Talk:Special relativity

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Former good articleSpecial relativity was one of the Natural sciences good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
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Next steps[edit]

New sections under consideration[edit]

After adding the section on Graphical representation of the Lorentz transformation, it became possible for me to move Causality and prohibition of motion faster than light from where it had been stuck to a more rational location in the article, and then to fence off the old legacy sections behind a "Warning! There be lions and tigers and bears (oh my) beyond this point!" sign.

There is obviously a lot left to be done. Optical effects ought to include relativistic aberration and maybe the Fizeau experiment??? Dynamics, of course, covers force, energy and momentum, collisions, and relativistic mass (and why the majority of physicists consider it to be a deprecated concept). Relativistic mass is a concept that most lay persons have heard about, and I'm sure that many visitors to this article page have been disappointed not seeing any mention of it.

I'm hoping that my reorganization should make it easier to add these additional topics. Prokaryotic Caspase Homolog (talk) 09:33, 11 November 2018 (UTC)Reply[reply]

Hmmm... it looks like I need to cover the magnet and conductor thought experiment as a preparatory step before covering relativistic aberration. Prokaryotic Caspase Homolog (talk) 06:48, 18 November 2018 (UTC)Reply[reply]

Should experimental results be blended with the main narrative or kept separate?[edit]

Currently, almost all discussion of the experimental justification for SR is sequestered in the Status section, not that there is very much of it.

Is this a desirable organization? Prokaryotic Caspase Homolog (talk) 20:49, 14 November 2018 (UTC)Reply[reply]

Suggestion to extend the section on relativity and quantum mechanics[edit]

I would recommend to add to that section a mentioning of the Thomas precession. An extremely clear, though still elementary, introduction to this effect is provided in the excellent textbook by Stepanov.Efroimsk (talk) 04:43, 10 September 2019 (UTC)Reply[reply]

Pre-relativistic understanding of length contraction and time dilation[edit]

@JRSpriggs: Please comment on the proposed revised statement+notes+references and suggest changes as necessary. Prokaryotic Caspase Homolog (talk) 07:47, 15 November 2018 (UTC)Reply[reply]

  • I had written the following:
In pre-relativistic physics, distance and time were considered to be independent measurements, and despite some puzzling experimental results, physicists had no inclination to believe that measured distance or time between events should change as a result of a shift in frame from which measurements are made.
  • You commented, "distance between events DOES change in prerelativistic physics as a result of a change in the reference frame, unless the time of the events is the same" and changed the wording to the following:
In pre-relativistic physics, distance and time were considered to be independent measurements, and despite some puzzling experimental results, physicists had no inclination to believe that measured time between events should change as a result of a shift in frame from which measurements are made.
  • Pre-relativistic views of length contraction and time dilation are rather complex to describe, and my initial phrasing was an (apparently futile) attempt to avoid going into extensive discussion of Lorentz's and Poincaré's speculations. I propose the following revision with notes and references:
In pre-relativistic physics, distance and time were considered to be independent measurements, and despite some puzzling experimental results, physicists had no inclination to believe that any "true" measured distance[note 1] or time[note 2] between events should change as a result of a shift in frame from which measurements are made.
  • I am quite aware that the final form of Lorentz ether theory predicts, within its domain of applicability, results which are identical to those of special relativity. LET, however, underwent extensive development between 1892 through 1905, and meant quite different things at different times. Just because the final form of the theory does not contradict Newton's third law, does not invalidate my statement in the notes that earlier versions had difficulties in conforming with classical mechanics.

Notes

  1. ^ The results of the Michelson–Morley experiment led George Francis FitzGerald and Hendrik Lorentz independently to propose the phenomenon of length contraction. Lorentz believed that length contraction represented a physical contraction of the atoms making up an object.[1]: 62–68  In his view, length contraction should result in compressive strains in an object that should result in measurable effects. Such effects would include optical effects in transparent media, including optical rotation[p 1] and induction of double refraction,[p 2] and the induction of torques on charged condensers moving at an angle with respect to the aether.[p 2] Lorentz was perplexed by experiments such as the Trouton–Noble experiment and the experiments of Rayleigh and Brace which failed to validate his theoretical expectations.[1]
  2. ^ For mathematical consistency, Lorentz proposed a new time variable, the "local time", which depended on the position of a moving body following the relation .[p 3] Lorentz considered local time not to be "real"; rather, it represented an ad hoc change of variable. Impressed by Lorentz's "most ingenious idea", Poincaré saw more in local time than a mere mathematical trick. It represented the actual time that would be shown on a moving observer's clocks. On the other hand, Poincaré did not consider this measured time to be the "true time" that would be exhibited by clocks at rest in the aether.[2] The multiplication of hypotheses led to disturbing conflicts with classical mechanics, including violation of Newton's third law of action and reaction.[1]: 39–42 

Primary sources

  1. ^ Lorentz, H.A. (1902). "The rotation of the plane of polarization in moving media" (PDF). Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW). 4: 669–678. Retrieved 15 November 2018.
  2. ^ a b Lorentz, H. A. (1904). "Electromagnetic phenomena in a system moving with any velocity smaller than that of light" (PDF). Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW). 6: 809–831. Retrieved 15 November 2018.
  3. ^ Lorentz, Hendrik (1895). "Investigation of oscillations excited by oscillating ions". Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies (Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern). Leiden: E. J. Brill. (subsection § 31).

References

  1. ^ a b c Miller, Arthur I. (1998). Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911). Mew York: Springer-Verlag. ISBN 0-387-94870-8.
  2. ^ Darrigol, Olivier (2005). "The Genesis of the Theory of Relativity" (PDF). Séminaire Poincaré. 1: 1–22. Retrieved 15 November 2018.
  • You are over-thinking this. I was not talking about length contraction or any such thing. The sentence which I changed said "... measured distance or time between events should change as a result of a shift in frame ..." (emphasis added). Before special relativity, we had Galilean relativity according to which the transformation law for frames of reference was:
.
The "− v t" term means that the location of an event depends on the time that its position is measured. So if you subtract two such locations to get the x-component of the distance, you will get a value which depends on the times of the events. That is my whole point. JRSpriggs (talk) 20:10, 15 November 2018 (UTC)Reply[reply]
Well, that does not represent what Purgy and I intended. Will have to do a major re-write. Prokaryotic Caspase Homolog (talk) 23:49, 15 November 2018 (UTC)Reply[reply]
More precisely one could perhaps write about coordinatizing two events
in two Galilean inertial frames in standard configuration
leaving separately both their time lapse
and their contemporal spatial distance
invariant.
Not talking about the boring coordinates, this could be also more detailed to
The space—time interweaving puts an end to identical time as well as to contemporality across non comoving frames. Sorry, I missed from the diff-view the suggestion below, and also had no edit conflict. Use to your liking. Purgy (talk) 09:17, 16 November 2018 (UTC)Reply[reply]

  • Let's try this:
In Galilean relativity, length ()[note 1] and temporal separation between two events () are independent invariants, the values of which do not change when observed from different frames of reference.[note 2][note 3]
In special relativity, however, the interweaving of spatial and temporal coordinates generates the concept of an invariant interval, denoted as :
[note 4]
The interweaving of space and time revokes the implicitly assumed concepts of absolute simultaneity and synchronization across non-comoving frames.

Notes

  1. ^ In a spacetime setting, the length of a rigid object is the spatial distance between the ends of the object measured at the same time.
  2. ^ The results of the Michelson–Morley experiment led George Francis FitzGerald and Hendrik Lorentz independently to propose the phenomenon of length contraction. Lorentz believed that length contraction represented a physical contraction of the atoms making up an object. He envisioned no fundamental change in the nature of space and time.[1]: 62–68 
         Lorentz expected that length contraction would result in compressive strains in an object that should result in measurable effects. Such effects would include optical effects in transparent media, such as optical rotation[p 1] and induction of double refraction,[p 2] and the induction of torques on charged condensers moving at an angle with respect to the aether.[p 2] Lorentz was perplexed by experiments such as the Trouton–Noble experiment and the experiments of Rayleigh and Brace which failed to validate his theoretical expectations.[1]
  3. ^ For mathematical consistency, Lorentz proposed a new time variable, the "local time", called that because it depended on the position of a moving body, following the relation .[p 3] Lorentz considered local time not to be "real"; rather, it represented an ad hoc change of variable.[2]: 51, 80 
         Impressed by Lorentz's "most ingenious idea", Poincaré saw more in local time than a mere mathematical trick. It represented the actual time that would be shown on a moving observer's clocks. On the other hand, Poincaré did not consider this measured time to be the "true time" that would be exhibited by clocks at rest in the aether. Poincaré made no attempt to redefine the concepts of space and time. To Poincaré, Lorentz transformation described the apparent states of the field for a moving observer. True states remained those defined with respect to the ether.[3]
  4. ^ This concept is counterintuitive at least for the fact that, in contrast to usual concepts of distance, it may assume negative values (is not positive definite for non-coinciding events), and that the square-denotation is misleading. This negative square lead to, now not broadly used, concepts of imaginary time. It is immediate that the negative of is also an invariant, generated by a variant of the metric signature of spacetime.

Primary sources

  1. ^ Lorentz, H.A. (1902). "The rotation of the plane of polarization in moving media" (PDF). Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW). 4: 669–678. Retrieved 15 November 2018.
  2. ^ a b Lorentz, H. A. (1904). "Electromagnetic phenomena in a system moving with any velocity smaller than that of light" (PDF). Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW). 6: 809–831. Retrieved 15 November 2018.
  3. ^ Lorentz, Hendrik (1895). "Investigation of oscillations excited by oscillating ions". Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies (Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern). Leiden: E. J. Brill. (subsection § 31).

References

  1. ^ a b Miller, Arthur I. (1998). Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911). Mew York: Springer-Verlag. ISBN 0-387-94870-8.
  2. ^ Bernstein, Jeremy (2006). Secrets of the Old One: Einstein, 1905. Copernicus Books (imprint of Springer Science + Business Media). ISBN 978-0387-26005-1.
  3. ^ Darrigol, Olivier (2005). "The Genesis of the Theory of Relativity" (PDF). Séminaire Poincaré. 1: 1–22. Retrieved 15 November 2018.
  • This edit rephrased the footnote defining "length" as a prima vista triviality. A prominent intent in me writing a "bulky" definition for this everyday notion was to introduce the notion of events in their fundamental role of establishing "length", the value of which will turn out as varying from frame to frame, because of varying coordinates of these events. I think the ladder paradox is directly connected here, and a caveat of carrying forward a sloppy notion of length into the realm of STR is appropriate. Purgy (talk) 11:10, 17 November 2018 (UTC)Reply[reply]
I know what you meant, but I found your original wording confusing. "In a spacetime setting the length of a rigid object is defined by the spatial distance of the two events made up of the ends of this object at the same time." The ends of the object are not events, but follow world lines. So you intended that the length of the object should mean the spatial distance between two events, having the same time coordinates, selected from the world lines of the two ends. This spatial distance would, in general, be less than the length measured in the rest frame of the object (i.e. its proper length). In the rest frame of the object, however, it is not at all necessary that the selected events have the same time coordinate.
All this amounts to a lot of superfluous detail, especially in a footnote for the Galilean scenario for which length is an invariant. Prokaryotic Caspase Homolog (talk) 13:45, 17 November 2018 (UTC)Reply[reply]
To me an end of an object at some point in time makes up a perfect event ("two events made up of the ends of this object at the same time"), and varying time traces out a world line, which is a certain collection of events; and I perceive no problem with getting acquainted to the notion of a time-varying lenght, as observed from different frames, never getting longer than some distinguished length, one might call a proper length. I do not know how fruitful it is to continue measuring lengths at different times, which only works in the rest frame of the object, and I expressed my doubts about leaving the notion of length in its "trivial" setting of Galileian spacetime.
I did not suggest a footnote pertaining to the Galileian notion of length, but a footnote to a sustainable notion of length in general, and to focus the attention to the upcoming change in the notion of length. I think the method of "how to measure length" should not be changed/restricted during migration to STR, and thus I am unaware of a "lot of superfluous detail", however, I consider a footnote, missing to warn about the upcoming subtleties, to be really superfluous. Lifting the wording above confusion (which I miss) to your standards is beyond me, disagreeing is not. :) Purgy (talk) 17:01, 17 November 2018 (UTC)Reply[reply]
In terms of English language usage,
  • I do not know what a "spatial distance of two events" means. I do know what a spatial distance between two events means.
  • I do not know what "two events made up of the ends of the object at the same time" means. I do know what two "ends of the object measured at the same time" means.
  • Applying the two "Englishian phrase transformations" essentially converts one phrase to the other, except for your use of "is defined by."
Prokaryotic Caspase Homolog (talk) 18:33, 17 November 2018 (UTC)Reply[reply]
An apology for lack in English idiomology is certainly nonsensical, I just regret it. In German the use of a genitive ("of") instead of a preposition ("between") is common habit, I do ask for improving my construction of "making up" events from their spatial and temporal coordinates (but leaving "events" in place), while talking about their "spatial distance", and, thirdly, after applying the EPT (see above) I do miss not only the rigor-effusing "is defined by", but also the mentioned "event", which is at the heart of post-Galilean spacetime.
I repeat the heart of my complaint: "prima vista triviality". If it were not for the last, innocuously sounding phrase ("measured at the same time"), the whole footnote would be absolutely "superfluous". My concern is to transport to the reader this essential condition not as a small closing phrase, but as an essential, concept transforming information, and I tried to do this via the demonstrative use of "defining" and "event". As usually, take what you like. Purgy (talk) 21:13, 17 November 2018 (UTC)Reply[reply]

No, it is not trivial. It is at the heart of the "brain freeze" that led to my oversight. I should have known better. I thank JRSpriggs for correcting me, and I thank you for introducing the original version of the footnote.

Pushed to main space. We can work on improving it later, but there are other topics to add. Prokaryotic Caspase Homolog (talk) 04:19, 18 November 2018 (UTC)Reply[reply]

I am afraid of being misunderstood. I never wanted to state that the footnote, as is stands now, were trivial. I want to express my perception that its current formulation lacks emphasis on the changing settings in Galilean and -say- Einsteinian spacetime. To my taste, it evokes a prima vista(=sometimes wrong!)-impression of not being that fundamental as it is, by putting a condition, generating the decisive difference, into a small appendix of the sentence. My pleadings just ask for more emphasis on the change, suggesting the use of the words "define" and "event". There is absolutely no need, for a statement to be correct, of conforming to my taste. Purgy (talk) 09:24, 18 November 2018 (UTC)Reply[reply]

I didn't go Deep Into the emission Theory but some of its starting lines say that light is emitted by a speed 'C' relative to the source which is indeed not true as experiments Would see that the speed of light won't increase if emitted from a moving object or from one at rest Om C Thorat (talk) 16:17, 23 January 2020 (UTC)Reply[reply]

Emission theory of light[edit]

The normal introductory dialog on relativity says "No aether could be found so there must be constant speed of light", and then we change basic constructs of time and space to fit. But the much more obvious explanation is the Emission theory. It occurred to me as a student, and to Newton long before that. And the binary star refutation was not produced until long after relativity, and Fox's refutation of that much later.

I believe this warrant some solid introductory text. Otherwise it simply does not make sense to anyone that does not already understand it. And it encourages the worst type of thinking in the sciences, merely repeating what authoritative people say without thinking about it.Tuntable (talk) 00:51, 4 April 2019 (UTC)Reply[reply]

"Intuition" in interpreting spacetime diagrams[edit]

@UKER: objected to the analogy used here, calling the analogy "childish":

While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. The frames are actually equivalent. The asymmetry is due to unavoidable distortions in how spacetime coordinates map onto a Cartesian plane. By analogy, planar maps of the world are unavoidably distorted, but with experience, one learns to mentally account for these distortions.

Uker replaced it with the following wording

While the observer frame is represented with space and time axes that meet at right angles, the axes for observers in different frames of reference are represented with their axes meeting at acute or obtuse angles. This unavoidable asymmetry stems from the way spacetime coordinates map onto a Cartesian plane, but it should not affect the intuition that all the represented frames of reference are equivalent.

It is not an "intuition" that all represented frames of reference are equivalent. Their equivalence is a fact, and recognition of their equivalence is not a native intuition, but rather is an element of knowledge that comes with experience.

Proposed compromise, removing the analogy, but correcting the introduced error of fact.

While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. The frames are actually equivalent. The asymmetry is due to unavoidable distortions in how spacetime coordinates map onto a Cartesian plane, but with experience, one learns to mentally account for these distortions.

Prokaryotic Caspase Homolog (talk) 12:24, 3 August 2020 (UTC)Reply[reply]

UKER's "the observer frame" sounds ambiguous. I'd prefer the first sentence of your version:
"While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. The frames are equivalent."
We don't need the pedagogic remark. But as always, to avoid this kind of back and forth, stick a good source to it and cast it in concrete. - DVdm (talk) 12:47, 3 August 2020 (UTC)Reply[reply]
I can agree with the primed/unprimed syntax. My issue, as DVdm says, is that comparison to cartographical maps, which seems targeted at a much lower level demographic than the whole rest of the article. --uKER (talk) 21:09, 3 August 2020 (UTC)Reply[reply]
The cartographical analogy is quite commonly used in describing spacetime diagrams, but I can understand why you do not think it appropriate. The learning "to mentally account for these distortions" is a paraphrase of Schutz, but including an actual reference to Schutz seems to be going too far. Overall, I think my proposed compromise should give us each half of what we want, leaving us each a bit disappointed that we didn't get all of what we want. That's the whole point of compromise, after all. Face-smile.svg Prokaryotic Caspase Homolog (talk) 21:48, 3 August 2020 (UTC)Reply[reply]
Ha, Schutz. Bring him on in a reference and let's close this Face-smile.svg. - DVdm (talk) 21:50, 3 August 2020 (UTC)Reply[reply]
Hmmm... "The prohibition against OR means that all material added to articles must be attributable to a reliable, published source, even if not actually attributed." When I look at the original section in Schutz,
I see discussion on various features of spacetime diagrams that take getting used to, illustrating the "inappropriateness of using geometrical intuition based on Euclidean geometry....[the student] has to adapt his intuition accordingly." Strictly speaking, a citation would be WP:SYN of separate sentences by a single author. Prokaryotic Caspase Homolog (talk) 06:13, 4 August 2020 (UTC)Reply[reply]
OK, we can leave it out. No big deal... - DVdm (talk) 08:33, 4 August 2020 (UTC)Reply[reply]

I saw your edit, but that sentence was cringe inducing in that it was written in what seemed like a pedantic-sounding first person, like saying "I'm so experienced I can mentally interpret them properly". Do we really need that remark? What value does it provide? Communicating the article's reader that there's people that can actually read the diagram despite some minor geometric incovenience? --uKER (talk) 02:19, 6 August 2020 (UTC)Reply[reply]

I'm OK with these latest changes of yours. It's only your ORIGINAL attempt at rewording that I had serious objections to. "It should not affect the intuition that all the represented frames of reference are equivalent" made me cringe. Face-smile.svg Prokaryotic Caspase Homolog (talk) 04:36, 6 August 2020 (UTC)Reply[reply]
Fair enough. Give it your best shot. :) --uKER (talk) 05:36, 6 August 2020 (UTC)Reply[reply]

Let's work out revisions to the Transverse Doppler effect section[edit]

@Gregor4: I understand what you are trying to do. But what you have written is verbose, rather confusing, and not written at a level appropriate for the target audience, which would be high school seniors to first year college students. Let's try and work out a better approach. I would recommend that we first review the presentation in Relativistic_Doppler_effect#Transverse_Doppler_effect which covers many of the same points that you wish to address. Thanks! Prokaryotic Caspase Homolog (talk) 08:28, 2 November 2021 (UTC)Reply[reply]

Answer by Gregor4 (talk) 02:40, 9 November 2021 (UTC) Sorry, I had not seen the document Relativistic_Doppler_effect#Transverse_Doppler_effect which gives a good explanation. I think, we should refer to that page, and I have rewritten a contribution for the page Special Relativity below.Reply[reply]

When I originally wrote the current short, highly abbreviated section on TDE in the Special relativity article, I had deliberately covered only the circular cases. Discussing the linear diagrams, as I did in Relativistic_Doppler_effect#Transverse_Doppler_effect, introduces a lot of complications. As I work on this section below, it keeps on getting bigger...and bigger... Face-sad.svg I'm not sure that what I'm creating here is an appropriate level of detail for Special relativity. Prokaryotic Caspase Homolog (talk) 18:08, 13 November 2021 (UTC)Reply[reply]
@Gregor4: Here is the result of my re-write. I don't like it. The level of detail seems out of proportion to what should be in an introductory article for Special relativity, although appropriate for Relativistic_Doppler_effect#Transverse_Doppler_effect. Prokaryotic Caspase Homolog (talk) 14:00, 15 November 2021 (UTC)Reply[reply]

I tried a new version. What do you think? Gregor4 (talk) 04:29, 17 November 2021 (UTC)Reply[reply]

@Gregor4: We need to emphasize Einstein's original formulation of relativistic Doppler shift, with the receiver pointed directly at where it perceives the image of the source to be at its closest point. Ninety-nine percent of all TDE experiments are devoted to this case. Start by reversing (B) and (A). Prokaryotic Caspase Homolog (talk) 14:35, 17 November 2021 (UTC)Reply[reply]

I have added a note about Einstein's formulation in the description of case (2). I do not want to change the order of A and B because the case (1) happens before case (2). Gregor4 (talk) 22:30, 17 November 2021 (UTC)Reply[reply]

Your 5-3a is way too busy. Since this illustration describes the situation in the frame of the source, the analysis should be an almost trivial application of time dilation. You do not need to illustrate any blueshift as the distance decreases in this diagram, because then you have redshift some time after the distance increases. You just confuse the reader. If you want to describe the point of zero Doppler shift, you should do so in a separate section via a separate diagram. Prokaryotic Caspase Homolog (talk) 04:29, 18 November 2021 (UTC)Reply[reply]

I have slightly revised Fig 5-3(a) and have rewritten the explanation for his case. I hope you lie it. Gregor4 (talk) 23:30, 21 November 2021 (UTC)Reply[reply]

Transverse Doppler effect[edit]

Figure 5–3. Transverse Doppler effect: Variant scenarios

The transverse Doppler effect (TDE) is one of the novel predictions of special relativity. Assume that a source and a receiver are both approaching each other in uniform inertial motion along paths that do not collide.

At the beginning, when the observer approaches the light source, the observer sees a blueshift, and later, when the distance with the source increases, he sees a redshift. The transverse Doppler effect describes the situation when the light source and the observer are close to each other. At the moment when the source is geometrically at its closest point to the observer, one may distinguish

  1. the light that arrives at the observer,
  2. the light that is emitted by the source, and
  3. the light that is at half distance between the source and observer.

The situation of case (1) is shown in Fig. 5-3(a) in the rest frame of the source. The frequency observed by the observer is blueshifted by the factor γ because of the time delation of the observer (as compared with the rest frame of the source). The dotted blue image of the source shown in the figure represents how the observer sees the source in his own rest frame.

The situation of case (2) is shown in Fig. 5-3(b) in the rest frame of the observer. This light is received later when the source is not any more at closest distance, but it appears to the receiver to be at closest distance. The observed frequency of this light is redshifted by the factor γ because of the time delation of the source (as compared with the rest frame of the observer). This situation was Einstein's original statement of the TDE [1]

In the situation of case (3), the light will be received by the observer without any frequency change.

Whether an experiment reports the TDE as being a redshift or blueshift depends on how the experiment is set up. Consider, for example, the various Mössbauer rotor experiments performed in the 1960s.[2][3][4] Some were performed with a rotating source while others were performed with a rotating receiver, as in Fig 5‑3(c) and (d). Fig 5‑3(c) and (b) are corresponding scenarios, as are Fig 5‑3(d) and (a).

References

  1. ^ Morin, David (2008). "Chapter 11: Relativity (Kinematics)" (PDF). Introduction to Classical Mechanics: With Problems and Solutions. Cambridge University Press. pp. 539–543. ISBN 978-1-139-46837-4. Archived from the original (PDF) on 4 April 2018.
  2. ^ Hay, H. J.; Schiffer, J. P.; Cranshaw, T. E.; Egelstaff, P. A. (1960). "Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in 57Fe". Physical Review Letters. 4 (4): 165–166. Bibcode:1960PhRvL...4..165H. doi:10.1103/PhysRevLett.4.165.
  3. ^ Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1965). "A time dilatation experiment based on the Mössbauer effect". Proceedings of the Physical Society. 85 (3): 583–593. Bibcode:1965PPS....85..583C. doi:10.1088/0370-1328/85/3/317.
  4. ^ Kündig, Walter (1963). "Measurement of the Transverse Doppler Effect in an Accelerated System". Physical Review. 129 (6): 2371–2375. Bibcode:1963PhRv..129.2371K. doi:10.1103/PhysRev.129.2371.