Talk:Spacetime/Archive 12

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.^[1]
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.^[2]

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)

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)

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.^{[1]: 1–30}

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.^[2]

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.^[3]

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

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.

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:

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)