Talk:Spacetime/Archive 17

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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:

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

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:

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

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

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".

I have just added numerous "Return to introduction" internal links that I would really have preferred to be "Return to Table of Contents" except that phones don't display a table of contents. Now, "Return to introduction" links are, to the best of my knowledge, not common on Wikipedia, and I somehow doubt that there is anything covering them in the MOS. Do you object to their usage because they violate your principle of least surprise?

I am trying to be an effective manager to keep the article coherent rather than letting it take the course of most technical articles that have suffered from total lack of management. I expect many changes by other contributors in the future, and so long as the article tells a coherent story at an appropriate level for the target audience, I'm fine with that. Stigmatella aurantiaca (talk) 08:37, 23 July 2017 (UTC)

Here is another example. Yohan suggested a reworking of the appearance of the Table of Contents. My reaction: I thought it was a worthwhile idea and spent a lot of effort trying to make it work, but I was ultimately defeated by the behavior of Wikipedia mobile on different devices.

Also, I am looking into cutting some pieces (that yes, I wrote) that are of lesser importance. Adding navigational aids only works so far. I am not, as you seem to think, in love with my own words. Eventually one has to look into what shortening the article can do to improve it. Stigmatella aurantiaca (talk) 17:21, 23 July 2017 (UTC)

Unadvertised feature

@Greg L: Because of the many differences in browsers and phones, I would much prefer that the intra-wiki links be something that phone users discover for themselves whether they are useful for their particular combination of phone and browser, rather than advertising loudly, HERE IS A NEAT FEATURE FOR YOU TO TRY. Quit screwing with them. Stigmatella aurantiaca (talk) 23:09, 22 July 2017 (UTC)

The intra-wiki links work perfectly on Desktops for all browsers that I've tested, on both Windows, Apple, and Linux machines. If nobody used mobile devices, I'd say, sure, go ahead and make your changes. But somewhere around 42-44% of our users are mobile users, and it is a fair guess that most of them are phone users rather than tablet users, and iOS and Android work differently. Because of the anomalies that I've found, I'd rather leave these features as neat things that desktop users may discover to be very useful, and phone users may or may not find useful. Stigmatella aurantiaca (talk) 23:55, 22 July 2017 (UTC)

See third paragraph, above. Greg L (talk) 04:13, 23 July 2017 (UTC)

Trimming stuff

Lots of examples were OK when the article was small. But with the article around 200K, we need to exercise some triage.
Example: Terence and Stella are at a 100 meter race. Terence is an official at the starting blocks, while Stella is a participant. At t = t′ = 0, Stella begins running at a speed of 9 m/s. At 5 s into the race, Terence, in his unprimed coordinate system, observes their mother, situated 45 m downfield from the starting blocks and 10 m to the left (45 m, 10 m, 0 m, 5 s), waving at Stella. Stella, in her primed coordinate system, observes their mother waving at her at x′ = x − vt = 45 m − 9 m/s × 5 s = 0 m, y′ = y = 10 m, i.e. she observes their mother as waving from directly to her left (0 m, 10 m, 0 m, 5 s).

One reviewer called the following "a cemetery of buzzwords." I agree.
Quantized spacetime
In general relativity, spacetime is assumed to be smooth and continuous—and not just in the mathematical sense. In the theory of quantum mechanics, there is an inherent discreteness present in physics. In attempting to reconcile these two theories, it is sometimes postulated that spacetime should be quantized at the very smallest scales. Current theory is focused on the nature of spacetime at the Planck scale. Causal sets, loop quantum gravity, string theory, causal dynamical triangulation, and black hole thermodynamics all predict a quantized spacetime with agreement on the order of magnitude. Loop quantum gravity makes precise predictions about the geometry of spacetime at the Planck scale.

Spin networks provide a language to describe quantum geometry of space. Spin foam does the same job on spacetime. A spin network is a one-dimensional graph, together with labels on its vertices and edges which encodes aspects of a spatial geometry.

Stigmatella aurantiaca (talk) 23:34, 24 July 2017 (UTC)

Simplified Doppler Effect discussion with removal of text and a diagram

Figure 3-6. Galilean spacetime diagrams of classical Doppler effect. (a) Source moving away from the receiver. (b) Receiver moving away from the source.

Semi-interesting stuff, but no real scientific/historical relationship between these early speculations and relativistic spacetime

Foreshadowings of the spacetime concept
In myth and literature
Incas regarded space and time as a single concept, referred to as pacha (Quechua: pacha, Aymara: pacha). The peoples of the Andes maintain a similar understanding.

Arthur Schopenhauer wrote in 1813: "...the representation of coexistence is impossible in Time alone; it depends, for its completion, upon the representation of Space; because, in mere Time, all things follow one another, and in mere Space all things are side by side; it is accordingly only by the combination of Time and Space that the representation of coexistence arises."

The idea of a unified spacetime is stated by Edgar Allan Poe in his essay on cosmology titled Eureka (1848) that "Space and duration are one". In 1895, in his novel The Time Machine, H. G. Wells wrote, "There is no difference between time and any of the three dimensions of space except that our consciousness moves along it", and that "any real body must have extension in four directions: it must have Length, Breadth, Thickness, and Duration".

Return to Introduction
In math and physics
In Encyclopedie, published in 1754, under the term dimension Jean le Rond d'Alembert speculated that duration (time) might be considered a fourth dimension if the idea was not too novel.

Another early venture was by Joseph Louis Lagrange in his Theory of Analytic Functions (1797, 1813). He said, "One may view mechanics as a geometry of four dimensions, and mechanical analysis as an extension of geometric analysis".

Concerning his development of the theory of quaternions in 1843, William Rowan Hamilton wrote, "Time is said to have only one dimension, and space to have three dimensions. ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions."

Various authors have credited W. K. Clifford with having anticipated the concept of curved spacetime as far back as 1870, although the actual extent to which Clifford anticipated spacetime curvature is debatable: in an 1876 publication, Clifford speculated that "curvature of space is what really happens in that phenomenon which we call the motion of matter", i.e. he wrote on the possibility of curved space without mentioning time.

Return to Introduction

Loedel diagrams are enlightening, but I didn't make use of them in the article.

For instance, whereas in conventional spacetime diagrams, the equivalence between the rest and moving frames is not immediately evident, if one chooses a third reference frame between the resting and moving frames with the two other frames moving in opposite directions with equal speed (the median frame), the result, often called a Loedel diagram (although it was independently developed by multiple authors), has equal units of length and time for both axes.

Stigmatella aurantiaca (talk) 11:35, 25 July 2017 (UTC)

Idiosyncratic coverage of a graduate-level topic.

Topology

The assumptions contained in the definition of a spacetime are usually justified by the following considerations.

The connectedness assumption serves two main purposes. First, different observers making measurements (represented by coordinate charts) should be able to compare their observations on the non-empty intersection of the charts. If the connectedness assumption were dropped, this would not be possible. Second, for a manifold, the properties of connectedness and path-connectedness are equivalent, and one requires the existence of paths (in particular, geodesics) in the spacetime to represent the motion of particles and radiation.

Every spacetime is paracompact. This property, allied with the smoothness of the spacetime, gives rise to a smooth linear connection, an important structure in general relativity. Some important theorems on constructing spacetimes from compact and non-compact manifolds include the following:

• A compact manifold can be turned into a spacetime if, and only if, its Euler characteristic is 0. (Proof idea: the existence of a Lorentzian metric is shown to be equivalent to the existence of a nonvanishing vector field.)
• Any non-compact 4-manifold can be turned into a spacetime.

Return to Introduction

Stigmatella aurantiaca (talk) 11:53, 25 July 2017 (UTC)

References

The results in the topology section are quite relevant and interesting. They could be reworded. I think the main message is that there are limitations imposed by the mathematical structure that limits the possible behavior of spacetime. Not every 4-D manifold can be endowed with a Lorentzian metric (whereas any manifold of whatever dimension can be endowed with a Riemannian metric). These excluded manifolds are thus not solutions of Einstein's field equations. (The stuff about the Euler characteristic translates to something like "spacetime can topologically be like a sphere, but not a torus", though not literally.) "Compact" can be perhaps reworded as "finite" (technically it is closed and bounded in any embedding in a flat space of higher dimension (they exist, at least in the Riemannian case)). "Paracompactness" (property possessed by any manifold) is purely technical. YohanN7 (talk) 08:13, 15 August 2017 (UTC)

45 years ago I might have attempted a reworking of the section along the lines that you suggest. Absolutely not now. Could you maybe show how you think the section ought to read? I see nothing of this in the main article Spacetime topology. Should the main article be reworked to include this missing material? Thanks! Stigmatella aurantiaca (talk) 15:20, 15 August 2017 (UTC)

If true, then yes. I took it all at face value. YohanN7 (talk) 14:28, 16 August 2017 (UTC)