I recently started trying to understand the theory of relativity and I have the following question. Because earth is orbiting the sun at approx 67,000 mph (and its my understanding time slows down the faster you are moving) what are the effect of time on earth compared to a completely stationary observer watching earth's orbit, from outer space? How would the twin paradox work with one twin on earth and the other twin completely stationary in outer space?
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$\begingroup$ This is a good question, but the only problem is that there is no stationary reference frame. No reference frame is preferred over any other. $\endgroup$– HDE 226868 ♦Commented Oct 31, 2014 at 18:34
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$\begingroup$ Can you elaborate please? $\endgroup$– user3151798Commented Oct 31, 2014 at 22:39
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$\begingroup$ I can try, but it probably won't be too good: No object can be said to be stationary relative to any other object. There is no "stationary" reference frame. $\endgroup$– HDE 226868 ♦Commented Oct 31, 2014 at 22:45
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$\begingroup$ Im going to have to look into that more to get a better understanding. To ask my question a different way: if a twin was on pluto which orbits at roughly 10,600 mph and the other twin was on earth which orbits at 67,000 mph. When the two met would the twin on earth be younger? $\endgroup$– user3151798Commented Oct 31, 2014 at 22:52
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$\begingroup$ @HDE226868 While you are technically correct, there are reference frames that experience less acceleration than we do on Earth. Here's an unhelpful link that at least shows astronomers do need to compensate for the Earth's acceleration when computing exact times: en.wikipedia.org/wiki/Barycentric_Dynamical_Time $\endgroup$– user21Commented Nov 1, 2014 at 14:07
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2 Answers
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Time dilation is a relative phenomenon, not a local phenomenon.
As adrianmcmenamin mentioned, Earth's motion around the sun is cause for no more time dilation than any other point in the universe. Consider that the sun is travelling around the galaxy at 200 km/s, and the Milky Way is approaching Andromeda at 130 km/s. We do not know at what speed we are approaching the great attractor, and I hope that at this point it becomes obvious that there is no difference in "us approaching the great attractor" to "the great attractor approaching us". Nothing is considered "stationary to the background" in an infinite, expanding universe as there is no "background" to measure against.
Consider the gedankenexperiment of comparing a clock on Earth to a clock orbiting the galaxy. Now compare those clocks to clocks outside the galaxy. You might consider the clock that ticks the most time away to be the "most at rest clock". Now I ask you, how will you compare the clocks? You must move at a significant portion of the speed of light for a very long time to get information from one clock to the next. Thus, the messenger would suffer the effects of Special Relativity, rendering the comparison meaningless.
To further the point, consider the development of International Atomic Time. I'll quote directly from wikipedia:
In the 1970s, it became clear that the clocks participating in TAI were ticking at different rates due to gravitational time dilation
Consider, those were clocks on Earth suffering from measurable time dilation due only to their latitude and altitude differences and the effect of moving information across the distances between them!
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Relativity (special and general) is founded on the theory - which has been well tested - that there is no fundamental reference frame in space and hence there can be no "completely stationary" observers at all.
All we can say is that observers move relative to one another.
The time dilation effect of the Earth's motion at 67,000 mph relative to another observer is actually very small, being inversely proportional to the square root of 1 minus the relative velocity squared divided by the speed of light squared - essentially this is a ratio of about 1.000000005 - a second in every seven years or so.
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$\begingroup$ So if I understand this correctly, time on Earth to some observers in the universe could be extremely slow and to other observers time on Earth could be extremely fast. Or to say it another way, to an observer somewhere in the universe our life span on Earth is only a few seconds and to other observers somewhere in space our life span on Earth may be millions of years? (theoretically of course) Due to the speed we're travelling relative to the speed the other observers our travelling? @dotancohen $\endgroup$ Commented Nov 3, 2014 at 17:01
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$\begingroup$ This answer is not completely correct. In ANY rest frame the Earth is moving around the Sun, because this movement is not rectilinear. $\endgroup$– EnviteCommented Dec 4, 2014 at 13:16