Talk:Spacetime/Archive 12

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Note on archiving of old talk page and semi-protection of the article

Hi all.

Looking over the previous version of this page, it became apparent all of it was unnecessary drama attempting to deal with a disruptive I.P. editor. That issue was resolved at this ANI. The remedy chosen by the admin was to semi-protect the Spacetime article as well as this talk page for two months; thus, the silver-colored padlock icon in the upper right-hand corners of both pages. This means only autoconfirmed and confirmed users may contribute to the Spacetime article as well as this talk page at the moment.

The semi-protection automatically expires after two months (at 17:05 UTC, 20 August 2017); thereafter, non-registered I.P. editors may once again contribute. However, problems with that particular disruptive I.P. user will likely not reoccur since the I.P. took the highly unusual step of requesting to have himself permanently blocked—and the request was granted.

In hopes we can take a deep cleansing breath and begin anew, I’ve archived the previous threads on this talk page here at Talk:Spacetime/Archive 11. Since the organization of large swaths of discussion threads on #11 was as clean as an accordioned hazmat train wreck, if you find you need a key text passage or a to-do list from the archive in order to start a new discussion here, please feel free to copy it and paste as required.

Note that the #11 archive does not appear in the ClueBot III archive index at right; it instead appears in the fourth pane down in the talk header at the top of this page. Greg L (talk) 02:16, 21 June 2017 (UTC)

It looks like some scheduled update process out of our direct control did the archive re-indexing? I see #11. Stigmatella aurantiaca (talk) 14:57, 22 June 2017 (UTC)

Oh. Yeah. There appears to be two methods for indexing the archive: the one in the talk header is much faster and could be part of MediaWiki (the software application foundation upon which Wikipedia is built) so the servers get to it within seconds. The ClueBot is more like WALL•E and takes its time to make its rounds to this neighborhood.

By the way, since MediaWiki is the world’s best tool for collaborative writing of extensive, structured content, I added MediaWiki to my business's website so FDA-type regulatory consultants and others could work together on submittals. MediaWiki is to Google’s on-line collaborative writing tools as a human is to a mouse. Greg L (talk) 16:26, 22 June 2017 (UTC)

A thought about cooperation here

This section was intended to be seen as intimately related to Greg L's archiving comment above (as of sign. date)

I apologize for this might be considered as off topic, but I do consider it relevant for the future development of this article. 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. Upholding that this one IP-47... certainly acted in a disruptive manner, I definitely want to point to the fact that an admin coined his edits as "appear to be well-intentioned and reasonably competent". Nevertheless, these edits weren't discussed at all, and no honest consent was aimed for, but he was, imho, really shouted down. Maybe, this is the only remedy for guys like him, but a specific (mentioned!) section by the above editor and my personal experience here, make it perhaps possible that there might be a small probability of professional technical writers being too parochial and offensive (herpes?).

I repeat my best wishes. Purgy (talk) 07:47, 21 June 2017 (UTC)

What is a 4-dimensional manifold?

@Stigmatella aurantiaca: I’m clearly not understanding the subtleties of a 4-D manifold, such as its broadest scope and the extent to which it applies to Minkowski space, relativity, etc. Will you explain to me what the distinction is between these two statements:

1. [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.
2. The spacetime of general relativity is an example of what mathematicians call a 4‑dimensional manifold.

Greg L (talk) 19:56, 24 June 2017 (UTC)

There is a difference between the physics of a situation, versus the mathematical framework with which one analyzes the physical situation.

• Intuitively, one can imagine a continuous gradation of spaces from ones which are highly curved, to ones which are hardly distinguishable from flat, to ones which are completely flat. This is an absolutely valid visualization of the underlying physics.
• "Minkowski space" refers to a construct within a particular mathematical formalism that Hermann Minkowski began working on even before Einstein published his 1905 paper on SR. To say the least, Minkowski felt somewhat scooped by his former student when he saw what Einstein had published, but he had the grace to avoid making any claims to priority, especially since Einstein had gone far beyond what Minkowski had accomplished in terms of actually applying the theory to physical situations. Minkowski was, after all, a mathematician and not a physicist, and he wasn't at first really into applications. Minkowski thought that Einstein's kinematic approach was rather klunky, but he took his time developing his geometric approach because he wanted to get it right. What Minkowski unveiled in 1908 was a sophisticated distillation of many years of development.
• The term "manifold" belongs to an entirely different branch of mathematics, Riemannian geometry.
• To say that Minkowski space is a manifold, is sort of like saying that in plane geometry, a plane represents the surface of a hemisphere of infinite radius.

Stigmatella aurantiaca (talk) 01:50, 25 June 2017 (UTC)

Re priority, Born wrote: "[...] 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." Stigmatella aurantiaca (talk) 12:56, 25 June 2017 (UTC)

So, some, but not all, spacetime is well described as being a 4-D manifold. Minkowski Space is not well described as a 4-D manifold; it is best described as a Lorentzian manifold, which is a class of pseudo-Riemannian manifold? Not that I’d advocate that any of this go in the lede. Greg L (talk) 18:28, 25 June 2017 (UTC)

BTW, I'm not seeing the above quote of Born in the article on Minkowski, which seems a shame. Greg L (talk) 23:47, 25 June 2017 (UTC)

I think that for Minkowski spacetime, for this article, you can skip "manifold" all-together. It is not foremost a manifold, while the spacetime of GR is. That said, if you (as a student) learn Minkowski spacetime (or SR or even EM) the "full-blown way" at the outset, then the passage to GR is much easier. One reference that takes this approach (from the physicists POV) is

• Landau, L.D.; Lifshitz, E.M. (2002) [1939]. The Classical Theory of Fields. Course of Theoretical Physics. Vol. 2 (4th ed.). Butterworth–Heinemann. ISBN 0 7506 2768 9. {{cite book}}: Invalid |ref=harv (help)

Other books take other approaches. One telling difference quickly telling which approach is used is the presence or absence of "covariant and contravariant indices". YohanN7 (talk) 07:35, 28 June 2017 (UTC)

@YohanN7: and @Stigmatella aurantiaca: Thank you very much, YohanN7. Is it correct to say the following(?):

1. Since the article title is “Spacetime”, this article broadly covers the full gamut of spacetime; not solely Minkowski space.
2. Minkowski space is an especially notable—actually the most notable—theoretical and mathematical framework of spacetime, and as such, the article places an appropriate level of emphasis on Minkowski space.

If the answer to the above two posits is ‘yes,’ then I would submit that the current degree of coverage on manifolds with regard to the spacetime of GR is appropriate. Yes? No? Greg L (talk) 04:17, 29 June 2017 (UTC)

Can we find a wording that is a good compromise between accessibility and precision?

With this edit, @Schlafly: changed

Mathematically, spacetime is a manifold, which is to say, it is a topological space that locally resembles Euclidean space near each point. By analogy, at small enough scales, a globe appears flat.
to

Mathematically, spacetime is a manifold, which is to say, it is a topological space that is locally homeomorphic to Euclidean space near each point. For example, each point on a globe has a neighborhood that can be flattened to be a planar region.

In the introduction section, this language, while precise, would be extremely scary to the target audience: interested laymen, young middle-school and high school students, etc. I will be reverting the language to the original language and pushing the more precise description into a note.

Is this an OK compromise for you? Stigmatella aurantiaca (talk) 08:08, 27 June 2017 (UTC)

References

Not really. If you want to make it more accessible, then get rid of "topological space". Saying "resembles Euclidean space" is very misleading, because it does not. It resembles a Lorentzian space in this case, not a Euclidean one. Also, saying that a globe appears flat is also confusing. It is tangent to a flat plane, but it is not flat. There are comments on this page that the "manifold" concept is confusing, and I have to agree. There are other articles on manifolds, and this one should be more accurate. Roger (talk) 14:51, 27 June 2017 (UTC)

I got rid of "topological space", but a high school student won't know the difference between "resembles" and "homeomorphic" even with prolonged explanation. Stigmatella aurantiaca (talk) 15:10, 27 June 2017 (UTC)

While we are simplifying, how about just "appears flat" or some variant thereof rather than "resembles Euclidean space"? Stigmatella aurantiaca (talk) 15:16, 27 June 2017 (UTC)

The edit in question was done very early in the article (third paragraph in the Definitions section, right under the lede). If wikipedians are going to contribute to this article, what is needed is more effort to make the early, introductory parts clearer and easier to gently ease the readership into this difficult subject matter (educate without losing them); not the other way around.

We aren’t writing to impress Ph.D.s; they don’t come here to to learn anything. And we don’t write to impress other wikipedians. Terminology like “homeomorphic” so early in an introductory part of the article that is used in an “Oh dear… didn’t-cha know?”-fashion (without a succinct explanation of what the term means) is the last thing this article needs and doesn’t help the target audience (visitors to a general interest encyclopedia).

Moreover, if a term like “homeomorphic” isn’t going to be repeatedly used throughout the rest of the article, then there’s no point to introducing it and defining it in the first place. As it stands, Stigmatella’s current “compromise”, where he transplanted “homeomorphic” to Note 2 is no improvement at all for our all-important readership; if someone doesn’t fix it (or better yet, delete it), I eventually will. As it stands now, Note #2 is purely the product of expertitis conflictus lingo-ralphus. We don’t need any of that here. Greg L (talk) 20:08, 27 June 2017 (UTC)

P.S. See this ∆ edit, Through an experiential based learning process, I used a cognitive disequilibrium approach for perceptibility; i.e. I wrote plainly. If I didn’t hit the technical nail on the head, I’m sure you guys can fix it. Greg L (talk) 20:38, 27 June 2017 (UTC)

"Spacetime in general relativity" section

I've moved the "Spacetime in general relativity section" here. I think there is some salvageable material. Stigmatella aurantiaca (talk) 17:16, 2 July 2017 (UTC)

---

In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor. In special relativity, the Riemann tensor is identically zero, and so this concept of non-curvedness is sometimes expressed by the statement Minkowski spacetime is flat.

The earlier discussed notions of time-like, light-like and space-like intervals in special relativity can similarly be used to classify one-dimensional curves through curved spacetime. A time-like curve can be understood as one where the interval between any two infinitesimally close events on the curve is time-like, and likewise for light-like and space-like curves. Technically the three types of curves are usually defined in terms of whether the tangent vector at each point on the curve is time-like, light-like or space-like. The world line of a slower-than-light object will always be a time-like curve, the world line of a massless particle such as a photon will be a light-like curve, and a space-like curve could be the world line of a hypothetical tachyon. In the local neighborhood of any event, time-like curves that pass through the event will remain inside that event's past and future light cones, light-like curves that pass through the event will be on the surface of the light cones, and space-like curves that pass through the event will be outside the light cones. One can also define the notion of a three-dimensional spacelike hypersurface, a continuous three-dimensional slice through the four-dimensional property with the property that every curve that is contained entirely within this hypersurface is a space-like curve.

Many spacetime continua have physical interpretations which most physicists would consider bizarre or unsettling. For example, a compact spacetime has closed timelike curves, which violate our usual ideas of causality (that is, future events could affect past ones). For this reason, mathematical physicists usually consider only restricted subsets of all the possible spacetimes. One way to do this is to study "realistic" solutions of the equations of general relativity. Another way is to add some additional "physically reasonable" but still fairly general geometric restrictions and try to prove interesting things about the resulting spacetimes. The latter approach has led to some important results, most notably the Penrose–Hawking singularity theorems.

References

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I’d just jettison the passage because it is the product of mathematicians arguing about their dislike of zeros. Like User:Dweller once wrote:

“ What consenting mathematicians get up to behind closed doors is their business, but please don't do it in public. ”

Until someone figures out how to make a good, long-lasting miniature black hole safely in the laboratory, astrophysicists will continue to imagine spacetimes curved beyond the speed of light. And mathematicians will continue to generate equations resulting in infinities and singularities, and they will swear that the universe is full of utter nonsense because their math produces utter nonsense.

What do bees and black holes have in common? They’ve both had times when experts declare that they violate the laws of physics in some way.

This state of affairs rather reminds me of aeronautical engineers in the early 50s who declared that the fact that bees fly violates the laws of aerodynamics. Anytime the experts declare that their formulas show that nature is doing impossible things, their calculations are being done correctly but they are missing a piece of relevant physics and the accompanying new mathematics. Which reminds me of another quote, this time by Richard Feynman:

“ Science is the belief in the ignorance of the experts ”

I’ve never much liked the astrophysicists’ explanations for why a singularity can have a polar moment of inertia; their reasoning comes across to me as “Pay no attention to that ‘zero’ behind the curtain; they spin.”

My personal favorite theory for avoiding singularities and the region between them and event horizons (where spacetime is distorted beyond the speed of light) is Dr. Samir D. Mathur’s “Fuzzballs,” which he arrived at via string theory. His calculations show that when a neutron star collapses to a black hole, what previously was essentially a 21 km-diameter ball of degenerate matter (neutron soup, and possibly even more degenerate forms of matter like quark soup, and hyperons) degenerates one final step: into a ball of strings.

According to Dr. Mathur, the physical surface of a fuzzball is located precisely at the event horizon (precisely where the acceleration required to escape the event horizon equals the speed of light), which is equal to the Schwarzschild radius. A stellar-mass black hole of 1.6 solar masses (just beyond the upper limit for a neutron star) has a diameter of 4.726 kilometers; quite a bit smaller than a Ø 21 km neutron star, but infinitely larger than zero.

Years ago, I corresponded many times with Dr. Mathur while revising our article on Fuzzballs. So I might be biased, but his theoretical solution passes my ‘grin test’ for resolving divide-by-zero. Greg L (talk) 19:59, 2 July 2017 (UTC)

OK. Consider the section completely jettisoned. You might also notice that I jettisoned my own section discussing Rindler space even though it represented several days of effort on my part. The section just wasn't working. A very important rule is not to become too wedded to your own work. What I substituted for what I threw out is far more important and, I think, far more interesting to the target audience. I think it represents the first effort anywhere on Wikipedia to explain the stress-energy tensor to the interested layman. I was inspired by Maschen's beautiful diagram on the contravariant components of the stress-energy tensor. The right artwork makes explaining abstruse concepts vastly easier! Stigmatella aurantiaca (talk) 21:10, 2 July 2017 (UTC)