Talk:Spacetime/Archive 8

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Technical difficulty

P.S. Some I.P. editor just visited the article and expanded the tag to declare that It may be too technical for most readers to understand. (*sigh*)

Greg L (talk) 16:23, 2 April 2017 (UTC)

@Greg L: Unfortunately, there is a limit to how non-technical I can make this. Discussing the twin paradox from the stay-at-home twin's point of view is trivial, but if I want to discuss the twin paradox from the traveling twin's point of view, I'm forced to add another equation

$tan\ \theta =v/c$

and to present some middle school geometry. I've been racking my brains here. I'll be introducing some background material in a few hours with the above scary equation. I'm not sure when I'll be able to do the actual twin paradox, since I need to mull over a lot as to the actual strategy that I will employ to present it. How much rigor, how much handwaving, how to avoid my discussion turning into an essay, etc. There are a fair number of decent attempts to explain the twin paradox out there, but unfortunately the best are non-encyclopedic essays. Stigmatella aurantiaca (talk) 18:18, 2 April 2017 (UTC)

Quoting you: “Unfortunately, there is a limit to how non-technical I can make this.” Agreed. After a hurculean effort, we're already at the editorial limit; improving it from γ =4 to to γ =20 isn't impossible; it just requires an impractical amount of extra editorial energy. The subject matter is what it is. Moreover, the tag's verbiage is likely not entirely accurate (“This article may be too technical for most readers to understand”). To precisely describe the conundrum would require a new kind of tag: “This article is too technical for some readers to understand.” But that's merely stating an objective truth. Greg L (talk) 18:37, 2 April 2017 (UTC)

I've added some material on transforming between reference frames and removed the cop-out "(It is beyond the scope of this introduction to explain how to calculate the transformed axes of the spacetime diagram for different reference frames.)" in the relativity of simultaneity discussion. Stigmatella aurantiaca (talk) 20:00, 2 April 2017 (UTC)

Back to Twin paradox

P.S. I read the link on the twin paradox you provided. Thanks. The world needs a still-better explanatory thought experiment showing how the twin paradox is no paradox.

I previously did a drive-by-shooting read on our Twin paradox article, which doesn’t seem to be particularly good or bad insofar as technical articles go on Wikipedia. I nonetheless had an epiphany that there are more than time differences going on that create the apparent paradox; there are also apparent differences in distance that factor into what each individual sees and which are important in showing how there is no paradox. I know: in light of “spacetime,” what I just wrote is obvious on its face.

One of the complexities with many of the available twin paradox thought experiments is they involve inbound and outbound trips in a spaceship, which adds extraneous doppler shift effects that do nothing but cloud the issue as the various authors labor to explain the effect. I think I'm beginning to wrap my mind around what is occurring and can now see that Einstein chose good words to describe the astronaut not aging as fast: it is merely a “peculiar” effect, and a “natural consequence” of special relativity.

I am quite intent on going to one of my sandboxes and working on my own twin paradox thought experiment entailing an astronaut who leaves earth and orbits the sun at a distance of 27.53 au (between the orbits of Uranus and Neptune) and which has a velocity, perpendicular to a radian from the sun to the International Celestial Reference Frame within the ecliptic plane, of 299,532,238 m/s (γ = 24). As viewed from earth, it takes the spaceship precisely 24 hours to orbit the solar system. Yeah, Neptune is way the hell out there. Moreover, as viewed from earth, laser strobes synched to the spaceship’s clock show its time advances only one hour per orbit.

Importantly, the astronaut sees his orbit as being smaller than it appears to us. Moreover, the astronaut would see both the sun and earth as shaped like an American football with their long axis at their poles.

I had another epiphany while at Twin paradox. If I achieve what I'm after, it won't be necessary to begin the thought experiment in earth's reference frame, before takeoff (with the twins hugging), and ending again in earth's reference frame after landing (with the twins seeing they've aged differently); that too would be excess thought-baggage.

In summary, I posit that there should be no differences between observations made by a passing alien (at the same velocity) who had never been in earth's inertial reference frame, and those made by an astronaut who took off from earth. I posit also—but am far from certain—that a clear and convincing refutation of the paradox can be made when examining earthbound and spaceship observations made only while the spaceship is in a stable orbit, which is to say, without consideration of accelerations and periods where the spaceship once shared earth's reference frame. Greg L (talk) 20:20, 2 April 2017 (UTC)

If you think that can improve Twin paradox, go right ahead. I have no intention of touching that article. Too many cooks. Just look at the number of archived discussions! I prefer working on less politically charged articles. I learned my lesson a while back. Stigmatella aurantiaca (talk) 00:15, 3 April 2017 (UTC)

Oh, hell no. I wouldn't try to contribute to the Twin paradox article. The editors over there rely heavily on the [undo] button to keep their life fuss-free and the article so splendiforous. The “undo” button: it’s one-click easy! Greg L (talk) 00:33, 3 April 2017 (UTC)

Length contraction will take a few days, mostly in working out the animated graphics. I don't see anything available in Commons that really appeals to me. It's somewhat more complicated to explain length contraction than time dilation. It's only after presenting multiple reference frames, relativity of simultaneity, time dilation, length contraction, the Terrell–Penrose effect (i.e. the difference between what one sees vs. what one measures), and mutual time dilation that I'll be ready to tackle the twin paradox. I'll get there eventually. There's a lot of background preparation involved, if I don't want the reader to feel cheated and/or mystified. The Twin paradox article doesn't supply that background. Stigmatella aurantiaca (talk) 22:06, 6 April 2017 (UTC)

Your addition of animations will probably be the biggest help of all in understanding this abstruse subject matter. I created this animation for the Thermodynamic temperature article (and most of the other animations and graphics). Although animations take a huge amount of time to make, they are worth the effort and have withstood the test of time over there. Greg L (talk) 00:04, 9 April 2017 (UTC)

Babies and bath water

heap someone has erased a very useful well explained part on the timelike space like etc equations it should be reposted! — Preceding unsigned comment added by 88.15.240.6 (talk) 12:02, 13 April 2017 (UTC)

Looking over the material that I deleted, there are several sections where I may have tossed out a baby. I will try to restore the content at an appropriate level of difficulty, which is to say, I wish the material in the Introduction section to be understandable by a typical high school science student who is willing to devote a reasonable (and not excessive!) amount of effort into absorbing the material:

• "Certain types of world lines are called geodesics of the spacetime – straight lines in the case of Minkowski space and their closest equivalent in the curved spacetime of general relativity. In the case of purely time-like paths, geodesics are (locally) the paths of greatest separation (spacetime interval) as measured along the path between two events, whereas in Euclidean space and Riemannian manifolds, geodesics are paths of shortest distance between two points.<ref group=note>This characterization is not universal: both the arcs between two points of a great circle on a sphere are geodesics. The concept of geodesics becomes central in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences."
• [For a timelike interval] "There exists a reference frame such that the two events are observed to occur in the same spatial location, but there is no reference frame in which the two events can occur at the same time."
• "In a light-like interval, the spatial distance between two events is exactly balanced by the time between the two events." [Restoring the definition of a light-like interval should be trivial.] took care of this Stigmatella aurantiaca (talk) 12:59, 30 April 2017 (UTC)

Stigmatella aurantiaca (talk) 08:56, 18 April 2017 (UTC)

My stab at an executive summary

@Greg L:Quite frankly, I don't like it. It starts off OK, but towards the end, since the reader has not been given adequate groundwork, it seems to me that the sentences turn into meaningless buzz.

Introduction

---

Summary

Definitions

• In classical mechanics, time is separate from space. In special relativity, time and space are fused together into a single 4-dimensional manifold called "spacetime."
• The technical term "manifold" and the great speed of light imply that at ordinary speeds, there is little that humans might observe which is noticeably different from what they would observe if the world followed the geometry of "common sense."
• Things that happen in spacetime are called events. Events are idealized, four-dimensional points. There is no such thing as an event in motion.
• The path of a particle in spacetime traces out a succession of events, which is called the particle's "world line."
• In special relativity, to "observe" or "measure" an event means to ascertain its position and time against a hypothetical infinite latticework of synchronized clocks. To "observe" an event is not the same as to "see" an event.

History

• 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.
• Einstein's theory of special relativity (1905), which was based on kinematics and a careful examination of the meaning of measurement, completely resolved the problems raised by the aforementioned experiments.
• Hermann Minkowski, in 1908, published a geometric interpretation of special relativity which has come to be known as Minkowski space, or spacetime.

Spacetime interval

• Time by itself and length by itself are not invariants, since observers in relative motion will disagree on the time between events or the distance between events.
• On the other hand, observers in relative motion will agree on the measure of a particular combination of distance and time called the "spacetime interval."
• Spacetime intervals can be positive, negative or zero. Particles moving at the speed of light have zero spacetime intervals and do not age.

Reference frames

• To simplify analyses of two reference frames in relative motion, Galilean (i.e. conventional 3-space) diagrams of the frames may be set in a standard configuration with aligned axes whose origins coincide when t = 0.
• A spacetime diagram in standard configuration is typically drawn with only a single space and a single time coordinate. The "unprimed frame" will have orthogonal x and ct axes. The axes of the "primed frame" will share a common origin with the unprimed axes, but its x' and ct' axes will be inclined by equal and opposite angles from the x and ct axes.

Light cone

• On a spacetime diagram, two 45° diagonal lines crossing the origin represent light signals to and from the origin. In a diagram with an extra space direction, the diagonal lines form a "light cone."
• The light cone divides spacetime into a "timelike future" (separated from the origin by more time than space), a "timelike past", and an "elsewhere" region (separated from the origin by a "spacelike" interval with more space than time).
• Events in the future and past light cones are causally related to the origin. Events in the elsewhere region do not have a causal relationship with the origin.

Relativity of simultaneity

• If two events are timelike separated (causally related), then their before-after ordering is fixed for all observers.
• If two events are spacelike separated (non-causally related), then different observers with different relative motions may have reverse judgments on which event occurred before the other.
• Simultaneous events are necessarily spacelike separated.
• The spacetime interval between two simultaneous events gives the proper distance. The spacetime interval measured along a world line gives the proper time.

Invariant hyperbola

• In a plane, the set of points equidistant from the origin form a circle.
• In a spacetime diagram, a set of points at a fixed spacetime interval from the origin forms an invariant hyperbola.
• Spacelike and timelike intervals form spacelike and timelike invariant hyperbolae.

Time dilation and length contraction

• If frame S' is in relative motion to frame S, its ct' axis is tilted with respect to ct.
• Because of this tilt, one light-second on the ct' axis maps to greater than one light-second on the ct axis. Likewise, one light-second on the ct axis maps to greater than one light-second on the ct' axis. Each observer measures the other's clocks as running slow.
• One light-second on the x' axis projects to less than one light-second on the x axis. Likewise, one light-second on the x axis projects to less than one light-second on the x' axis. Each observer measures the other's rulers as being foreshortened.

Measurement versus visual appearance

• Because it takes time for light to travel from different points of an object to an observer, the visual appearance of an object traveling at high speed will not correspond to its measured dimensions.
• For example, a high speed object passing by an observer will not appear length contracted, but rotated. This is known as "Terrell rotation".
• Apparent faster-than-light jets of matter ejected by black holes also represent optical illusion.

Twin paradox

• To beginners, mutual time dilation seems self-contradictory because two observers in relative motion will each measure the other's clock as running more slowly.
• Careful consideration of how time measurements are performed reveals that there is no inherent necessity for the two observers' measurements to be reciprocally "consistent."
• In the twin paradox, one twin makes a journey into space in a high-speed rocket, returning home to find that the twin who remained on Earth has aged more.
• The twin paradox is not a paradox because the twins' paths through spacetime are not equivalent.

Gravitation

• In the absence of gravity, spacetime is flat, is uniform throughout, and serves as nothing more than a static background for the events that take place in it.
• Gravity greatly complicates the description of spacetime. In general relativity, spacetime is no longer a static background, but actively interacts with the physical systems that it contains.

Definitions

Non-relativistic classical mechanics treats time as a universal quantity of measurement ... blah, blah ... Stigmatella aurantiaca (talk) 11:35, 13 April 2017 (UTC)

@Stigmatella aurantiaca. I'm sorry to say that I agree with you. What you've got here is more of a glossary than a primer. And that's not a wasted effort; I actually added a glossary to a complex Wikipedia article before.

Hmmm... a Summary section at the end of the Introduction section, rather than a misguided attempt to give the reader a prequel? That might work... Stigmatella aurantiaca (talk) 21:33, 14 April 2017 (UTC)

I think I can help you write a primer by asking you to explain some things to me; I'll serve as the “fool” in the exercise of making something foolproof. Allow me to explain my idea here:

Let's assume that the readers coming here are reasonably well educated, bright, have an interest in the subject matter, and—most importantly—have a basic awareness of Einstein's theory of relativity and its time and space dilation. Let's further assume that the reason they are visiting this website is to not only understand what timespace *is*, but to also understand how timespace is distinct from what Einstein had advanced in 1905.

As I see it, Einstein’s On the Electrodynamics of Moving Bodies was, according to Einstein's own abstract, advanced to make two important points: A) light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body, and B) there is no “absolutely stationary space” in which special electromagnetic processes take place.

But Einstein also clearly saw that both spatial coordinates and time varied depending upon one's relative motion. After all, the title of ¶3 is “Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former.” He obviously saw the measurement of both time and space as being affected by the relative motion of observers. Yet, if I understand your take on the matter, Einstein did not see these simultaneous variations of time and space geometrically as movements within a unitary “timespace.”

(Stop me if I'm wrong on any of that preceding paragraph and correct me. If, on the other hand, what I wrote above is actually perfectly spot on, then that should serve as the framework upon which you expand your verbiage.)

So I'll play the roll of “visitor” here and you explain it to me. Let me challenge you to do the following in only 500–750 words plus one or two illustrations (or animations) with captions: Explain to me what Einstein taught insofar as how time and space both changed depending on the relative motion of two observers. But remember, you wouldn't want to use graphics that uniquely illustrate Minkowski's spacetime. Nor do you want your verbiage to intrude into Minkowski's spactime's turf. Why? Because the distinction of Minkowski's space will be the second half of the challenge (coming up later).

This role, by the way, is easy for me because, I suppose, I don't get it. After looking at Einstein's paper and how he was simultaneously addressing temporal and spatial transformations, it really rather escapes me why a unified spacetime was lost on the guy. We can either see-saw our way up the learning curve on this via your starting with a nugget of your verbiage, or you can lay it on me. Whatever works and is fun; we weren't drafted into the Army here. Greg L (talk) 01:03, 14 April 2017 (UTC)

I think that I should be able to come up with an explanation that will make you happy. Give me a couple of days. Looking over my explanation for length contraction, there are points that I didn't explain clearly. Making sure that my explanations are clear and accurate is the priority. Stigmatella aurantiaca (talk) 21:33, 14 April 2017 (UTC)

I can't follow Einstein's math, but I can (I think) parse the logic of his verbiage as he introduces and summarizes his formulas. Maybe this is the key distinction between Einstein's 1905 theory of relativity and Minkowski space: It looks like Einstein had separate formulas for transformations upon shapes and for transformations on time; I haven't yet spotted verbiage where he introduces calculations for performing transformations upon anything akin to a 4D manifold of spacetime. If my understanding (no single formula upon a 4D manifold) is correct, then that is the key distinction between Einstein's teachings and those of Minkowski.

It may well be that the graphs typically used to illustrate Einstein's formulaic concepts unfortunately exhibit too much of Minkowski's graphical view. Perhaps the principle challenge with illustrating Einstein's view will be in choosing illustrations that graphically represent his two distinct formulas (time and space) as faithfully as possible without overdoing the “geometric” implications. Yes?

I also note where Einstein wrote as follows (my emphasis):

“ A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion—viewed from the stationary system—the form of an ellipsoid of revolution with the axes. ”

It may be that the most effective illustration in a primer for this half (the spatial half) of Einstein's formulas could be something as simple as an plain old illustration of an ellipsoid—a properly CADed ellipsoid—with a caption explaining that Einstein had a formula for the transformation of space that described how a spherical body would appear to an observer with a relative velocity. Greg L (talk) 01:34, 15 April 2017 (UTC)

P.S. Since Einstein's transformations on time and space were still Lorentz transformations, one could have illustrations of those, but they wouldn't be uniquely Einstein's contributions. Can the distinctive advancement of Einstein's teachings over Lorentz’ work be captured in an illustration? Or can it only be described in body text? All I can come up with for illustrating Einstein's distinctive contribution comes from merely looking at the principle points of his abstract at the start of his paper:

“ A) light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body, and B) there is no “absolutely stationary space” in which special electromagnetic processes take place. ”

In my mind, both A and B could be captured by a picture of two trains (rather like this image) showing that just like sound in still air, the speed of the signal doesn't change; only its pitch. The caption could then explain that Einstein's second point (there is no absolute stationary space) effectively means that from the point of view of any observer, it's as if one’s “luminiferous aether” moves with them. Thus, this one graphic and a caption could capture the distinctive points of Einstein's teachings? Greg L (talk) 17:43, 15 April 2017 (UTC)