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limitations of the equivalence principle
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by
on 2008-04-09 03:26:24 (edited 2008-04-09 03:42:31)
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I will demonstrate how, under certain conditions, Einstein's equivalence principle can be violated. According to the principle, a man in an elevator should not be able to distinguish gravitational force from acceleration. For example, the man may experience weightlessness, which may be due to free-fall towards a planet, or the lack of any close planet. Similarly, if the man experiences normal gravity, it could be due the elevator at rest relative to a close-by Earth-sized planet, or the upwards acceleration of 9.8m/s2, Earth's surface gravity equivalent. However, this upward acceleration could not be kept up forever. There is a limit to how long a body can maintain this acceleration. This is because there is a limit to how fast a body can move, namely, the speed of light. Some simple arithmetic shows that it would take just over 354 days to reach the speed of light while maintaining aforementioned acceleration. So, if Einstein stuck me in an elevator for a year, then asked me if I was accelerating out in space of sitting still on Earth the whole time, I'd sock him in the teeth. 
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Re: limitations of the equivalence principle
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But at that point, the elevator would no longer be accelerating at g, so your situation is no longer one described by this principle. Instead let's make this a rocket elevator with enough fuel to burn continuously for a year with exactly enough thrust to accelerate at g. As the year approaches, things would start fucking up if we tried to observe/contact him since he's approaching the speed of light relative to the starting point. However, he still thinks that he's accelerating at 9.8m/s2. The fact that we're moving away at a tremendous speed has no effect on the ability of the rocket to generate a certain amount of thrust.
10 more years!
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