# Talk:Time dilation/Archive 2

## Etiology

I re-worded some of the introduction to mention the transverse doppler effect.

I could not find any free illustration software, so I just drew the necessary diagrams on my whiteboard and took a picture of them. The result is, shall we say, less than professional. Someone more graphically atuned than I should probably re-draw them. There are also layout issues.

The proposed explanation is, however, about as simple as you can possibly get. It is likely accessible to the aforementioned "12th grader" (though I recall being taught Euclidean geometry well before then), despite the fact it does have some diagrams and some simple algebra. Frankly, graphs and math are going to form part of the description. This is physics.

I am well aware the explanation is hardly a proof, but I assert this is not the place to deal with what happens when the clock is moved along it's axis, spatial isotropy, realizing the implicit experiment (the problem of doppler) and the like. "Just the facts."

If this proposal more or less stands, I think the sections from "Temporal coordinate systems" to "Time dilation and space flight" can be removed -- in this, I completely agree with "Anon" in that they are unnecessarily complicated. mdf 13:59, 24 October 2005 (UTC)

mdf, Why use the word "appears"? We already all agreed that time dilation has a real component. I think we need to agree on terminology. No enclosed experiment can detect the differing rates of ticking (this is because people and things inside such a lab are also affected). However, using somewhat complicated math and knowledge of the theory, it is possible to continuously measure this using the NIST time-sync protocol for satellites by sending a signal to said satellite and comparing the time signal as received at the satellite with those at the ground stations. So the local measurement of time appeared fine in all respects, except that the dilation was exactly measured in the end. In other words, ignoring relativistic simultaenity for a moment, since we're only talking about satellite speeds here for now, you could write a program to calculate earth-time and satellite-time and continuously verify it with the NIST time-sync system and watch the 2 *computed* clocks fall slowly out of sync, gaining or losing time and also hope to one day bring the calculated clock back to the earth if some nae-sayers still wanted to argue with its reality as compared to the clock on earth. The problem with "appears" is the same as ems's associating my use of "laymen" as implying I am clergy, this is the wrong use of the word in the context. A layman is a non-pro in the context given(..and I'm a buff, not a pro). Similarly "appears" in your context is supposed to mean "is seen to", but a layman wandering by might read it as "only appears to be as the reality is different". Jok2000 15:20, 24 October 2005 (UTC)
He uses "appears" because velocity time dliation is symmetrical: Each clock is found to be running slow in the other frame of reference, but physically the clocks are running at the same rate. None-the-less your semantic point is well taken, which is why I used "is found to be" above in the place of "appears". Hopefully that would alleviate your concern. --EMS | Talk 16:44, 24 October 2005 (UTC)
How does EMS know that "physically the clocks are running at the same rate"? E4mmacro 06:51, 29 December 2005 (UTC)

This new section of yours has a lot of issues. The big problem is that it collides with Cleon's animated GIF, which for me is a better way of explaining the same thing. However, there are others as discussed below. So I will revert it out.

I asked you before to establish a sandbox version of this article. That means placing a copy in a location like User:mdf/sandbox/Time dilation, and playing with it there. Efforts like that should be commented on first before being placed before the world.

That is a nice experiment that you did with the new section and the illustration. However, I think that the contents should be placed in a seperate article called Mathematics of velocity time dilation. Also, Wikipedia has adequate facilities for formatting mathematics. There is no need to clutter up an illustration with it, especially since that math needs some supporting text to make is accessible to readers who are initially unfamiliar with this material. --EMS | Talk 16:05, 24 October 2005 (UTC)

It was clear to me that had I established a "sandbox version" you would have ignored it. Instead, I chose to be bold. Don't you remember telling me to do that as well? Or did you mean I was only allowed to be bold' in ways that you would ultimately approve? And as far as I know, no material in the wikipedia needs to be "commented on" prior to being "placed before the world". If I am incorrect in this assumption, then please cite relevant wikipedia policy on my talk page that supports your contention in this regard.
As I noted, it is basically impossible to not use a diagram, and some simple mathematics, to explain the cause of time dilation. The material you left basically proves this point: it is virtually an unreadable mass of confusion. Clock synchronization? Temporal coordinate systems? Totally beside the point, as my submission shows.
Your complaints that the graphics had the math are simply style vs. substance. I invited improvements. I guess that would have been hard, eh? Easier to just revert.
But on a deeper level, I find it perplexing that a few sentences and a simple diagram that more or less explain the phenomena in the simplest manner is somehow lacking compared to the stream-of-consciousness confusing babble that you left. What, exactly, was defective in my submission? Can you offer anything quantifiable, beyond your Royal Say-So? What "supporting text" was needed? Can you explain, clearly, why I or anyone else shouldn't just revert your reversion?
Fortunately for you, though, you don't need to answer any of these questions: as I said above, one revert and I'm gone. mdf 17:39, 24 October 2005 (UTC)
It is easier to destroy than to create, and that goes for the both of us. In any case, to be more specific:
1. You hand drawing covers the same ground as the animated GIF in the section Time_dilation#The_Space-time_geometry_of_velocity_time_dilation. I would prefer that the explanation of that be modified.  ::#* You put your eitology before my text defining what in the most general terms time dilation is. So it is misordered IMO
2. The math clutters up the second illustration, and the lack of supporting text means that t is not explicitly defined.
3. I can't see how this stuff is any less a "stream of consciousness" than what is already there
4. It is not integrated at all with what is already there. Instead if covers the same ground in a different fashion, potentially confusing readers.
I assure you that you are wrong about my not worrying about a sandbox page. Myself and a few others will, given an announcement of it, establish watches on it and actively give you feedback (and some added editting also). This approach has been used successfully by a number of editors, including myself.
You impress me as someone with potential, but you need a chance to play around with this medium and get used to it. Also, be advised that this page needs a good, solid, thoughtful rewrite. I don't want it to be clutterred up with your text and mine and Cleon's with each going off in a different direction. Instead I was something that can act as a coherent whole.
In any case, please don't be put off by my reverting your section. You edit to the intro caused me to remove some of my own text, and if you can moot the section on coordinate systems and/or Cleon's animated GIF, then I will let those go away too. However, your writing this time was not of that level. Just remember that if you don't try again you can't fall flat on your face again, but neither can you succeed in producing something good. --EMS | Talk 19:45, 24 October 2005 (UTC)

I think you guys are talking about 2 different things. mdf's diagram explains the real time dilation (bring 2 clocks back together and they are different), while the animated .gif explains a purely symmetric observational time dilation of 2 ships who do not wish to establish their intertial reference frame nor necessarily ever directly compare their clocks. As such, I propose that the page be broken down into "purely observed" and "real" time dilation halves.Jok2000 20:29, 24 October 2005 (UTC)
"purely observed" time dilation is the "real" time dilation! The same symmetry exists for the mdf's diagram even if he did not show it. --EMS | Talk 21:05, 24 October 2005 (UTC)

Nope, its not symmetric. You should read the twin paradox page closely. This isn't even controversial. It's on PBS or Discovery like twice a week. This page is grossly in error, and quite obviously so. When are you going to put in the "disputed" thing, by the way?Jok2000 01:54, 25 October 2005 (UTC)
I think the "cleanup" tag is mor effective IMO (although that is not my doing). As for the twin "paradox", that includes an acceleration on the part of one of the twins, making their referece frames non-equivalent. (That is a good point however, and should be covered in the article.) --EMS | Talk 05:54, 27 October 2005 (UTC)

## Restoration of Eitology section

I think that I would like it better if it did not make this article look more like a used book store than a well organized article. I won't contest its restoration, but this article needs to have someone "take the bull by the horns" and really redo it a ways. (I regret that I am too busy for that at this time.) --EMS | Talk 06:00, 27 October 2005 (UTC)

Okay, cleanup can be be based on the expert opinion at http://scienceworld.wolfram.com/physics/TimeDilation.html for the non-symmetric part, and the symmetric space-ship fleet .gif then works best if it contains a third body like the Earth.Jok2000 12:23, 27 October 2005 (UTC)

I'm not a user of Wikipedia, however, I am very familiar with time dilation. You need to word the article better. I am familiar with time dilation, but I don't even want to read the article because the first few sentences are so complicated. You need to word it in more "user-friendly' terms so it is easier to read. http://www.geocities.com/superstringtheory42

---above by anon

Well, when you learn to read, come back and check the version history of this topic and suggest some changes that might survive the reversionists. My reference to a very easy to understand book on time was reverted a long time ago. The "symmetric" part is not really relevant to time dilation and can go, IMHO, unless it takes on the idea of propogation delay and doesn't pretend to describe time dilation. Here, I'll put it back in and see what happens.Jok2000 18:34, 1 December 2005 (UTC)

## question

Is the idea that at the speed of light no time passes and time travelled = distance in light years? So if you travelled to the end of the universe (15 billion light years) at light speed it would seem instantaneous for you, but you would arrive in 15,000,002,005 AD ??? Astrokey44 11:29, 2 December 2005 (UTC)

Try Talk:Time_dilation/Archive_1#Recent_edits_by_ems57fcva Jok2000 14:19, 2 December 2005 (UTC)

They seem to only talk about speeds which approach light speed, what about travelling at light speed itself. looking through that led me to this table from an older version of the page, would this be any use in the current article? Astrokey44 14:41, 2 December 2005 (UTC)
v (%c) length due to length contraction time due to time dilation
0 1.000 1.000
10 0.995 1.005
50 0.867 1.155
90 0.436 2.294
99 0.141 7.089
99.9 0.045 22.366
99.999 0.00448 224.658

## "proper time locally"

It says now: "Time dilation is the phenomenon of proper time passing at a different rate for a remote and/or moving object than it does locally. " That's certainly not yet optimal, for here "proper" and "local" mean effectively the same thing, similar to writing "local position is measured far away at a different location than locally".

That may be an improvement, but I'm sure we can do better than that. For example:

"Time dilation is the phenomenon of time passing at a different rate for a remote and/or moving clock than it does locally and/or in rest."

or, IMO again better:

"Time dilation refers to the phenomenon that the proper time rate of a remote and/or moving clock differs from that of a reference clock."

Cheers, Harald88 18:28, 12 December 2005 (UTC)

Regretfully, I find the last proposal insufficient: in the phrase

"Time dilation is the phenomenon of proper time being observed to pass at a different rate for a remote and/or moving object than it does for the observer",

the words "observed" and "observer" may cause confusion. On top of that, "observer" is jargon that risks to be interpreted at face value, causing considerable misunderstandings. Thus I'll do an attempt to do better. Harald88 08:35, 13 December 2005 (UTC) PS I did not include "proper time" in the intro sentence, as it's not necessary and a burden for newbees. It should be mentioned somewhere later though. Harald88 08:58, 13 December 2005 (UTC)

I think that you have done a good job of capturing the essense of my sentence, so I will not quibble. You are however quite right that proper time needs to be mentioned here somehow. (At the least we have gotten beyond the weird edit whereby the into was talking about "accelerated clocks".) --EMS | Talk 19:15, 13 December 2005 (UTC)

## Seems accurate on a glance

Why is the factual accuracy of this article disputed? I didn't read the whole thing, but what specifically has been called into question? --Monguin61 03:20, 15 December 2005 (UTC)

The green ships / red ships explanation does not agree entirely with the Twin paradox resolution. More precisely "both the green and the red fleet are entitled to consider themselves as "non-moving" in their own frame of reference." from this page and "The usual resolution of the paradox is that the twins are not symmetrical: the travelling twin has a "turnaround" and not all reference frames are equivalent." from the Twin paradox page are not in agreement. Jok2000 04:04, 15 December 2005 (UTC)

*Sigh*. The twin paradox page explicitly notes that in that "paradox" three interial frames are involved. In this write-up, only two inertial frames are involved. As for the statement "not all reference frames are equivalent": That is true. However, in SR, all inertial frames are equivalent. I will look at the twin paradox article and see if I can clarify the point being made there. However, that {{disputed-section}} tag is IMO inappropriate, and I will remove in within 24 hours unless you can make a better case for its being there. --EMS | Talk 05:03, 15 December 2005 (UTC)
Okay, sure, the ships came from somewhere, either 1 or 2 other inertial reference frames. How's that? ..however I'll caution you not waste much effort debating me, as I don't have much to say. I'm the kind of guy, to borrow a line from Dire Straits, who if I see two guys claiming to be Jesus, might say "1 of them must be wrong", not because I deny Jesus and can be excommunicated by the Pope, but rather, have employed logic that even the Pope cannot deny. Jok2000 13:04, 15 December 2005 (UTC)
This is irrelevant. While each observer remains in the same inertial frame, the reciprocity of this effect applies. For example, how do you know that these are not aliens on stars which are passing each other? In that case, they have been in those frames of reference throughtout their lives! What more do you want?
Kindly note that this is the reason why the twin paradox is such a perpetual nuisance! For example, if traveling twin has a time dilation factor of 0.5 (which means v = 0.866c) and his trip lasts 10 years in the view of the stay-at-home twin, the traveling twin must see the stay-at-home twin pass through 20 years if his coordinate time with the stay-at-home twin's clock ticking at half-time all the while. Because of how the traveling twin's perception of spacetime changes at turnaround, that is indeed the case. (This is something that the twin paradox page itself should cover. Maybe someday I will take care of that.)
I hope that this satisfies you. In any case, I kindly request that you remove that tag now. I principle, you "own" the tag. However, your failure to understand that section does not mean that it is wrong. The tag therefore is more a form of harrassment than a bona-bide warning of a conflict between groups of editors. --EMS | Talk 15:41, 15 December 2005 (UTC)
I think there's a term in psychiatry for imagined harrassment. However, like I said, I don't have much to say. You clearly think space is empty and the time dilation follows the object. I haven't been to the vatican recently to see if that's part of accepted canon, however the boys on the inertia page are busy debating even inertia ad nauseum, so its good you removed the disputed tag -- we barely exchange a harsh syllable any more. Actually, I was hoping you'd have changed it to "disputed section" shortly after I added it, but then I went off to more productive topics and the dispute kinda fizzled. Jok2000 20:30, 15 December 2005 (UTC)

## The GIF-animation is sufficient

Time dilation in transversal motion.

In the GIF-animation the fleet do compare their clocks!
The lightpulses that are being emitted at regular intervals provide the information that allows the ships of the respective fleets to maintain constant distance to each other, and for each fleet the regular lightpulses serve to maintain a single fleet-time.
Pulses traversing from one fleet to another are equally informative and meaningful.
Every second of red time a time-bearing pulse is sent to the green fleet, and the green fleet counts two seconds of green time between each pulse recieved from the reds.
Conversely: every second of green time a time-bearing pulse is sent to the red fleet, and the red fleet counts two seconds of red time between each pulse recieved from the greens. They do compare their respective rates of proper time, that is what the pulses traversing from one fleet to the other are all about.

The GIF-animation is designed in such a way that the time-bearing pulses of light are a true indicator of the way the rates of proper time of the reds and the greens relate to each other. It is in this GIF-animation a true indicator because it is designed in such a way that involvement of classical Doppler effect is avoided.

Recapitulating: the twin scenario entails that two space-ships depart from each other, and later make a rendez-vous, and if one spaceship has traveled more distance than the other, they will on rendez-vous be seen to not have had the same lapse of proper time.

I suppose that it is tempting to believe that to defer the comparison of lapse of proper time to when the rendez-vous point has been reached is a more solid comparison. Is it more physical to compare clocks that have been brought into co-moving status? There is no support for such a hypothesis. There is no support for thinking that the twin scenario singles out something that is somehow more physical than what is depicted in the GIF-animation.

Any of the ships of either of the fleets can make a U-turn at some stage, and have a rendez-vous with a ship that has been passed by earlier. The ship that has made a U-turn in order to get to the point of rendez-vous will then be seen to have had less lapse of proper time. If both a "red ship" and a "green ship" make a U-turn, then both will have less lapse of proper time than the ships they rendey-vous with.

I vote to not discuss the twin scenario in this article. There is a separate wikipedia article for the twin paradox. Of course, the two subjects are interrelated, but I think discussing the twin scenario in the time dilation article is unnecessary duplication.

The GIF-animation is designed to emphasize the symmetry that is at the heart of special relativity: the principle of relativity of inertial motion. --Cleon Teunissen | Talk 14:58, 15 December 2005 (UTC)

Yeah, the twins thing doesn't belong here. Let's delete the green & red ships nonsense completely. Jok2000 15:10, 15 December 2005 (UTC)

Also, quoting Cleon: involvement of classical Doppler effect is avoided. The issue is that Transverse Doppler effects are related to the time dilation. Its a terribly contrived example ignoring several major points. The best 2 sentence description for both time dilation and the twins thing is here: Wolfram We really need to delete misleading fluff out of this article. Jok2000 19:39, 15 December 2005 (UTC)

Then name the points that are being ignored. IMO, that GIF needs a much better description, but overall is quite accurate and useful. That rewrite has been on my to-do list for some time, and this may just force the issue. In the meantime, that {{disputed}} tag has been removed. You have not shown me that there is anything to dispute here. --EMS | Talk 20:04, 15 December 2005 (UTC)
I had a look at the Wolfram intro: "Time Dilation : The apparent shortening of time relative [...]" -> hardly possible to be more confusing than that, since length contraction means the apparent decrease of a rod's length unit, and time dilation the apparent increase of a clock's time period ... Harald88 22:07, 15 December 2005 (UTC)
In reply to Jok2000: The name 'transverse Doppler effect' is a misnomer. Time dilation in transversal motion is unrelated to classical Doppler effect. The two have only one thing in common: a shift of the frequency of signals; the causative mechanisms of the frequency shifts are unrelated. Trying to force a comparison with classical Doppler effect would only introduce confusion.
I checked out the Wolfram link. Sure, it's concise, it's also so incomplete that it is incorrect.
I also feel that the current time dilation article is overburdened, but by the looks of it I would delete quite different passages compared to what you would delete.--Cleon Teunissen | Talk 22:21, 15 December 2005 (UTC)
I fully agree with Cleon that "transverse Doppler effect" is a misnomer, despite it being rather standard jargon. It has nothing to do with Doppler's theory, it just happens to be part of the same measurement. For explaining such mix-up terms are counter productive.

BTW, which passages are proposed for deletion? Harald88 22:28, 15 December 2005 (UTC)

Okay, let's suppose we fix up the wording of the green & red ships part. I must take exception with Harald88's edit of 15:40 27 November 2005 that prompted me to finally put the disputed-tag in there. He changed "is" to "seems to". Time dilation is an experimentally verified phenomenum. The article shouldn't need wishy-washy language. The "considering yourself non-moving" bit in the green and red ships section is also superfluous to the discussion, or at least in the wrong place. What EMS said about aliens and what not is utterly irrelevant. There are no meteorites landing on earth with odd half-lives of radioactive elements or any such thing, well that's an exaggeration, the equivalence principle takes care of physical experiments on that scale. Most assuredly, if the green ships were launched from earth and the red ships were parked relative to the Earth, the GIF would be totally incorrect -- again, experimentally verified. Haefel-Keating trumps all this thought-experiment silliness. So I still propose that the green/red ships part be deleted, it only agrees with Haefel-Keating if the green ships are still relative to the Earth or sun or something not moving too quickly around these parts. :) Jok2000 02:24, 16 December 2005 (UTC)

SRT is about observations, whereby what is measured (seems to be so) from one point of view (inertial coordinate system) is measured differently (does not seem so) from another point of view. Now that is a fact about the theory. If you remove the "seems to" at inappropriate places, you end up with self contradiction (or a multi-universe, but that is not officially agreed on!). Such sloppyness is exactly the cause of much confusion and debate in literature and it is good to avoid that mess here. Harald88 08:01, 16 December 2005 (UTC)
Haefel-Keating is not relevant to this since it combines general relativity and special relativity. Like it or not, that GIF is correct for green ships launched from the Earth that then go out a ways, turn around, and zoom past the Earth and the red fleet before turning around again and coming back home. However, the GIF is only concerned with the part where the green fleet zooms by the red fleet, or in between (and not including) the turnarounds. By contrast, the twin paradox does include a turnaround, and Haefel-Keating is was done on a spatially closed path. All that you are demonstrating is a lack of understanding about what time dilation and the twin paradox are about.
BTW - We may not have meteorites with strange half-lives around, but muons created in the upper atmosphere regularly make it down to the surface of the Earth even though is takes many, many times the half-life of the muon to get down here even at nearly the speed of light. The trick is that they are time dilated as they come on down. How that occurs is very much described that GIF. --EMS | Talk 03:18, 16 December 2005 (UTC)

## What provides the clearest window on time dilation

I copy and paste from above.

Most assuredly, if the green ships were launched from earth and the red ships were parked relative to the Earth, the GIF would be totally incorrect Jok2000 02:24, 16 December 2005 (UTC)

Again, your objection seems to stem from a conviction that time dilation occurs if and only if a traveller makes a turnaround and rejoins the people he has departed from.

The GIF depicts the situation of, say, the outbound leg of the journey of the travellers. Let a string of space stations be situated from the Earth to Sirius, each say, one lightweek apart. Let those be the "reds". Let a fleet of traveling "green" ships travel to Sirius. The GIF dipicts the situation during the journey from Earth to Sirius. The GIF depicts how the lapse of green proper time and the lapse of red proper time relate to each other.

It a philosophical point, I suppose, as to what provides the clearest window on the properties of time dilation. An example: let there be two space-ships, one is moving inertially, the other is using rocket thrust to circle around the non-accelerating ship. That is an a-symmetrical situation and then the circling ship has consistently less lapse of proper time than the non-accelerating ship. Accumulation of time dilation is a function of difference in pathlength; the circling ship is clocking up more mileage, and in accordance with that the circling ship has less lapse of proper time. --Cleon Teunissen | Talk 10:18, 16 December 2005 (UTC)

Cleon - Good explanation. I will only add a couple points to it:
1. See the proper time article for the math relating to Cleon's last example.
2. Not only does the GIF work for the outbound leg of a round trip to Sirius, but aslo the inbound leg. That is the crux of the twin paradox. It fails in the view of the "green" fleet at turnaround because of how turnaround affects the green view of spacetime.
--EMS | Talk 11:34, 16 December 2005 (UTC)
My main conviction is that the GPS satellite system works. The red/green diagram requires the reader to make an assumption for it to be true, that is, it must be executed in a particular way to come out as stated. EMS loves to call it lack of understanding, but I did actually read the article the way you folks are arguing it the first time through, however I never operate with unwise assumptions, and went back through the argument leaving out the assumptions and discovered rather quickly that it is in error. Jok2000 13:51, 16 December 2005 (UTC)
The GPS is a gravitational time dilation phenomenon. That material used to be a part of this page, but was exported some months ago to the other page, although this page still references it. Gravitational time dilation involves accelerated frames of reference, while velocity time dilation in an effect of inertial frames of reference. There is a difference:
1. In the velocity case, each observer sees the other clock as running slow.
2. In the gravitational potential case, if one observer sees the other clock as running slow, then in the view of the other observer the first clock is running fast.
You are correct that there is an apparent contradiction in each clock ticking slow in the other's viewpoint. However, when you work through the math, you find the Lorentz contraction and the relativity of simultaneity combine to with time dilation to make special relativity self-consistent. So whether you like it or not, the GIF is correct. --EMS | Talk 18:39, 16 December 2005 (UTC)
I don't know if it's much of a reference, since I wrote it, but the math you deleted the first time I edited this page about 2 months ago, which I've seen in several reputable sources, states that the GPS system's time dilation is a combination of 3 factors, SR, GR and something I am wholely unfamilar with, the Sagnac effect. The GIF cannot be correct, because it suffers from the same issue as the Twin Paradox, when it is viewed as a paradox (as opposed to when it is resolved). It is easy to see from the GPS SR equation that the effect is continuous, not at turn-around. Suppose a budding GPS (or Gallileo) engineer came to this page? He'd be fired on the spot if he quoted it without laughing. You seem to want to describe propagation delay, although you do seem to know what time dilation is. Jok2000 20:34, 16 December 2005 (UTC)
Excellent! I now understand your gripe.
This is as I thought: You do not appreciate the symmetry of the SR time dilation effect. You are quite correct that the GPS effect is asymmetrical, while what is being displayed here is symmetrical. However, just look at your own writing:
the GPS system's time dilation is a combination of 3 factors, SR, GR and something I am wholely unfamilar with, the Sagnac effect.
So SR is not the whole story here. You also note that
It is easy to see from the GPS SR equation that the effect is continuous
which is true, but it is also true of the red-green ships model in either frame of reference. In general, the GPS time dilation factors are computed for an Earth-centered inertial frame of reference. In a GPS-based frame of reference, the same SR slowdown would be present for the Earth, but different GR values (and to a minor extent Sagnac effect values) would be present to compenstate for the SR effect being symmetrical.
A warning - You are not going to resolve this philosophically. SR is based on mathematics, and to show a problem you must show that the math is inconsistent. People have been trying that for over 100 years, and noone has succeeded. In fact, the success is Hermann Minkowski's 1908 proof that SR is really self-consistent. --EMS | Talk 21:55, 16 December 2005 (UTC)
My guess is that the depiction in the GIF seems incorrect to you, because somewhere along the line you make some inappropriate assumption. The GIF is not intended as paradoxical. The GIF depicts aspects of motion in Minkowski space-time. It is an axiom of special relativity that Minkowski space-time geometry is the proper geometry to use. The GIF depicts a theorem of Minkowski space-time geometry.--Cleon Teunissen | Talk 21:53, 16 December 2005 (UTC)

## Rate versus amount of lapse of proper time

In my previous entry I used the expression 'accumulation of time dilation'. That needs some clearing up, I think.

In the case of time-dilation-in-transversal-motion (depicted in the GIF) there is not a one-on-one relation between red proper time and green proper time. The situation is symmetrical however; red is to green what green is to red. What is compared in the GIF is rate of lapse of proper time, and the determining factor is relative velocity.

In the a-symmetrical case of one space-ship in inertial motion, and another space-ship using rocket thrust to circle around it, there is a non-symmetrical time dilation and consequently a buildup of difference in amount of elapsed proper time. For difference in amount of elapsed proper time the determining factor is difference in pathlength.

Earlier I glossed over that by using the expressions 'less lapse of proper time' and 'more lapse of proper time', not specifying whether it referred to 'comparative rate of proper time' or 'amount of proper time'.

Presumably the symmetrical time dilation and the a-symmetrical time dilation are different aspects of the same thing, but I find it not straighforward to envision how they are related. The a-symmetrical time dilation is still somewhat intuitive, it's the symmetrical time dilation that boggles the mind.

I concentrated on the symmetrical case because (1) the muon example (2) generally, symmetry is the physicist's best friend. --Cleon Teunissen | Talk 12:39, 16 December 2005 (UTC)

There is in principle no difference between "symmetrical time dilation" and "a-symmetrical time dilation": they are both calculated with the same equations, relative to inertial frames. Harald88 12:50, 16 December 2005 (UTC)

## Time dilation aspects of the GPS technology

I copy and paste from above:

I don't know if it's much of a reference, since I wrote it, but the math you deleted the first time I edited this page about 2 months ago, which I've seen in several reputable sources, states that the GPS system's time dilation is a combination of 3 factors, SR, GR and something I am wholely unfamilar with, the Sagnac effect. Jok2000 20:34, 16 December 2005 (UTC)

OK, lets review the GPS.
The Sagnac effect is a fundamental geometric effect. Let's put it this way: the Sagnac effect is a theorem of light propagation in newtonian absolute space and time, it's a theorem of Minkowski space-time geometry, and it's a theorem of the Riemannian geometry that is applied in GR. It's a theorem of any geometry that is suitable for modeling physics. The Sagnac effect is so fundamental that all theories predict it.

All terrestrial clocks that are located at sealevel have the same rate of proper time as compared to each other, and thus keep running in synchrony with very little adjustment. For a satellite in orbit there are two time dilation factors.
(1) Since it is orbiting, the satellite is clocking up more mileage than the terrestrial clocks, wich corresponds to less lapse of proper time than terrestrial clocks. This is non-symmetrical time dilation.
(2) Since the satellite is higher up in the Earth's gravitational well there is correspondingly more lapse of proper time. This is also non-symmetrical time dilation.
For GPS-satellites, in their orbits with a period of 12 hours, the gravitational time dilation is the strongest contribution, and for the clocks on the GPS satellites there is more lapse of proper time as compared to terrestrial clocks.

I have familiarized myself with the physics problems that the engineers of the GPS system have solved, and it is with that knowledge as background that I present my views on time dilation. --Cleon Teunissen | Talk 22:06, 16 December 2005 (UTC)

## Possible new animated GIF

Cleon -

I have an idea for a new animated GIF that may help people like Jok2000 to see what is going on with velocity time dilation being symmetrical. What you need to show is the red fleet passing the green fleet. Notice my emphasis on the word "fleet". This would not be one ship, but each as a series of ships. The ships will have spaced thenselves out at intervals of 0.866 light-seconds, so that a red ship will move between successive green ships in one second in the green ship frame of reference and vice-versa. Note that this spacing out and a clock synchronization was done within each fleet, with the master clocks (in the lead read and green ships) set so that they would read zero as they passed each other.

Now look at this in the red frame of reference. At red time t=0 all red clocks read t=0. Alao, the lead green clock reads t=0. Furthermore, the red ships are at locations 0, 1, 2, 3, 4, ..., but the green ships are at locations 0, -1/2, -1, -3/2, -2, ... . This is of course due to the Lorentz contraction. Even more interesting are the clock settings in the green fleet at t=0: 0, 3/4, 3/2, 9/4, 3, ... . This is due to the relativity of simultaneity. Now here is a table noting the places of the green fleet in the red reference frame (in units of 0.866 light-seconds), and the clock times of the green fleet and 1/2 second intervals of red time:

Red time Green ship 1 Green ship 2 Green ship 3 Green ship 4 Green ship 5 Notes
place clock place clock place clock place clock place clock
0.0 0 0 -0.5 .75 -1.0 1.5 -1.5 2.25 -2.0 3.0 Green ship 1 at Red ship 1
0.5 0.5 0.25 0 1.0 -0.5 1.75 -1.0 2.5 -1.5 3.25
1.0 1.0 0.5 0.5 1.25 0 2.0 -0.5 2.75 -1.0 3.5 Green ship 1 at Red ship 2
1.5 1.5 0.75 1.0 1.5 0.5 2.25 0 3.0 -0.5 3.75
2.0 2.0 1.0 1.5 1.75 1.0 2.5 0.5 3.25 0 4.0 Green ship 1 at Red ship 3

Notice some things: When Red ship 1 is next to green ship 2, the green clock reads 1 second! Simlarly, when red ship 2 is next to green ship 1, the red clock also reads 1 second. So there is the symmetry, courtesy of the time offset of the relativity of simultaneity. This possibly could be animated for better effect. --EMS | Talk 04:01, 17 December 2005 (UTC)

Good idea! Indeed, that's much more clear. Harald88 05:09, 17 December 2005 (UTC)

Hi EMS,

the reason the GIF came out as it did is that I tried to steer away from explicit depiction of length contraction, as that would add complexity. Of course, time dilation, length contraction and relativity of simultaneity are interconnected; any animation that has one of them has (implicitly or explicitly) all three of them.

My view is that the article should in equal measure acknowledge the two aspects of velocity time dilation.
(1) Symmetrical velocity time dilation. Comparative rate of lapse of proper time. It is determined by relative velocity.
(2) Non-symmetrical velocity time dilation. Comparison of amount of proper time that has elapsed. It is determined by difference in pathlength. (Example: one spaceship moving inertially, a second space-ship circling the first. The second ship's worldline in space-time is longer then.)

What needs to be avoided in the article is a suggestion that acceleration is a determining factor in any form of time dilation. Acceleration breaks symmetry, but time dilation is not a function of acceleration.

As it is, the article is not consistent. The statement, "gravitational time dilation involves accelerated frames of reference" is untenable. Satellites in orbit are moving inertially, and for satellites orbiting at different altitudes a non-symmetrical time dilation is observed: different amounts of lapse of proper time as compared to each other.( see the entry about GPS-technology for more details) --Cleon Teunissen | Talk 09:54, 17 December 2005 (UTC)

There is a gravitational (or acceleration) field between ourselves and the satellites. So the vicinity of the Earth is an accelerated frame of reference. It also is a curved spacetime. I personally would like to leave GR out of this mix, although some reference is needed. In the end, you have really hit the nail on the head by noting the path length is what is important. However, you have goofed in one respect: The "length" of a world line is the proper time elapsed while traveling along it: When the second ship is circling the first (and the first ship is moving inertially), it is the first ship that has the "longer" world line.
As for the proposed GIF: This may not be the right place for it, but I think that it may be useful. --EMS | Talk 16:21, 17 December 2005 (UTC)
The problem, if I understand it correctly, is that EMS defends Einstein's original GRT interpretation while Cleon defends the current mainstream interpretation. If I'm right about this, then also Cleon was right with his objection: if the statement "gravitational time dilation involves accelerated frames of reference" is disputed, it can not be presented as fact. Harald88 17:42, 17 December 2005 (UTC)
You gentlemen have discussed and expanded on my original quibble admirably, and why it did not qualify as a dispute and a resolution is a bit of a puzzle, however I'll assume its just semantics. I'm off on a trip for a couple of weeks, so I'll leave you with a thought while I'm gone: symmetry is easily achieved with only 2 frames of reference, however with 3 one is forced to re-evaluate the situation. As much as the sci-fi fans might like 2 fleets of spaceships, aliens and distant outposts in the galaxy, we have an active system (GPS) we can study closer to earth and if this were my article, I would give priority to the material and the here and now. So as a minimum, the spaceships .gif would require a 3rd reference frame, the one they originated from, preferably the earth, and then proper calculations could be made. As for philosophical points, I have read Einstein's "Ideas and Opinions" and it speaks volumes for the general scientific philosophy of the 1950s. Jok2000 16:47, 18 December 2005 (UTC)
EMS is of course correct in pointing out that in Minkowski space-time geometry the natural definition of length-of-a-worldline is the proper time along that worldline. In the example of one space ship moving inertially and a second spaceship circling the first then as measured in the inertial frame (co-moving with the first ship), the spatial length of the two paths is different, the circling path being longer spatially.
It is my understanding that the amount of gravitational time dilation is a function of how deep a clock is down a gravitational well, but that it is not directly a function of whether the clock is resting on the surface of a gravitating body, or in orbit around the gravitating body. (For the clock in orbit there will be an asymmetrical velocity time dilation, in accordance to the orbital motion.)
The expression 'being-in-an-accelerated-frame of reference', is not quite synonymous to 'being in curved space-time'. The expression 'being-in-an-accelerated-frame of reference' also emcompasses 'being in an uniform gravitational field'. Gravitational time dilation correlates with 'being-in-curved-space-time. So when an object is being accelerated while moving in Minkowski space-time, I categorize the asymmetrical time dilation associated with that as an aspect of velocity time dilation.
I agree with EMS that it is best to discuss first velocity time dilation, and treat gravitational time dilation separately. I'm currently working on another animation, which I hope will be useful. I will keep my big mouth shut until that is finished. By the way, my signature is changed, I have been granted a change of user name from Cleon Teunissen to Cleonis. --Cleonis | Talk 21:45, 20 December 2005 (UTC)
Harald88 wrote "The problem, if I understand it correctly, is that EMS defends Einstein's original GRT interpretation while Cleon defends the current mainstream interpretation."
It does seem a matter of interpretation. See also the following article by Peter M. Brown, about GR interpretation (PDF 67 KB). I am committed to the interpretation where the concept of gravitational field is exclusively associated with curvature of space-time. Einstein disagreed with that, as a matter of principle, and he did have a point, it's worthwile to appreciate the depth of Einstein's considerations. --Cleonis | Talk 21:45, 20 December 2005 (UTC)
*Sigh*. As a practial matter, gravitational time dilation is associated with gravitational potential, and there are no "asymmetrical" time dilation effects that do not fall into that category. In the rotating disk example, the central observer is not in an accelerated frame of reference, but because of his rotation his view of spacetime is accelerated. Because inertially moving objects are accelerated in this frame of reference, I say that a gravitational field exists in this view of spacetime. It is as simple as that. Curved spacetime makes it so that all observers will perceive inertially moving objects accelerating with respect to themselves in at least some regions of the spacetime. Yet to me a gravitational field is defined by the result and not the cause. --EMS | Talk 05:15, 21 December 2005 (UTC)
That will soon (hopefully) be handled in the Twin paradox, as originally it was about Einstein's relativity concept. Harald88 07:59, 21 December 2005 (UTC)