Quote:
Originally Posted by arkain101
I believe this is an accurate expression of a paradox based on a specific conception of time. That is, "Time: Something a clock measures".
Scenario:
Three reference frames:
a)We have a person on earth with a digital clock (Person "E" / Clock "E")
b)We have a person in space orbiting earth 1000km away at a very high velocity. (Person "S" / Clock "S")
c)We have a star "The sun" (to actual scales)
Because of the simplicity of this paradox we can fast forward to some hypothetical results.
At the beginning of the experiment, Clock E and S are synchronized.
Then one year later:
When clock E strikes 12:00pm Person E observes clock S is 5 minutes behind and reads 11:55am.
Also,
When clock S strikes 12:00pm person S observes clock E is 5 minutes ahead and reads 12:05pm.
If this is true, then Person E has experienced 5 minutes more of "time" than person S.
This should suggest that when person E and S observe the sun they observe the sun over a 5minute time difference. This would suggest that the sun is now existing in two different realms of "time"; A realm of time for person S and a realm of time for person E.
This is the paradox. The sun does not and is not existing in two different realms of time. Especially understandable if person S returns to earth and shakes the hand of person E and they both observe the sun with their clocks differing by 5 minutes.
Again this is a paradox if we accept that (the digital) clocks measure time.
If we perform this thought experiment again, only, we do not use digital clocks, we use atomic clocks and get the same results, I believe we could conclude the following.
Time is not only something that a clock measures, but also strictly and independently an intimate part of electromagnetism.
Either way. Is this paradox correct, and if so, is it solvable?
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CraigD answered this in by assuming that you meant one thing by "observe the sun over a 5minute time difference", And I'll answer it assuming you meant another.
From the way you stated the problem, I'm going to assume you meant that they will observe the Sun at different points of it's path in the sky. (one will see the Sun at its noon position, and one will see it at a 5 mins from noon position.) The reason I'm making this assumption is that I have run across others who have tried to make this argument.
Be assured,
this will not happen, and is not what Relativity predicts will happen.
Both E and S see the Sun in the same position at the end, They will just disagree as to how much time passed from the start of the experiment to the finish. If the Sun started at its noon position and returned to its noon position one year later according to E, then it started at the noon position, and returned to the noon position one year minus 5 min later according to S.
IOW, according to S, the Earth simply took a little less than 24 hrs to complete each Solar day(The Earth rotated faster according to S)
No paradox.
