# Talk:Spacetime

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One of the 500 most frequently viewed mathematics articles.

## Expressing math notation, units of measure, buzzwords, and linking

Overview
Wikipedia’s Manual of Style: Dates and Numbers (WP:MOSNUM) has some wonderful guidance on expressing units of measure. I was tempted to transplant a small bit of cherry-picked examples from its guidance here, but realized it is so well written and succinct, it’s best just to provide the link. So…

The following are my thoughts on how WP:MOSNUM’s principles apply to some specifics of our Spacetime article.

Avoid “sciencey” math notation
Notwithstanding that experts in a field will understand what 1.2 m·s−2 means, instead writing 1.2 meters/second2 makes the measure fully accessible to a larger segment of our visiting readership. Wikipedia is a general-interest encyclopedia; Ph.D.s don’t come to Wikipedia to learn something within their field of expertise. When doing technical writing, one must always consider the gamut of the target audience and try to make the article accessible to the lowest level of that gamut.

Where practical, spell out unit names unless the unit symbol is ubiquitous in everyday life
Take this example of of two unit symbols (km and s):

nearly 300,000 km in space being equivalent to 1 s in time
nearly 300,000 km in space being equivalent to 1 second in time.

Note how “s” became “second” but “km” remained as a unit symbol. Why? Except for in America, both “km” and “km/hr” are seen so often in real life, they become spelled-out units of measure in its own right even though they are technically unit symbols. We also take into consideration the assumed expertise of the readership of the article; writing for our Dog article is different from our Year article, which is different from our Spacetime article. As for Americans and their Customary units of measure in normal life, we can safely assume Americans visiting this particular article are familiar with “km” and “km/hr”. However, “km/s” is not on traffic signs. This principle of spelling out units of measure should generally be adhered to unless doing so makes a paragraph or article section tedious and cumbersome for our readership. On that subject…

Properly introduce “sciencey” unit symbols before using them
If a cumbersome (lengthy and multi-syllabic) scientific unit of measure (one not frequently encountered in real life) repeatedly appears in the same article section and is getting tedious to read, then writers should parenthetically introduce the unit symbol before employing it. Thus, the first occurrence in the section that looks like this:

30 MeV
30 million electron volts (MeV)

After a proper parenthetical introduction, authors may then use the unit symbol (30 MeV) throughout the rest of the passage. The point of using unit symbols where they are frequently encountered isn’t to save ourselves time when writing, but to save our readers mental energy and make the text faster to read.

Authors should also consider allowing greater repetition of a spelled-out unit of measure (avoiding unit symbols) if it is short or monosyllabic, like meter, volt, watt, hertz, lux, year, hour, and joule. A paragraph containing three or four instances similar to the following…

A total surge energy of 30 joules caused the expected damage.
is more natural to read than…
A total surge energy of 30 J caused the expected damage.

…without undue tediousness.

Avoid Click To Learn & Return©™®. Don’t require readers to click links to understand the material at hand
It is good to avoid the overused Wikipedia practice of “We have links, so let’s embrace Click To Learn & Return©™®.” If a noun, term, or phrase is specialty lingo within an art, we shouldn’t use it in an “Oh… didn’t-cha know?”-fashion and expect the mere presence of a link to be sufficiently informative without the courtesy of also providing a simple explanatory parenthetical. Take, for instance, our article on the Space Needle; verbiage like this:

An imitation carillon was installed in the Space Needle.
An imitation carillon (a multi-bell musical device) was installed in the Space Needle.

As an alternative to parentheticals, Click to Learn & Return can be avoided fluidly and naturally by explaining the concept first and then adding a clause to introduce the specialty lingo, like the following example with the term “manifold”:

By combining space and time into a single manifold called Minkowski space in 1908, physicists significantly simplified a
[Minkowski] fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space, what mathematicians refer to as a type of 4‑dimensional manifold.

Italicizing to set off lingo-speak is an option to employ depending upon nuances such as whether it is a compound noun or the lingo-speak is especially obscure.

In all cases when doing technical writing, one carefully considers the sophistication level of the target readership. Clearly, if the vast majority of the target readership can be expected to be familiar with buzzwords common to an art, we wouldn’t speak down to the audience by pulling out the Ernie & Bert puppets to explain the obvious. For instance, an article on a particular kind of musical instrument requires no explanatory verbiage for terms like frequency or musical note; the link alone is sufficient.

Greg L (talk) 18:27, 23 June 2017 (UTC)

### Protest

I want to express my strong objection, firstly to placing the above essay-like variations on the theme of WP:MOS on the talk page of the article entitled Spacetime, because it has no relation to its specific content, and secondly to the content of this comment, trying to prescribe a style, partly inappropriate for an encyclopedia, and not being fully covered by the established policies of WP. Purgy (talk) 13:10, 26 June 2017 (UTC)

What part of “The following are my thoughts”… did you find confusing, Purgy? Methinks thou dost protest too much. If you have a good idea on how we can improve the article, ample digital whitespace is available for constructive help, such as writing your own WP:Essay; they exist for a reason. Greg L (talk) 20:50, 27 June 2017 (UTC)
The problem is not me, in finding things confusing, but you, in repeatedly(!) violating established WP policies, e.g. in editing my intended and coherent layout. I will not elaborate on your efforts to commandeer this whole article, including this talk page, even when being rather clueless on any stringent background of the topic. I cite: "We don’t need any of that here." Meanwhile, others try to discuss the matter. Roma locuta? Purgy (talk) 06:15, 28 June 2017 (UTC)
I see. As regards my above WP:essay on how to keep things as easy as possible to read on an already exceedingly technical article, you are just wrong; an essay on such a topic is perfectly OK. I suggest you read the link I provided.
As regards me and others “violating established WP policies”, where I edited text of yours you felt was “intended” and “coherent”, try not to take the collaborative writing process so personally; it is inherent to the Wikipedia experience for others to discuss and change something you wrote. With specific regard to that edit you seem to be chaffing about, User:Stigmatella aurantiaca responded to you personally as follows (∆ edit here):
You've made some good suggestions in the past, but English does not appear to be your native language. So I've taken your suggested changes here where you and User:Greg L can work on them together. Hope you don't mind too much?.
On a final note, you made a comment here, (∆ edit) where you wrote…
I did not quit cooperation on it for the behaviour of one single disruptive IP-editor, but I explicitly declared four contributors as causing me troubles in cooperating.
Going forward, collaboration usually works better if you don’t bitterly and explicitly complain about the behavior of virtually the entire population of editors who are active on this article. Regards. Greg L (talk) 19:01, 28 June 2017 (UTC)
Evidently, I lack the required professionalism to formulate text in a way that is sufficiently accessible to you in its fundamental details (layout vs content, placement vs existence of essays, talk pages vs articles, ... ). Therefore, I walk away from the carcass of this discussion like from beating a dead horse. Purgy (talk) 06:01, 29 June 2017 (UTC)

I think it is important to keep in mind and coordinate on who our target readership is as we go forward on this article. Material I write for guys with slide rules is very different from that for managers. Furthermore, content written for a diverse crowd (like a general interest encyclopedia) must have a much greater range to its difficulty level; the initial portions must be informative and interesting for beginners while allowing advanced readers to wade further to material they find informative.

It’s also crucial to consider the likely (middle of the bell curve) level of familiarity the target readership has with the lingo and background of a given art. Someone who is visiting our Trombone article is usually already familiar with musical concepts like “pitch” and “notes.”

Because Wikipedia is a general interest encyclopedia directed to a diverse readership, here are some principles I believe we should keep in mind as it relates to an exceedingly technical subject like spacetime:

1. The average age of a Wikipedia reader is 36 years, ranging from 14 to 92.

2. Wikipedia's pithy and succinct ledes (the opening paragraphs before the index) are one of the features that makes Wikipedia so popular. Readers driving to the library and digging out an Encyclopedia Britannica can be expected to wade a long ways into the article whereas an Internet-based readership has a large portion of an attention deficit crowd who wade no further than our ledes.

3. Ledes should clearly explain the subject so that the reader is prepared for the greater level of detail that follows. Ledes should establish significance and be written in a way that makes readers want to know more. Ledes should answer two questions for the nonspecialist reader: “What is the subject?” and “Why is this subject distinctive and notable?”

4. Because our readership is so diverse, it is important that not only should the entire article start out simply (made as accessible as possible), but—particularly in the early sections—individual sections should be as accessible as practicable in the early paragraphs, carefully transitioning to increasing difficulty within the section.

5. Keep it simple. We are writing only for non-experts; true experts in any given subject matter don’t come to Wikipedia to learn anything. I’ve corresponded with Ph.D.s who published papers I had cited in various Wikipedia articles and quickly found they had zero interest in Wikipedia; in fact, they were incredulous that someone would waste their time contributing to a project where 16-year-old kids could revert your material. With two-thirds of my patents in PEM fuel cells, I can attest that a long time ago, I once scrolled through our article on that subject… just to see how long it was; I didn’t read a word of it and have zero interest in it.

6. As regards the Spacetime article, we can assume that the middle-of-the-bell-curve reader (the mode, mean, and median) is already familiar with Einstein and the basics of his Theory of Special Relativity, and has come here to understand what is distinctive about spacetime.

Greg L (talk) 18:52, 8 July 2017 (UTC)

### Dissenting opinion

I do not want to let the above stand as if its content as a whole were based on general consensus. I do neither agree to the semi-educated, unsourced pseudo-statistics, nor to the claims about the "non-expert, potential readers" of Wikipedia.

I consider this to be just another (text-) wall, intended to prohibit contributions from outside the editor's narrow scenery. Purgy (talk) 07:52, 9 July 2017 (UTC)

Hmmm. With language like “semi-educated”, you’re obviously just trying to ‘mix it up’ and be nothing but provocative. Before trying to be inflammatory on the project, I suggest you think twice before weighing in when you don’t have any idea what you’re talking about.
I linked the statistic about the age of our readership; it’s from Mani Pande of the Wikimedia Foundation. You can complain to him about his “pseudo-statistics.” Tell him Purgy knows better.
As for what ledes are supposed to accomplish, that came right out of Wikipedia:Writing better articles. And if you think published Ph.D. experts come to Wikipedia to read up on the latest & greatest truths of their art, you go find one who does that.
Finally, my suggestion that we ‘write for the target readership’ is common-sense stuff that comes from Technical Writing 101.
If you want to be constructive to the project, you can consider User:Stigmatella aurantiaca’s offer (∆ edit here): You've made some good suggestions in the past, but English does not appear to be your native language. So I've taken your suggested changes here where you and User:Greg L can work on them together. Hope you don't mind too much?.
That was a perfectly reasonable and generous offer for us to devote extra amounts of our all-volunteer time to assist you in contributing. But all we received from you was yet another of your protests where you complained (∆ edit here) that you have problems with four editors here, which amounts to pretty much every single contributor who was active on this page! The other passengers on a plane tend to be disinclined to see your point of view when you’re trying to open the cabin door mid-flight while complaining that everyone is out to get you.
Your persistent sniping here is bordering on being nothing but disruptive. I suggest you take this English idiom under advisement: you best let it go. You wrote earlier that you had done so (“Therefore, I walk away from the carcass of this discussion like from beating a dead horse”) but temptation seems to have gotten the better of you. Greg L (talk) 15:43, 9 July 2017 (UTC)

## Genesis of the spacetime concept

Schlafly is correct in his latest edit. The history of special relativity and the history of spacetime take a branch-and-merge somewhere around Lorentz and Poincare. Minkowski actually began work on his ideas about spacetime before 1905, and was stunned by Einstein's 1905 publication, since it expressed various conclusions that Minkowski had already (privately) arrived at concerning such things as the meaning of local time etc. Although he felt scooped, Minkowski never attempted to claim priority, and was always generous in giving Einstein credit. He did, however, think that Einstein's kinematic presentation was klunky.

I'm working to re-introduce some of the historical background that Geoffrey deleted since he wished to give more emphasis to spacetime as opposed to special relativity. This weekend has been busy, however... Stigmatella aurantiaca (talk) 12:38, 9 July 2017 (UTC)

I saw the edit and assumed it was correct. Thanks for confirming. Greg L (talk) 15:33, 9 July 2017 (UTC)

P.S. Historical tidbits such as what you wrote above about Minkowski easily passes a simple Technical Writing 101 grin test as being informative and interesting for the target readership. That clearly belongs in the historical section and should be restored. The previous version of the historical section may have been a bit long, but if someone is getting tired of reading that section, they can skip it.
Geoffrey’s edit, which pruned the History section down to its roots in order to “give more emphasis to spacetime as opposed to special relativity,” makes zero sense to me and is far from an improvement. Almost everyone who is interested in reading the History section will already have a general familiarity (or want to be familiar) with the basic principles of special relativity (maybe general relativity too), and will be interested in learning how the various theories paralleled each other and pollinated each other.
That Minkowski had been one of the profs for a 16-year-old Einstein was an interesting tidbit I added to the lede specifically because it was germane to the objective for all of Wikipedia's ledes: Ledes should establish significance and be written in a way that makes readers want to know more. Going forward, the historical relationship of how Minkowski fits relative to other significant Lorentz/Einstein/spacetime events begs to be fleshed out in an interesting way in the History section.
My most general advise would be to restore roughly two-thirds of what had previously been there, and arrange it in a semi-chronological fashion (you’ve seen movies and documentaries adopt that kind of flow presentation) so that important “elevator ride” nuggets like what you wrote here on this thread appear early in the section, and really ‘detaily’ stuff that is harder to remember appears later. Greg L (talk) 22:50, 9 July 2017 (UTC)
PPS: I'd be happy to collaborate in detail on a History section within a green-div here on this page. That is, unless you’ve had an epiphany on a sweet way to do it. Greg L (talk) 00:19, 10 July 2017 (UTC)
If you could work on this, I'd much appreciate it. My wife fell down and is currently nearly bedridden, so the amount of time that I can spend on this subject is somewhat limited, between trips to the doctor, taking her to physical therapy, going to my regular job, etc. I've been somewhat overwhelmed these last few weeks.
Disentangling the numerous threads of "who believed what and when" is very complex. The reason, of course, is that many researchers were hot on the trail of what was ultimately to be special relativity, and most historians agree that if Einstein hadn't been first, someone else would have arrived at the same conclusions within a very few years at most. Two highly useful sources on Minkowski's contributions are
One should be very careful of how one interpret's Minkowski's statement to Born that I had quoted to you before, because (1) local time is only one of a number of issues dealt with by Einstein in his 1905 paper, and (2) Poincare had already made statements to that effect, so I'm puzzled because, so far as I can tell (beware of wp:OR on my part!) Minkowski should have stated that he had been scooped by Poincare on this point, not Einstein(!!!) Then there is the matter of Sommerfeld's redaction of Minkowski's 1907 article for its posthumous 1915 publication, which muddies the waters a lot. In addition, Minkowski continued to use the word "ether" until shortly before he died. There are contradictory viewpoints on how much Minkowski truly understood of the import of Einstein's contributions, etc etc. Stigmatella aurantiaca (talk) 03:12, 10 July 2017 (UTC)
I’m very sorry to hear about your wife. I hope she recovers quickly.
I could help you with the French-like presentation of the meal, but on material of this nature, I’d screw up (big time) if I tried my hand at an original recipe. This is supposed to be a hobby that’s enjoyable for you. Anything and everything here can wait until real life for you gets a tad monotonous and you actually look forward to getting back into the kitchen to mix up a little something special.
If someone else here doesn’t step in and do some magic with the History section, what I might do is look over the previous version of it and see if I can jigger it. Greg L (talk) 04:59, 10 July 2017 (UTC)
It is a mistake to have so much on Einstein in the introductory sections. He had very little to do with the concept of spacetime. There are separate articles on the history of relativity.
Some of what is there is not quite right. Transformations mixing space and time predate the 20th century and Einstein. So did the constant speed of light. Saying that Einstein's 1905 paper was a breakthrough over Lorentz and Poincare is debatable, and not really relevant to spacetime. It would be more relevant to say whether Minkowski's work was a breakthrough, but there is no need to insert historical opinions here anyway. Roger (talk) 05:03, 12 July 2017 (UTC)

## Draft of revised history section for discussion

There is very little solid evidence indicating the path whereby Minkowski developed his geometric concept of spacetime. Much of what is written is based on arcane deconstruction of what was crossed out in drafts of Minkowski's lectures, extensive speculation on why Minkowski had omitted mentioning Poincare in his 1908 lecture, etc. etc. I've tried to avoid such speculative analysis. Stigmatella aurantiaca (talk) 09:20, 11 July 2017 (UTC)

Figure 1-2. Michelson and Morley expected that motion through the aether would cause a differential phase shift between light traversing the two arms of their apparatus. The most logical explanation of their negative result, aether dragging, was in conflict with the observation of stellar aberration.
{Text struck through to denote that it is no longer in service. Greg L (talk) 21:52, 18 July 2017 (UTC)

By the mid-1800s, various experiments such as the observation of the Arago spot and differential measurements of the speed of light in air versus water were considered to have proven the wave nature of light as opposed to corpuscular theory.[1] Waves implied the existence of a medium which waved, but attempts to measure the properties of the hypothetical luminiferous aether implied by these experiments provided contradictory results. For example, the Fizeau experiment of 1851 demonstrated that the speed of light in flowing water was less than the sum of the speed of light in air plus the speed of the water by an amount dependent on the water's index of refraction. Among other issues, the dependence of the partial aether-dragging implied by this experiment on the index of refraction (which is dependent on wavelength) led to the unpalatable conclusion that aether simultaneously flows at different speeds for different colors of light.[2] The famous Michelson–Morley experiment of 1887 (Fig. 1‑2) showed no differential influence of Earth's motions through the hypothetical aether on the speed of light, and the most likely explanation, complete aether dragging, was in conflict with the observation of stellar aberration.[3]

George Francis FitzGerald in 1889 and Hendrik Lorentz in 1892 independently proposed that material bodies traveling through the fixed aether were physically affected by their passage, contracting in the direction of motion by an amount that was exactly what was necessary to explain the negative results of the Michelson-Morley experiment. (No length changes occur in directions transverse to the direction of motion.)

By 1904, Lorentz had expanded his theory such that he had arrived at equations formally identical with those that Einstein were to derive later (i.e. the Lorentz transform), but with a fundamentally different interpretation. As a theory of dynamics (the study of forces and torques and their effect on motion), his theory assumed actual physical deformations of the physical constituents of matter.[4]:163–174 Lorentz's equations predicted a quantity that he called local time, with which he could explain the aberration of light, the Fizeau experiment and other phenomena. However, Lorentz considered local time to be only an auxiliary mathematical tool, a trick as it were, to simplify the transformation from one system into another.

Other physicists and mathematicians at the turn of the century came close to arriving at what is currently known as spacetime. Einstein himself noted, that with so many people unraveling separate pieces of the puzzle, "the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905."[5]

An important example is Henri Poincaré,[6][7] who in 1898 argued that the simultaneity of two events is a matter of convenience. In 1900, he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by proposing an explicitly operational definition of clock synchronization assuming constant light speed. In 1900 and 1904, he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the principle of relativity, and in 1905/1906[8] he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with the postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional space-time by defining various four vectors, namely four-position, four-velocity, and four-force.[9][10] He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems the best suited to the description of our world".[10] Furthermore, even as late as 1909, Poincaré continued to believe in the dynamical interpretation of the Lorentz transform.[4]:163–174. For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity.[7][4]

In 1905, Einstein introduced special relativity (even though without using the techniques of the spacetime formalism) in its modern understanding as a theory of space and time.[7][4] While his results are mathematically equivalent to those of Lorentz and Poincaré, it was Einstein who showed that the Lorentz transformations are not the result of interactions between matter and aether, but rather concern the nature of space and time itself. Einstein performed his analyses in terms of kinematics (the study of moving bodies without reference to forces) rather than dynamics. He obtained all of his results by recognizing that the entire theory can be built upon two postulates: The principle of relativity and the principle of the constancy of light speed. In addition, Einstein in 1905 superseded previous attempts of an electromagnetic mass-energy relation by introducing the general equivalence of mass and energy, which was instrumental for his subsequent formulation of the equivalence principle in 1907, which declares the equivalence of inertial and gravitational mass. By using the mass-energy equivalence, Einstein showed, in addition, that the gravitational mass of a body is proportional to its energy content, which was one of early results in developing general relativity. While it would appear that he did not at first think geometrically about spacetime,[11]:219 in the further development of general relativity Einstein fully incorporated the spacetime formalism.

When Einstein published in 1905, another of his competitors, his former mathematics professor Hermann Minkowski, had also arrived at most of the basic elements of special relativity. Max Born recounted a meeting he had made with Minkowski, seeking to be Minkowski's student/collaborator: "[…] I went to Cologne, met Minkowski and heard his celebrated lecture 'Space and Time' delivered on 2 September 1908. […] He told me later that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery."[12] Minkowski had been concerned with the state of electrodynamics after Michelson's disruptive experiments at least since the summer of 1905, when Minkowski and David Hilbert led an advanced seminar attended by notable physicists of the time to study the papers of Lorentz, Poincare et al. However, it is not at all clear when Minkowski began to formulate the geometric formulation of special relativity that was to bear his name, or to which extent he was influenced by Poincaré's four-dimensional interpretation of the Lorentz transformation. Nor is it clear if he ever fully appreciated Einstein's critical contribution to the understanding of the Lorentz transformations, thinking of Einstein's work as being an extension of Lorentz's work.[13]

Figure 1-3. Hand-drawn transparency presented by Minkowski in his 1908 Raum und Zeit lecture.

Minkowski introduced his geometric interpretation of spacetime to the public on November 5, 1907 in a lecture to the Göttingen Mathematical society with the title, The Relativity Principle (Das Relativitatsprinzip). In the original version of this lecture, Minkowski continued to use such obsolescent terms as the ether, but the posthumous publication of this lecture in the Annalen der Physik (1915) was edited by Sommerfeld to remove this term. Sommerfeld also edited the published form of this lecture to revise Minkowski's judgement of Einstein from being a mere clarifier of the principle of relativity, to being its chief expositor.[12] On December 21, 1907, Minkowski spoke again to the Göttingen scientific society, and on September 21, 1908, Minkowski presented his famous talk, Space and Time (Raum und Zeit),[14] to the German Society of Scientists and Physicians.[note 1]

The opening words of Space and Time include Minkowski's famous statement that "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence." Space and Time included the first public presentation of spacetime diagrams (Fig. 1‑3), and included a remarkable demonstration that the concept of the invariant interval (discussed shortly), along with the empirical observation that the speed of light is finite, allows derivation of the entirety of special relativity.[note 2]

Einstein, for his part, was initially dismissive of the Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[4]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime.

Brief summary

• To mid-1800s scientists, the wave nature of light implied a medium that waved. Much research was directed to elucidate the properties of this hypothetical medium, called the "luminiferous aether". Experiments provided contradictory results. For example, stellar aberration implied no coupling between matter and the aether, while the Michelson–Morley experiment demanded complete coupling between matter and the aether.
• FitzGerald and Lorentz independently proposed the length contraction hypothesis, a desperate ad hoc proposal that particles of matter, when traveling through the aether, are physically compressed in their direction of travel.
• Henri Poincaré was to come closer than any other of Einstein's predecessors to arriving at what is currently known as the special theory of relativity.
• "The special theory of relativity ... was ripe for discovery in 1905."
• Einstein's theory of special relativity (1905), which was based on kinematics and a careful examination of the meaning of measurement, was the first to completely explain the experimental difficulties associated with measurements of light. It represented not merely a theory of electrodynamics, but a fundamental re-conception of the nature of space and time.
• Having been scooped by Einstein, Hermann Minkowski spent several years developing his own interpretation of relativity. Between 1907 to 1908, he presented his geometric interpretation of special relativity, which has come to be known as Minkowski space, or spacetime.

References

1. ^ Hughes, Stefan (2013). Catchers of the Light: Catching Space: Origins, Lunar, Solar, Solar System and Deep Space. Paphos, Cyprus: ArtDeCiel Publishing. pp. 202–233. ISBN 9781467579926. Retrieved 7 April 2017.
2. ^ Stachel, John (2005). "Fresnel’s (Dragging) Coefficient as a Challenge to 19th Century Optics of Moving Bodies.". In Kox, A. J.; Eisenstaedt, Jean. The Universe of General Relativity. Boston: Birkhäuser. pp. 1–13. ISBN 081764380X. Archived from the original (PDF) on 2017-04-13.
3. ^ French, A.P. (1968). Special Relativity. Boca Raton, Florida: CRC Press. pp. 35–60. ISBN 0748764224.
4. Pais, Abraham (1982). ""Subtle is the Lord-- ": The Science and the Life of Albert Einstein (11th ed.). Oxford: Oxford University Press. ISBN 019853907X.
5. ^ Born, Max (1956). Physics in My Generation. London & New York: Pergamon Press. p. 194. Retrieved 10 July 2017.
6. ^ Darrigol, O. (2005), "The Genesis of the theory of relativity" (PDF), Séminaire Poincaré, 1: 1–22, Bibcode:2006eins.book....1D, ISBN 978-3-7643-7435-8, doi:10.1007/3-7643-7436-5_1
7. ^ a b c Cite error: The named reference Miller was invoked but never defined (see the help page).
8. ^ Poincare, Henri (1906). "On the Dynamics of the Electron (Sur la dynamique de l’électron)". Rendiconti del Circolo matematico di Palermo. 21: 129–176. Retrieved 15 July 2017.
9. ^ Zahar, Elie (1989) [1983], "Poincaré's Independent Discovery of the relativity principle", Einstein's Revolution: A Study in Heuristic, Chicago: Open Court Publishing Company, ISBN 0-8126-9067-2
10. ^ a b Walter, Scott A. (2007). "Breaking in the 4-vectors: the four-dimensional movement in gravitation, 1905–1910". In Renn, Jürgen; Schemmel, Matthias. The Genesis of General Relativity, Volume 3. Berlin: Springer. pp. 193–252. Archived from the original on July 14, 2017. Retrieved 15 July 2017.
11. ^ Schutz, Bernard (2004). Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity (Reprint ed.). Cambridge: Cambridge University Press. ISBN 0521455065. Retrieved 24 May 2017.
12. ^ a b Weinstein, Galina. "Max Born, Albert Einstein and Hermann Minkowski's Space-Time Formalism of Special Relativity". arXiv. Cornell University Library. Retrieved 11 July 2017.
13. ^ Galison, Peter Louis (1979). "Minkowski's space-time: From visual thinking to the absolute world". Historical Studies in the Physical Sciences. 10: 85–121. doi:10.2307/27757388. Retrieved 11 July 2017.
14. ^ Minkowski, Hermann (1909). "Raum und Zeit" [Space and Time]. Jahresberichte der Deutschen Mathematiker-Vereinigung. B.G. Teubner: 1–14.

References

1. ^ The geometry of Minkowski spacetime is closely connected to certain variants of sphere geometry (such as Lie sphere geometry or Conformal geometry) developed in the 19th century. For instance, the Lorentz transformation is a special case of spherical wave transformations. In particular, as pointed out by Poincaré (1912) and others, it is simply isomorphic to the Laguerre group which transforms spheres into spheres and planes into planes. The isomorphism between the Möbius group (which is isomorphic to the group of isometries in hyperbolic R3) and the Lorentz group is also well known.
2. ^ (In the following, the group G is the Galilean group and the group Gc the Lorentz group.) "With respect to this it is clear that the group Gc in the limit for c = ∞, i.e. as group G, exactly becomes the full group belonging to Newtonian Mechanics. In this state of affairs, and since Gc is mathematically more intelligible than G, a mathematician may, by a free play of imagination, hit upon the thought that natural phenomena actually possess an invariance, not for the group G, but rather for a group Gc, where c is definitely finite, and only exceedingly large using the ordinary measuring units." Minkowski (1909), op cit.

### Discussion of Green-div

On a side note, it is clear that Minkowski way gritting his teeth, perhaps on part of all of the mathematical community. (It wasn't the first or last time such things happened.) From Space and time]:
With respect to this it is clear that the group ${\displaystyle \displaystyle G_{c}}$ in the limit for ${\displaystyle \displaystyle c=\infty }$, i.e. as group ${\displaystyle \displaystyle G_{\infty }}$, exactly becomes the full group belonging to Newtonian Mechanics. In this state of affairs, and since ${\displaystyle \displaystyle G_{c}}$ is mathematically more intelligible than ${\displaystyle \displaystyle G_{\infty }}$, a mathematician may, by a free play of imagination, hit upon the thought that natural phenomena actually possess an invariance, not for the group ${\displaystyle \displaystyle G_{\infty }}$, but rather for a group ${\displaystyle \displaystyle G_{c}}$, where c is definitely finite, and only exceedingly large using the ordinary measuring units. Such a preconception would have been an extraordinary triumph for pure mathematics. Now, although mathematics only shows irony at this place, still the satisfaction remains for it, that thanks to its fortunate antecedents by its senses sharpened in free remote-view, it is instantly able to grasp the deep consequences of such a modification of our view of nature. (Extra emphasis mine.)
(The group ${\displaystyle \displaystyle G_{\infty }}$ is the (homogeneous) Galilean group and the group ${\displaystyle \displaystyle G_{c}}$ the Lorentz group.) YohanN7 (talk) 10:34, 11 July 2017 (UTC)
Then the history of GR is, from a competitive perspective (who comes up with it first?), even more interesting. E. had more or less promised a new theory for a lecture, but with months, weeks, and then days remaining until the scheduled lecture, he had no theory. And — Hilbert was on the chase (tipped off by E himself a couple of years earlier in a letter). YohanN7 (talk) 10:44, 11 July 2017 (UTC)
@YohanN7: I confess that I had only skimmed Minkowski's lecture, relying mostly on secondary sources, but that is a great quote! The bulk of it needs to go into a note, of course, but I will definitely find a place to reference it in the text. I haven't tested [itex] \displaystyle on Microsoft Edge, only [itex] but I may need to change it to HTML if MediaWiki goofs up in the small font. Stigmatella aurantiaca (talk) 14:27, 11 July 2017 (UTC)
Some suggestions:

I’ve got some ‘real life’ to attend to, but a speed-read of this seemed very nicely written and interesting… quite enjoyable. I’ll be back to this later this evening. Greg L (talk) 17:11, 11 July 2017 (UTC)

@D.H: Thanks for the references! I had the impression that something very strange was going on between Minkowski and Poincaré, but I didn't have a diverse enough selection of sources to feel comfortable about making any sort of summary statement. Some of the sources that I had available to me had a very opinionated point of view, far from neutral. And the relationships that you point out between the Lorentz transformation and spherical wave transformation, and with spherical geometry in general, are also quite interesting. Stigmatella aurantiaca (talk) 18:20, 11 July 2017 (UTC)

I must leave it up to you guys to ensure the material is factually correct, but I thoroughly enjoyed reading that. I think this section is world-class informative and very useful. I made three relatively minor edits (∆ here) for clarity.

There is only one sentence I find confusing or ambiguous: The spacetime of special relativity has since come to be known as Minkowski spacetime. Apparently, there are other types of spacetime whereby Minkowski's is but one type (the “spacetime of special relativity”). This seems to be an equivocation out of the blue. Perhaps the fine distinction is buttressing (prophylactic textus fineprintus) in anticipation of editorial drive-by shootings by proponents of other types of spacetime with different dimensions… I don’t know. But if the entire History section is discussing nothing but the spacetime of special relativity, then the distinction should be explained with either a preceding caveat (e.g. Whereas there are alternative theories where space has other than three dimensions…), or there should be a pithy parenthetical explaining the prophylactic textus fineprintus. Greg L (talk) 19:33, 11 July 2017 (UTC)

Well, for starters there is the curved spacetime of general relativity. Hmmm... Do I want to discuss that in the Introduction??? Stigmatella aurantiaca (talk) 20:35, 11 July 2017 (UTC)
Even if other types of spacetime can be covered elsewhere, such as in the Introduction, important concepts on arcane technical matters can benefit from some repetition. I think such an abrupt hyperfine distinction at the end of the History section should have its foundation smoothly established; something like this(?): Though there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. I’ll add it up in the green-div as a straw man. Greg L (talk) 21:27, 11 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── The green-div receives two thumbs up from me. Whenever you guys are done with the factual stuff and citations, I think it’s ready for primetime. Greg L (talk) 21:36, 11 July 2017 (UTC)

### Arbitrary section break #1

@YohanN7: Please check my wording. Thanks! Stigmatella aurantiaca (talk) 06:02, 12 July 2017 (UTC)

Minkowski's statement there doesn't make much rigorous sense. In order to frame it rigorously, I believe one has to resort to group contraction (see example two there). But this doesn't matter much. I also don't remember (and don't have the time to find out right now) whether M. there is including or excluding translations. Just strike out the parenthetical "homogeneous" and our naming of the groups is correct (by abuse of terminology) whether translations are included or not. It can always be made more precise later. YohanN7 (talk) 08:17, 12 July 2017 (UTC)
Done. Stigmatella aurantiaca (talk) 09:45, 12 July 2017 (UTC)

@D.H: Added note to text. Haven't gotten to your references yet. Stigmatella aurantiaca (talk) 06:25, 12 July 2017 (UTC)

This history is pretty good, but it suffers from some unnecessary opinions. This article is on spacetime, so we do not need opinions on the credit for special relativity. For that, refer the reader to Relativity priority dispute.

"proposed that material bodies traveling through the fixed aether were physically affected" - more precisely, they proposed that the lengths of material bodies traveling through the fixed aether were affected.

"but with a fundamentally different interpretation" - I would strike this, as Einstein denied that he had a different interpretation.

"Lorentz considered local time to be only an auxiliary mathematical tool" - this is disputed, and is an unnecessary slam on Lorentz.

"continued to believe in the dynamical interpretation" - this is dubious, and should be omitted. You are documenting the history, not blaming people for beliefs.

Since the article is on spacetime, it is much more important to point out that Poincare was unequivocally the first to publish a description of spacetime as a 4D space, with metric and symmetry group. Furthermore, Minkowski's first paper references Poincare's spacetime paper. Those are facts. Maybe Minkowski got spacetime from Poincare or maybe figured it out for himself, he doesn't say. There is no need to speculate. Roger (talk) 06:37, 12 July 2017 (UTC)

@Roger I disagree with your disagreements with the following statements
• proposed that material bodies traveling through the fixed aether were physically affected
• but with a fundamentally different interpretation
Followers of Lorentz fully expected, in such experiments as the Trouton–Noble experiment, the Trouton–Rankine experiment, the Experiments of Rayleigh and Brace, and so forth, to be able to observe secondary effects due to compressive strains and so forth, whereas SR makes clear from the very start why such experiments would inevitably fail to achieve positive results.
While it is true that after such experiments as the above provided negative results, Lorentz was able revise his theory so as to explain the results as being logical consequences of his theory, he did not predict their negative results ahead of time.
• Lorentz considered local time to be only an auxiliary mathematical tool
We have Lorentz's own words on this point. "If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity by which the theory of electromagnetic phenomena in moving systems gains a simplicity that I had not been able to attain. The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time, and that my local time t' must be regarded as no more than an auxiliary mathematical quantity." Lorentz in a note that he added to the second edition of his "Theory of Electrons" (1916).
• continued to believe in the dynamical interpretation
It's late and I need to get to bed. I'll get to the matter of what Poincare believed later. Stigmatella aurantiaca (talk) 07:31, 12 July 2017 (UTC)
Your counterclaim goes strictly against the views of the great majority of historians of science. For instance, Scott Walter, in Poincaré on clocks in motion writes, "The concept of time deformation employed by Poincaré in Göttingen and thereafter was quite distinct from that of Einstein and Minkowski. For the latter theorists, time dilation and length contraction were kinematic eﬀects or consequences of the four-dimensional (3+1) metric of spacetime, respectively. According to Poincaré, the velocity dependence of measured lengths and durations was best understood as a result of compensating deformations of meter sticks and timekeepers. In the wake of Minkowski spacetime, the absolute space and time of Newtonian mechanics took on a conventional nature for Poincaré, for whom the concept of Galilei spacetime had not lived out its utility for science, and would not do so for some time." Stigmatella aurantiaca (talk) 12:00, 12 July 2017 (UTC)
In addition to the 1916 paper cited by Stigmatella aurantiaca, there are additional occasions at which Lorentz described local time as an auxiliary variable. He did it in his 1914 paper on Poincaré ("auxiliary quantities whose introduction is only a mathematical artifice"), or in this 1928 paper ("heuristic working hypothesis"). Also Einstein remarked in this 1907 paper: "One had only to realize that an auxiliary quantity introduced by H. A. Lorentz and named by him "local time" could be defined as "time" in general. --D.H (talk) 14:44, 12 July 2017 (UTC)
If you want to say that followers of Lorentz had an expectation in 1900 that Einstein did not have in 1905, then that would be more accurate. But still not correct, as Poincare was a follower of Lorentz without that expectation. And this is of questionable relevance to a history of spacetime. If you are trying to make the point that later work had the benefit of knowledge gained by later experiments, isn't that obvious?
You could say that Lorentz credited Einstein with achieving a simplicity, but the explanation given is inaccurate, misleading, and inappropriate. The above text implies that Lorentz was just using a mathematical trick/transformation with no physical significance. That is not true, as Lorentz was using that transformation to explain Michelson-Morley. For a history of spacetime, it is better to just explain what Lorentz did, and not give dubious explanations for why he did not achieve the simplicity of later scholars.
You refer me to criticism of Poincare's conventionalist philosophy. That might be interesting in an article on the history of the philosophy of physics, but in an article on the history of spacetime, the pertinent fact is that Poincare was the first to publish a mathematically and physically correct account of spacetime. Roger (talk) 16:14, 12 July 2017 (UTC)

This is again a side note, not intended to reply to anything in particular.

One sharp point that is tacitly, but not explicitly there is that foundational physics was in a state of utter confusion until Einstein's publication, whether practiced by mathematicians or physicists. It is probably not true that partial physical results (and this includes physical interpretation of mathematical formulas) were obtained before E. It is rather true that correct formulas, and correct observations about e.g. the Maxwell equations were there, but based either on incorrect physical assumptions or no physical assumptions.

I have read the above very sharply (and reliably) formulated somewhere, just can't remember exactly where. I'll try to. The point is this: It doesn't matter much what Minkowski, Poincaré et. all. actually thought before Einstein, because what they thought was physically wrong, or physically void. (What they thought after E. needs to be backed up with references of course, see next paragraph. Not all saw the light right away.)

It is also true (by the same source, but surely others as well) that SR only enjoyed gradual acceptance. So, when referring to 1906-20 papers in turn referring to pre-1905 papers, though it is interesting that bits and pieces (without much physics) of SR was there before Einstein, some (most!) of these bits and pieces were purely coincidental. Interestingly, since Sommerfeld is involved, he himself had the corresponding piece of luck with his formula for the hydrogen energy spectrum.

In summary, a description of the historical emergence of SR should, in my opinion, not be including even the possibility that it emerged as a collaborative effort, even tough E would perhaps not have discovered SR without the efforts of his predecessors and competitors. Am I obscure?

An excellent summary. I had never really thought things through as well as you put them, but I agree (almost) completely! Stigmatella aurantiaca (talk) 14:36, 12 July 2017 (UTC)
Regarding the "collaborative effort", here is an Einstein quote about Lorentz: "The enormous significance of his work consisted therein, that it forms the basis for the theory of atoms and for the general and special theories of relativity. The special theory was a more detailed exposé of those concepts which are found in Lorentz's research of 1895. (Pais, Subtle is the Lord, p. 169). --D.H (talk) 14:44, 12 July 2017 (UTC)
Do you have an original Lorentz reference? According to Scientific publications of H.A. Lorentz, there are no published works from 1895. I am curious whether the 1895 results would stand up to modern day scrutiny. This, of course, I am probably not able to decide by myself, but I'd still like to read it. YohanN7 (talk) 07:14, 13 July 2017 (UTC)
Check the complete bibliography, year "1895b". The English translation is available at
Here is another quote of Einstein (as quoted in Born (1955), Physics in my Generation, p. 101 and Keswani (1965), Origin and Concept of Relativity, p. 33, see also history of special relativity for sources): "There is no doubt, that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already recognized that the transformations named after him are essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further. Concerning myself, I knew only Lorentz's important work of 1895 – "La theorie electromagnetique de MAXWELL" and "Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern" – but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense my work of 1905 was independent. [..] The new feature of it was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the "Lorentz invariance" is a general condition for any physical theory. This was for me of particular importance because I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity.". Note that the first paper cited by Einstein was actually published in 1892. Btw, also Poincaré clearly noted that the Lorentz transformations applies not only to Maxwell's equations. --D.H (talk) 09:09, 13 July 2017 (UTC)
Thanks. I look forward to reading. Your "btw" is definitely interesting: "Btw, also Poincaré clearly noted that the Lorentz transformations applies not only to Maxwell's equations.". SR is no less and not much more than Lorentz invariance. If "not only Maxwell's equations" were replaced by "all equations" (including those describing mechanics), then full SR emerges. YohanN7 (talk) 09:27, 13 July 2017 (UTC)
Wow, that's a big paper... YohanN7 (talk) 09:30, 13 July 2017 (UTC)

An Einstein quote: I do not recognize my theory since the mathematicians got hold of it. (Or something like that...) I'll try to locate a source. YohanN7 (talk) 13:46, 12 July 2017 (UTC)

Found it: Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore. Quoted in P A Schilpp, Albert Einstein, Philosopher-Scientist (Evanston 1949). YohanN7 (talk) 13:56, 12 July 2017 (UTC)

...and an excellent quote, as well. I had actually been debating whether to include it or not (in a slightly different translation). I guess I should. Stigmatella aurantiaca (talk) 14:36, 12 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I partially disagree with one opinion stated by Roger: This article is on spacetime, so we do not need opinions on the credit for special relativity. For that, refer the reader to Relativity priority dispute. Here's why:

1. Since Minkowski spacetime is irrevocably intertwined with the theory of special relativity, it would be impossible to have a useful History section here without touching factually—and in an interesting way—on SR and who was responsible for its development.

2. God does too play dice with the universe—at least when it comes to who gets notable public recognition for famous ideas. Turbo code vs. Gallager codes is just one example of the dust being blow off of long-forgotten papers written by damned smart people who only received recognition for their insights after they died.

3. As mere wikipedians, we can’t fix #2, above, by practicing the art of reading deeply into primary sources such as the physicists’ published papers. And we must be terribly cautious when we look up their famous quotes and start performing a rain dance looking for inspiration as to the significance and truthfulness of the quote. For the most part, we must look towards what the reliable sources are saying insofar as who deserves credit for what on special relativity.

4. Referring readers to Relativity priority dispute is no option at all for a fluid, interesting, and informative reading experience because A) doing so would merely be practicing Click to Learn & Return©™®, and B) that article sucks because it’s as interesting to read as the Warren Commission’s report on the assassination of president Kennedy.

5. To save time, we can merely refer to the Undisputed and well-known facts section of Relativity priority dispute as we craft our green-div here.

6. The lede of Relativity priority dispute states this: Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. I note the operative word “Subsequently,” and submit that for the purposes of the History section here, it is beyond scope to be blowing the dust off of papers that failed to receive due recognition at the time.

7. We may fairly limit ourselves—to a large extent—to what was notable at the time (circa 1887–1916), and add a clause or parenthetical akin to while modern historians believe other individuals should be credited for the development of spacetime and special relativity-like formulas and theories. It’s not our concern to future-proof the History section of this article against the possibility that an archivist at Princeton might dig up some guy’s masters dissertation from 1882.

Greg L (talk) 17:49, 12 July 2017 (UTC) I disagree with the above side note that says "foundational physics was in a state of utter confusion until Einstein's publication" and "SR only enjoyed gradual acceptance". This is an article about spacetime, not Einstein or SR. Historians mostly agree that Einstein's 1905 paper did not have a big impact at the time, but Minkowski's version of spacetime and SR enjoyed extremely rapid acceptance after Minkowski's famous 1908 paper. The latter point is worth making. Roger (talk) 18:13, 12 July 2017 (UTC)

Roger. The article is about spacetime. But any proper treatment in a History section must necessarily discuss Einstein and a variety of other physicists and theories that impact the history of spacetime; ergo, my point #1, above. Greg L (talk) 19:02, 12 July 2017 (UTC)
Fine, mention Einstein and SR all you want, but please don't skip essential facts in the history of spacetime. The above history skips the generally-accepted facts that (1) spacetime was first published by Poincare, based only on Lorentz, and (2) Minkowski got the idea from Poincare, expanded on it, and then wrote the essay that sold everyone on it. However important Einstein was to SR, he really was not important to the development of spacetime. See for example this quote from the Galison paper cited above (and behind a paywall, unfortunately). Roger (talk) 01:45, 13 July 2017 (UTC)
In sum Minkowski still hoped for the completion of the Electromagnetic World Picture through relativity theory. Moreover, he saw his own work as completing the program of Lorentz, Einstein, Planck, and Poincare. Of these it was Poincare who most directly influenced the mathematics of Minkowski's space-time. As Minkowski acknowledges many times in "The Principle of Relativity," his concept of space-time owes a great deal to Poincare's work.35 [Galison,1979]

──────────────────────────────────────────────────────────────────────────────────────────────────── @Roger: I think all our objectives are aligned. The above green-div is the ultimate in collaborative writing tools whenever the going gets double-tough. Everyone can contribute to a green-div and tinker and fidget with much reduced pressure. Do you want Stigmatella aurantiaca to incorporate your suggested material into the green-div? Or do you see a fine place to shoehorn it into? Greg L (talk) 02:08, 13 July 2017 (UTC)

I did not realize that the green box was open for editing. There was a call for comments, and I commented. So go ahead and let the editor do a revision. Roger (talk) 04:27, 13 July 2017 (UTC)
OK. Thanks! Greg L (talk) 04:51, 13 July 2017 (UTC)

### Arbitrary section break #2

I think it is worth asking the question whether anyone of Minkowski, Poincaré and Lorentz published mathematically correct formulas with the correct (according to modern formulations of SR) physical premises and interpretations before 1905. I have been taught that this is not the case. But references where someone quotes someone (that sometimes again quote someone else), and the fact that all decent scientists are eager to pay their dues to their predecessors (sometimes perhaps too generously) suggests otherwise. YohanN7 (talk) 07:07, 13 July 2017 (UTC)

That is, would these papers stand up to present day scrutiny by physicists and mathematicians as opposed to historians of science? Einsten's 1905 work does stand up to scrutiny (which is why SR has the status it has still today), though, perhaps, his and (many other physicists) mathematical presentations on occasion brings tears to the eyes of the mathematically inclined reader YohanN7 (talk) 07:22, 13 July 2017 (UTC)

@Schlafly: @Greg L: I'll do my best to come up with an appropriate addition that properly credits Poincare and his importance to Minkowski. I had thought it was obvious in the section as written that Einstein's role in the development of the spacetime of special relativity was minor at best. Give me a day or two. I've just finished purchasing Space and Time: Minkowski's papers on relativity (\$5) so that I can read The Relativity Principle in translation, to supplement my use of secondary sources. My German is unfortunately very flaky. Stigmatella aurantiaca (talk) 08:15, 13 July 2017 (UTC)
Spacetime of special relativity is fixed by special relativity, which is fixed by Einstein. Development of various equivalent formalisms can be credited to others, but, please, don't say that "Einstein's role in the development of the spacetime of special relativity was minor at best". YohanN7 (talk) 08:52, 13 July 2017 (UTC)
I'll find a more accurate manner of expressing what I was trying to say. But first I need to do more research on Poincare. Stigmatella aurantiaca (talk) 10:10, 13 July 2017 (UTC)
@YohanN7: When it comes to part 2 of Einstein's 1905 paper (what Einstein considered to be the important part, otherwise why give his paper the title that he did?), I find myself much preferring Jackson. Stigmatella aurantiaca (talk) 08:15, 13 July 2017 (UTC)
I don't understand what you mean. Possibly you mean that old papers are almost invariably painstaking to read. I'd agree with that. Not uncommonly, some people take pride in reading only historical references, so that they can obtain a "superior view". Almost without exception, those who do get it all wrong, which has been a source for substantial disputes and frustration. YohanN7 (talk) 08:52, 13 July 2017 (UTC)
painstaking to read - Yes, that is pretty much what I meant. Despite Wikipedia's wp:NOR policy, one does need to refer to primary sources to establish "ground truth".
off-topic side note - An amusing recent example of where I had to do a bit of primary source digging to resolve an issue where different secondary sources were copy-pasting each other was Talk:Fizeau–Foucault_apparatus#313000 or 315000?. The title of the Fizeau–Foucault_apparatus article, incidentally, was a neologism coined by an currently blocked Wikipedia editor who was ignorant of the difference. There are no references in the literature to this non-existent experimental mishmash prior to 2002 (i.e. the creation date of the Wikipedia article). Stigmatella aurantiaca (talk) 10:00, 13 July 2017 (UTC)
@Schlafly: @Greg L: I'll also need to visit the university library for some materials that are behind a paywall. Stigmatella aurantiaca (talk) 08:45, 13 July 2017 (UTC)
For your research on Poincaré, you may find the list of secondary sources on Poincaré and relativity useful, which I compiled some years ago. --D.H (talk) 11:15, 13 July 2017 (UTC)
That's a long list! I sorted through the available abstracts for the articles that you listed, and tonight or tomorrow, I'll be visiting the university library to follow up on the papers with interesting abstracts that are behind paywalls. It will depend on the state of my wife's health. Stigmatella aurantiaca (talk) 18:19, 13 July 2017 (UTC)
Quoting YohanN7: Spacetime of special relativity is fixed by special relativity, which is fixed by Einstein. I second that motion.
I think it’s obvious from the many (and extensive) biographies and documentaries on Einstein that he was an original thinker who had zero need to read every scientific paper in existence at the time.
Merely because modern historians can point to the existence of other papers where people were thinking along similar lines doesn’t diminish the fact that Einstein had intellectual prowess, nor the importance of his mental feat in connecting the dots between electrodynamics and the implications of the Michelson–Morley experiment, and it certainly doesn’t take away from the historical perception that “Einstein = special relativity.”
It’s clear (to me anyway), that Einstein had a big take-away with the Michelson–Morley experiment and gave much thought to what the universe would look like from the point of view of someone riding a light beam. It’s also beyond clear from his paper On the Electrodynamics of Moving Bodies that he was merely trying to say that “moving a conductor through a stationary magnetic field” is the same as “moving a magnetic field over a stationary conductor.” Ergo, he mentions Maxwell prominently in his paper because electrodynamics viewed in a new light was the point of his paper.
To Einstein, the Michelson–Morley experiment was merely a historical experiment (Einstein was eight years old at the time) that established one simple fact: light has only one speed for all observers irrespective of the source’s relative motion. Though Michelson & Morley’s raw observations of light’s speed were exacting and correct, Einstein jettisoned Michelson & Morley’s presumed existence of an ether as a carrier for electromagnetic propagation. Einstein perceived no need to cite their work; they merely made a measurement.
Finally, Einstein mentioned only Planck and Lorentz in the footnote of his paper because those physicists’ principles and math were merely ‘cute mathematical window dressing’ attempting to explain the natural world. When one properly viewed electrodynamics in terms of the profound underlying principle of the constancy of the speed of light, these three fundamentally deep truths underlying the natural world became evident:
1. “The same laws of electrodynamics and optics will be valid for all frames of reference.”
2. There is no “luminiferous ether.”
3. There is no such thing as an “absolutely stationary space.”
From these universal truths sprang math—featuring the same transformations as those from Lorentz—describing still other truths such as how different observers will measure where and when events occur differently.
Einstein's insight was a classic case of the phenomenon the famous computer researcher Alan Kay spoke of: “A change in perspective is worth 80 IQ points.” Einstein deserves full credit for special relativity. Efforts to diminish the implications of his insight, in my opinion, are just historical revisionism by authors and others who are anxious to make a name for themselves because they purport to be able to see truths that elude the mere masses. Greg L (talk) 20:43, 14 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── @Schlafly: I've added a long paragraph on Poincaré to the history, but I find little justification for your attempts to claim that he had not only scooped Einstein on special relativity, but had also scooped Minkowski in developing four-dimensional spacetime. Technically speaking, yes, Poincaré was first to demonstrate the possibility of expressing physics in four-space, but he did not pursue the effort. Stigmatella aurantiaca (talk) 05:13, 15 July 2017 (UTC)

I can only hope that the balance you are striking here is in accordance with WP:WEIGHT, which starts out as follows: Neutrality requires that each article or other page in the mainspace fairly represent all significant viewpoints that have been published by reliable sources, in proportion to the prominence of each viewpoint in the published, reliable sources. My takeaway from that principle, as it applies to the present debate, is that the extent to which we dwell on Poincaré should mirror the coverage that the best RSs have to say on the guy. Greg L (talk) 05:37, 15 July 2017 (UTC)
I believe that Schlafly will agree to trimming the paragraph on Poincaré in view of what I have to say concerning his non-importance in the development of the spacetime concept. Spending several sentences on his non-role indeed involves a WP:WEIGHT issue. I only put as much up there as I did to show Schlafly what he was getting into. Stigmatella aurantiaca (talk) 05:53, 15 July 2017 (UTC)
@D.H: I came away from the library with lots of great material on Poincaré. He was an amazing figure. After I digest this stuff, I might see if I can contribute to his Wiki article. Thanks again for all of your research! I'm coming away from this with a new favorite scientist to stand on my shelf alongside a long list including, in no particular order, Feynman (I once stood beside him perched on top of the same umbrella table. Long story...), Max Delbrück (I once babysat his children), Barbara McClintock (great lady!), Einstein, Faraday, Lucy Shapiro, Dale Kaiser, Maxwell, etc. etc. Stigmatella aurantiaca (talk) 05:53, 15 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── The sentences marked off in yellow are my attempt to accommodate Roger's insistence that we include mention of Poincaré's pioneering use of 4-dimensional spacetime a couple of years ahead of Minkowski's public lectures introducing the concept. It is my belief that, since Poincaré never really took the concept anywhere, that cramming this material in violates WP:WEIGHT. I propose that it be deleted. Stigmatella aurantiaca (talk) 06:07, 15 July 2017 (UTC)

With regard to your suggestion that the crammed material violates WP:WEIGHT, I would say our weight should mirror how modern and particularly good RSs give weight (or not) to Poincaré. It is not the duty of mere wikipedians to pretend that we’re the cigar-chomping editor of the Washington Post and we’re going to decided whether to give Nixon a break or not. You’ve obviously read this stuff. I encourage you to be bold and abide by the weight of the good RSs. Damn the dissenting wikipedians; full RS ahead. Greg L (talk) 06:27, 15 July 2017 (UTC)
P.S. Reading the paragraph on Poincaré—without any knowledge of the extent to which the RSs balance any discussion of him—it seems informative, balanced, topical, and (importantly) interesting and as if it belongs in a proper historical treatment of the subject. Having said that, it still seems to me to give the guy a tad too much credit. Here's why:
The history of special relativity and how Einstein and others like Poincaré were thinking along similar lines around the same time reminds me of history of atomic fission and the atomic bomb. Upon the late-1938 discovery of the true extent of the physics underlying nuclear fission (the release of 200 MeV of kinetic energy and the release of two free neutrons), pretty much every atomic physicist had the same epiphany at the same instant. The extent to which one executes on that epiphany is an altogether different matter.
Alas, it seems to me that Poincaré’s suggestion regarding the “inherent undetectability of the aether” comes miles short of Einstein’s conclusion that there is no ether because light’s speed is intertwined with the fundamental physical nature of the universe. I submit that this bit The logical consequences of these two propositions can be said to encompass the entirety of special relativity might be editorializing too much unless it is cited to good R.S. Since it’s only a green-div, I took the liberty of deleting that bit. Greg L (talk) 06:19, 15 July 2017 (UTC)
On Mondays, Wednesdays and Fridays, it seems, Poincaré still believed in the existence of the aether, while on Tuesdays, Thursday, and Saturdays he didn't. Who knows what he believed on Sundays? I'm still trying to figure out what "other reasons" to include as regards most science historians not crediting Poincaré with actually discovering special relativity. The aether issue was one of them. Stigmatella aurantiaca (talk) 06:25, 15 July 2017 (UTC)
We had wikipedians out trying to change the world with the use of “16 gibibytes” of RAM because “gibibyte” was a suggested standard. Though virtually no one in the computer industry observed the practice, we had editors who shoehorned the terminology literally overnight into hundreds of articles. It’s not our role to champion change, right wrongs, or remedy historical injustice unless, on balance, the RSs do. As wikipedians, we follow, not lead. WP:WEIGHT is clear. I don’t know what the RSs are saying but I have every confidence you do. Greg L (talk) 06:32, 15 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── On second thought, this bit For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity, nor did he play any major role in the development of the spacetime concept, makes the paragraph look like a case of unadulterated wikipedian conflictus textitis. I’m going to go trim that paragraph. Stand back for a bit. Greg L (talk) 06:37, 15 July 2017 (UTC)

Done. It now seems to place proper weight on Poincaré given how the RSs view his contributions. Greg L (talk) 07:01, 15 July 2017 (UTC)

### Arbitrary section break #3

• Ummm. No. Will fix later. Stigmatella aurantiaca (talk) 07:37, 15 July 2017 (UTC)
• Roger does need a chance to see what the paragraph looked like with reference to Poincare's work on four-dimensional spacetime, since that was Roger's big thing. Stigmatella aurantiaca (talk) 07:33, 15 July 2017 (UTC)

Henri Poincaré was to come closer than any other of Einstein's predecessors to arriving at what is currently known as the special theory of relativity. In 1900, Poincaré recognized that Lorentz's "local time" is actually what is indicated by moving clocks, and he proposed an explicitly operational definition of clock synchronization.[1] In 1904, Poincaré suggested the inherent undetectability of the aether. The logical consequences of these two propositions can be said to encompass the entirety of special relativity. Moreover, in his 1906 paper On the Dynamics of the Electron,[2] Poincaré introduced the innovative concept of a 4-dimensional space-time while discussing various hypotheses on gravitation. He did not pursue the 4-dimensional formalism very far, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding that "that three-dimensional language seems the best suited to the description of our world".[3] Furthermore, However, even as late as 1909, Poincaré continued to believe in the dynamical interpretation of the Lorentz transform.[4]:163–174 For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity, nor did he play any major role in the development of the spacetime concept.

References

1. ^ Cite error: The named reference Miller was invoked but never defined (see the help page).
2. ^ Poincare, Henri (1906). "On the Dynamics of the Electron (Sur la dynamique de l’électron)". Rendiconti del Circolo matematico di Palermo. 21: 129–176. Retrieved 15 July 2017.
3. ^ Walter, Scott A. (2007). Renn, Jürgen; Schemmel, Matthias, eds. The Genesis of General Relativity, Volume 3. Berlin: Springer. pp. 193–252. Archived from the original on July 14, 2017. Retrieved 15 July 2017.
4. ^ Cite error: The named reference Pais was invoked but never defined (see the help page).

I don't know why you guys are arguing about what Poincare believed about the aether, or what a great genius Einstein was, or who should get credit for special relativity. There are other WP pages for those topics. This article is on spacetime. It does not matter if Poincare was an astrologer or if he believed the Earth was flat. A history of spacetime should state the objective fact that Poincare first created the concept.

"since Poincaré never really took the concept anywhere" - Do you realize that Minkowski died soon after his famous paper, and so he never went any further with it either?

"Who knows what he believed on Sundays?" - Do you realize that many great scientists had peculiar religious beliefs, and thus believed odd things on Sundays? Many also have odd beliefs on philosophical and political matters. Why are you trying to pass judgment on his beliefs? Why do you care?

Some of Poincare's statements do seem contradictory if you do not understand his conventionalist philosophy. Same with Einstein, for that matter, as he sometimes said there was an aether and sometimes that there was not. And you might also be confused by what modern physicists say about the aether. But if this issue really interests you, then please move it over to one of the WP articles on the aether. This article is on spacetime, not the aether.

"I find little justification for your attempts to claim that he [Poincare] had not only scooped Einstein on special relativity, but had also scooped Minkowski in developing four-dimensional spacetime." - I am not really claiming that Poincare scooped anyone. Poincare wrote a paper on spacetime. Minkowski did some subsequent research that made use of Poincare's results and developed them further. There is some suggestion that Minkowski got some of the ideas independently, but neither Minkowski nor anyone else has made this claim with any specificity. From what we know, Minkowski developed his spacetime from Poincare, and Poincare developed his from Lorentz.

"nor did he [Poincare] play any major role in the development of the spacetime concept" - What historian says that? I just quoted Galison saying "Of these it was Poincare who most directly influenced the mathematics of Minkowski's space-time." Spacetime is clearly defined in Poincare's paper. Maybe not as clearly as Minkowski's paper, but it is there and no one can dispute that.

"Henri Poincaré was to come closer than any other of Einstein's predecessors to arriving at what is currently known as the special theory of relativity." - This is a very strange thing to say in an article on spacetime. What is currently known as special relativity (according to the textbooks I have) includes the spacetime concept, and Einstein never had that until he got it from Minkowski. It would be more accurate to say that Poincaré came closer than any other of Minkowski's predecessors to arriving at what is currently known as the special theory of relativity. Whether you agree with that or not, there is a separate article on History of special relativity. The concern is whether he published the spacetime concept.

You guys are getting way off-topic here. Just give the history of spacetime in the spacetime article. Roger (talk) 08:21, 15 July 2017 (UTC)

@Schlafly: You wrote, quote:

(1) spacetime was first published by Poincare, based only on Lorentz, and
Technically, yes, in "On the Dynamics of the Electron"
However, Poincare specifically stated that this line of research seemed to "entail great pain for limited profit", and his ultimate conclusion was "that three-dimensional language seems the best suited to the description of our world".
(2) Minkowski got the idea from Poincare, expanded on it, and then wrote the essay that sold everyone on it.
Minkowski's mathematical inspirations were primarily from Lorentz and Poincare. He took Poincare's abandoned idea of four-dimensional spacetime, expanded on it, and presented a sales pitch for spacetime that made him famous. Given Poincare's negative writings on the probable utility of the spacetime concept that he originated, I am very puzzled on why you insist on wishing to exaggerate Poincare's importance in its development.
(3) However important Einstein was to SR, he really was not important to the development of spacetime.
We all here are perfectly aware of your belief that Einstein ruined physics, thank you. I am doing my best to separate your statements of fact versus your statements of interpretation, and to assign proper weight to your views, accommodating as many of your factual observations as will fit with the rest of the section.
Now, let me correct the main green div area. As it stands, it does not reflect the consensus of reliable sources. I am quite sure that you do not want me to insert the statements marked yellow in the small green div area.
Stigmatella aurantiaca (talk) 12:45, 15 July 2017 (UTC)

@Schlafly: Your edit summary for your above post states that you object to the “spurious slams on Poincare”, which translates to “harsh criticisms of Poincaré that aren’t what they purport to be.” You see a prescient genius in what Poincaré accomplished in his time. However, the only thing that matters is what the historians are saying today.

Like User:YohanN7 wrote, Spacetime of special relativity is fixed by special relativity, which is fixed by Einstein. It's utterly impossible to have a proper historical treatment of spacetime without discussing special relativity; the RSs thoroughly cover the development of SR in a historical discussion of spacetime, and so too must we.

All Stigmatella, YohanN7, and I are trying to accomplish with our history section is to mirror, per WP:WEIGHT, how modern, good RSs give credit and weight to everyone’s contributions to the understanding of spacetime, Poincaré included. It would be very wrong for mere wikipedians vary from the RSs; anything else would be a major disservice to our readership.

IF what is currently in the small green-div is true, that most modern historians feel Poincaré had no major role in the development of spacetime, then I would argue that the amount of airtime given to Poincaré in the big green-div is appropriate as its general tone (though it is in need of some factual correction).

My take-away from our treatment of Poincaré is that he was a notable example of one of the many physicists standing at the party, wine glass in hand, talking about what was on a lot of others’ minds, but failed to go back to his study and do the hard work. If my take-away mirrors what the RSs are saying, then I’d say our current treatment in the big green-div strikes the proper gist and weight. Greg L (talk) 16:26, 15 July 2017 (UTC)

We seem to have a general consensus as to how our History section should touch upon the contributions of Poincaré. I suggest you revise the big green-div in a way that best reflects the weight given by the RSs and we move on. After your edit, we should have a short pause for final comments to discern if we truly do have a general consensus. Greg L (talk) 15:38, 15 July 2017 (UTC)

These are spurious slams on Poincare: "Poincare's abandoned idea", "Poincare's negative writings on the probable utility of the spacetime concept", "most modern historians feel Poincaré had no major role in the development of spacetime", "failed to go back to his study and do the hard work".
If anyone, it was Einstein who was negative about the utility of spacetime. Poincare did predict that 3D language would be preferred for most purposes, and he was completely correct about that. As I thumb thru some physics journals today, most of the articles still use the 3D language. And I say that Poincare should be credited for his work regardless of whether his predictions about future utility were correct or not.
Can you show me even one modern historian who says "Poincaré had no major role in the development of spacetime"? I pointed out that Galison, in the article already cited in the green-div, says that Poincare did have a major role. The article text should accurately reflect its sources. Also, no one says that spacetime was "fixed by Einstein". Everyone agrees that the spacetime concept, spelled out by Poincare and Minkowski, was news to Einstein.
There are no historians that say that only Einstein did the hard work, or that Poincare abandoned spacetime, or any of that nonsense. I am the one here who is sticking to the facts that are generally accepted.
There are historians who credit Einstein for relativity, as explained in Relativity priority dispute. There reasons are somewhat peculiar and off-topic here, as they usual define special relativity to exclude 4D spacetime. You can refer the reader to that article for details, but this article is about spacetime. Roger (talk) 17:40, 15 July 2017 (UTC)
Mmmm. Quoting you: no one says that spacetime was "fixed by Einstein". Indeed. No one here said that.
As regards this statement you made: And I say that Poincare should be credited for his work regardless of whether his predictions about future utility were correct or not, many here would like to play Perry White and make policy decisions on how history ought to be treating this individual or that. Alas, we place great weight on what the reliable secondary sources say.
It's clear to me that Stigmatella aurantiaca has no axe to grind here one way or another and is exceedingly well versed in both the primary and secondary sources. I propose that he do his best to adhere to the best interpretation of the truth (mostly secondary sources with a careful dash of his own interpretation of the primary sources), declare it ready and hoist it as a straw man to see if we have a consensus. “Consensus,” by the way, does not mean “unanimous” and it never did. Greg L (talk) 21:14, 15 July 2017 (UTC)
YohanN7 wrote "Spacetime of special relativity is fixed by special relativity, which is fixed by Einstein." No historian or reliable source says this. Let's get the facts right, and then discuss how "history ought to be treating this individual or that". Roger (talk) 00:41, 16 July 2017 (UTC)
I don't know about historians, but mathematicians and physicists know, and write things like "despite many efforts of Lorentz, Poincaré and many others, the situation in theoretical physics was generally murky before Einstein in one blow clarified matters". (V. S. Varadarajan in Supersymmetry for mathematicians) In the same paragraph it is, if I recall correctly, also mention that the mathematical structure of spacetime was then fixed as well.
Regardless of what sources by historians say, it is a fairly easy (but non-trivial) matter to derive only from the fact that there is a universal velocity that the symmetry group of spacetime is a subgroup of the conformal group. (Ruling out purely conformal transformations (and landing at the Poincaré group) requires either, in addition, the second postulate, or the (weaker) observation that the Maxwell equations with sources aren't conformal invariant.) Saying that special relativity does not imply the mathematical structure of spacetime is, forgive me, no rudeness intended, pure nonsense. YohanN7 (talk) 06:57, 17 July 2017 (UTC)
@Schlafly: It appears to me that you were confused by Yohan's use of the term "fixed". He used "fixed" in the sense of "is uniquely determined by". You were apparently reading "fixed" in the sense of "was repaired by", which doesn't make too much sense. Stigmatella aurantiaca (talk) 10:17, 17 July 2017 (UTC)

### (Purgy's) Section break #4

I have no problem with pondering the diverging educated and sourced opinions about topics wrt their belongings to a spacetime article or not, nor with the weighing of contributions by Poincare to this or that, not even to him standing with wine glass in hand (per se a perfidious insinuation to this important scientist), and I too trust in Stigmatella aurantiaca being fair and open to contributions, even to those he currently opposes. However, I do have strong reservations against professional writers, firstly proclaiming consensus on just their own behalf about themata they are absolutely clueless, and secondly, transferring this usurped right to one editor of his selection; and all this before there was any substantial discussion at all. I do hope that the repeatedly obtruded dogmata, only rudimentarily founded in WP directives (I opposed already), and the fully causeless arrogated competence, will not detriment the development of this article. Purgy (talk) 07:24, 16 July 2017 (UTC)

(*Yoda accent*): ‘Brushing up on your wiki-insults have you?’
It appears you devoted much time to researching wiki-smack and leaning elegant new English words in a dictionary. But please desist with your highbrow name-calling and whining. I count a half-dozen multisyllabic words in your above rant that Koko, the sign-language gorilla could easily parse and translate into “Greg L stinky bad; Purgy nice smelling smart.” Yeah… we get your message; doesn’t impress.
You complained earlier (∆ edit) that you have problems with four editors here, which amounts to pretty much every single contributor who was active on this page! Tilting at four windmills makes it perfectly clear where the problem lies. Regrouping and coming back to single out an individual windmill and start tilting at that one doesn’t help your cause.
If you want to be constructive to the project, you can consider User:Stigmatella aurantiaca’s offer (∆ edit here): You've made some good suggestions in the past, but English does not appear to be your native language. So I've taken your suggested changes here where you and User:Greg L can work on them together. Hope you don't mind too much?.
OK. Maybe that sort of comment stings for someone who believes himself to possess exemplary English-language, encyclopedic technical writing skills. But consider what the famous astronomer, Neil deGrasse Tyson once wrote: “Imagine a world in which we are enlightened by objective truths rather than offended by them.” Stigmatella aurantiaca’s offer was a perfectly reasonable and generous offer for us to devote extra amounts of our all-volunteer time to assist you in contributing. You clearly weren’t interested in taking him up on his offer.
You wrote earlier as follows: “Therefore, I walk away from the carcass of this discussion like from beating a dead horse.” But you didn’t. You came back again… twice… with protests that accomplish nothing. Curious.
Now, I invite you to improve this article with prose that is A) factual, B) is compliant with all of Wikipedia’s rules, C) is well crafted English prose with an encyclopedic tone, and which D) makes an already complex and abstruse article easier to understand. That would be a big improvement over your incessant harping and raging at those you blame for the slings and arrows of your outrageous misfortune. If the prospect of that isn’t your cup of tea, then try acting like an adult for once and do the right thing. Greg L (talk) 00:04, 17 July 2017 (UTC)

The above history section contains entire passages on aether experiments and Lorentz, while Poincaré's contributions and even Einstein's are hardly mentioned. Therefore, I propose the following additions (there is certainly some room left for a short history of curved spacetime.) --D.H (talk) 08:31, 16 July 2017 (UTC):

@D.H: Excellent suggestions, as usual, many of your points being expressed better than what I could have come up with! I will put together a merge of your proposal with the rest of the history above. I do not foresee that I will need to make any changes, except in minor points of grammar. You will need to wait a few hours. My wife and I are celebrating our 34th anniversary, so this weekend has been busy. Stigmatella aurantiaca (talk) 12:32, 16 July 2017 (UTC)
Wow, happy anniversary!! PS: The last hours I spent watching TV to see Federer win Wimbledon 2017 -;). Greetings, --D.H (talk) 15:31, 16 July 2017 (UTC)

{{{Unchanged: Three passages on aether and Lorentz}}}

{Text struck through to denote that it is no longer in service. Greg L (talk) 19:11, 18 July 2017 (UTC)}

Other physicists and mathematicians at the turn of the century came close to arriving at what is currently known as spacetime. Einstein himself noted, that with so many people unraveling separate pieces of the puzzle, "the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905."[1]

An important example is Henri Poincaré,[2][3] who in 1898 argued that the simultaneity of two events is a matter of convenience, in 1900 he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by proposing an explicitly operational definition of clock synchronization assuming constant light speed, in 1900 and 1904 he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the principle of relativity, and in 1905/1906[4] he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with the postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional space-time by defining various four vectors, namely four-position, four-velocity, four-force.[5][6] He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems the best suited to the description of our world".[6] Furthermore, even as late as 1909, Poincaré continued to believe in the dynamical interpretation of the Lorentz transform.[7]:163–174. For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity.[3][7]

In 1905, Einstein introduced special relativity (even though without using the techniques of the spacetime formalism) in its modern understanding as a theory of space and time.[3][7] While his results are mathematically equivalent to those of Lorentz and Poincaré, it was Einstein who showed that the Lorentz transformations are not the result of interactions between matter and aether, but rather concern the nature of space and time itself. Einstein performed his analyses in terms of kinematics (the study of moving bodies without reference to forces) rather than dynamics. He obtained all of his results by recognizing that the entire theory can be built upon two postulates: The principle of relativity and the principle of the constancy of light speed. In particular, Einstein in 1905 superseded previous attempts of an electromagnetic mass-energy relation by introducing the general equivalence of mass and energy, which was instrumental for his subsequent formulation of the equivalence principle in 1907. Namely, this principle states the equivalence of inertial and gravitational mass, and by using the mass-energy equivalence, Einstein showed that also the gravitational mass of a body is proportional to its energy content, which was one of early results in developing general relativity. While it would appear that he did not at first think geometrically about spacetime,[8]:219 in the further development of general relativity Einstein fully incorporated the spacetime formalism.

When Einstein published in 1905, another of his competitors, his former mathematics professor Hermann Minkowski, had also arrived at most of the basic elements of special relativity. Max Born recounted a meeting he had made with Minkowski, seeking to be Minkowski's student/collaborator: "[…] I went to Cologne, met Minkowski and heard his celebrated lecture 'Space and Time' delivered on 2 September 1908. […] He told me later that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery."[9] Minkowski had been concerned with the state of electrodynamics after Michelson's disruptive experiments at least since the summer of 1905, when Minkowski and David Hilbert led an advanced seminar attended by notable physicists of the time to study the papers of Lorentz, Poincare et al. However, it is not at all clear when Minkowski began to formulate the geometric formulation of special relativity that was to bear his name, or to which extent he was influenced by Poincaré's four-dimensional interpretation of the Lorentz transformation. Nor is it clear if he ever fully appreciated Einstein's critical contribution to the understanding of the Lorentz transformations, thinking of Einstein's work as being an extension of Lorentz's work.[10]

{{{Unchanged: Image and two passages on Minkowski}}}

Einstein, for his part, was initially dismissive of the Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[7]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime.

1. ^ Born, Max (1956). Physics in My Generation. London & New York: Pergamon Press. p. 194. Retrieved 10 July 2017.
2. ^ Darrigol, O. (2005), "The Genesis of the theory of relativity" (PDF), Séminaire Poincaré, 1: 1–22, Bibcode:2006eins.book....1D, ISBN 978-3-7643-7435-8, doi:10.1007/3-7643-7436-5_1
3. ^ a b c Cite error: The named reference Miller was invoked but never defined (see the help page).
4. ^ Poincare, Henri (1906). "On the Dynamics of the Electron (Sur la dynamique de l’électron)". Rendiconti del Circolo matematico di Palermo. 21: 129–176. Retrieved 15 July 2017.
5. ^ Zahar, Elie (1989) [1983], "Poincaré's Independent Discovery of the relativity principle", Einstein's Revolution: A Study in Heuristic, Chicago: Open Court Publishing Company, ISBN 0-8126-9067-2
6. ^ a b Walter, Scott A. (2007). "Breaking in the 4-vectors: the four-dimensional movement in gravitation, 1905–1910". In Renn, Jürgen; Schemmel, Matthias. The Genesis of General Relativity, Volume 3. Berlin: Springer. pp. 193–252. Archived from the original on July 14, 2017. Retrieved 15 July 2017.
7. ^ a b c d Cite error: The named reference Pais was invoked but never defined (see the help page).
8. ^ Schutz, Bernard (2004). Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity (Reprint ed.). Cambridge: Cambridge University Press. ISBN 0521455065. Retrieved 24 May 2017.
9. ^ Weinstein, Galina. "Max Born, Albert Einstein and Hermann Minkowski's Space-Time Formalism of Special Relativity". arXiv. Cornell University Library. Retrieved 11 July 2017.
10. ^ Galison, Peter Louis (1979). "Minkowski's space-time: From visual thinking to the absolute world". Historical Studies in the Physical Sciences. 10: 85–121. doi:10.2307/27757388. Retrieved 11 July 2017.

## I believe the section to be ready for transfer to article space.

D.H's suggested revisions correct what I felt to be deficiencies in the narrative that I had developed with help from all of the rest of you, but which I wasn't quite able to pinpoint. At this point, I believe that the history is ready to transfer to article space.

I will begin the process of transfer immediately after this post.

Thanks to everybody who helped out! Stigmatella aurantiaca (talk) 02:30, 17 July 2017 (UTC)

I'm reading through and it so far is quite natural to read, interesting, and logical. I am confused about this sentence: In 1900, he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by proposing an explicitly operational definition of clock synchronization assuming constant light speed. What does “explicitly operational definition of clock synchronization”mean? Can you flesh that out within the sentence? Greg L (talk) 04:39, 17 July 2017 (UTC)
P.S. Very good! I went all the way through it and made only a few minor edits for clarity. I found it very easy to understand with the exception of what I wrote in the preceding paragraph. Greg L (talk) 04:52, 17 July 2017 (UTC)
"fleshing out" is on my to-do list. Should get to it in a day or so. Stigmatella aurantiaca (talk) 11:08, 17 July 2017 (UTC)
Geoffrey left a trail of typos and careless edits, not just here but in Special relativity. I didn't go around following him closely to proofread his work, although I obviously should have. I had assumed that a working physicist would be more careful than he actually was. So I'm taking care of those items first. Mea culpa. Stigmatella aurantiaca (talk) 18:04, 17 July 2017 (UTC)
Your culpa runneth over with goofs to fix.
With regard to “…an explicitly operational definition of clock synchronization assuming constant light speed,” an alternative way to address insider-speak like that would be to give it a more general treatment, e.g. In 1900, he recognized that Lorentz's "local time" was actually more akin to what Einstein later posited five years later.
Alternatively, a more detailed but plain-speak treatment. For instance (though I have no idea it is technically correct): In 1900, he recognized that Lorentz's "local time" is actually as Einstein would describe five years later, where ‘time’ (when events occur on a clock) must necessarily vary for different observers in a universe where the speed of light has one fixed value regardless of the two observers’ relative velocities to an observed light source. Greg L (talk) 18:50, 17 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Clearer? Stigmatella aurantiaca (talk) 06:51, 18 July 2017 (UTC)

Very. I enjoyed the learning process, so it’s good stuff. Greg L (talk) 17:18, 18 July 2017 (UTC)
You're welcome. Galison's book is a great read, by the way. Stigmatella aurantiaca (talk) 18:00, 18 July 2017 (UTC)
Translations of Poincare frequently have him using the word "convenience", which was used in D.H's text. I suspect it may be a case of one or another of Poincare's translators settling on the wrong English word to express some subtle nuance of the French. "Convention" makes more sense in most instances. Stigmatella aurantiaca (talk) 18:00, 18 July 2017 (UTC)
I know someone who speaks fluent French. She’s a French citizen, born in France, and married to an American. Would you like to share the precise passage with me and I’ll have her look at it? Greg L (talk) 19:07, 18 July 2017 (UTC)
I'll need to track down the original French for these passages that I know only in translation. This may take a while. Stigmatella aurantiaca (talk) 22:39, 18 July 2017 (UTC)
By the way, she's a language genius. She and her husband play Scrabble in any language so long as it is one of the Romance languages. She and her husband (my boss at the time, though we really had more of a Darren Stevens / Larry Tate relationship) came to me requesting a ruling: she wanted to play Scrabble in Korean, which wasn’t originally a Romance language but only recently has received government-endorsed “official” translations into the English alphabet. I ruled in his favor (I’m no fool). Whatever verdict you obtain regarding her native French, well, you can take it to the bank. Greg L (talk) 00:52, 19 July 2017 (UTC)

## Sections too long

Sections longer than, say, half a screen, are possibly intimidating. An easy way around this is to create sub- (subsub-) sections. If you worry that the TOC becomes too long, it can be made to diplay only down to a chosen depth. YohanN7 (talk) 08:57, 18 July 2017 (UTC)

I'm worried that the fonts of level 4 and deeper subsection headers are indistinguishable. I sort of got around this for • Active, passive, and inertial mass, • Pressure as a gravitational source, and • Gravitomagnetism by adding dots, but it was a kludge solution that I really didn't like. Is there some more elegant way of customizing subheader fonts? Stigmatella aurantiaca (talk) 11:38, 18 July 2017 (UTC)
Don't know. Maybe have a look here. YohanN7 (talk) 12:04, 18 July 2017 (UTC)
TOC could stand a bit of abbreviation. I'll try limiting its depth. Stigmatella aurantiaca (talk) 15:30, 18 July 2017 (UTC)
Trying to figure out visual cues that would work to break up a wall of text, not necessarily subsections. Stigmatella aurantiaca (talk) 15:44, 18 July 2017 (UTC)
Sometimes very simple page layout elements can be employed to break up long stretches of text to alleviate the mind’s energy devoted to eye tracking. Sidebars are a common way in print; though I think it’s possible, I haven’t personally seen them used on Wikipedia.
Bullets, enumerated lists, and cquotes are other examples that break up visual monotony, can easily be used on Wikipoedia, and all of which require minimal-to-zero truncation of text material.
In the History section, as an example of what I’m talking about, I converted an imbedded quote in an already tortuously long paragraph into a cquote, which also effectively bifurcated that long paragraph. All in all, that single giant paragraph became three elements, which I find to be much easier to read because the mind doesn’t have to struggle so hard to direct the eye.
Before and after.
Greg L (talk) 17:40, 18 July 2017 (UTC)
Thanks! Stigmatella aurantiaca (talk) 17:48, 18 July 2017 (UTC)

The {{TOC limit|3}} moved the lede to below the table of contents (funkiness here). I repositioned the tag (∆ edit) to restore the wiki-standard convention of having the lede before the TOC. Greg L (talk) 21:44, 18 July 2017 (UTC)

whoops! Stigmatella aurantiaca (talk) 00:16, 19 July 2017 (UTC)

This version doesn't look too shabby. Then for sectioning without sectioning, one could just play around with standard emphasis.

This topic can be roughly be broken uo into (one), (two), ...

Sure, why not? I just reverted your self-revert! Stigmatella aurantiaca (talk) 07:39, 19 July 2017 (UTC)
How about this version, where I've lumped all of the legacy sections under "Technical topics"? Stigmatella aurantiaca (talk) 07:52, 19 July 2017 (UTC)
Probably a good idea. The separate topics don't really each warrant a top level section. YohanN7 (talk) 08:20, 19 July 2017 (UTC)
That's what I thought, too. So I reverted my self-revert. Stigmatella aurantiaca (talk) 08:29, 19 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── My two cents? It’s a really bad idea. It certainly looks better (there’s no doubting that bit) but the tradeoff in functionality is overly steep.

As wikipedians, we tend to get used to what is what and where things are located after working on a single article for a long while. However, the experience for long-time visitors, who are accustomed to Wikipedia conventions but are new to this article will be VERY different. I can guarantee you that many readers will have experiences like this:

We don’t make a city smaller and easier to drive through by tearing pages out of its telephone book. I think you two just suffered from an industrial-grade case of groupthink.

It takes, what, a half-second longer to scroll through a two-level TOC with a modern trackpad or mouse? Greg L (talk) 15:54, 19 July 2017 (UTC)

I've set limit=3. Let's see how this works. I'm at work right now, so can't check its appearance/functionality on a tablet. Could somebody with a tablet and someone with a minitab check how the full site and the mobile site look on a tablet and minitab? Changes won't make any difference to a phone. Wikipedia mobile on a phone size screen doesn't show TOC at all. Stigmatella aurantiaca (talk) 17:29, 19 July 2017 (UTC)
TOC left|limit=2 looked fine on minitablets in Desktop view.
TOC left|limit=3 looks bad on minitablets in Desktop view.
TOC left|limit=2 looked fine on full size tablets in Desktop view.
TOC left|limit=3 looks marginal on full size tablets in Desktop view.
Stigmatella aurantiaca (talk) 21:26, 19 July 2017 (UTC)
On an iPad running iOS 10.3.2, four hierarchical levels show in Safari in desktop view and they aren’t numbered. On a laptop running MacOS 10.12.5, two levels show (no more than 3.1, for instance) in both Chrome and Safari. Greg L (talk) 21:37, 19 July 2017 (UTC)
And I thought I had near-OCD levels of perfectionism. Two levels on a desktop is fine. Four levels for some tablets isn’t a deal breaker because just a flick of the finger is plenty fast. Greg L (talk) 21:40, 19 July 2017 (UTC)
I was using an online simulator, trying out different virtual tablets and minitablets. The simulator is not always accurate, so I trust your report more than I trust the simulator. The question was how the LEFT option looks. I can tell that the online simulator goofs up in how it handles TOC in Mobile view. The only accurate way to judge definitively is with actual tablets.
It looks like we have to go with a regular display, if we want limit=3.
LEFT with limit=2 looked nice and clean, though, on all displays. Stigmatella aurantiaca (talk) 21:57, 19 July 2017 (UTC)
"On an iPad running iOS 10.3.2, four hierarchical levels show in Safari in desktop view and they aren’t numbered." - AAARGH!!!! Stigmatella aurantiaca (talk) 22:00, 19 July 2017 (UTC)
I conceived of and designed the {{val}} and {{xt}} templates we enjoy today and take for granted; I sweated atomic-level details like this during their development. But the TOC is established business that isn’t going to be changing. These huge TOC differences are all due to vast differences on the consumption end of things. Optimizing the experience for desktop at two levels showing (e.g. “3.1” via TOC3) is best, IMHO, even though other platforms are compromised in different ways. Look at the bright side: There are no “errors” in the TOC regardless of what platform is being used; the only difference is hierarchical depth, which is just a grayscale judgement call anyway. Greg L (talk) 22:08, 19 July 2017 (UTC)
Actually, that was iPad running iOS 10.3.2 in mobile view. One way or another, my reaction is still AAARGH!!! Stigmatella aurantiaca (talk) 21:28, 21 July 2017 (UTC)

Here's a thought. I’ve never seen intra-page hyperlinks denoted by bolding before. Is that something relatively new to Wikipedia, or is it a home-brewed thing?

If home brew, I propose that 1) to better clue readers to the availability of these convenient hyperlinks, 2) and to better embrace the principle of least astonishment, and 3) to avoid such links being essentially an Easter egg, we try something like the following:

We were discussing the genesis of spacetime in early July when…

Now that I think about it, I might have encountered this situation before in a previous article (it might have been our Kilogram article) and ended up with this sort of solution. It works quite well and best serves our readership because it’s perfectly clear and unambiguous. Greg L (talk) 22:57, 19 July 2017 (UTC)

Bold intra-page hyperlinks are already very common in mathematics articles for linking to a numbered formula. For example: Acceleration (special relativity). Various of the numbered formulas are referenced within the text by a bold formula number. I am merely extending the use slightly. Stigmatella aurantiaca (talk) 23:49, 19 July 2017 (UTC)
Since it is a convention that isn't exactly ubiquitous on Wikipedia, would you mind if I changed the non-math ones to what I am proposing above? I think it will be helpful to non-expert users of Wikipedia. Greg L (talk) 01:46, 20 July 2017 (UTC)
The links are already very prominently blue because of the boldness, and it is not necessary for readers to click on them to understand the article. You will notice that there is usually a gentle hint of some sort associated with the links that the reader is encouraged to explore their use: "Click here for a brief section summary", "invariant interval (discussed shortly)", "(see Fig. 1‑1)", "Fig. 2‑9 illustrates that...", "As we have discussed in the previous section on four-momentum", etc.
There is also the issue that many of the links don't necessarily work the first time for phone users, and even more importantly, phone users don't have a good way to return to where they were, especially since they do not have the benefit of a table of contents. The "back" < button often leaves them stranded after a javascript-assisted leap.
The lack of TOC for phone users is an exceptionally irritating point to me, since it makes navigation through the article extremely difficult. I would like to be able to have a "click here to return to TOC" or some sort, but it would only function for Desktop users, who don't need such a feature.
What the MediaWiki "jeniouses" should have done was provide an initially collapsed TOC for phone users. <sarcasm> But no, that was too hard for them to implement. </sarcasm>
So no, don't add the extra verbiage, since except for "Click here for a brief section summary" where I have explicitly provided a "back" mechanism, I don't want to rub phone user's faces into the fact that desktop users have available to them a feature that they may be very hesitant to use.
Re the math intra-wiki link templates, they are incompatible with "collapsing" formulas that compress on a narrow screen, otherwise I would have used them in a couple of points in the Spacetime article. Instead, I rearranged the text so that discussion about a formula was always immediately adjacent to the formulas being discussed, which were hence not necessarily located in the positions where their display may have been most natural. I also completely omitted discussion of one formula (of lesser importance, admittedly) where I couldn't resolve the placement issue. Stigmatella aurantiaca (talk) 05:37, 20 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I tried putting a note at the beginning that the Section Summaries can be read as a stand-alone "Introduction to Spacetime", but I had to undo because of anomalies that phone users experience if they make the Section Summaries their first point of entry. Stigmatella aurantiaca (talk) 13:04, 20 July 2017 (UTC)

OK. It’s not a big deal anyway. I should think though that what the mathematics editors are up to insofar as using bold to indicate intra-article hyperlinks is one thing; using the convention in this more general fashion is an uncommon interface element that doesn’t appear in WP:LINKS and runs an increased risk of suffering frustrating drive-by shootings in the future. I think you are setting yourself up for needless hassle in the future.
With regard to your mention of a lack of an explicitly provided "back" mechanism, that issue doesn’t appear to be relevant since providing an intra-article hyperlink imbedded in the phrase is functionally identical to imbedding the link a few words adjacent in a parenthetical.
I’ll change just one of those links as an example to consider. I hope you ruminate on my example link (near the bottom of the section, here) for a good while before acting. I think you’ll soon conclude that it reads exceedingly close to what you had before, is typographically elegant, is fully compliant with WP:LINKS (and what our users are accustomed to), makes the experience no different for users on mobil devices, and—very importantly—fully and unambiguously communicates to all users what they can expect if they click the link, which is a fundamental imperative of all good man-machine interface guidelines. Greg L (talk) 16:23, 20 July 2017 (UTC)
With regard to your mention of a lack of an explicitly provided "back" mechanism, that issue doesn’t appear to be relevant It's far, far worse than that. Your linking to a top-level section works fine on a phone, because the top level section exists even when the section has not been expanded, and the "back" arrow works fine. But when you experiment with wikilinks to destinations at deeper levels, you will find that the implementation of Wikipedia mobile has a lot of flaky elements that leave you absolutely exasperated, and the back arrow can take you to completely unexpected destinations. Stigmatella aurantiaca (talk) 16:40, 20 July 2017 (UTC)
Agreed. But we’re still talking past each other. My point is only as follows:
This example of trying to understand our target readership (discussed above)
…is functionally identical (mobil users included) to this:
This example of trying to understand our target readership (discussed above)
The blue color in both methods makes it clear that there’s a link. The only differences between the two examples are that 1) the second example fully complies with WP:LINKS, and 2) the second example makes it perfectly clear the reader will be taken to an intra-article location and won’t be taken to another article.

## Current deficiencies in article coverage

Purgy's latest revisions and my (mostly favorable) reaction to them made me think again about current deficiencies in article coverage that stand out immediately to anybody giving this article even a casual read.

Remembering that the goal is to present the material in a form accessible to high school students (or at most, first-year college physics/calculus students):

• There is no discussion of strong fields.
• There is no discussion of the left-hand side of the Einstein field equations.

To keep the article length from spiraling out of control, there are a number of items that could easily be tossed out. The Stella and Terence examples, for instance, were introduced when the article was half its current size, and are disposable. If an adequate presentation of the left side of the Einstein field equations could be developed, we could toss out the Riemannian geometry and Curved manifolds sections, which I currently have parked in the "Technical topics" storage attic for legacy material that I couldn't bring myself to throw away.

The problem is, try as I may, I can't really think of a unique high-school-level take on either topic that

1. Does the topic justice
2. Is not already covered, more or less (in)adequately, in the General relativity and Introduction to general relativity articles (which still deserve their Featured Article status, years after their award).

Any suggestions? Stigmatella aurantiaca (talk) 18:13, 21 July 2017 (UTC)

The intent would not be to provide a sweeping overview of the missing topics. Providing a general, sweeping overview is the job of the General relativity and Introduction to general relativity articles. Those two articles provide exemplary "Wow" and "Gee-whiz" presentations of their subject matter. I have nothing against "Wow" and "Gee-whiz" presentations. It's just that what those articles are doing is not what this article is attempting to do.
"Instead, the focus [of the Introduction to curved spacetime section has been] to explore a handful of elementary scenarios that serve to give somewhat of the flavor of general relativity."
Stigmatella aurantiaca (talk) 23:35, 21 July 2017 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I can offer thoughts one step at at a time. I’ve happy with the lede, Definitions, and History. Next on the list is Spacetime interval. I note that it quickly launches into math-speak, which I suggest should be done very gently so early in the article. We should ease readers into this complex material, step by step. Math terms which seem blindingly obvious to us, such as delta, need to be explained as we ease readers into this material. As an example, here’s what’s currently there:

In three-dimensions, the distance between two points can be defined using the Pythagorean theorem:

${\displaystyle d^{2}=\Delta x^{2}+\Delta y^{2}+\Delta z^{2}}$

Although two viewers may measure the x,y, and z position of the two points using different coordinate systems, the distance between the points will be the same for both (assuming that they are measuring using the same units). The distance is "invariant".

In special relativity, however, the distance between two points is no longer the same…

I’m still not sure of what I’m doing because the current verbiage isn’t sufficiently clear for me to be sure I have a full grasp of the subject matter before trying to simplify the text. But (suspecting I understand it), I propose something like this:

Pythagorean theorem
With space represented along side a, and time along side b a spacetime interval is measured along the hypotenuse, c.

Note the graph at right showing a right triangle. Spacetime diagrams typically represent three-dimensional space by reducing it to a single dimension, which is charted along the horizontal X axis. The single dimension of time is then charted along the vertical Y axis.

Generally, the two axis are scaled proportionally to each other so one light second of distance along the X axis is the same distance on the graph as one second of time on the Y axis (or a light year paired to year, et cetera). Thus, something traveling at the speed of light makes a path at a 45-degree angle.

When measuring distances between any two points in all three dimensions of space (x, y, and z axis), the mathematical relationship is governed by a 3-D version of the Pythagorean theorem:

${\displaystyle d^{2}=\Delta x^{2}+\Delta y^{2}+\Delta z^{2}}$

…where ${\displaystyle \Delta }$ (delta) represents the distance traveled along the given dimension. The distance between two points in 3-D space is merely the square root of ${\displaystyle d^{2}}$.

Although two viewers may measure the x, y, and z position of the two points using different coordinate systems, the distance between the points will be the same for both (assuming that they are measuring using the same units). The distance is "invariant".

In special relativity, however, the distance between two points is no longer the same!

Did I understand my material right? How’d I do? If not, please bring out the Ernie & Bert puppets and help me here by correcting this. Greg L (talk) 23:07, 22 July 2017 (UTC)

We have to assume a certain amount of math literacy. The main target are high school students going up through first year college physics/math. We are not aiming for seventh graders. Look, I'm going bonkers trying to figure out whether there is a feasible means of explaining the basic ideas behind Christoffel symbols, Bianchi identities, Ricci tensors etc. without inundating the reader with the actual math, and you are focused on the Pythagorean theorem??? Stigmatella aurantiaca (talk) 23:22, 22 July 2017 (UTC)
This article is insanely too God-damned big and complex; over and over, every editor in talk-space and behind the scenes has been reinforcing that consistent message, yet you kept shoveling technical coal into the boiler. And now you’re worrying at this late stage about how to make advanced concepts like Christoffel symbols and Bianchi identities more accessible before ensuring that basic concepts are smoothly and properly introduced in the earliest of sections.
You are going to learn soon enough (weeks, months) that with this article in this state of affairs, as soon as you take a two-week-long break, it will be subjected to an series of drive-by shootings such that you’ll scarcely recognize it. Only there’s a 90% chance that those doing the drive-by shootings won’t be as knowledgeable as you. I warned you the first time around that your weird crap like forking the background information to another article entirely was going to receive pushback and you wouldn’t listen until you learned the hard way.
Your tendency towards WP:OWN is disheartening. So you just do what you fucking want then. Greg L (talk) 03:48, 23 July 2017 (UTC)
Who is expressing OWNERSHIP? I have a strong VISION of how the article ought to be. I have expressed it repeatedly:
• This should be an article aimed at high school to first year college students that explains spacetime, primarily within the context of relativity theory.
• This article does not take a "Wow" and "Gee whiz" approach to explaining the subject, but instead focuses on expressing relativistic topics using a consistent spacetime approach rather than the kinematic approach adopted by most popular treatments. (Unfortunately, to keep ramp-up to a minimum, I decided early that a Taylor-Wheeler approach to explaining spacetime was inappropriate. However much I love their way of explaining things, it requires early introduction to the concept of rapidity.)
• There are already two great articles on Wikipedia taking a "Wow" and "Gee whiz" approach to explaining general relativity. This article should not copy them.
• Unlike most technical articles on Wikipedia, this article should not be allowed to grow "like Topsy" resulting in the undecipherable mishmash with which I started back in March.
Within the context of my vision, I have accepted MAJOR CHANGES to the article. You come in and expand the lede from its original one paragraph to its current five paragraphs. My reaction: Sure, it was overly terse. Let Greg take over here. Yohan adds a bit of technical material to "Rapidity" that is a bit of a stretch for the target audience. My reaction: Great stuff, but let's move some of it to a note. Geoffrey comes in and moves the "Measurement versus visual appearance" section to Special relativity. My reaction: Hey, you're right! He rewords a significant fraction of my writing. My reaction: Most of it is somewhat better than my writing, some of it is a bit worse, but I wish he could have been more careful in copy-editing. He deletes "Maxwell's contributions". My reaction: yes, I understand. He chops out most of the History section. My reaction: Geoffrey has a point. Let's all get together and put together a History section that emphasizes spacetime. Purgy decides to rewrite "Light cone". My reaction: Sure. Let's just not toss in stuff about spooky action at a distance.
The article has, as you pointed out, grown to be quite long. A great deal of my effort has been to make it effectively shorter by providing summaries and navigation aids. Much of my effort has been hampered by technical issues having to do with how Wikipedia mobile works on phones. The "Section summaries" can be read as an integrated "Introduction to spacetime".