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Sorry that's the best wording for a title I could come up with. Anyhoo my question is one that I have wondered about for a long time, and I am prompted to post now after seeing this article on the new atomic clock.
Let's assume that we have clocks that can measure time to an arbitrarily accurate degree. If a clock was sitting at the surface of the Earth, what is the minimum height it would need to be elevated in order to detect the dilation of time.
For example. I'm fairly sure that if this clock was moved from the ground to a 1 metre high table, that we can already detect that level of time dilation in practice. So I'm now wondering what is the theoretical limit, and by that I mean if the time dilation for a given elevation got down to the Planck length then that would be a theoretical limit.
So... Could we measure in principle the dilation if the clock was raised 1 cm? 1mm? one...?
I'm guessing that the answer is routine math but I do not have the skill to do the math.
Let's assume that we have clocks that can measure time to an arbitrarily accurate degree. If a clock was sitting at the surface of the Earth, what is the minimum height it would need to be elevated in order to detect the dilation of time.
For example. I'm fairly sure that if this clock was moved from the ground to a 1 metre high table, that we can already detect that level of time dilation in practice. So I'm now wondering what is the theoretical limit, and by that I mean if the time dilation for a given elevation got down to the Planck length then that would be a theoretical limit.
So... Could we measure in principle the dilation if the clock was raised 1 cm? 1mm? one...?
I'm guessing that the answer is routine math but I do not have the skill to do the math.