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Two questions

In the Hafele-Keating like experiments there are always two accelerated reference frames. However, in the Twin Paradox thought experiments there is never more than one accelerated frame. How can one consider the Hafele-Keating experiments germane to the paradox?

Could you explain why atmospheric mesons, which are nearly inertial reference frames, decay slowly in the Earth’s nearly uniform weak field? It appears to me that using the weak field transforms their clocks are supposed to run fast. —Preceding unsigned comment added by Emagnus3 (talk • contribs) 04:39, 13 March 2010 (UTC)[reply]

First things first: Welcome to Wikipedia! :)
In answer to your first question: 'These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks.'. This is from Science's abstract for the second paper. I know that a lot of other authors agree. I think that your question has merit, though. There are authors who disagree about the relevance of experiments to solving a paradox arising from a thought experiment, so this will have to be mentioned when the corresponding sources arrive here.
Your second question has a simple answer: The special relativistic effect of slowing down the aging rate of the moving particle is several orders of magnitude larger than the slowing down of ground clocks due to gravitational time dilatation. Happy editing, Paradoctor (talk) 12:09, 13 March 2010 (UTC)[reply]
It's ridiculous to claim that physical experiments are not relevant to solving a thought experiment. Strictly speaking, it's probably true that authors have made this claim, because people do write ridiculous things. But, for example, Newton's first law of motion is essentially a gedanken, as completely force free laboratories containing frictionless ramps and pulleys are in short supply.

While not explained sufficiently in this article, Hafele-Keating and related experiments are versions of the rotational type of twin paradox mentioned in the final section, and these rotational versions are logically related to the "standard" linear versions. There is a nice, not overly complicated discussion of this in sections 2, 3, and 4 of this paper, which would serve as an excellent reference to flesh out the final section of the article here. Tim Shuba (talk) 17:23, 13 March 2010 (UTC)[reply]

"It's ridiculous": So are Time Cube and Paris Hilton. As long as we can source it to reliable sources, and in accordance to WP:DUE and whatever else applies, not only can we insert it, we have to, I'm afraid.
"authors have made this claim": You'll probably find more philosophers than physicists among them, but the answer is "affirmative".
"would serve as an excellent reference to flesh out": I'll be the last to hold you back from adding statements from a reliable source. ;) Paradoctor (talk) 18:30, 13 March 2010 (UTC)[reply]

Regarding the Viewpoint of the traveling twin

First, I would like to thank Paradoctor for his warm welcome and wish him well on his anticipated paper.

A successful analysis of Hafele-Keating included an analysis of the effects of Special Relativity. Similarly Paradoctor’s successful analysis of the decay of atmospheric mesons included an analysis of the effects of Special Relativity.

It is not clear to me that, in this section, there has been any analysis, during the period of acceleration, for the effects of Special Relativity. Emagnus3 (talk) 23:07, 3 April 2010 (UTC)[reply]

That's kind of the holy grail here. Einstein claimed in his 1918 paper that special relativity is not applicable to accelerated frames of reference. Others (too lazy to look up now) have stated that you can extend SR to accelerated observers, and get the expected results. There are lots of other opinions, ranging from "trivial, no paradox, really" to "ZOMG, Einstein lied to us!". There is no single consensus solution, but among physicists in general, there is a general, if not universal, feeling that the twin paradox is no threat to SR's logical consistency. Philosophers are somewhat more skeptical, and my favorite nutjobs cranks crackpots fringe theorists often use the paradox to prove that their favorite TOE is needed to repair physics in general. If you ask me, uncle Al has left us with another fine mess. ;) Paradoctor (talk) 23:36, 3 April 2010 (UTC)[reply]

Decrepitude

I appreciate that the stationary twin will have aged more, but would they also exhibit greater decrepitude? DynamoDegsy (talk) 15:33, 27 April 2010 (UTC)[reply]

Not if the time was spent in a nice comfy cryochamber. ;) Paradoctor (talk) 16:38, 27 April 2010 (UTC)[reply]
And if there wasn't a nice comfy cryochamber? :o) DynamoDegsy (talk) 07:30, 28 April 2010 (UTC)[reply]
There is always S.E.N.S.. ^_^ Paradoctor (talk) 16:13, 28 April 2010 (UTC)[reply]
My query results from a discussion amongst colleagues (engineers not scientists). My contention is that Paul Langevin's "striking example" means that, when the travelling twin returns to earth, he will have incurred only 2-years of decrepitude, and all his earthbound contemporaries will have incurred 200-years of decrepitude, i.e. they are dead. Whereas, my colleagues contend that although only two years have elapsed for the travelling twin, he too will have incurred 200-years of decrepitude. I believe that decrepitude is a function of time (and lifestyle), and as time has slowed for him, then so will his decrepitude. DynamoDegsy (talk) 07:41, 29 April 2010 (UTC)[reply]
According to Eddington, you have every reason to believe your colleagues are in error. If that doesn't convince them (it won't), ask them to cite their sources, I'm interested. If this argument is something they came up by themselves, please inform them that "decrepitude" does not seem to be a term appearing in relativity. ;) Paradoctor (talk) 16:17, 29 April 2010 (UTC)[reply]

Experimental proof

For me, the clocks in planes not really convincing, since the difference is so tiny so that one might say, that other reasons cause the tiny delay. But, I think, experiments with decaying particles in accelerators are much more convincing, since the effect is much larger due the higer velocity close to the speed of light.— Preceding unsigned comment added by 95.222.228.77 (talk • contribs)

Please sign your talk page messages with four tildes (~~~~). Thank you. DVdm (talk) 08:23, 28 April 2010 (UTC)[reply]

A remark and a question

Remark You write

They know that the distant star system and the Earth are moving relative to the ship at speed during the trip.

In my humble opinion that should be

They know that the distant star system and the Earth are moving relative to the ship at speed during the trip.

This will have no effect on the calculations.

Question According to the travelers' calculation they will arrive home having aged 5.14 years. How much would the people of the earth-based mission control have aged according to the travelers' calculation? —Preceding unsigned comment added by 84.83.33.64 (talk) 15:09, 9 June 2010 (UTC)[reply]

Please put new remarks at bottom of page and sign with four tildes (~~~~)? Thanks.
About the remark. Speed is always positive. Normally when -v is used, we talk about velocity, which has a direction. In that case velocity -v is in the opposite direction as velocity v. When we talk about speed, the direction is either explicitly stated, or silently assumed, which is the case here. So the sentence is correct.
About the question: When the calculation is made from the traveller's viewpoint, they will calculate that the Earth-people age 10.28 years. The calculation is a bit trickier because during the trip the travellers live in two different inertial frames: one frame for the outbound part and another frame for the inbound part. At the turnaround event, there is a sort of "simultaneity-with-the-earth-jump" between the event immediately before the turnaround and the event immediately after. You find a more rigorous treatment and an example (A) in [1] which is a reference for the section Twin paradox#Difference in elapsed times: how to calculate it from the ship. IIRC this question was asked a while ago on Wikipedia:Reference desk/Science. You can search the archives. DVdm (talk) 15:32, 9 June 2010 (UTC)[reply]

The bibliographies

The Benton bibliography is now available at s:The clock problem (clock paradox) in relativity. I'll add the bibliographies of Benton (240 entries), Arzeliés (109), Marder (241), and Chang (35) to Further reading later on. Paradoctor (talk) 18:45, 9 June 2010 (UTC)[reply]

Correction request

First, excuse me if I'm not getting this right. My request would be to find a better name for so called "simultaneity planes" on this image: http://en.wikipedia.org/wiki/File:Twin_Paradox_Minkowski_Diagram.svg As this other image calls "plane of simultaneity" those points in spacetime that are separated by only space in a given inertial frame: http://en.wikipedia.org/wiki/File:Relativity_of_Simultaneity_Animation.gif So for the first image we can't simply talk about a single plane of simultaneity, since it's relative to an observer's inertial frame, and we have two of them. I think those lines are important, just the name is wrong, because it's ambiguous if we try to Google it. Thanks! —Preceding unsigned comment added by 78.92.229.174 (talk) 23:20, 17 June 2010 (UTC)[reply]

Welcome to Wikipedia!
"excuse me if I'm not getting this right": Nothing to apologize for being WP:BOLD. ;)
I updated the the file on Commons as requested. Regards, Paradoctor (talk) 03:58, 18 June 2010 (UTC)[reply]

Omg, I wasn't right: We had 3 and not 2 inertial frame, but they were correctly named simultaneity planes. With the new naming, it can be easily seen. Thanks! —Preceding unsigned comment added by 78.92.229.174 (talk) 09:25, 18 June 2010 (UTC)[reply]

Ok, so I noticed: At every examined point on the diagram, there is a black line, which is the path of the twin, and since relativity, it's his ct' axis. And we have colored lines crossing are the according x' axis. So coloring the according black lines to blue/red could make the understanding even easier, since every inertial system would have a consistent color. Or not... It's up to you. Thanks for helping! MoZo1 (talk) 13:13, 18 June 2010 (UTC)[reply]

experimental set-up

Supposing we choose a different thought-experimental set-up. Twin A sets off and after a brief spurt of acceleration his engine cuts out and he is now coasting at near-light speed. Or to put it another way, he is stationary and twin B is coasting away from him at near-light speed. Their relative velocities are (by definition) identical. An outside observer C chooses a time when the twins are equidistant from him. Presumably they appear to him to be aging/have aged by the same amount. This is presumably also true of any number of outside observers (each equidistant from the twins) at any point in the voyage. Including the time when twin A rejoins twin B. Or is there a point when a sudden discrepancy is observed by an outside observer?Escoville (talk) 15:46, 19 June 2010 (UTC)[reply]

Please take this to the science reference desk. This page is for discussing the form and content of the article, not of the subject itself. Thanks. DVdm (talk) 15:58, 19 June 2010 (UTC)[reply]
I've watchlisted the science reference desk, and will answer there if you ask your question there. Paradoctor (talk) 15:11, 20 June 2010 (UTC)[reply]
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