talk) 04:51, 11 October 2018 (UTC)
 * It looks ok, but I can't spend an hour for scrutinizing now—just a few minutes every now and then. Maybe later - DVdm (talk) 10:37, 11 October 2018 (UTC)

Is this section original research?
After I removed the Landau & Lifshitz reference as being unsuitable, this section was left with no sourcing. Although the derivation appears correct to me, Wikipedia is not a place for original research. Can somebody find appropriate sourcing that documents this section's approach to deriving the longitudinal Doppler effect? Prokaryotic Caspase Homolog (talk) 15:40, 11 October 2018 (UTC)

Longitudinal Doppler effect analyzed using Lorentz transforms

Let us repeat the derivation more systematically in order to show how the Lorentz equations can be used explicitly to derive a relativistic Doppler shift equation for waves that themselves are not relativistic.

Let there be two inertial frames of reference, $$S$$ and $$S'$$, constructed so that the axes of $$S$$ and $$S'$$ coincide at $$t = t' = 0$$, where $$t$$ is the time as measured in $$S$$ and $$t'$$ is the time as measured in $$S'$$. Let $$S'$$ be in motion relative to $$S$$ with constant velocity $$v$$; without loss of generality, we will take this motion to be directed only along the x-axis. Thus, the Lorentz transformation equations take the form

 * $$\begin{align}

x &= \gamma \left( x' + \beta ct' \right) \\ y &= y' \\ z &= z' \\ ct &= \gamma \left( ct' + \beta x' \right) \\ \frac{dx}{dt} &= \frac{v + \frac{dx'}{dt'}}{1 + \frac{v}{c^2}\frac{dx'}{dt'}}. \end{align}$$

See velocity-addition formula, where $$\beta = v/c$$ and $$\gamma = (1 - \beta^2)^{-\frac{1}{2}}$$, and $$c$$ is the speed of light in a vacuum.

The derivation begins with what the observer in $$S'$$ trivially sees. We imagine a signal source is positioned stationary at the origin, $$O'$$, of the $$S'$$ system. We will take this signal source to produce its first pulse at time $$t_1' = 0$$ (this is event 1) and its second pulse at time $$t_2' = 1/f'$$ (this is event 2), where $$f'$$ is the frequency of the signal source as the observer in $$S'$$ reckons it. We then simply use the Lorentz transformation equations to see when and where the observer in $$S$$ sees these two events as occurring:

The period between the pulses as measured by the $$S$$ observer is not, however, $$t_2 - t_1$$ because event 2 occurs at a different point in space to event 1 as observed by the $$S$$ observer (that is, $$x_2 \neq x_1$$) — we must factor in the time taken for the pulse to travel from $$x_2$$ to $$x_1$$. Note that this complication is not relativistic in nature: this is the ultimate cause of the Doppler effect and is also present in the classical treatment. This transit time is equal to the difference $$x_2 - x_1$$ divided by the speed of the pulse as the $$S$$ observer sees it. If the pulse moves at speed $$-u'$$ in $$S'$$ (negative because it moves in the negative x-direction, towards the $$S$$ observer at $$O$$), then the speed of the pulse moving towards the observer at $$O$$, as $$S$$ sees it, is:
 * $$-u = \frac{-u' + v}{1 + (-u') \frac{v}{c^2}},$$

using the Lorentz equation for the velocities, above. Thus, the period between the pulses that the observer in $$S$$ measures is:
 * $$\begin{align}

\tau &= t_2 - t_1 + \gamma \frac{v}{f'} \left( \frac{u' - v}{1 - \frac{v u'}{c^2}} \right)^{-1} \\ &= \frac{\gamma}{f'} + \frac{\gamma}{f'} \frac{v}{u' - v} \left(1 - \frac{v u'}{c^2} \right). \end{align}$$

Replacing $$\tau$$ with $$1/f$$ and simplifying, we get the required result that gives the relativistic Doppler shift of any moving wave in terms of the stationary frequency, $$f'$$:
 * $$f = \gamma \left( 1 - \frac{v}{u'} \right) f'.$$

Ignoring the relativistic effects by taking $$v \ll c$$ or $$c \rightarrow \infty$$ (equivalent to $$\gamma \rightarrow 1$$) gives the classical Doppler formula:
 * $$f = \left( 1 - \frac{v}{u'} \right) f'.$$

For electromagnetic radiation where $$u' = c$$ the formula becomes
 * $$f = \gamma \left( 1 - \frac{v}{c} \right) f' = \gamma \left( 1 - \beta \right) f' = f' \sqrt{\frac{1 - \beta}{1 + \beta}}$$

This expression may be compared to the classical Doppler effect. In the latter case, one has

 * $$f = \left( \frac{c + v_\text{r}}{c + v_\text{s}} \right) f' \,$$
 * where
 * $$c \;$$ is the velocity of waves in the medium;
 * $$v_\text{r} \,$$ is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);
 * $$v_\text{s} \,$$ is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).

In terms of wavelength, one can write
 * $$\lambda = \lambda' \sqrt{\frac{1 + \beta}{1 - \beta}},$$

where $$\lambda'$$ is the wavelength of the source at the origin $$O'$$ as the observer in $$S'$$  sees it. In these equations v (and thus β) is assumed positive when the source is receding from the observer, and negative when approaching.

For electromagnetic radiation, the limit to classical mechanics, $$c \rightarrow \infty$$, is instructive. The Doppler effect formula simply becomes $$f = f'$$. This is the "correct" result for classical mechanics, although it is clearly in disagreement with experiment. It is "correct" since classical mechanics regards the maximum speed of interaction — for electrodynamics, the speed of light — to be infinite. The Doppler effect, classical or relativistic, occurs because the wave source has time to move by the time that previous waves encounter the observer. This means that the subsequent waves are emitted further away (or closer) to the observer than they otherwise would be if the source were not in motion. The effect of this is to stretch (or compress) the wavelength of the wave as the observer encounters them. If however the waves travel instantaneously, the fact that the source is further away (or closer) makes no difference because the waves arrive at the observer no later or earlier than they would anyway since they arrive instantaneously. Thus, classical mechanics predicts that there should be no Doppler effect for light waves, whereas the relativistic theory gives the correct answer, as confirmed by experiment.

Assessment
You have done a TREMENDOUS job!!! Great! IMO the previous treatment of Motion in arbitraty direction  was not so bad. The author replaced $$\theta_o$$ with $$\theta_s$$, inserting the formula for relativistic aberration. The author demonstated how relativitic aberration formula "ties" angle of emission $$\theta_s$$ with angle of reception $$\theta_o$$. In simple words it looks like that: TDE redshift appears when $$\theta_o = \pi/2$$, i.e the receiver is "looking" through his tube - telescope  at right angle to direction of motion of the source. In this case the source (since it "moves" in the receiver's frame) MUST "to take into account" relativistic aberration and turn laser pointer backward at angle $$\theta_s$$, if it wants to send the light pulse at normal to its path and to hit the target, i.e. the receiver's telescope. The TDE blueshift appears when we work in the source's frame, i.e. the source is "at rest" and it doesn't "think" about aberration, so the angle of emission $$\theta_s = \pi/2$$. The source emits at right angle towards the path of motion of the receiver, but in this case, due to relativistic aberration of light the receiver MUST turn his telescope forward at angle $$\theta_o$$ in accordandce with relativistic aberration angle formula, if it "wishes to see" the source. Naturally, for null - shifted TDE the source emits backward and the emitter looks forward at the equal angles, because they share full amount of relative velocity "fifty - fifty" and the both "take the abberration into account" to the same extent. Albert Gartinger (talk) 14:55, 13 October 2018 (UTC)

The closer observer's velocity is to that of light, the the lower above the horizon is the visible position of the source, although in fact at the moment of measurement the source is directly above the head, or at points of closest approach. Albert Gartinger (talk) 15:03, 13 October 2018 (UTC)

Yes, I see that the source of the former analysis in the Motion in an arbitrary direction was this chapter at Mathpages http://www.mathpages.com/rr/s2-04/2-04.htm Albert Gartinger (talk) 16:21, 13 October 2018 (UTC)

Something wrong with this animation

I have removed this animation. I am not sure that the animation is wrong, but the caption most certainly is. It speaks of the "oblate shape" of the sphere, "as seen from our perspective."

The effects of Terrell rotation mean that the sphere will not appear oblate from our perspective. There is a profound difference between what is measured versus what is seen in special relativity.

Given that the caption's description of the perceived shape of the sphere from our perspective is wrong, I wonder what else about this animation is wrong. Prokaryotic Caspase Homolog (talk) 22:21, 15 October 2018 (UTC)
 * After studying this animation a bit more, the answer is, "Pretty much everything." Prokaryotic Caspase Homolog (talk) 22:54, 15 October 2018 (UTC)
 * It's all like that, the animation is confusing, I looked at it. In fairness it must be said, that the "rotated Terrell's sphere" is also a bit confusing since it is only a special case. It depends on spatial position of the camera wrt the sphere. The Terrell's photo was taken at the moment when the sphere had already flown far away. What for? Terrell photographs the image that was radiated at the moment of closest approach.  While this image "flies" to the camera, the sphere moves away. You can change the reference frame and make the camera moving wrt "stationary" sphere. That makes clear that the "rotated sphere" is just a photo taken from the side. For example, you ask me to take your photo, and I photograph one of your ears from the side. Then I publish a scientific paper that Mr. PCH appears rotated on photographs. Very entertaining!  If you take a photo at that moment when the sphere is directly opposite the camera, it will not be rotated, but $$\gamma$$ times elongated because of the Lorentz contraction of the film, with the both ears clearly visible. There are parallels with transverse Doppler blueshift at points of closest approach. Albert Gartinger (talk) 06:28, 16 October 2018 (UTC)
 * If an observer thinks that he is "moving" in the sphere's frame, then he is free to choose non - standard synchronization (Reichenbach's) of clocks in his frame (one - way speed of light will be slow "forward" and fast "backward" and the sphere will be measured as "stretched" fully in accordance with that picture as taken by "moving" camera at point of closest approach. Albert Gartinger (talk) 06:42, 16 October 2018 (UTC)
 * For comparison, most (but not necessarily all) of the animations on the SpaceTimeTravel.org site are correct. I remember writing to the authors of this site about some detail or other about some figure/animation that seemed a bit off. I don't remember what the detail was, and I don't see the figure/animation to jog my memory, so I think that the figure/animation that I had questions about may have been taken off. Anyhow, the geometric distortion seen in the animation that I took off corresponds to those seen in the movie labeled "Movie: Soccer ball - 90% of the speed of light, length contraction omitted This simulation is not relativistically correct!" Prokaryotic Caspase Homolog (talk) 08:41, 16 October 2018 (UTC)

What do you think of replacing the other animation with this static figure? By comparing the relativistic prediction with the non-relativistic one, it illustrates better the differences between relativistic Doppler shift/aberration and the Newtonian prediction. I don't know if the quantitative details are correct (gridline spacing), but qualitatively (color effects), it seems OK. In order to check the quantitative details, I would have to do a bit of computer programming, and I don't have time to do that right now. Prokaryotic Caspase Homolog (talk) 09:12, 16 October 2018 (UTC)
 * It looks good. I believe that colors are fine. Maybe the grid must be worked out even though it seems convincing. Albert Gartinger (talk) 09:32, 16 October 2018 (UTC)
 * Thanks! Prokaryotic Caspase Homolog (talk) 12:09, 16 October 2018 (UTC)

I'm not sure I want to get into observational evidence for relativistic Doppler shift
$$z$$ is the fundamental observable in cosmological distance calculations.

I just finished deleting a few lines showing a calculation of $$z$$ in terms of relativistic Doppler shift. But the relativistic Doppler shift of special relativity is, strictly speaking, associated with Minkowski spacetime (i.e. flat spacetime). Other contributions to the observed value of $$z$$ are the cosmological redshift and gravitational redshift.

This is way too big a subject to cover adequately in this article, and I do not pretend to be any sort of expert in general relativity or cosmology. Best to leave discussion of $$z$$ to the articles on redshift, Hubble's law, Cosmology etc. which hopefully are being edited by people who know more about the subject than I do.

Prokaryotic Caspase Homolog (talk) 18:36, 17 October 2018 (UTC)

I guess that I'm pretty much finished with what I wanted to change
With my last edit clarifying the scope of the article, I think that I'm basically finished. It probably needs some tweaks, but I can't think of anything major that I want to add. Hope you like the result. Prokaryotic Caspase Homolog (talk) 20:33, 17 October 2018 (UTC)
 * Congratulations! Of course I like it! Obviously, it has become more systematic and informative. I believe, that in general it is one of the best. You have done a great job! You make amazing charts and diagrams! --Albert Gartinger (talk) 14:56, 18 October 2018 (UTC)
 * Remember, you helped! Prokaryotic Caspase Homolog (talk) 16:19, 18 October 2018 (UTC)

Question about section Systematic derivation for inertial observers (currently retitled)
(Current title of this section is Longitudinal Doppler effect analyzed using Lorentz transforms)

I have been doing rearrangement and cleanup of this article. Just a few hours ago, I added missing sources for the section on the Longitudinal Doppler effect

I note that you are principal editor of the section on using Lorentz transforms to derive the longitudinal Doppler effect. The single reference that you provided at the end, to Landau & Lifshitz volume 2, pp 1–3, did not work as a reference to back up the approach to deriving the longitudinal Doppler effect that you used in this section. Their treatment of the Doppler effect, on pp 116–117, uses the transformation of four-vectors.

I have no issues with the derivation itself. I just reviewed it, and it looks OK to me. But Wikipedia is not supposed to be a place where people publish their own original research.

I have been searching articles and textbooks to find one which employs the approach that you used. Could you help me out by supplying a reference? Prokaryotic Caspase Homolog (talk) 15:16, 11 October 2018 (UTC)

Sorry, I have just noticed the ping. Yes, I wrote most of that section, you are correct. As for sources, I honestly can't remember what, if any, I used. Looking back at it, I would certainly agree that the final paragraph, where the consequences of the classical Doppler effect on EM radiation is discussed, should have a source. As for the derivation itself, by the strict guidelines of WP:OR it probably does fail, but I think a sensible person would not regard the derivation as "original research" (since it's just a trivial application of the LTEs).

But, to be honest, I no longer care about adding good physics to Wikipedia: the guidelines simply prohibit it, and in good part due to WP:OR. There are caveats in the guidelines (e.g. here) but these are just afterthoughts and anyway are mostly ignored by overzealous editors; the whole exercise is just a losing battle to the pedants. So, I'm not going to waste time trying to remember or find sources, sorry. It's a shame that it will go, since to a struggling undergrad it might have been useful to see things explicitly done, but I accepted a long time ago that that's just how things happen on Wikipedia. Good luck with your efforts. Krea (talk) 23:24, 1 November 2018 (UTC)

 * Original research would be fine if Wikipedia had procedures in place for expert peer review. It does not. A competitor to Wikipedia, Citizendium, which was started by Wikipedia co-founder Larry Sanger in 2006, had attempted to put in place a peer review system, but it encountered an issue: How do you judge who is an expert? Although it launched with major fanfare, the true experts mostly left within a few years, and the editors currently remaining include a fair number of crackpots.

 * So we are left with Wikipedia with its free-wheeling, "anyone can edit" model. The result, quite frankly, is that a lot of junk is mixed in with decent writing. Consider, for instance, the article that you contributed to, Relativistic Doppler effect, and which I worked on intensively for two weeks. In particular, consider the mess that I started from. It opened with large, beautiful animations by a person who really didn't know anything about relativity, in particular how Terrell rotation means that there is a profound difference between measurement versus visual appearance. Yet these two animations had been viewed by hundreds of thousands of visitors to this article with no one noticing that, in the one case, the animation was misleading, and in the other case, the animation was total nonsense.

 * The "Motion in arbitrary inertial frames" section was adequately sourced, but the writer completely misunderstood his source material!

 * Other sections had inconsistent focus. For example, nobody accessing an article on relativistic Doppler effect should have to read a simplistic description of a pitcher tossing balls to a catcher.

 * "No original research" is an unreliable tool for distinguishing between good writing and nonsense. In the article on Special relativity which I am currently working on, I have left in place two large sections of unsourced material because the sections appear to be well written (even if at too high a level for the typical encyclopedia user), and they cover important material. As soon as material becomes available that is written at a more appropriate level for first and second-year undergraduate students (which I consider to be the main target audience), I intend to delete these two sections. My main concern will not be that the sections are unsourced, but because they are written at an inappropriate level.

 * In the case of your contribution, I moved it to the talk page mainly because a perfectly adequate and well-sourced derivation of the longitudinal Doppler effect exists in the article, and there is no real need to present an alternative derivation. Not being sourced was only a secondary consideration in my move. My main concern was to keep the article focused and without unnecessary redundancy.

 * If you ever do find reliable sourcing, I would encourage you to create a section titled "Alternative derivations" at the end of the article and to move your contribution from the Talk page to this section. I would be perfectly happy with you doing this. The important thing to me is that you keep this material at the end of the article and not interrupt the main flow of the article with what would essentially be a large digression.

 * Prokaryotic Caspase Homolog (talk) 22:23, 2 November 2018 (UTC)

 * I'm not suggesting Wikipedia move to a peer-reviewed model, I agree it would not work. Although most -- if not all -- of the physics articles are a mess, perhaps the correct solution is to do exactly what you are doing and simply reorganize and edit the articles so that they are not so patchwork. My grievance against the "no original content" policy is due to its abuse by some editors to push through poor material over good material that was difficult to source. Perhaps that is inevitable and the price that one has to pay for an encyclopaedia of the breadth of Wikipedia. Frankly, the mathematics articles are an even worse mess; some of the maths pages on physics related things are of no real help to anyone who has need to be there. I think the page on the Hodge star was one; I used to have more examples, but I can't remember anymore...

 * As I said before, unfortunately I don't have the time or the inclination to search undergrad notes or books to find a good source, but perhaps one day the fancy might take me. A long time ago I wanted to write an article on the maximum speed of propagation of interaction and its implications on physics, and since I came to that idea after writing that section on the Doppler effect, if I ever find the time to write that article I might find a good source for the Doppler section too.

 * Looking at the relativistic Doppler effect page now, there are a few things that are bugging me:

 * Firstly, the Relativistic Doppler effect subsection does not make clear that the result quoted is only for light waves. There is a tendency for people to think that the relativistic Doppler effect only applies for light waves, which is incorrect. The article should strive not to imply this. The way I wrote my section was to make it clear that I was deriving a relativistic expression for any waves, and that we could use it quite trivially to get an expression for light waves by simply setting the speed of the wave to $$c$$. This analysis is presented at the end, but it really ought to be the main focus of the page. Also, it is in the "Derivation" section, even though there is no derivation presented, and it is very muddled about what it is trying to say. For example:

 * Relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, is often derived as if it were the classical phenomenon, but modified by the addition of a time dilation term. This is the approach employed in first-year physics or mechanics textbooks such as those by Feynman or Morin. Following this approach towards deriving the relativistic longitudinal Doppler effect, assume...

 * This really adds nothing to the discussion, and is potentially misleading. The final result is indeed diluted by $$\gamma$$, but presented here the derivation is insubstantial. To say it is classical but with time dilation is not particularly graceful. Feynman's derivation would be nice here, but the "derivation" presented is actually just a restatement of this observation.

 * Secondly, that analysis I mentioned just now, namely Relativistic Doppler effect is a very elegant derivation, but more technical than the one I wrote. When I wrote my derivation, I explicitly chose to do it from the LTEs for two reasons: first, that it is a simple application of the LTEs and shows that if ever you are stuck you can resort to them; and second, to make clear that whenever the LTEs are used you must always be mindful of what you are doing and to consider that when events that are displaced in space take place you cannot neglect the time it takes for that information to reach the observer. Students sometimes slip up on this point when they do derivations like this for the first time. Ideally, both my derivation and the one in the article ought to be present as two ways in which one can derive the correct result, mine a formulaic derivation and the one currently present as a more elegant way of essentially doing the same thing. The derivation that appears in Feynman would be nice to see too.

 * Note that in the current derivation, the sentence "$$v_s$$ and $$v_r$$ are assumed to be less than $$c_s,$$ since otherwise their passage through the medium will set up shock waves, invalidating the calculation" is, frankly, hilarious. How will the receiver/source create shock waves? What does that mean? Why does it invalidate the derivation? No. The assumptions being made are clear to see from the construction of the setup and can just be read off the Minkowski diagram. Since the source and receiver are within the forward light cone of the event at $$O$$ then you are assuming that $$|v_r| < c$$ and $$|v_s| < c$$. By construction you are also assuming that $$|v_r| < |c_s|$$ from the perspective of an observer stationary at $$O$$. The derivation doesn't assume that $$|c_s| < c$$, but for general considerations it ought to be assumed too.

 * Also the captions in the figures are bad. A caption should briefly explain what the figure is about, not just give a brief title to the figure.

 * I haven't checked the other sections for mistakes. They are probably fine. But I will say that I think it is commendable that you are putting some effort into making things better. I only wish I cared like I used to. Hopefully you can at least make things a little better.

 * Just out of curiosity, which two sections in the SR page are you referring to? I gave the page a quick scan, and the only thing I noted was that the "Spacetime" section just seems like a collection of results. Its contents ought to be put into the rest of the article at the appropriate points. The invariant interval should follow straight after the LTEs, and that would lead quite nicely into a discussion of Lorentz covariance and then relativistic kinematics. That's just my thoughts, though.

 * Krea (talk) 22:44, 6 November 2018 (UTC)

 * Thanks for the critiques!!! A person is generally a poor judge of his own writing, and having objective criticism of one's writing by a knowledgeable person is something that I don't experience often enough on Wikipedia. You are dead on in identifying Special relativity as being a highly problematical collection of results. I shuttled that material to the end because it was not written at a level appropriate for what I deem to be the main target audience for the article (high school through lower division undergradtuate), and I am busy trying to write sections to replace material that is missing. I recently expanded Thomas Rotation from a three line discussion to its current level, and cannibalized Relativistic Doppler effect to add the current subsection. I agree with you that invariant interval should follow straight after the LTEs. In fact, I am working on a section concerning the invariant interval right now. I would appreciate your monitoring my contributions and making the changes that you deem necessary.
 * The derivation that you termed "insubstantial" was in fact mostly the original material that I started with, which was rather muddled. I did the bare minimum that I could to clarify it, then went on to other sections.
 * Wikipedia style guides prefer short captions, with most discussion in the main body of text.

 * I encourage you to make changes to my work! The whole point of the collaborative model of article development used in Wikipedia is that you will see defects that I didn't notice in my writing, and I will see things that you didn't notice about your writing. I have a good thick skin. You don't have to worry about offending me, although I will fight back to defend what I think is right.
 * It will be great to collaborate/bump heads/argue constructively with another knowledgeable individual! Prokaryotic Caspase Homolog (talk) 23:26, 6 November 2018 (UTC)

 * It is tempting, I will admit, but I know how Herculean the task is. It requires such an amount of determination that I would be unsuitable to the task. I and a few other editors tried to rewrite the physics page many many years ago, and it fell apart. For my part, I couldn't accept the definition in the lead section: it was ugly, clumsy, inelegant; completely unacceptable to me for the definition of physics, but there were others who argued for it. Our endeavour collapsed. I think it's better that you follow through with your vision on how things should be. I will just make corrections to any mistakes I see when I can muster the spirit to do so! I'll take a look over the SR page on the weekend; you're welcome to send me a message and I can take a look over anything specific, or just send me a message on anything you like. Just don't expect speedy responses :)
 * Seeing as you're writing a section on the invariant interval now, I recommend Landau and Lifshitz. From memory, their discussion on SR is very elegant: there's always a gem to be found in Landau and you might find it helpful. It's in the Classical Field Theory volume. Check out the arxiv too. There might be some interesting papers on there about the foundations/principles of SR. Also, look for books by the masters themselves. Dirac, Heisenberg, Einstein, Schroedinger etc. have all written books, and when they write their introduction sections they are incredibly perspicacious (as you would expect). I can attest for Dirac (Principles of Quantum Mechanics) and Schroedinger (Space-Time Structure) personally.
 * Krea (talk) 23:09, 7 November 2018 (UTC)

Archives?
Is there an objection to establishing automatic archiving (> 1 year)? Purgy (talk) 07:41, 7 November 2018 (UTC)

Relativistic longitudinal Doppler effect derivation is blatantly wrong
Neither of two sources mentioned at the end contain this derivation. Morin, David (2008) actually has these formulas but for the case when receiver moves towards the source whereas the article considers receiver moving away and some of the formulas are taken from the part where receiver's reference frame is considered whereas the article claims to use source's reference frame. Two errors are made in the article which compensate each other in order to arrive at the correct formula:

1. The wavefront moves with speed $$c\,$$, but at the same time the receiver moves away with speed $$v$$ during a time $$t_s = 1/f_s = \lambda_s/c$$.

Actually this must be during a time $$t_{r,s}$$ as measured in the frame of the source. The wording is correct (at the same time) but the formula is not. From this "the period of light waves impinging on the receiver, as observed in the frame of the source." is $$t_{r,s} = t_s/(1-\beta)$$ which is the formula you can see in Morin, David (2008) (though with different sign for beta due to opposite direction)

2. $$t_{r,s}$$ is measured between two wavefront hits in the source's reference frame. These events are separated in space there. Receiver measures these events in the same point in space (proper time), so the time between wavefronts measured by receiver is smallest, it's $$t_r = t_{r,s} / \gamma$$, not $$t_r = t_{r,s} \gamma$$ (which, again, you can see in Morin, David (2008), all this on page XI-33 in Remark section)  — Preceding unsigned comment added by Panda34 (talk • contribs) 18:14, 8 April 2019 (UTC)

Clarify Reference Frames
Einstein's formula is only valid if the source and receiver were both stationary in the same reference frame at some point in their past and one of them remains so. Otherwise their relative velocity is given by the velocity addition formula as u = +/-( v2 - v1 ) / ( 1 - v1 * v2 / c^2 ) where v1 and v2 are reckoned in the original, common reference frame. The more general case is f1 / f2 = gamma1 / gamma2 / ( 1 + u / c ). --Relativity Guy (talk) 22:10, 26 May 2019 (UTC)

 * Is there a WP:reliable source to back this up? Otherwise it would be wp:original research. - DVdm (talk) 08:23, 27 May 2019 (UTC)
 * I cannot find any documentation about this, but according to our local relativity expert (http://physics.usask.ca/~dick/251.htm), it is a well known fact amongst GR theorists, which is consistently ignored in SR textbooks. It follows from conservation of momentum, since the reference frame in which the net 3-momentum is zero has the maximum possible lapse of proper time. --Relativity Guy (talk) 01:45, 28 May 2019 (UTC)
 * Please indent all your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.
 * Some professor's personal webpage is not sufficient. Wikipedia needs reliable wp:secondary sources for all challenged new content. See wp:RS and wp:BURDEN. - DVdm (talk) 08:12, 28 May 2019 (UTC)
 * I am not aware of any published material that addresses this issue, but the statement "In order to know which time is dilated, we recall that {\displaystyle t_{r,s}} {\displaystyle t_{r,s}} is the time in the frame in which the source is at rest." is problematic for astronomical redshift because being at rest implies the maximal possible lapse of proper time. Neither the Earth nor the distant galaxy can lay claim to that perspective. The rest frame is almost certainly somewhere in between, in which case t0 = gamma1 * t1 = gamma2 * t2. --Relativity Guy (talk) 03:36, 29 May 2019 (UTC)
 * Please indent all your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.
 * Without published material Wikipedia cannot take it on board—by design. - DVdm (talk) 07:44, 29 May 2019 (UTC)
 * Are you saying that the scientists who analyze redshift data are using the wrong formula? That seems unlikely. --Relativity Guy (talk) 01:55, 30 May 2019 (UTC)
 * As far as I can tell, the GR metric for cosmological redshift is ds^2 = c^2 dt^2 - a(t)^2 dr^2, where the factor ‘a’ represents the expansion of the universe as a function of coordinate time. The metric distance ’s’ is presumed to represent proper time in the local reference frame but it actually represents proper time in the centre of momentum reference frame (i.e. the Big Bang.) The correct metric is: dt1^2 = dt2^2 ( 1 - a(s)^2 v2^2 / c^2 ) /( 1 - a(s)^2 v1^2 / c^2 ) where the relative velocity is ( v2 + v1 ) / ( 1 + v1 * v2 / c^2 ). Hubble’s law and galaxy rotation curves would appear to be in error. That's not good. I would think Wikipedia should at least identify the issue as an on-going investigation. --Relativity Guy (talk) 03:35, 30 May 2019 (UTC)
 * Third time: please indent all your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. I fixed it, again.
 * As for the content, see wp:RS and wp:BURDEN, also, again. - DVdm (talk) 08:23, 30 May 2019 (UTC)
 * I think I see what’s going on. The GR metric for a cosmological model is centred on the cosmic rest frame, which is to say that the cosmic rest frame has the maximum possible lapse of proper time. In that context, any redshift (or blueshift) can be attributed entirely to Hubble expansion (or contraction.) The speed of the Earth in that context is ascertained by other means and turns out to be non-relativistic (1,330,000 kph) See http://www.astronomy.ohio-state.edu/~dhw/A5682/notes3.pdf for example. It may be a dubious assumption, but the equations are being applied correctly and your formula is correct for that use case. It probably won't work for galaxy rotation curves though. --Relativity Guy (talk) 19:39, 5 June 2019 (UTC)
 * Dang! This is hard. The general case is f1/f2=gamma1*gamma2*(1-v1*v2)*(1+u/c). This reduces to your formula when v1=0. You can derive this formula yourself with this recipe: (1) Transform RF1 into rest frame, in which the net momentum is zero; (2) Transform rest frame into RF2. (3) Solve for t2/t1 when x1=0.--Relativity Guy (talk) 23:30, 8 June 2019 (UTC)

Inconsistent/undefined units
We generally have v^2/c^2. However, the rotation section uses normalised units for R with no definition or guidance for the reader. There are many other similar things, though not necessarily relayed to units. Consequently, the reader needs an unnecessary level of background to make sense of the article.PhysicistQuery (talk) 22:08, 10 August 2019 (UTC)

 * In the case of $$ \frac{\nu '}{\nu} = \left( \frac{1 - R^2 \omega ^2 }{ 1 - R' ^2 \omega ^2 } \right) ^{1/2} ,$$ I was aware of and very much concerned with the inconsistency of the units used in this equation with those used in the rest of the article. The question is, how much are we allowed to change the form of the equation from that found in the original source material before any changes we make would be considered wp:NOR? In the end, I settled on leaving the notation used in this equation inconsistent with the rest of the article, even though the changes necessary to make it consistent with the rest of the article would be fairly straightforward. As you point out, this decision may have been a mistake.
 * On a related note, the history of the section on Relativistic longitudinal Doppler effect shows successive editors each believing that the previous editor messed up and/or wasn't as clear as they should have been, and the combined effect of multiple editors working on this section is a derivation that, so far as I can see, is not traceable to any source, and would therefore constitute original research. Perhaps this section needs to be rewritten so that the derivation used can be step-by-step correlated with a single reliable source? Prokaryotic Caspase Homolog (talk) 13:56, 11 August 2019 (UTC)

Trying to locate who did the following change (monkbot admin "Trappist the monk" said it was not him)
https://en.wikipedia.org/w/index.php?diff=882618498&oldid=880179841&title=Relativistic_Doppler_effect

is the narrowest timeline I could focus on to locate the crooked change:

<<< The converse, however, is not true. The analysis of scenarios where both objects are in accelerated motion requires a somewhat more sophisticated analysis. Not understanding this point has led to confusion and misunderstanding. >>>

probably as a biased response to the controversy about the novelly discovered extra-energy-shift between emission and absorption resonant lines concerning Mössbauer spectra for a co-orbiting source and absorber at the rotor rim the way first tackled by Walter Kündig (1960s).

Firstly, does anyone know who is responsible for this addition?

Secondly, please modify the indicated passage in terms of the following list of references where Prof. Kholmetskii et al. have dismantled all such notions of so-called "relativistic solutions" (such as the debunked "synchronization effect") that allegedly clear away "confusion and misunderstanding":

[1]	KHOLMETSKII A. L., MISSEVITCH O. V. and YARMAN T., Phys. Scr., 78 (2008) 035302.

[2]	KHOLMETSKII A. L., YARMAN T., MISSEVITCH O. V. and ROGOZEV B. I., Phys. Scr., 79 (2009) 065007.

[3]	KHOLMETSKII A. L., YARMAN T. and ARIK M., Ann. Phys., 363 (2015) 556.

[4]	YARMAN T, KHOLMETSKII A. L. and ARIK M., Eur. Phys. J. Plus, 130 (2015) 191.

[5]	KHOLMETSKII A. L., YARMAN T. and ARIK M., Ann. Phys., 374 (2016) 247.

[6] YARMAN T, KHOLMETSKII A. L. and ARIK M., et al., Can. J. Phys., 94 (2016) 780.

[7]	KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., Eur. Phys. J. Plus, 133 (2018) 261.

[8]	KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., J. Synchrotron Radiat., 25 (2018) 1703.

[9]	KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., Ann. Phys., 411 (2019) 167912.

[10] KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., Int. J. Mod. Phys. D, 28 (2019) 1950127.

[11] KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., Ann. Phys., 409 (2019) 167931.

[12] KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., Ann. Phys., 418 (2020) 168191.

[13] KHOLMETSKII A. L., YARMAN T., YARMAN O. and ARIK M., J. Synchr. Rad., 28 (2021) 78.

Prof. Dr. Ozan Yarman --Ozan Yarman — Preceding undated comment added 14:23, 14 February 2021 (UTC)

Radiant intensity changes with the reciprocal of Doppler factor
Regarding the sentence, "This implies that the total radiant intensity (summing over all frequencies) is multiplied by the fourth power of the Doppler factor for frequency." Isn't it the *reciprocal* of the Doppler factor? Doppler factor is fs/fr. If for example the receivers frequency doubles, then the Doppler factor is half, but the radiant intensity increases by 2^4. — Preceding unsigned comment added by 2603:8000:E500:E39:DD3E:37DE:5C8C:9DBB (talk) 02:36, 5 December 2021 (UTC)
 * Your understanding is correct. On the other hand, I have no idea what is "the Doppler factor for frequency". The sentence should be reworded. Evgeny (talk) 11:42, 5 December 2021 (UTC)

"One object in circular motion around the other

...If an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation.[6]

The converse, however, is not true. The analysis of scenarios where both objects are in accelerated motion requires a somewhat more sophisticated analysis. Not understanding this point has led to confusion and misunderstanding."

The first sentence in the second paragraph needs more explanation to make it clearer what you are trying to say. The converse of a situation where the source is accelerated is not one where source and receiver are accelerated, it is one where only the receiver is accelerated.Rine111 (talk) 15:18, 28 March 2022 (UTC)

Amplitude transformation is missing?
Great work on this article! May I ask if there is a philosophy behind leaving out the amplitude transformation? Einstein published this in 1905 (§7 - see link below) but I cannot find it anywhere in modern literature. If you make an open Google search on “does doppler effect change amplitude”, the first three hits will tell you that it doesn’t. I believe this is true for sound waves, but not in the case of EMR where the amplitude transforms with the same factor as the frequency. You will find a simple derivation of the equation in this preprint https://osf.io/wn3br that may be useful.

Einstein: http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf MadsVS (talk) 10:31, 5 February 2023 (UTC)

 * Hi people. Since no one is sharing their opinion, I will go ahead and add a section on the Amplitude transformation. Inputs are welcome. MadsVS (talk) 06:45, 27 March 2023 (UTC)

Suggested addition
I suggest the following changes: Line 1: The relativistic Doppler effect is the change in frequency, wavelength and amplitude of light,...

After the section "Visualization" we add the following section

Doppler effect on amplitude
The amplitude of an electromagnetic wave transforms with the same factor as the frequency. A blue shifted wave will have a larger amplitude while a red shifted will have a smaller. The general transformation equation was first presented by A. Einstein in 1905 [REF]. This wave property is often left out in textbook treatments of the Doppler effect. The amplitude transformation can be derived by considering the force a plane electromagnetic wave exerts on a charge in motion. Consider the force in an instance where the electric wave has amplitude $$A_E$$, and the magnetic wave has amplitude $$A_B $$. The relation between the electric and magnetic amplitude is $$\boldsymbol{B} = \frac{1}{c} \widehat{\boldsymbol{K}} \times \boldsymbol{E}$$, where $$\widehat {\boldsymbol{K}} $$ is a unit vector in the direction of propagation of the radiation. To simplify the algebra we limit the velocity of the charge to the xy-plane, while having the electric field in the z-direction, and $$\widehat {\boldsymbol{K}} $$ in the positive x-direction. This gives us the following vectors. $$ \begin{align} \widehat{\boldsymbol{K}}=\hat{i} \qquad \qquad \boldsymbol{E} = A_E\hat{k} \qquad \qquad  \boldsymbol{B} = \frac{1}{c} A_E \hat{i} \times \hat{k} = - \frac{1}{c} A_E \hat{j} \qquad \qquad \boldsymbol{v}=v \left( cos \theta \hat{i} + sin \theta \hat{j}  \right) \end{align} $$ Here $$ \mathbf{v} $$ is the velocity vector of the charge, and $$\theta $$ is the angle between $$ \widehat{\boldsymbol{K}}$$ and $$\mathbf{v} $$. The coulomb force on the charge is then

$$ \begin{align} \boldsymbol{F} = q \left( \boldsymbol{E} + \boldsymbol{v} \times \boldsymbol{B} \right) = q \left( A_E \hat{k}- \frac{v}{c} A_E \left( cos \theta \hat{i} + sin \theta \hat{j}\right) \times \hat{j} \right)= q A_E \left( 1-\beta cos \theta  \right) \hat{k} \end{align} $$ To find out how $$ A_E $$ transforms we can compare this to the force in the rest frame of the charge. Primed letters will be used in this frame. Since the charge is at rest there will be no magnetic force, and we have

$$ \begin{align} \boldsymbol{F}' = q A'_E \hat{k} \end{align} $$ Relativistic force transformations can now be used to link $$ \boldsymbol{F} $$ and $$ \boldsymbol{F}' $$. With the chosen orientation of the vectors, all forces are perpendicular to $$ \boldsymbol{v} $$, and the force transformation reduces to $$ \boldsymbol{F}' = \gamma \boldsymbol{F} $$. Inserting the results above we get $$ q A'_E \hat{k} = \gamma q A_E \left( 1-\beta cos  \theta  \right) \hat{k} $$ which reduces to

 * $$   $$ A'_E = \gamma\left( 1 - \beta cos \theta  \right) A_E

$$ The analysis was made in the receivers frame of reference, and the amplitude transforms in the same way as the frequency in $$. If the electric field is not perpendicular to the motion of the charge, the force can have a longitudinal component. This reflects that $$ \widehat{\boldsymbol{K}}' \neq \widehat{\boldsymbol{K}}  $$ due to aberration. MadsVS (talk) 15:37, 14 April 2023 (UTC)

 * As was explained on your talk page User talk:MadsVS in 2019, original research is against Wikipedia's policies. - DVdm (talk) 15:46, 14 April 2023 (UTC)
 * This is not original research. As i point out the equation was published by Einstein in 1905. See §7 "Theory of Dopplers principle and aberration" http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf
 * If you think the way i derive it is too original, that is something we can discuss. Aside from the way I derive it, do you have any arguments of why equation should not be included? MadsVS (talk) 20:38, 14 April 2023 (UTC)
 * One equation published by Einstein, and the remainder original research of the purest kind - see, again wp:OR, and wp:SYNTH. Clearly, wp:CALC does not even remotely apply.
 * Without a reliable textbook source for the entire thing, none of this will be allowed here. We can't even discuss it here per wp:Talk page guidelines and simply because of wp:NOTCHAT, aka What Wikipedia is not. - DVdm (talk) 20:48, 14 April 2023 (UTC)
 * As @DVdm correctly points out, Einsteins paper is a primary source. I have added a couple of secondary sources, and removed the calculations. Hope this new version is in agreement with the policies.
 * == Doppler effect on amplitude ==
 * The field amplitude of an electromagnetic wave transforms in the same way as the frequency.
 * $$  $$ A_r = \gamma\left( 1 - \beta cos \theta_s  \right) A_s $$.
 * Eq. 9 was first published in 1905 by A. Einstein . The Amplitude transformation is often left out of textbook ,
 * but it is found in use in treatments of scattering problems and Doppler Broadening. MadsVS (talk) 13:33, 18 April 2023 (UTC)
 * Eq. 9 was first published in 1905 by A. Einstein . The Amplitude transformation is often left out of textbook ,
 * but it is found in use in treatments of scattering problems and Doppler Broadening. MadsVS (talk) 13:33, 18 April 2023 (UTC)
 * but it is found in use in treatments of scattering problems and Doppler Broadening. MadsVS (talk) 13:33, 18 April 2023 (UTC)
 * but it is found in use in treatments of scattering problems and Doppler Broadening. MadsVS (talk) 13:33, 18 April 2023 (UTC)

 * We can simply include the formula for the transformation of the field amplitudes:
 * $$ A' = \gamma \left( 1 - \beta cos \theta \right) A $$
 * with the citation
 * Extract of page 164
 * But of course we cannot mention the fact that it is not published in two other (standard) text books, as that would be original research again - DVdm (talk) 14:43, 18 April 2023 (UTC)

Great that you have found a textbook reference @DVdm :-) Do you maybe want to edit the page your selv, or shall I do it? I think it is important to use the formulation "field amplitude", as you doo, since this is what the equation describes (and the potential amplitude is unaffected by the doppler shift). Also we should either translate Einstein's notation into the notation of this article (with "r" and "s" subscripts), or just refer to Eq. 7 of the article, which is a translated version of Einstein's frequency transformation. MadsVS (talk) 07:39, 19 April 2023 (UTC)

 * I don't think we need a separate subsection for this, so I have added a little comment at the end of the section Relativistic Doppler effect. See . - DVdm (talk) 09:20, 19 April 2023 (UTC)
 * I agree. First line should also be changed to make it consistent: The relativistic Doppler effect is the change in frequency, wavelength and amplitude of light... MadsVS (talk) 11:52, 19 April 2023 (UTC)
 * Let's be careful about that. I couldn't find a source that directly ties this change in amplitude as part of the Doppler effect. Usually the Doppler effect pertains to frequency and wavelength only, not necessarily to amplitude. As you can see in the source on pages 162, 163, and 164, the Doppler effect is treated in subsection 10.6.2 (The Doppler effect and aberration of light), whereas the amplitudes are mentioned in a separate subsection 10.6.3 (Derivation of the radiation energy transformation). That's why I carefully mentioned it as sort of another effect of relativity, besides the Doppler effect, and without explicitly saying so . Without a source that does it explicitly, I think we shouldn't mention it in the lead. - DVdm (talk) 14:31, 19 April 2023 (UTC)
 * I see that you already had made the change while I was writing the above. I have undone it for now, pending a good explicit source for it. Somehow I doubt we'll find one.... - DVdm (talk) 17:04, 19 April 2023 (UTC)
 * Sorry for rushing ahead DVdm. I thought we had it covered. In Einstein's article they are placed in the same section, and states clearly in the introduction that the Amplitude transformation is part of the Doppler effect. He refers to a textbook by T. P. Gill (The Doppler Effect), but I did not manage to access it online. MadsVS (talk) 17:42, 19 April 2023 (UTC)
 * No problem. But I got another one:
 * Extract of page 22.
 * I restored your version of the lead with this ref. Excellent! - DVdm (talk) 20:07, 19 April 2023 (UTC)
 * Nice work . MadsVS (talk) 07:09, 20 April 2023 (UTC)

title: Talk:Relativistic Doppler effect