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== Let's work out revisions to the Transverse Doppler effect section ==
== Thought experiments ==


{{reply to|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 ] which covers many of the same points that you wish to address. Thanks! ] (]) 08:28, 2 November 2021 (UTC)
In his popular and semi-popular writings, Einstein was well-known for illustrating basic concepts of relativity with the aid of thought experiments.


Answer by ] (]) 02:40, 9 November 2021 (UTC)
Am I simply missing it, or does there not exist an article in Misplaced Pages devoted to "Special relativity thought experiments"?
Sorry, I had not seen the document ] 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.


: 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 ], introduces a '''lot''' of complications. As I work on this section below, it keeps on getting bigger...and bigger... ] I'm not sure that what I'm creating here is an appropriate level of detail for ]. ] (]) 18:08, 13 November 2021 (UTC)
Would creation of such an article be desirable? Or would such an article violate ]?
: {{reply to|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 ], although appropriate for ]. ] (]) 14:00, 15 November 2021 (UTC)


I tried a new version. What do you think?
] (]) 03:24, 5 April 2018 (UTC)
] (]) 04:29, 17 November 2021 (UTC)


:I think that it would be a good article to have, if it is framed as an article about the history of relativity and limited to sourced thought experiments devised by Einstein himself. ] (]) 04:24, 5 April 2018 (UTC) : {{reply to|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). ] (]) 14:35, 17 November 2021 (UTC)


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).
:: Definitely it needs to be a sourced article. If we wish to make it an historical article strictly about Einstein's unique approach to conceptualizing complex scientific ideas, then the article name could be "Einstein's thought experiments", that would describe the ones that he devised not just for special relativity, but also ones that he devised for general relativity and for quantum mechanics. ] (]) 10:11, 5 April 2018 (UTC)
] (]) 22:30, 17 November 2021 (UTC)


:: {{reply to|JRSpriggs}} I have created ]. I hope you find it decent. ] (]) 17:14, 28 April 2018 (UTC) : 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. ] (]) 04:29, 18 November 2021 (UTC)


I have slightly revised Fig 5-3(a) and have rewritten the explanation for his case. I hope you lie it.
:::Yes, thank you. ] (]) 01:39, 29 April 2018 (UTC)
] (]) 23:30, 21 November 2021 (UTC)


====Transverse Doppler effect====
== Measurement versus visual appearance ==
]


The transverse ] (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.
Triggered by recent edits ... While I have no (perceived) problem in the original, probably terse version of identifying the "measured shape" of an object as a collection of 3d-space-coordinates, obtained from a section of spacetime coordinates, and appropriately associated to corresponding object-inherent coordinates, revealing the length contraction in the direction of the velocity, I am unsure about the term "snapshot" in the current version. I think "snapshot" is "taking a picture", and induces inherently propagation of light, which is carefully excluded in "observing", i.e. taking spacetime coordinates.


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
I must admit that the notion of "visual appearance" is a bit bewildering to me in both versions. I think this is now about taking a "snapshot", which involves a central projection, including dependencies on distance between the object and the observer, the direction of the velocity, and what not.
#the light that arrives at the observer,
#the light that is emitted by the source, and
#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 {{math|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.
I think that the presented material is excellent, but the presentation is not fully rigorous and sufficiently explicative, and I am unsure, whether the edits constitute an improvement. 12:29, 10 September 2018 (UTC)


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 {{math|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 <ref name=Morin>{{cite book |title=Introduction to Classical Mechanics: With Problems and Solutions |chapter=Chapter 11: Relativity (Kinematics) |chapter-url=http://www.people.fas.harvard.edu/~djmorin/chap11.pdf |first1=David |last1=Morin |publisher=] |year=2008 |isbn=978-1-139-46837-4 |pages=539–543 |archive-url=https://web.archive.org/web/20180404002006/http://www.people.fas.harvard.edu/~djmorin/chap11.pdf |archive-date=4 April 2018}}</ref>
: Can you suggest a better wording? Now that you bring it up, I can see the problem that you might have with the word "snapshot" as a means of describing the "measured shape" of an object. ] (]) 02:14, 12 September 2018 (UTC)


In the situation of case (3), the light will be received by the observer without any frequency change.
:: I am sorry, but my reservations, and only sometimes direct suggestions for marginal improvements, are all I can provide. I am an intuition-less non-expert in STR, heavily suffering from the total collapse of the concept of ''rigid body'' in STR already in '''1''' dimension (rockets with string). Additionally, I disagree with certain adhered to concepts (necessity of talking about moving observers vs. light sources) claiming to be based on Einstein, and I do not feel adequately versed in the use of this non-native tongue, to express such delicate matters. ] (]) 08:02, 12 September 2018 (UTC)
::: Hmmm... You bring up a variety of issues unrelated to your original concern. ] and ] are not covered in the article as presently written, but one could argue that they need to be covered. One could also argue that coverage of those topics would represent unnecessary digressions, given the article's other deficiencies. The collective authorship paradigm that Misplaced Pages follows, while very good for developing articles in history, biography, etc. has not proven itself very well adapted to the development of technical articles like special relativity. In common with most other technical articles, the current article is a hodgepodge of parts with widely differing levels of difficulty. It needs a thorough overhaul by a person with a clear vision of how the article should be structured and what the target audience is supposed to be.
::: However, giving this article a thorough overhaul is beyond my competency. I can only focus on the little bits and pieces that I myself have added. The best that I can promise is that I'll continue to think about the points that you raised. Maybe somebody else will find a better wording. ] (]) 23:39, 12 September 2018 (UTC)


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 ] performed in the 1960s.<ref name=Hay>{{cite journal|author1=Hay, H. J. |author2=Schiffer, J. P. |author3=Cranshaw, T. E. |author4=Egelstaff, P. A. |date=1960|title=Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in <sup>57</sup>Fe|journal=Physical Review Letters|volume=4|issue=4|pages=165–166|doi=10.1103/PhysRevLett.4.165|bibcode=1960PhRvL...4..165H}}</ref><ref name=Champeney>{{cite journal|author1=Champeney, D. C. |author2=Isaak, G. R. |author3=Khan, A. M. |date=1965|title=A time dilatation experiment based on the Mössbauer effect|journal=Proceedings of the Physical Society|volume=85|issue=3|pages=583–593|doi=10.1088/0370-1328/85/3/317|bibcode = 1965PPS....85..583C }}</ref><ref name=Kundig>{{cite journal|author=Kündig, Walter|date=1963|title=Measurement of the Transverse Doppler Effect in an Accelerated System|journal=Physical Review|volume=129|issue=6|pages=2371–2375|doi=10.1103/PhysRev.129.2371|bibcode = 1963PhRv..129.2371K }}</ref> Some were performed with a rotating source while others were performed with a rotating receiver, as in Fig&nbsp;5&#8209;3(c) and (d).
::::I really had no intention to bring up these topics as ''issues'' of this article (in need of covering), but only as prominent in causing me troubles in developing a good intuition about STR. I feel quite similar to the description of your last paragraph, just additionally handicapped by the necessity to use a non-native language.
Fig&nbsp;5&#8209;3(c) and (b) are corresponding scenarios, as are Fig&nbsp;5&#8209;3(d) and&nbsp;(a).
::::Triggered by your remarks, I want to mention a thorough attempt -not too long ago- to deal with this article in the perspective you mentioned, which seems to have failed the target, but certainly has brought about significant improvements. BTW, I strongly object to the ''collective authorship paradigm'' being any good for questionable articles in history or biography. All the best, ] (]) 07:13, 13 September 2018 (UTC)
::::: '''''This''''' article? The last really major revamping that I recollect was the decision in mid-2015 to delete as being an even worse hodgepodge than the main article. ] (]) 07:52, 14 September 2018 (UTC)


::::::I am deeply concerned by me sloppily mixing up ''this'' article with ], which encountered heavy efforts of targeted improvement in 2017. My attention here was by far too focused on the "snapshooting" of "spacetime vectors", i.e., just on the local changes, being related to STR. Pardon! ] (]) 09:36, 14 September 2018 (UTC)

::::::: The strength (and weakness!) of ] as currently written was the principal editor's determination to adhere, as much as possible, to a purely geometric approach to presenting the material. There are neither trains nor lightning bolts in ]. For the most part, the geometric demonstrations are logically presented, but by their very nature, the demonstrations are somewhat divorced from intuitive understanding. Most people, including myself, are rather more comfortable with a kinematic approach, i.e. with railway cars and spaceships. The problem is, how to add this introductory material? Most "Introduction to" articles get only a few percent of the readership of their associated main articles. Instead of trying to resurrect (which needs to stay dead), I wonder if such material could be added as an extended introductory section to the current article? Against this idea would be the following objections:
::::::: 1) Such material could very easily violate ].
::::::: 2) Such an introductory section could easily double the size of this article.
::::::: 3) A featured wikibook exists on which has the merits of being principally authored by a single knowledgeable editor. It has a consistent presentation and relatively clear focus, and as a wikibook, it was allowed to take on textbook aspects. Despite this, I'm not very happy with it. Could somebody like myself do any better? Absolutely not.
::::::: Thoughts? ] (]) 15:17, 14 September 2018 (UTC)

::::::::... thinking ... ] (]) 08:35, 15 September 2018 (UTC)

{{od}}
I take back part of what I said about the wikibook. I'm '''''very''''' unhappy with it. If you're going to write a textbook on special relativity, you need problems with solutions, or at least lots of example scenarios. ] (]) 11:10, 15 September 2018 (UTC)

:To start with the result of my thinking: I have none. I agree on your verdict the wikibook not making me happy, I do not cling to the WP:NOTTEXTBOOK beyond not allowing for collections(!) of examples (paradigmata are a core necessity in WP! imho), yes, the danger of doubling the length is dangling, and finally, given my engagement and eruditeness on this matter, I am convinced I could not do half as good as you.
:As an aside, I am very skeptical about the usual intuition on kinetics. All this rubbish about "moving observers" stems imho from "intuitively" "observing" '''TWO''' reference frames, thereby silently introducing a '''third''' frame, leaving the uninitiated confused.
:Sorry, I think the best I can do, is commenting from the off sometimes. Please, do never assume any malevolence from my side. ] (]) 07:36, 18 September 2018 (UTC)

== Rearranging the sections, and now I'm stuck ==

I've been rearranging the sections of this article so as to put them into a more rational order, and now I'm stuck.

There are a variety of approaches to teaching relativity:
* The dominant approach found in most college textbooks is begin with the "two postulates" (almost always starting with a stronger, less intuitive form of the second postulate than that adopted by Einstein in his 1905 paper) and to proceed through relativity of simultaneity, time dilation, length contraction etc. to the Lorentz transformations. While traditional, this principle-based approach has many issues. As has noted, "Teaching STR that way is especially problematic because, unlike the case of classical thermodynamics which is also taught as a principle theory, the two postulates or principles in the case of STR are strongly counterintuitive when taken together."
* Several textbooks begin with Minkowski spacetime as the central focus, often approaching Minkowski spacetime through constructive arguments. This, for instance, is the approach adopted by Taylor & Wheeler's ''Spacetime Physics''. The article ] attempts consistently to follow this approach, how successfully, I'm not sure.
* Some authors advocate beginning with the Lorentz transformations as the first principle. I know of '''''no''''' introductory college textbook that teaches special relativity this way.

This article starts off as if it were following a two-postulates presentation, and then suddenly switches over to presenting the Lorentz transformations as the first principle, from which everything else derives.

How should I go from here? Any suggestions? ] (]) 08:53, 28 October 2018 (UTC)

: I think that I've managed a kludgy fix by adding some transitional commentary about different approaches to presenting special relativity. ] (]) 10:00, 28 October 2018 (UTC)

:: I personally am not happy with basing special relativity on the single postulate of universal Lorentz covariance, but that's the way the article appears to have been written. ] (]) 15:36, 28 October 2018 (UTC)

== I need help here ==

Does this section really provide a comprehensible explanation of why FTL is impossible? All it does is state that "one can show" that causal paradoxes can be constructed. ] (]) 03:24, 29 October 2018 (UTC)
: It makes sense to me. It explains how FTL travel would violate causality. There’s no proof of causality but it’s intuitively very appealing as without causality paradoxes arise, so is widely accepted as being true. And if you accept causality then FTL travel must be impossible.--<small>]</small><sup>]</sup><sub style="margin-left:-2.0ex;">]</sub> 03:47, 29 October 2018 (UTC)
:: I restored the section, but I still don't like it. At the very least, it needs a second Minkowski diagram showing how, through the exchange of FTL signals, one can generate a causality-violating scenario. As currently written, it demands an act of faith on the part of the reader. I suppose I could draw the necessary diagram and modify the text to work with the new figure. I don't see a ready-made figure on Commons that will do. ] (]) 04:57, 29 October 2018 (UTC)
:::It’s alright to me. It’s the sort of thing that’s hard to draw as it quickly gets cluttered, but if you’ve looked at enough such diagrams you can visualise it in your head. Or follow the logic of the text which does not really depend on the diagram except to initially establish the relationship between A, B and C.

:::I’m removing the text too now it’s back in the article; it’s still in the page history if there’s any need to refer to it.--<small>]</small><sup>]</sup><sub style="margin-left:-2.0ex;">]</sub> 09:44, 29 October 2018 (UTC)

::::I suggest to get rid of one spatial dimension in the relevant pic. An (x/t + x'/t')-diagram would do the job (there is already a comment about this in the article text) better than this fancy x/y/t-cone. Maybe it is helpful to hint to the trivial fact that any line in the upper half of the first quadrant through the origin and an arbitrary event represents a t'-axis, with an appropriate x'-axis (symmetrically to x = t), whereas any lines through an event in the lower half can only be an x'-axis, because reverse interpretations have no real solutions within the Lorentz transformation (for the less mathy inclined: there is no meaningful place to put the respective other axis ).
::::As an aside: maybe Occham's razor can be considered applicable not only in reducing the number of dimensions in diagrams but also for reducing the number of premises to derive STR from. ;) ] (]) 15:44, 29 October 2018 (UTC)
::::: I was already considering replacing the fancy x-y-t light cone diagram with an x-t diagram. The extra dimensions don't add anything to the presentation, and the current figure occupies a disproportionate amount of real estate. John makes a good point about how cluttered a spacetime diagram illustrating causality violation can be. Use of color can be helpful, but I have to be careful not to rely too much on color. Also, since we have already established that the article begins with universal Lorentz covariance as the central principle for its development of special relativity, it would be better to show this using the LTs rather than with a spacetime diagram. However, I have to mind ]. Anything I add has to be sourced, and the references that I have in mind to use to source my additions all use spacetime diagrams as the simplest way to illustrate their discussion. ] (]) 16:12, 29 October 2018 (UTC)

{{od}}
I am heavily concerned that I cause so much sighs, really. I was aware that my Spacetime effort would have some superior formulation, but I was convinced that the "1800s" are no good either.

... and now I gave some more chance to ''sigh deeply'' about ''this here'' article, but again I am convinced that I implemented some hints to a substantial improvement of the status quo ante. BTW, I left the latter part of the paragraph untouched. Simply throw it all away ... I do not mind too much. ] (]) 08:49, 30 October 2018 (UTC)

== Let's talk about your proposed changes ==

Let's talk about your proposed changes. I'm also working on changes at the same time. ] (]) 12:45, 30 October 2018 (UTC)

===Causality and prohibition of motion faster than light===
]

In Fig.&nbsp;10&#8209;4 the interval <math>\text{AB}</math> is 'time-like'; i.e., the line connecting <math>\text{A} = (x = 0, ct= 0)</math><ref group=note>Unnecessary to explain that A is at the center of the unprimed coordinate system</ref> and <math>\text{B} = (x=x_\text {B}, ct=t_\text{B})</math><ref group=note>Unnecessary to explain that B is at the coordinates of B.</ref> can be taken as a <math>ct'</math>-axis, that establishes with the line symmetric to <math>ct=x</math> an <math>x'/ct'</math>-frame,<ref group=note name=scenario>Not illustrated. You force the reader to have to draw the scenario, either in his/her head or on paper.</ref> in which events <math>\text{A}</math> and <math>\text{B}</math> occur in the primed frame at the same spatial coordinate <math>x'=0</math>, separated by a time interval of length <math>t'_\text{B}.</math><ref group=note name=verbose>Verbose restatement of the original.</ref> The event <math>\text{A}</math> precedes <math>\text{B}</math> in all frames possible under Lorentz transformation (<math>ct'</math>-axis within the light cone).<ref group=note>Unnecessary additions to "A precedes B in all frames"</ref> It is feasible to observe from the <math>x/ct</math>-frame a matter-/information-transport from <math>\text{A}</math> to <math>\text{B}</math><ref group=note>Jargonese rewording of "It is hypothetically possible for matter (or information) to travel from A to B"</ref> at some speed smaller than lightspeed,<ref group=note name=implying>Are you implying here that FTL is possible?</ref> so the event <math>\text{A}</math> can ''cause'' the event <math>\text{B}</math>, if this speed can be achieved by the transport.<ref group=note name=implying/>

The interval <math>\text{AC}</math> is 'space-like'. Since the Lorentz transformation prohibits a <math>ct'</math>-axis within the shaded cone, the line connecting <math>\text{A}</math> and <math>\text{C}</math> ''cannot'' be taken for this, but only as an <math>x'</math>-axis.<ref group=note name=scenario/> The suitable <math>x'/ct'</math>-frame is again symmetric to the <math>ct=x</math>-line,<ref group=note name=scenario/> and in this frame the events <math>\text{A}</math> and <math>\text{C}</math> occur at the same temporal coordinate <math>ct'= 0.</math> So for all events <math>\text{E}</math> within the shaded cone there exists a primed frame in which <math>\text{A}</math> and <math>\text{E}</math> are simultaneous, separated by some spatial distance.<ref group=note name=verbose/> Besides this frame with simultaneity, there are frames in which <math>\text{A}</math> precedes <math>\text{C}\; (t'_\text{C} >0),</math> but also frames in which <math>\text{C}</math> precedes <math>\text{A}\; (t'_\text{C} <0).</math> Naively, some speed above lightspeed (determined by the slope of the line connecting <math>\text{A}</math> and <math>\text{C}</math>) would allow for the latter frames a transport between the spatial coordinates of <math>\text{A}</math> and <math>\text{C}</math> that triggers an event there, prior to the transport's depart, as observed in the <math>x/ct</math>-frame, thereby violating causality.<ref group=note name=verbose/> However, the Lorentz transformation does not yield a solution for such frames.<ref group=note>Why not? What happens to the LT that prohibits this?</ref>

{{reflist-talk|title=Notes|group=note}}

:I care about my wordings, but I do not add much to a stranded investment, I just stand prepared to answer any follow up. I plan for more global remarks in the reply to the second set of notes.
:#It's about making a coordinate ''explicit'', even when it is 0, not about explaining the origin.
:#It's (again) about making the coordinate <math>x_B</math> explicit, soon afterwards there will be an <math>x'_B,</math> too. It's a flaw of math to rely on microscopic differences in notation.
:#I hoped for getting it illustrated.
:#(a) I'd say it's about different frames. (b) No, E is a totally new event. (c) ??? It's the first occurrence of "causality".
:#They're intended as an introduction to the non-existence of <math>ct'</math>-axes in the shaded cone.
:#Jargon in math is at the core of unique meaning, avoiding the "lyrics" of popular introduction (lyrics = much emotion, no precision, just a good feeling for high volume intuition pumping)
:#By no means! Should I have mentioned that worldlines in the first quadrant with slopes greater 1 represent speeds below lightspeed, and that <math>\infty</math> is rest = observer?
:#No real solutions exist, because <math>\gamma</math> isn't a real factor anymore.
:I'll take some time for the announced 2. part, since I want to avoid a TL;DR, but want to say sooo much. :) ] (]) 17:36, 31 October 2018 (UTC)

===I'm concurrently working on additions to the text based on this diagram===
{{multiple image
| width = 160
| image_gap = 4
| image1 = Causality violation 1.svg
| image2 = Causality violation 2.svg
| alt2 = Three small white and yellow flowers before green-leaf background
| footer_align = center
| footer = Figure 10-5. Causality violation
}}

The narrative will go more or less like this: C and D are on a high speed train. A and B are on the ground. D passes B just as the lottery winning numbers are announced. B tells D the winning numbers. D uses his ] to instantaneously inform his partner, C, of the lottery results. C, who is passing A at that moment, informs A of the winning numbers. A user her ansible to instantly flash the numbers to B, who writes the numbers on his lottery ticket, submitting it before the drawing. ] (]) 13:26, 30 October 2018 (UTC)

:For the sake of simplification, you could just omit B and C, and have the whole thing go between A and D. I made a rather crude simplified version of the diagram, adding a marker for an example location of the lottery draw. --] (]) 14:02, 30 October 2018 (UTC)

:: Looking at your diagram, the lottery event needs to be placed on D's world line, otherwise there would be a communications delay.
:: There is another issue, however, and that is ]. I based my diagrams on a published reference. Too much deviation from the diagrams and narrative that I used as my source would constitute original research. ] (]) 14:45, 30 October 2018 (UTC)

:The location of the lottery is fine as long as 1. it's in the past light cone of the moment the moving subject sends the info backwards, and 2. it's in the future light cone of the moment when the stationary subject receives it. About keeping your diagrams, yeah, you probably have a point. --] (]) 18:56, 30 October 2018 (UTC)

:: There are lots of spacetime diagrams to choose from to illustrate the paradox. I've seen this one in multiple contexts. I first came across it several years ago in "The Einstein Paradox and other Science Mysteries Solved by Sherlock Holmes" by ], in "The Case of the Faster Businessman". Then I encountered the same diagram in in David Morin's book, and now, doing a web search, I see it in the Each source accompanies what is essentially the same diagram with a different narrative. On Quora, I remember a soldier being warned just in time not to step on an IED after the driver of a passing troop carrier witnesses the soldier getting his foot blown off. Maybe a Sherlock Holmes mystery would be more appealing and less gory? ] (]) 22:49, 30 October 2018 (UTC)

===Purgy's comment===
*I trimmed my thoughts above and removed the paragraphs at the end to which I deny any comment. I hope you did allow for this.
*I cannot comment much on my suggestion, beyond what I stated already: I am convinced that it is by far more consistent than the status quo, and I concede that it maybe hard to read for the details,<ref group=note>VERY hard to read!</ref> which I consider to be necessary for a thorough understanding.<ref group=note>In general, encyclopedia entries are expected to provide a sketch of a proof, not attempt to provide the entire proof in detail, which is usually impossible within the space limitations of an article.</ref> To my taste there is way too much lyrics around about STR.<ref group=note>What do you mean by "lyrics"?</ref>
*I would gladly defend my proposition, but do not know against what and I also would enjoy seeing it improved, I would clarify all I can<ref group=note>Excessive detail does not clarify, but obscures.</ref> and I can even accept it being ignored, BUT:
*May I plead for reconsidering the inclusion of -say- fictional devices in an explanation, intended to be serious? I object with all my argumentative strength against including this "ansible"-story. This is ''explosion'' (ex falso quodlibet), but no serious argumentation. I cannot accept a claim being refuted because some contradictory device had lead to a contradiction. This is abuse of space time diagrams, rape of LT, cheap baiting with fraudulent gambling, ...
Primarily, I fully accept and support your prerogative on this article. ] (]) 16:01, 30 October 2018 (UTC)

:: Thought experiments invoke particulars that are irrelevant to the generality of their conclusions.
:: You object to the use of these fictional devices. However, it is precisely the invocation of these particulars that give thought experiments their experiment-like appearance. A thought experiment can '''always''' be reconstructed as a straightforward argument, without the irrelevant particulars. ], a well-known philosopher of science, has noted that "a good thought experiment is a good argument; a bad thought experiment is a bad argument."<ref name="Norton1991">{{cite book|author1=Norton, John|year=1991|chapter=Thought Experiments in Einstein's Work |editor1-last=Horowitz|editor1-first=Tamara|editor2-last=Massey|editor2-first=Gerald J.|title=Thought Experiments in Science and Philosophy |publisher=Rowman & Littlefield|isbn=9780847677061|pages=129–148|url=http://philsci-archive.pitt.edu/3190/1/8_norton.pdf |archiveurl=https://web.archive.org/web/20120601110138/http://philsci-archive.pitt.edu/3190/1/8_norton.pdf |archive-date=June 1, 2012}}</ref>
:: When effectively used, the irrelevant particulars that convert a straightforward argument into a thought experiment can act as "intuition pumps" that stimulate readers' ability to apply their ''intuitions'' to their understanding of a scenario.<ref name="Brendel2004">{{cite journal|last1=Brendel|first1=Elke|title=Intuition Pumps and the Proper Use of Thought Experiments |journal=Dialectica|date=2004|volume=58|issue=1|pages=89–108|accessdate=28 April 2018 |url=https://pdfs.semanticscholar.org/fbf3/641682da1249147aaabce84fd99392f0d701.pdf |archiveurl=https://web.archive.org/web/20180428150735/https://pdfs.semanticscholar.org/fbf3/641682da1249147aaabce84fd99392f0d701.pdf|archivedate=28 Apr 2018}}</ref>
:: I ''could'' use the spacetime diagrams to support a straightforward argument demonstrating that FTL communications implies violation of causality, but the ensuing description would be verbose and relatively nonintuitive.] (])
{{reflist-talk}} {{reflist-talk}}
=====The effect's "novelty" is exaggerated=====
{{reflist-talk|group=note|title=Notes}}
: The "transverse Doppler" phenomenology isn't as novel to SR as you might think. A similar effect seems to show up in almost any theory where the motion of the emitter has at least ''some'' influence on how light propagates.
: Take nasty old ballistic emission theory as an example. If an object moving through the lab throws light at what ''it'' believes to be "90 degrees" to its relative motion vector, a lab onlooker will see that ray to be advancing at the same rate as the object, and therefore angled to point slightly forward. If the lab onlooker aims a narrow-angle detector at lab-90 degrees to the path of the object, the light that registers on the detector does not belong to the transverse-aimed ray, but a different ray that was originally aimed slightly to the rear, and is therefore expected to include a recession redshift component.
: As a result, emission theory predicts a similar (actually ''stronger'') redshift to SR's, and pretty much any dragged-light or dragged-aether model that predicts a transverse-aimed ray being deflected forward in the lab frame will predict that the ray ''seen'' at 90 degrees in the lab frame will be seen to be redshifted. ] (]) 21:38, 27 August 2023 (UTC)


== "In Galilean relativity, length..between two events not change when observed from different frames of reference." ==
:::Well, protest as announced: I neither buy the necessity of "irrelevant particulars", not even their usefulness, nor do I believe that they "always" can be removed later on, leaving something that is a real argument. I resort to the opinion ''this thought experiment is a bad argument'' (Norton is fine), and I do not want to see "intuition pumps" (Brendel is rubbish) included in WP, but rather -especially in scientific articles- valid arguments, doubly checked for their validity. However, since you seem to be petrified to include this subspace communications, ... I do not bother for your arguments how to render that "ansibles" as irrelevant for the story or how to reconstruct it as a ''straightforward argument'', when it is just a silly story (there are far more respectable time travels in the pertinent literature), as well as I do not ask any longer for any specific leaks or obscurities in my formulations (that you wanted to discuss!?). May you find a fake, that looks like an experiment that helps others. ] (]) 19:03, 30 October 2018 (UTC)
:::: This obviously cannot be a matter of my strong opinion against your strong opinion, but will require consensus with others' inputs.
:::: By the way, I '''am''' looking closely at your revised proposal. I just can't pay a lot of attention to it right at the moment, since I work for a living. I'll return to examining it tonight.
:::: The results of our previous discussions have always been improvements in the articles in question. I value your comments, even when I disagree wholeheartedly! {{smiley}} ] (]) 21:07, 30 October 2018 (UTC)
{{od}}
If you are against colorful descriptions with multi-million dollar lotteries, Sherlock Holmes mysteries, soldiers on tour in Iraq and the like, how about this:


That's not correct. The length of an ''object '' is invariant in Galileo's world, but the distance/length between ''events ''is not invariant (when two frames are moving with respect to each other). This is an error I've seen before. ] (]) 11:02, 2 April 2023 (UTC)
:Consider the spacetime diagrams in Fig.&nbsp;10&#8209;5. A and B stand beside railroad tracks. A high speed train passes by with C riding in the last car of the train and D riding in the leading car. The world lines of A and B are vertical reflecting the stationary position of these observers on the ground, while the world lines of C and D are tilted forwards, reflecting the rapid motion of these observers in the train.
:Indeed, good catch.
# Fig.&nbsp;10&#8209;5a. B flashes a message to D as the leading car passes by.
:That is why a note is sticking to the expression <math>\Delta r</math>: {{!xt|"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'''."}} (emphasis added).
# D passes the message back to C using an instantaneous communication device. The signal follows along the <math>x'</math> axis, which is a line of simultaneity between C and D.
:For clarity and precision, I have changed that to: {{xt|"In a spacetime setting, the ''length'' of a '''moving''' rigid object is the spatial distance between the ends of the object measured at the same time. '''In the rest frame of the object the simultaneity is not required'''."}} In Galilean relativity, the simultaneity in the "moving frame" implies that in the rest frame of the object.
# Fig.&nbsp;10&#8209;5b. C flashes the message to A who is standing by the railroad tracks.
:I have also changed the phrase {{!xt|''...length and temporal separation between two events...''}} to the more precise {{xt|'''''an object's''' length and '''the''' temporal separation between two events...'}}
# A passes the message forwards to B via the instantaneous communication device. The signal follows along the <math>x</math> axis, which is a line of simultaneity between A and B.
:Change diff: - ] (]) 13:53, 2 April 2023 (UTC)


== Einstein's mechanics ==
Such a description is not very far off from a straightforward argument with none of the "irrelevant particulars" to which you take offense. ] (]) 00:49, 31 October 2018 (UTC)


Special relativity is occasionally referred by this name, both in and in . Is it common enough to mention this alternative name in the beginning and to make a redirect? I ask it here so it's not lost in the edit history. ] (]) 10:49, 26 July 2023 (UTC)
:''Edit conflict with the creation of the newest section, will reply there separately.''
:It's easy to refer to single notes:
:#Yes, it does not belong to my strengths to write directly to the heart, I'm more the nitpicking type, but I am convinced that deep understanding needs deep arguments.
:#I'm not requesting formal proofs (Four color theorem), but I oppose, as strong as is possible to me, to pseudo-explanations for "some thing", like
:::{{Talkquote|The assumption of the "existence of ansibles" (a logical constant 'False' in the theory)<br>''explains'' "some thing".}}
::&nbsp;&nbsp;&nbsp;3. See previous comment of mine.
::&nbsp;&nbsp;&nbsp;4. See #1.: "deep"
:As regards my general impression about explanations of counter-intuitive consequences in STR, I perceive a desire to flesh these out with most spectacular details (twins, pole in a barn, rockets and ropes, ansibles, Holmes, Iraq war, riches, ... ), even when the coexistence of arbitrarily many observers (~frames), all of them at rest in their respective frames, is not fully appreciated by a good deal of the audience. Oblique coordinate systems, unacquainted by themselves, and, additionally, describing a spatially just one-dimensional world and its temporal sections, should be treated with greater care (=detail!), imho. I appreciate the remark that an ansible works along the x-axis, but I miss the emphasis that it is about simultaneity within the -say- unprimed frame, only, and that there is ''no connection'' possible to the primed frame supported by LT.
:I understand that me being satisfied by the non-existence of a world line from A to C does not pertain to all readers, but I am really convinced that this is the core of the story, and all involvements of additional frames and actors, stories and whatnot impossibilities, only blur the core fact: {{tq|NO worldline from A to C!}} As is usual in logic, any assumption to the contrary (e.g.: existence and use of ansibles) allows derivation of ''all'' claims, true ones and false ones (I referred to this in my proposal by using the word "naively"). I deeply regret that my idiomatic abilities cannot provide a text with the necessary ease of readability.
:To my understanding an encyclopedia might (should!) contain information about the most wide spread and most surprising, most funny, ..., stories of counter-intuitivities, but should not(!) involve them in attempts of explanations. Here I am with my personal POV that I only alter for arguments, but not for just "consensus in WP". However, as said already, this won't cause any effects in WP-texts. No edit-warring for me, just TP-skirmishes.
:You may pump as you might, I won't develop any intuition about ansibles. I do however enjoy any of your appreciations. ] (]) 09:24, 1 November 2018 (UTC)


:I don't think it is common enough name to be mentioned in the lead. A redirect can certainly be made, but should probably point to ] instead of this article. ] (]) 11:22, 26 July 2023 (UTC)
==LT vs. two postulates vs spacetime approaches to understanding SR==


== Special relativity postulates ==
Mathematically, it is '''extremely simple''' to establish the non-existence of a world line from A to C, end of story, no need to go any further. But for most, the pure mathematical demonstration doesn't satisfy the need for an intuitive understanding of why that should be so. That is why I am so unhappy about the decision of the original authors of this article to develop special relativity starting with the single postulate of universal Lorentz covariance.


I think it would be interesting that a citation and comment of the following article would be inserted: https://doi.org/10.1119/1.10490
The appeal of the two-postulates development of special relativity is how, starting with these intuitive principles, one can arrive at all sorts of fantastic results, including the Lorentz transformation. But many people just don't ''get'' the deductive style of the two-postulates approach. They get lost at the very start trying to understand relativity of simultaneity, and if one gets stuck there, there is no going forwards.
It shows that the Lorentz transformations and the existence of an invariant speed can be derived based on the principle of relativity and homogeneity of space–time, isotropy of space–time, group structure, causality condition.
It is quite an impressive result that there should be a "limit speed" based on these hypotheses onuly. In this presentation, light does not play such an important role in the elaboration of the theory. ] (]) 09:26, 7 February 2024 (UTC)
:Old hat. Already covered in section ]. - ] (]) 18:11, 7 February 2024 (UTC)
::ok noted. There is no reference to the paper by Levy-Leblond, however. ] (]) 08:20, 8 February 2024 (UTC)
::: The current little section is properly sourced from a textbook and another journal article, so there's no need to add another source. - ] (]) 10:46, 8 February 2024 (UTC)
== "]" listed at ] ==
]
The redirect <span class="plainlinks"></span> has been listed at ] to determine whether its use and function meets the ]. Readers of this page are welcome to comment on this redirect at '''{{slink|Misplaced Pages:Redirects for discussion/Log/2024 October 2#Special relativity (simplified)}}''' until a consensus is reached. <!-- Template:RFDNote --> ]]] 13:57, 2 October 2024 (UTC)


== the section Twin paradox ==
Then there is the spacetime approach, which is frequently taught from a ''constructive'' standpoint through analogies with Euclidean geometry. If you buy the analogies and accept the results of experiment, that is the best approach for many people.


]
What I am trying to get at is that your reservations seem, '''to me''' anyway, mostly that you are most comfortable with a pure mathematics approach to understanding special relativity, which is why you are so dead set against ''irrelevant particulars'', ''intuition pumps'' etc. You are not a thought experiments sort of guy.

] (]) 23:14, 1 November 2018 (UTC)

Using the LTs, Fig. 10-5 can be explained in just three lines. Let S and S' be two frames in in standard configuration, and let <math>\text{E}</math> be the event corresponding to the crossing of the B and D world lines. Then <math>\beta = c t_E/x_E = v/c.</math> The event coordinates <math>(x_E, ct_E)</math> in frame S transform to <math>(x_E/\gamma, 0)</math> in frame S'. An instantaneous signal from <math>\text{E}</math> in frame S' intersects <math>(0,0),</math> and an instantaneous signal from the origin intersects <math> (x_E, 0)</math> in frame S, preceding event <math>\text{E}</math> by <math>t_E.</math> This is totally trivial math, but it does not leave me with any sense of satisfaction that I understand what is going on. It's just symbol manipulation. The spacetime diagram, however, is different. I get a visual handle on the transformation that I simply do not get working the symbols. I can '''see''' the effect of increasing the speed of the train, and I understand ''visually'' why even a speed infinitesimally greater than <math>c</math> can result in causality violation. ] (]) 03:22, 2 November 2018 (UTC)

:Your nice interest in my opinion keeps me quite busy these days. :) I start with the most easy comments.
:I frankly admit to be "most comfortable with a pure mathematics approach" (especially as long as the math is simple enough to my abilities), but I strongly refuse not being accessible by thought experiments. Any of the many indirect proofs I valuate much are such (Let blabla, then ..., therefore ¬blabla.), and I often see essential gain in accessibility by affixing a funny hat (''irrelevant particular'') to some entity (Four ''color'' theorem - not very funny, but famous). For reasons given already by elementary formal logic, I am, however, strongly averse to introducing evident antinomies, like ansibles, in any proof of any claim. (Assume "False", then "Anything". &ndash;is a tautology.) I would agree to disproving the existence of ansibles, relying on geometry or LT and causality, but I disallow for calling any disquisition on anything, which involves the use of an ansible, a proof of anything (repeating: ex falso quodlibet). I accept the path, leading from the ''assumption'' of a speed, ''infinitesimally'' (yuck) larger than lightspeed, to violation of causality, but I am in serious doubt, whether this path is easier to describe and(!) to follow, than the attempt of getting familiar with ct'-axes being restricted to the light cone, and x'-axes to the dark cone, converging with increasing speed to the useful limiting case of ct' and x' coinciding along the propagation of light in all frames (with common origin), the ubiquitous simultaneity. Personally, I perceive the introduction of two additional comoving frames as making things more complex (BTW, the Twin paradox in STR gains its life from the ''frame change'' of the twin.)
:The following is less apodictic and more personal: Dealing with verbally formulated principles is a language game, hard to join in non-native languages, so my primary effort is to create formal tools, independent of natural language, applicable also in hard to understand, in counter intuitive, in surprising, ... situations. To me these tools are the LT. I confess getting lost along so called derivations &ndash;often enriched with ''irrelevant particulars, intuition pumps'', and other distracting stuff, just there to hide the leaks or even flaws (like using ansibles!) within logic&ndash; but with the help of LT I am able to overcome my resentments and arrive at a stable understanding(?)/manipulation, reinforcible at any time by some calculation, even of matters like lost simultaneity. (As an aside, I am not sure, if an "intuitive" understanding of "relative simultaneity" is possible, at all.)
:Imho, there is no "Euclidean" geometry in the spacetime diagrams: it's about the ''difference'' of squares and not their ''sum''. The connecting line of two events in these diagrams is quite misleading wrt their spanned spacetime interval. (I recall to have had a hard time myself to get rid of the Euclidean intuition.) E.g.: Summing the two legs in the twin paradox is "shorter" than the direct connection. I would rather fight Euclidean associations within the x/ct-frame than further them.
:As for your second part, I am perfectly aware that neither my scaring efforts nor your discouraging formulations are very invitational to read, but I rather accept frightening hardship than logical disaster. Maybe there is an intuitively viable path from the slopes of the axes representing the speed and its reciprocal, converging at light propagation, where I started with "Naively, some speed above lightspeed ..."? Anyhow, you decided to take your road.
:Anticipating your objection regarding NOR, may I report that I was moved almost to tears by the ] by ]. For heavens sake, what is done here, in this context, at this level, is '''NO research''', so it cannot be ''original research''. All this is just a "making explicit" of reproducible, trivial math, not to be published for higher academic merit, but to aid the interested reader in his struggle to understand physics beyond falling apples. Are the publishers of books about popular interest topics afraid of losing their clientele to WP? There is so much published rubbish, why shouldn't WP contain some coherent information, without calling it ''research''. ] (]) 16:30, 2 November 2018 (UTC)

:: Your opinion is valuable, even if we disagree a lot. Note now the narrative to the FTL spacetime diagram does not mention lotteries or Sherlock Holmes or soldiers getting their feet blown off by an IED. Your doing! {{smiley}} And I agree that the section is better because of your pushing.
:: In regards to NOR, see my reply to Krea '''].''' ] (]) 22:57, 2 November 2018 (UTC)

:::It's not the first time while being around in WP that I enjoy disagreement, but it's a rare moment still - thanks. Thanks also for correcting my link; I am sorry not to have checked it myself. I would not have bothered to notify Krea myself, but I understand that it could be considered appropriate, and misspelling the name was certainly inappropriate. Just for completeness sake, I assume that we also disagree about the level, above which even well-written paragraphs in scientific articles are to be removed for being ''not properly sourced''. Finally, I announce some boldness of mine, and humble ask for it being kindly checked. Cheers, ] (]) 09:01, 3 November 2018 (UTC)
:::: Looks fine to me. You've achieved the greater precision that you wanted without loading it down with the excessive parenthetical digressions that, to my mind, made your previous attempt unreadable. {{smiley}}
:::: By the way, the other reason for pushing Krea's contribution to Talk was that it was not written in any sort of encyclopedic style, violating ] in a rather extreme fashion. I also disagreed with some sections that, while not technically incorrect, made somewhat misleading points. You can read his writing ''']''' and judge for yourself. ] (]) 11:52, 3 November 2018 (UTC)

== Proposed section revision ==

<strike>The proposed section revision below represents a distinct issue from Purgy's proposed rewording of the opening two paragraphs for greater precision at the cost of lesser clarity, which Purgy considers a good trade-off. '''Hence, this can be deployed separately from any decision regarding Purgy's proposed revisions.'''</strike>

: Issues concerning rewording have been resolved. ] (]) 14:13, 3 November 2018 (UTC)

I do have a question about placement. The article as written uses the single postulate of universal Lorentz covariance as its basic starting principle.
* In terms of ''subject matter'', it belongs in '''Other consequences.'''
* However, it uses Minkowski diagrams to perform the demonstration rather than Lorentz transforms. Therefore, in terms of ''presentation'', it belongs in '''Spacetime.'''

Where should it go? ] (]) 08:27, 1 November 2018 (UTC)

*'''Spacetime''': "No FTL", even when less important, is similarly elementary as contraction and dilation. The current "Other consequences", while certainly worth mentioning, are by no means elementary in the same way.
:This is not say that I perceive the structure of this article as perfect. The mass-energy-equivalence is most certainly not derived from the LT, what is the difference between "derived" and "other" consequences, the LT takes good care about the whole spacetime-space, ... ] (]) 14:38, 1 November 2018 (UTC)
:: OK. I'll keep it there. I could easily have recast the whole argument in terms of the LT, except that would have constituted original research. There is already too much original research in this article that I have been reluctant to throw away. ] (]) 15:03, 1 November 2018 (UTC)

Also, it appears that there is plenty of real estate if we want to reinstate the 3-dimensional light cone diagram that was originally Fig.&nbsp;10&#8209;4. Do we want to revert? ] (]) 08:31, 1 November 2018 (UTC)

*'''No revert''': A flat spatial geometry in two dimensions offers no additional effects relevant to the question of FTL, when compared to a one-dimensional geometry. Since any picture is a projection to two spatial dimensions, the thereby induced spatial ambiguities do not pay the rent, and a higher artificial appeal is just cheating. The troubles of staying aware of a temporal dimension with different metric properties being projected to a spatial dimension is sufficiently bewildering. ] (]) 14:38, 1 November 2018 (UTC)
:: OK. I had no preference for the 2D drawing ''just because I drew it.'' Rather, I want what is best for the article. ] (]) 15:03, 1 November 2018 (UTC)

===Causality and prohibition of motion faster than light===

<span style="color:darkred">'''Section has been transferred to the article via .'''</span>

:Besides the reservations rolled out in previous comments, this version has run to fat for explaining that no infinite speed is necessary to derive a contradiction from a contradiction. Sorry, I had to. ;) ] (]) 14:38, 1 November 2018 (UTC)
:: It is not obvious from the figure that a ''slightly'' greater than light-speed signal would lead to paradox. Either I had to draw a new figure, or I had to explain how a revised figure would look. Since how a revised figure would look is documented in the supplied reference, that appeared to be the preferable route. ] (]) 15:03, 1 November 2018 (UTC)

== I'm going to have to squeeze in an "Introduction to spacetime diagrams" somewhere ==

Although everything in special relativity can be derived from the Lorentz transforms, spacetime diagrams are a highly useful tool for visualization.

The two big elephants in the room are the two sections ] and ], neither of which were written at a level appropriate for what I deem the prime target audience for this article, high school through lower division college students. The two sections are inadequately sourced, and some of the writing may represent original research. For these reasons, I pushed these sections to the end. I have, however, been exceedingly reluctant to delete them, since technically I have found nothing wrong with them.

Somehow or other, I'm going to have to squeeze in a quick "Introduction to spacetime diagrams", since five spacetime diagrams are used in this article without adequate explanation about how they may be interpreted, and as I continue to edit this article, I may introduce more spacetime diagrams. Yes, there will be redundant overlap with the ] section, but that seems an unavoidable evil with the article in its current state. (Despite my efforts so far, I personally would rate the article, in its current state, as ] because it does not meet the "Readers are not left wanting" criterion necessary to meet B-class.) ] (]) 23:13, 5 November 2018 (UTC)

:Some fringe thoughts, triggered by the above concerns.
:- There is an article ], a redirect from "spacetime diagram", that also ''does not'' emphasize that the diagrams are just visualizations of the LT.
:- I dispute the general pedagogic value of deriving STR from principles beyond deriving the LT, as well as of a "constructive" approach to STR. E.g., only the most hardcore intuitive physicists develop an intuition of ''squished EM-fields'' and how to express them, imho.
:- WP is not very apt to address a specific cross-section/level-set of its readership, so I would shed some tears over shooting the elephants. Maybe a title, referring to greater advancedness, and leaving them to the end of the article would help, already.
:- Classifying any article with a scientific topic is hard (WP-rules are contradictory, incoherent, rudimetary, ... ''rubbish''). I ''do not'' argue for or against any capital letter: to suggest the worst, let WMF decide. ] (]) 10:49, 6 November 2018 (UTC)
:: It is possible to develop STR starting from the single postulate of Minkowski spacetime, treating the LTs as a derived principle. Given the emphasis of '''this''' article, starting with universal Lorentz covariance as the fundamental principle underlying STR, the approach taken by ] would be completely incorrect.
:: I fully intend to mention that practical computations in STR usually start with the LTs and/or the fundamental effects immediately derived from the LTs. Minkowski diagrams are most useful as a tool for visualization. They are less useful as a tool for computation.
:: Spacetime diagrams will be treated as derived from the LTs. I intend only a bare minimum introduction, with wikilinks to other articles developing them in greater detail. Thanks for the reference to ], by the way!
:: Shuttling legacy and/or limited-interest advanced topics beyond freshman-sophomore college level to the end and clearly labeling them as "advanced" is the strategy employed in a variety of articles on Misplaced Pages. For example, see ] and ]. Rather than euthanization, that would probably be my choice of what to do with these sections, except that ] is not an advanced topic. This section should not be caged with the others. It needs a separate home.
:: ] and ] are illogical separations of topic. I'm thinking of the following reorganization, taking some inspiration from Rindler:
::: Kinematics: RoS, TD, LC, Thomas rotation, causality and prohibition of FTL
::: Optical effects: Doppler, measurement vs visual appearance
::: Dynamics: mass-energy equivalence, how far can one travel
:: That allows me to cage the two old beasts separately from the others. I can only do this reorganization after developing the "Introduction to spacetime diagrams" section, because of how much use both the RoS and Causality sections make of spacetime diagrams.
:: Different people learn differently. Constructive and deductive approaches are both important.
:: ] (]) 12:25, 6 November 2018 (UTC)

== Doubting ... ==

I am disturbed about the last preparatory edits. I did not like the previous setting either, but I sense further blurring.

- The transformation equations do not relate arbitrary 'measurements', but strictly ''spacetime coordinates''. Hopefully, the measurements are 'covariant', and the appropriately formulated laws of physics confirm this.

- May I suggest to get rid of the "relatively moving observers", at least in new edits? I see an effort to introduce a "standard frame", that is exactly ''the observer'' (at rest!) and his frame. It is ''this frame'', in which ''further'' frames move and can be said to move relatively wrt each other. (I tried to emphasize this less ambiguous POV in my last edit of a caption). Referring to an ''observer'' in one of these further frames, makes this frame the new ''standard frame'', in which coordinates wrt the former standard frame are calculated via the inverse LT of the LT transforming from the old standard to the new (embarrassing).

- It should be made explicit that the parallel orientation of the spatial axes and the orientation of the velocity along the x-axis is a simplifying assumption. (I would not dig deep in the hyperbolic rotation, imho applicable only under this restriction.)

- BTW, what is the origin in spacetime diagrams? Is it the spatial origin, only? Does it make sense to talk about "whereabouts" of an origin at some time?

Just noise from the off. ] (]) 08:24, 8 November 2018 (UTC)

: I made some changes in the wording.
: Re your other comment, I thought I was ''already'' being very explicit that use of standard configuration represents a simplifying assumption, which with care would allow simpler math without invalidating the generality of the conclusions.
: ] (]) 08:59, 8 November 2018 (UTC)

: Spacetime diagrams usually compare two frames in standard configuration. So the origin represents <math>t = t' = 0</math> where all the spatial coordinates line up. The preparatory work is to (1) enable a bare minimum introduction to spacetime diagrams, since they are currently used in the article with no explanation; (2) allow derivation of the invariant interval from the LTs for the simple case of frames in standard configuration. ] (]) 09:22, 8 November 2018 (UTC)

::I was primarily triggered by the diff-display and expected some immediate treatment of spacetime diagrams (x/ct), and so I think I misunderstood not only the term "standard configuration", in wrongly binding it to a frame with ''orthogonal'' temporal and spatial axes, but also the term "origin", as the event with full blown coordinates (0,0,0,0), and no worldline of (0,0,0). Looking at the whole section, I understand your hint to "already", nevertheless, I still think that S and S' are depicted as spatial coordinates, whereas the section deals with spacetime coordinates. I experience this as potentially misleading. Let me know, please, when I get a nuisance. ] (]) 13:42, 8 November 2018 (UTC)

::: The treatment of Minkowski spacetime diagrams in progress begins with the spatial diagram as a starting point. It probably won't be ready to upload until the weekend. I have been delayed by libsvg bugs. You wouldn't believe how much trouble I had trying to draw a simple green line! I finally gave up on green lines, in favor of another color. ] ] (]) 15:41, 8 November 2018 (UTC)

== Let's discuss ==

I don't mind adding in motivations, etc. but your additions need a bit of work. Will add edits with notes in a bit. Mostly considerations of language and target audience, etc. ] (]) 10:39, 10 November 2018 (UTC)

:::Well, I don't mind being given the chance to learn on improvements to my writing. I will abuse the tq-template in inserting my remarks directly into your structure. If this intrusion is considered or turns out as inappropriate for some reason, do not hesitate to simply revert my edit. ] (]) 19:50, 10 November 2018 (UTC)
* Edit 1: In everyday experience, people do not routinely measure or think about SQUARED distances or times. A bit verbose.
::{{tq|I was aware of having been wordy, but I am convinced that hammering on the facts that spacetime coordinates have both spatial and temporal components pays the rent for newbie readers. Maybe, hammering that the <math>\Delta</math>'s (pls, allow for the idiotic apostrophe) in <math>x</math> and <math>t</math> are squared differences and not differences of squared values, but with <math>s</math> it's about the difference of squares, and the "square" has here the meaning of, hmm, what?, is too much. I'm always unsure how to be wordy enough, but not too much. I definitely want the items <math>\Delta t^2</math> '''and''' <math>\Delta x^2</math> to appear separately, to contrast these two independent Galilean invariants to the only one remaining STR invariant <math>\Delta s^2.</math>}}
* Edit 2: I believe that a majority of working physicists consider classical physics to mean non-quantum physics, i.e. relativity would be a classical theory.
::{{tq|I give in to "classic" being wrong, but I do want some serious physics in there, to have some contrast to the non-scientific "everyday" experience: Galilean, pre-Einsteinian, non-relativistic, ...}}
::: How about "pre-relativistic physics"?
* Edit 3: Counterintuitive to whom? Let's not scare the audience too soon. Also, how new is new? I think 100+ years is not new. :-)
::{{tq|We are acquainted to two Galilean (near)-invariants, and the spacetime interval is in a non-trivial way a new one. I gave two reasons,''at least'', for counterintuitivity. I thought nowadays they scream for trigger-warnings, mine should scare them away? ;) }}
* Edit 4: Most students who have learned about Cartesian coordinates are perfectly comfortable with positive and negative distances, times, temperatures etc. Reference to "positive definite", "imaginary time" and "metric signature" should be relegated to a Note, since no attempt is made to provide an inline definition for the reader. They are just "throwaway" terms.
::{{tq|In math, "distances" are non-negative, it takes "pesudo-distances" (like pseudo-Riemannian) to let them be negative. I have no precise notion covering "throwaway term", I introduced these terms for the possibly rare species that wants to connect their acquaintance with STR with rigorous math, or to satisfy their free associations (i² {{=}} -1).}}
::: Pushing to a note preserves your thoughts on this while not interrupting the flow for most readers.
* Edit 5: I'll try putting this chunk and the last chunk of text that I deleted into Notes, to see how putting them into Notes work for you. They are obviously matters that are important to you.
::{{tq|I prefer the "Pythagoras" to "The complete form", because it gives a reason (I like to hammer on), and it strengthens the relation to coordinate values. (less wordy?)}}
::: How about "an expanded form"? "Pythagorean" is confusing because of the minus sign, and I'm not sure I want to spend the time to explain '''here''' its significance. It is certainly an important topic, but I don't want to digress too much. Maybe expand the note?
* Edit 6: I like the overset def. I presume this is a standard form in the math literature?
::{{tq|It is one of the notations I have seen, I prefer it to the \equiv for the latter's many other meanings, I myself used the ":{{=}}" which is deprecated in WP, I think for the computer scientists sake. However, I think it is not appropriate at the second occurrence. It is a def the first time ("along a straight line"!), then it is just a consistent repetition in a detailed section.}}
::: Two dimensions versus four dimensions does not seem overmuch a repetition.
* Edit 7: Restoring deleted chunk of text as a note.
::{{tq|Note is probably fine.}}
* Edit 8: Restoring deleted chunk of text as a note.
::{{tq|See #5}}
* Edit 9: Minor copyedits, both in my language and in yours.
::{{tq|"as such" {{=}} "as an invariant": This constitutes the content of the derivation.}}
::: I understand what you were trying to say now.

<span style="color:darkred"> </span>

== Latest suggestion ==

{{Talkquote|In pre-relativistic physics, measured distances (<math>\Delta x</math>) and time lapses (<math>\Delta t</math>) between events were assumed to be independent invariants, and there were just, then only recently, emerging ideas that these measurements could change when taken in another frame. In special relativity the intrinsic interweaving of spatial and temporal coordinates fundamentally destroys this separate invariance, supported from everyday life, leaving just the ''difference'' of the squares of these quantities, denoted as <math>\Delta s^2</math>, as invariant. The invariance of this quantity can be deduced in a straightforward manner from the Lorentz transform.
: <math>\Delta s^2\;\overset{def}{=}\; c^2 \Delta t^2 - \Delta x^2.</math><ref group=note>This concept is counterintuitive at least for the fact that, in contrast to usual concepts of ], it may assume ''negative'' values (is not ] for non-coinciding events), and that the ''square''-denotation is misleading. This ''negative square'' lead to, now not broadly used, concepts of ]. It is immediate that the negative of <math>\Delta s^2</math> is also an invariant, generated by a variant of the ] of spacetime.</ref>

Expanding the linear spatial distance <math>\Delta x</math> with Pythagoras' theorem makes the invariant interval applicable to the general transformation between ''any'' two Cartesian inertial frames, which may include, in addition to the standard Lorentz transformation, rotations, translation in space, and translations in time (i.e. a ]).<ref name="Rindler1977">{{cite book |last1=Rindler |first1=Wolfgang |title=Essential Relativity |date=1977 |publisher=Springer-Verlag |location=New York |isbn=0-387-10090-3 |edition=2nd}}</ref>{{rp|33–34}}
: <math> \Delta s^2 = c^2 \Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2).</math>
}}
{{reflist-talk}}
{{reflist-talk|group=note|title=Notes}}

Rationale:
*Making <math>\Delta x</math> and <math>\Delta t</math> explicit makes it easier to hint to the special feature of "minus"(!) in the Minkowski metric. I think this remains hard enough to keep in mind when looking at spacetime diagrams, when the "obvious sum" of two triangle sides is "shorter" than the "longest" side. Furthermore, I believe reasons to assume non-invariance did emerge then.
*Recalculating the Euclidean "unique linear spatial distance" via "Pythagoras" is no "re-definition", superseding the previous one. I inserted the parens and exchanged the "-"s for making Pythagoras more obvious. I settle on agreeing on disagreement.

May I ask that you include as much as is to your liking, I consider in any case my ideas as sufficiently considered. ] (]) 09:54, 11 November 2018 (UTC)

Mentioning asides: Shouldn't ] be moved up to Consequences ..., too. More distant: I was very proud about me writing in the lead the "causing - caused" play on words, because I hoped someone were reminded of Wheeler's "how to move - how to curve", but I fully understand that it might not be good English. :) Sorry, ] (]) 11:04, 11 November 2018 (UTC)

: Much improved! You've bypassed my objections to <math>\Delta x^2</math> and <math>\Delta t^2</math>, but I still think it is a bit verbose and overly coy in hinting at (but not actually describing) the "emerging ideas" (i.e. Lorentz, Poincaré). Let me re-read some relevant chapters in Arthur I. Miller's ''Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911)'' before responding. You make me '''WORK!''' I'm still uncertain about Pythagoras. ] (]) 12:23, 11 November 2018 (UTC)

{{od}}
OK, how about this? There is absolutely no need to ''(hint, hint)'' at the "emerging ideas that these measurements could change when taken in another frame" since those ideas had already been quickly suggested in the Introduction, and a link to ] had been provided.
{{Talkquote|In pre-relativistic physics, measured distances (<math>\Delta x, \Delta y, \Delta z</math>) and time lapses (<math>\Delta t</math>) between events were assumed to be independent invariants. In special relativity, the intrinsic interweaving of spatial and temporal coordinates fundamentally destroys these separate invariances, supported from everyday life, leaving just the ''difference'' of the squared time lapse and the summed squares of the spatial quantities, denoted as <math>\Delta s^2</math>, as invariant:
: <math> \Delta s^2 \; \overset{def}{=} \; c^2 \Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2).</math>

The invariance of this quantity can be deduced from the Lorentz transform.<ref group=note>This concept is counterintuitive at least for the fact that, in contrast to usual concepts of ], it may assume ''negative'' values (is not ] for non-coinciding events), and that the ''square''-denotation is misleading. This ''negative square'' lead to, now not broadly used, concepts of ]. It is immediate that the negative of <math>\Delta s^2</math> is also an invariant, generated by a variant of the ] of spacetime.</ref> This invariant interval, related to the Pythagorean theorem, is in fact applicable to the general transformation between ''any'' two Cartesian inertial frames, which may include, in addition to the standard Lorentz transformation, rotations, translation in space, and translations in time (i.e. a ]).<ref name="Rindler1977">{{cite book |last1=Rindler |first1=Wolfgang |title=Essential Relativity |date=1977 |publisher=Springer-Verlag |location=New York |isbn=0-387-10090-3 |edition=2nd}}</ref>{{rp|33–34}}

For simplified scenarios such as in the analysis of spacetime diagrams, a reduced-dimensionality form of the invariant interval is often employed:

: <math>\Delta s^2 \, = \, c^2 \Delta t^2 - \Delta x^2.</math>

Demonstrating that the interval is invariant is straightforward for the two dimensional case and with frames in standard configuration:<ref name=Morin2007/>
}}
{{reflist-talk}}
{{reflist-talk|group=note|title=Notes}}
] (]) 08:44, 13 November 2018 (UTC)

:Only because you asked for it explicitly:
:Omitting the (hint, hint) is fine if hinting was already done (note the "are" in the text now); Euclidean metric (= Pythagoras = SUM of squares) is well known, but I would avoid mentioning Pythagoras, when the spacetime metric (= DIFF of squares) is addressed nearby. How about renaming the first occurrence of <math>\Delta x</math> to <math>\Delta r</math>? I simply like the ultimately terse definition of the spacetime metric, in contrast to the Euclidean metric, as the difference of <math>c^2\Delta t^2</math> and <math>\Delta r^2</math> much better than the one with a boring list of components (x,y,z). Orthogonal decomposition of a strictly 1-dim property into three components is no rocket science. Stripped by all refs, and cramming in some wild beasts to put into footnotes or to annihilate totally, this would look like:

{{Talkquote|In pre-relativistic physics, measured distances (<math>\Delta r</math>) and time lapses (<math>\Delta t</math>) between events are independent invariants. In special relativity, the intrinsic interweaving of spatial and temporal coordinates radically destroys these separate invariances, supported by everyday life experience; just the ''difference'' of the squared time lapse and the squared spatial distance, denoted as <math>\Delta s^2</math>, remains as the ''invariant spacetime interval'', demonstrating a fundamental discrepancy between Euclidean and spacetime distances.

:<math> \Delta s^2 \; \overset{def}{=} \; c^2 \Delta t^2 - \Delta r^2.</math>

In three spatial dimensions <math>\Delta r^2</math> can be expanded, according to Pythagoras' theorem, to

:<math> \Delta s^2 = c^2 \Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2),</math>

but in simplified 1-dimensional scenarios, as in the analysis of spacetime diagrams, the reduced-dimensionality form from above is often employed.

The invariance of the quantity <math>\Delta s^2</math> is a property of the general Lorentz transform (also ]), making it an ] of spacetime. The general Lorentz transform between ''any'' two Cartesian inertial frames covers, in extension to the standard Lorentz transform, which deals just with translations (]s) in x-direction, all other ] and ] in space and in time, and also all transformations that keep the origin fixed (]).

Demonstrating ...}}

: rank the various revised versions of the section, both yours and mine, about three grade levels more difficult to read than what is currently in place. Now, I believe that the first paragraph in any section needs to be maximally accessible, and the difference in difficulty level between the suggestions offered here and what is in place is quite dramatic. As I've stated before, a successful compromise leaves '''neither''' person completely happy. I will push as much as I can of your suggestions into main article space to achieve the additional precision of expression that you desire, but I insist on the readability of the first paragraph. Neither of us will get entirely what we want, but that's the nature of compromise... ] (]) 23:18, 13 November 2018 (UTC)

::Who were I, if I dared to discuss the readability of my English babbling? <small>There is just a faint doubt about the feasibility of "deep learned" programs significantly judging roughly five(!) sentences for their readability.</small> I myself wrote about me ''cramming in'' topics I consider interesting for a reader passing by (sometimes with the intent to trivialize high brow lingo). I really feel honored by any small phrase of mine that makes it into an accepted version. I see my cramming in as just offering on topic window shopping for things I find didactically valuable and generally interesting.
::Besides being quite satisfied as it stands, there is just this
:::<math> \Delta s^2 = c^2 \Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2),</math>
::or worse in its original form
:::<math> \Delta s^2 = c^2 \Delta t^2 - \Delta x^2 - \Delta y^2 - \Delta z^2,</math>
::being preferred to
:::<math> \Delta s^2 = c^2 \Delta t^2 - \Delta r^2</math>
::that I do not understand. The latter version easily focuses on the important NEW temporo-spatial metric (with its ''minus''), emphasizes the one-dimensionality of distance and is way shorter and therefore way more clearly laid out. I am convinced that the embedding of one-dimensional spatial distances in 3-dimensional Euclidean spaces via Pythagoras as
:::<math> -\Delta r^2 = - (\Delta x^2 + \Delta y^2 + \Delta z^2)</math>
::convinces even the faintest hearted. I admit that I am not a fan of this "standard configuration", with its dragging along of two parasitic spatial dimensions, adding ''nothing'' to substantial understanding at this level.
::Please, do not bother to proselytize me to opinions in reliable sources, I really accept the versions that you find fit for WP. ] (]) 10:10, 14 November 2018 (UTC)

== Next steps ==

=== New sections under consideration ===

After adding the section on ], it became possible for me to move ] 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. ] (]) 09:33, 11 November 2018 (UTC)

=== Should experimental results be blended with the main narrative or kept separate? ===

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

Is this a desirable organization? ] (]) 20:49, 14 November 2018 (UTC)

== Pre-relativistic understanding of length contraction and time dilation ==

{{reply to|JRSpriggs}} Please comment on the proposed revised statement+notes+references and suggest changes as necessary. ] (]) 07:47, 15 November 2018 (UTC)
* 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{{refn|group=note|The results of the ] led ] and ] independently to propose the phenomenon of ]. Lorentz believed that length contraction represented a ''physical contraction'' of the atoms making up an object.<ref name="Miller1998">{{cite book |last1=Miller |first1=Arthur I. |title=Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911) |date=1998 |publisher=Springer-Verlag |location=Mew York |isbn=0-387-94870-8}}</ref>{{rp|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<ref name="LorentzPolarization" group=p>{{cite journal |last1=Lorentz |first1=H.A. |title=The rotation of the plane of polarization in moving media |journal=Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW) |date=1902 |volume=4 |pages=669–678 |url=http://www.dwc.knaw.nl/DL/publications/PU00014324.pdf |accessdate=15 November 2018}}</ref> and induction of double refraction,<ref name="LorentzElectromagnetic" group="p">{{cite journal |last1=Lorentz |first1=H. A. |title=Electromagnetic phenomena in a system moving with any velocity smaller than that of light |journal=Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW) |date=1904 |volume=6 |pages=809-831 |url=http://www.dwc.knaw.nl/DL/publications/PU00014148.pdf |accessdate=15 November 2018}}</ref> and the induction of torques on charged condensers moving at an angle with respect to the aether.<ref name=LorentzElectromagnetic group=p/> Lorentz was perplexed by experiments such as the ] and the ] which failed to validate his theoretical expectations.<ref name="Miller1998"/>}} or time{{refn|group=note|For mathematical consistency, Lorentz proposed a new time variable, the "local time", which depended on the position of a moving body following the relation <math>t'=t-vx/c^2</math>.<ref name="Lorentz1895" group=p>{{cite book |last1=Lorentz |first1=Hendrik |title=Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies (Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern) |date=1895 |chapter=Investigation of oscillations excited by oscillating ions |chapter-url=https://en.wikisource.org/Translation:Attempt_of_a_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Bodies/Section_III |at=(subsection § 31) |publisher=E. J. Brill |location=Leiden |url=https://en.wikisource.org/Translation:Attempt_of_a_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Bodies}}</ref> 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.<ref name="Darrigol2005">{{cite journal |last1=Darrigol |first1=Olivier |title=The Genesis of the Theory of Relativity |journal=Séminaire Poincaré |date=2005 |volume=1 |pages=1–22 |url=http://www.bourbaphy.fr/darrigol2.pdf |accessdate=15 November 2018}}</ref> The multiplication of hypotheses led to disturbing conflicts with classical mechanics, including violation of Newton's third law of action and reaction.<ref name=Miller1998/>{{rp|39–42}} }} 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 ] 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.
{{reflist-talk|group=note|title=Notes}}
{{reflist-talk|group=p|title=Primary sources}}
{{reflist-talk}}


I disagree with the statement "in order for the two observers to compare their proper times, the symmetry of the situation must be broken: At least one of the two observers must change their state of motion to match that of the other." And this is depicted in Figure 4.4 when the traveling twin (which I'll call #2) reaches the destination (3 light-years away) and heads back home.
: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 <u>events</u> should change as a result of a shift in frame ..." (emphasis added). Before special relativity, we had ] according to which the transformation law for frames of reference was:
::<math>\begin{align}
t' &= t \\
x' &= x - v t \\
y' &= y \\
z' &= z ,
\end{align}</math>.
:The "&minus; ''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. ] (]) 20:10, 15 November 2018 (UTC)


But actually, #2 doesn't need to do anything more after he reaches the destination. In the 1st diagram, #1 sends his 2nd annual message, which will arrive at the destination when #1 has aged 5 years (#1 time).&nbsp; #2 also knows this, but when he receives the message at the destination, he has aged only 4 years (#2 time).
:: Well, that does not represent what Purgy and I intended. Will have to do a major re-write. ] (]) 23:49, 15 November 2018 (UTC)


Similarly, in the 2nd diagram, when #2 sends his 4th message (from the destination), #1 receives it in his 8th year (#1 time), and subtracting the 3-year propagation delay, he knows that he had aged 5 years (#1 time) when #2 sent the message (after only 4 years of #2 time).<br> ] (]) 16:32, 6 November 2024 (UTC)
:::More precisely one could perhaps write about coordinatizing two events
::::<math>\text{E}_i ,\quad i\in \{1,2\}</math>
:::in two Galilean <math>(t'=t;\;x'=x -vt;\; y'=y;\;z'= z)</math> inertial frames in standard configuration
::::<math>E_i \mapsto \{(t_i,x_i,y_i,z_i),\;(t'_i,x'_i,y'_i,z'_i)\},</math>
:::leaving separately both their time lapse
::::<math>\Delta t= t_2 - t_1= t'_2- t'_1</math>
:::and their contemporal <math>(t_1=t_2)</math> spatial distance
::::<math>\Delta r^2= (x_2 - x_1)^2+ (y_2 - y_1)^2+ (z_2 - z_1)^2= (x'_2 - x'_1)^2+ (y'_2 - y'_1)^2+ (z'_2 - z'_1)^2</math>
:::invariant.
:::Not talking about the boring coordinates, this could be also more detailed to
::::<math>\Delta r= r_2- r_1= (r_2- vt_2) - (r_1-vt_1)= r'_2- r'_1.</math>
:::The space&mdash;time interweaving puts an end to identical time as well as to contemporality across non comoving frames. <small> Sorry, I missed from the diff-view the suggestion below, and also had no edit conflict. Use to your liking. </small> ] (]) 09:17, 16 November 2018 (UTC)


:The statement is properly sourced. Our personal analysis and views are really off-topic here. See ]. - ] (]) 17:18, 6 November 2024 (UTC)
<hr/>
* Let's try this:
:: In Galilean relativity, lengths (<math>\Delta r</math>){{refn|group=note|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.}} and temporal separation between two events (<math>\Delta t</math>) are independent invariants, the values of which do not change when observed from different frames of reference.{{refn|group=note|The results of the ] led ] and ] independently to propose the phenomenon of ]. 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.<ref name="Miller1998">{{cite book |last1=Miller |first1=Arthur I. |title=Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911) |date=1998 |publisher=Springer-Verlag |location=Mew York |isbn=0-387-94870-8}}</ref>{{rp|62–68}}
<br/>&nbsp;&nbsp;&nbsp;&nbsp;
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<ref name="LorentzPolarization" group=p>{{cite journal |last1=Lorentz |first1=H.A. |title=The rotation of the plane of polarization in moving media |journal=Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW) |date=1902 |volume=4 |pages=669–678 |url=http://www.dwc.knaw.nl/DL/publications/PU00014324.pdf |accessdate=15 November 2018}}</ref> and induction of double refraction,<ref name="LorentzElectromagnetic" group="p">{{cite journal |last1=Lorentz |first1=H. A. |title=Electromagnetic phenomena in a system moving with any velocity smaller than that of light |journal=Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW) |date=1904 |volume=6 |pages=809-831 |url=http://www.dwc.knaw.nl/DL/publications/PU00014148.pdf |accessdate=15 November 2018}}</ref> and the induction of torques on charged condensers moving at an angle with respect to the aether.<ref name=LorentzElectromagnetic group=p/> Lorentz was perplexed by experiments such as the ] and the ] which failed to validate his theoretical expectations.<ref name="Miller1998"/>}}{{refn|group=note|For mathematical consistency, Lorentz proposed a new time variable, the "local time", which depended on the position of a moving body following the relation <math>t'=t-vx/c^2</math>.<ref name="Lorentz1895" group=p>{{cite book |last1=Lorentz |first1=Hendrik |title=Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies (Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern) |date=1895 |chapter=Investigation of oscillations excited by oscillating ions |chapter-url=https://en.wikisource.org/Translation:Attempt_of_a_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Bodies/Section_III |at=(subsection § 31) |publisher=E. J. Brill |location=Leiden |url=https://en.wikisource.org/Translation:Attempt_of_a_Theory_of_Electrical_and_Optical_Phenomena_in_Moving_Bodies}}</ref> Lorentz considered local time not to be "real"; rather, it represented an ad hoc change of variable.
<br/>&nbsp;&nbsp;&nbsp;&nbsp;
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.<ref name="Darrigol2005">{{cite journal |last1=Darrigol |first1=Olivier |title=The Genesis of the Theory of Relativity |journal=Séminaire Poincaré |date=2005 |volume=1 |pages=1–22 |url=http://www.bourbaphy.fr/darrigol2.pdf |accessdate=15 November 2018}}</ref>}}


I am quoting just our article, which is someone's interpretation of the source. Where is the policy that says it's "off topic" to question an editor's interpretation? I am also an editor, and my interpretion of the figure presented as evidence does not support the statement.<br>
::In special relativity, however, the interweaving of spatial and temporal coordinates generates the concept of an '''invariant interval''', denoted as <math>\Delta s^2</math>:
--] (]) 23:56, 6 November 2024 (UTC)


: I am the principal author of this particular section, so I am of course concerned in instances where I may have failed to express myself with perfect clarity. Perhaps you would prefer if I rephrased the sentence, "in order for the two observers to '''''perform side-by-side comparisons''''' of their proper times, the symmetry of the situation must be broken: At least one of the two observers must change their state of motion to match that of the other"? Your proposed counterexamples are not side-by-side comparisons of proper time, but rather #1's and #2's respective '''''calculations''''' of what they think would be observed by the other. ] (]) 04:18, 7 November 2024 (UTC)
::: <math> \Delta s^2 \; \overset{def}{=} \; c^2 \Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2) </math><ref group=note>This concept is counterintuitive at least for the fact that, in contrast to usual concepts of ], it may assume ''negative'' values (is not ] for non-coinciding events), and that the ''square''-denotation is misleading. This ''negative square'' lead to, now not broadly used, concepts of ]. It is immediate that the negative of <math>\Delta s^2</math> is also an invariant, generated by a variant of the ] of spacetime.</ref>


Thank you. I am deleting my first long-winded answer, because there is a more direct way to have this discussion.&nbsp; #1 receives #2's 4th annual message in year 8, even if #2 keeps going in the same direction (no asymmetry). If so, then isn't that still a paradox? (because the classical expectation would be 4 years to reach the star + 3 years to receive the message = 7 years)<br>
::The interweaving of space and time revokes the implicitly assumed concepts of absolute simultaneity and synchronization across non-comoving frames.
--] (]) 14:46, 8 November 2024 (UTC)


:No, mere disagreement of special relativity with classical prediction does not constitute a paradox. Please note that these talk pages are intended for suggestions leading to improvement of the article, and are '''''not''''' intended for general discussion of the subject. You may wish to reply to me on my personal talk page, but not here. ] (]) 06:42, 11 November 2024 (UTC)
{{reflist-talk|group=note|title=Notes|colwidth=30}}
{{reflist-talk|group=p|title=Primary sources|colwidth=30}}
{{reflist-talk|colwidth=30}}

Latest revision as of 20:47, 16 December 2024

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

@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)

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.

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... 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)
@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)

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

@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)

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)

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)

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)

Transverse Doppler effect

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

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. 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 Fe". 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.
The effect's "novelty" is exaggerated
The "transverse Doppler" phenomenology isn't as novel to SR as you might think. A similar effect seems to show up in almost any theory where the motion of the emitter has at least some influence on how light propagates.
Take nasty old ballistic emission theory as an example. If an object moving through the lab throws light at what it believes to be "90 degrees" to its relative motion vector, a lab onlooker will see that ray to be advancing at the same rate as the object, and therefore angled to point slightly forward. If the lab onlooker aims a narrow-angle detector at lab-90 degrees to the path of the object, the light that registers on the detector does not belong to the transverse-aimed ray, but a different ray that was originally aimed slightly to the rear, and is therefore expected to include a recession redshift component.
As a result, emission theory predicts a similar (actually stronger) redshift to SR's, and pretty much any dragged-light or dragged-aether model that predicts a transverse-aimed ray being deflected forward in the lab frame will predict that the ray seen at 90 degrees in the lab frame will be seen to be redshifted. ErkDemon (talk) 21:38, 27 August 2023 (UTC)

"In Galilean relativity, length..between two events not change when observed from different frames of reference."

That's not correct. The length of an object is invariant in Galileo's world, but the distance/length between events is not invariant (when two frames are moving with respect to each other). This is an error I've seen before. Johanley (talk) 11:02, 2 April 2023 (UTC)

Indeed, good catch.
That is why a note is sticking to the expression Δ r {\displaystyle \Delta r} : "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." (emphasis added).
For clarity and precision, I have changed that to: "In a spacetime setting, the length of a moving rigid object is the spatial distance between the ends of the object measured at the same time. In the rest frame of the object the simultaneity is not required." In Galilean relativity, the simultaneity in the "moving frame" implies that in the rest frame of the object.
I have also changed the phrase ...length and temporal separation between two events... to the more precise an object's length and the temporal separation between two events...'
Change diff: - DVdm (talk) 13:53, 2 April 2023 (UTC)

Einstein's mechanics

Special relativity is occasionally referred by this name, both in educational resources and in research papers. Is it common enough to mention this alternative name in the beginning and to make a redirect? I ask it here so it's not lost in the edit history. Tarnoob (talk) 10:49, 26 July 2023 (UTC)

I don't think it is common enough name to be mentioned in the lead. A redirect can certainly be made, but should probably point to Relativistic mechanics instead of this article. Jähmefyysikko (talk) 11:22, 26 July 2023 (UTC)

Special relativity postulates

I think it would be interesting that a citation and comment of the following article would be inserted: https://doi.org/10.1119/1.10490 It shows that the Lorentz transformations and the existence of an invariant speed can be derived based on the principle of relativity and homogeneity of space–time, isotropy of space–time, group structure, causality condition. It is quite an impressive result that there should be a "limit speed" based on these hypotheses onuly. In this presentation, light does not play such an important role in the elaboration of the theory. 88.180.38.188 (talk) 09:26, 7 February 2024 (UTC)

Old hat. Already covered in section Special relativity#Relativity without the second postulate. - DVdm (talk) 18:11, 7 February 2024 (UTC)
ok noted. There is no reference to the paper by Levy-Leblond, however. 88.180.38.188 (talk) 08:20, 8 February 2024 (UTC)
The current little section is properly sourced from a textbook and another journal article, so there's no need to add another source. - DVdm (talk) 10:46, 8 February 2024 (UTC)

"Special relativity (simplified)" listed at Redirects for discussion

The redirect Special relativity (simplified) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Misplaced Pages:Redirects for discussion/Log/2024 October 2 § Special relativity (simplified) until a consensus is reached. 1234qwer1234qwer4 13:57, 2 October 2024 (UTC)

the section Twin paradox

Figure 4-4. Doppler analysis of twin paradox

I disagree with the statement "in order for the two observers to compare their proper times, the symmetry of the situation must be broken: At least one of the two observers must change their state of motion to match that of the other." And this is depicted in Figure 4.4 when the traveling twin (which I'll call #2) reaches the destination (3 light-years away) and heads back home.

But actually, #2 doesn't need to do anything more after he reaches the destination. In the 1st diagram, #1 sends his 2nd annual message, which will arrive at the destination when #1 has aged 5 years (#1 time).  #2 also knows this, but when he receives the message at the destination, he has aged only 4 years (#2 time).

Similarly, in the 2nd diagram, when #2 sends his 4th message (from the destination), #1 receives it in his 8th year (#1 time), and subtracting the 3-year propagation delay, he knows that he had aged 5 years (#1 time) when #2 sent the message (after only 4 years of #2 time).
Bob K (talk) 16:32, 6 November 2024 (UTC)

The statement is properly sourced. Our personal analysis and views are really off-topic here. See WP:TPG. - DVdm (talk) 17:18, 6 November 2024 (UTC)

I am quoting just our article, which is someone's interpretation of the source. Where is the policy that says it's "off topic" to question an editor's interpretation? I am also an editor, and my interpretion of the figure presented as evidence does not support the statement.
--Bob K (talk) 23:56, 6 November 2024 (UTC)

I am the principal author of this particular section, so I am of course concerned in instances where I may have failed to express myself with perfect clarity. Perhaps you would prefer if I rephrased the sentence, "in order for the two observers to perform side-by-side comparisons of their proper times, the symmetry of the situation must be broken: At least one of the two observers must change their state of motion to match that of the other"? Your proposed counterexamples are not side-by-side comparisons of proper time, but rather #1's and #2's respective calculations of what they think would be observed by the other. Prokaryotic Caspase Homolog (talk) 04:18, 7 November 2024 (UTC)

Thank you. I am deleting my first long-winded answer, because there is a more direct way to have this discussion.  #1 receives #2's 4th annual message in year 8, even if #2 keeps going in the same direction (no asymmetry). If so, then isn't that still a paradox? (because the classical expectation would be 4 years to reach the star + 3 years to receive the message = 7 years)
--Bob K (talk) 14:46, 8 November 2024 (UTC)

No, mere disagreement of special relativity with classical prediction does not constitute a paradox. Please note that these talk pages are intended for suggestions leading to improvement of the article, and are not intended for general discussion of the subject. You may wish to reply to me on my personal talk page, but not here. Prokaryotic Caspase Homolog (talk) 06:42, 11 November 2024 (UTC)
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