Talk:Relativistic Doppler effect

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.

${\begin{aligned}{\widehat {\boldsymbol {K}}}={\hat {i}}\qquad \qquad {\boldsymbol {E}}=A_{E}{\hat {k}}\qquad \qquad {\boldsymbol {B}}={\frac {1}{c}}A_{E}{\hat {i}}\times {\hat {k}}=-{\frac {1}{c}}A_{E}{\hat {j}}\qquad \qquad {\boldsymbol {v}}=v\left(cos\theta {\hat {i}}+sin\theta {\hat {j}}\right)\end{aligned}}$

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

${\begin{aligned}{\boldsymbol {F}}=q\left({\boldsymbol {E}}+{\boldsymbol {v}}\times {\boldsymbol {B}}\right)=q\left(A_{E}{\hat {k}}-{\frac {v}{c}}A_{E}\left(cos\theta {\hat {i}}+sin\theta {\hat {j}}\right)\times {\hat {j}}\right)=qA_{E}\left(1-\beta cos\theta \right){\hat {k}}\end{aligned}}$

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

${\begin{aligned}{\boldsymbol {F}}'=qA'_{E}{\hat {k}}\end{aligned}}$

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 $qA'_{E}{\hat {k}}=\gamma qA_{E}\left(1-\beta cos\theta \right){\hat {k}}$ which reduces to

Eq. 9 :    $A'_{E}=\gamma \left(1-\beta cos\theta \right)A_{E}$

The analysis was made in the receivers frame of reference, and the amplitude transforms in the same way as the frequency in Equation 7. 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 Wikipedia:What Wikipedia is not#Wikipedia is not a publisher of original thought. - 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.

Eq. 9:   $A_{r}=\gamma \left(1-\beta cos\theta _{s}\right)A_{s}$.

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)

References

@MadsVS: 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

Ta-Pei Cheng (2013). Einstein's Physics: Atoms, Quanta, and Relativity - Derived, Explained, and Appraised (illustrated, reprinted ed.). OUP Oxford. p. 164. ISBN 978-0-19-966991-2. 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)

@MadsVS: 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#Motion in an arbitrary direction. See [1]. - 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)

@MadsVS: 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)

@MadsVS: No problem. But I got another one:

Daniel Kiefer (2014). Relativistic Electron Mirrors: from High Intensity Laser–Nanofoil Interactions (illustrated ed.). Springer. p. 22. ISBN 978-3-319-07752-9. 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)