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This is probably answered many times, but my confusion is the following.

In special relativity it is said that there is no preferred coordinate system. Does that mean that for the people at rest (any rest frame of reference) things happen at same rate ? But just are seen from other system as delayed. So that people live to same age or particles decay at same life times in any rest frame.

The GPS satellite clocks run at different rate as seen from earth. But the atomic clock should run in space at same rate as the one on earth. (not taking into account the gravity effects)

With all of the above said my question is simply: can we conclude from having same physics in all rest frames (that are non accelerating) that it does not matter with what speed we travel we should always have same time rates for particle decays, life span.. Yes, no answer will be perfect.

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Technically NO, Logically YES. –  Red Jun 22 '13 at 18:44

3 Answers 3

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can we conclude from having same physics in all rest frames (that are non accelerating) [...] same time rates for particle decays, life span..

No.
Quite the contrary:
From "having the same physics" for all participants (beginning with the same physics being used for determining which participants are "at rest" to each other, and which are not) we have, for instance, the means of comparing life spans of instable particles to each other, from trial to trial, in the first place;
without having to resort to any "foregone conclusions" or expectations, for instance about any life spans being equal, between any particular trials.

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Thank you. No would mean velocity matters and same physics do not guarantee same time intervals in different rest frames. –  Anonymous Jun 23 '13 at 0:56
    
You're welcome. To repeat and re-enforce: yes, velocity matters (or more generally: geometric relations matter) when trying to compare "life spans" of different participant with each other; especially if they are separated from each other. And using the same physics for defining "life span" as a physical, measurable quantity and for comparing values of "life span" between distinguishable participants does not imply or guarantee equality of those particular participants by this particular measure. –  user12262 Jun 24 '13 at 19:20

Time and speed are relative. Let's say I'm watching you. The faster you move relative to me, the slower you age relative to me. However, relative to yourself you age at the same rate no matter how fast you go.

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No you cannot conclude that all non-accelerating frames run at the same rate. There is no such thing as the "same rate" in two different frames. You can't compare them. Both non-accelerating frames will see that the time rates in the other one as slower. There is no way to say that they are both the "same rate" until you bring them back together which of necessity requires acceleration.

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