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Physics, Astronomy & Cosmology / Re: The TWINE Paradox
« on: 03/09/2006 15:23:21 »
Alberto - re: "hammers" - sorry, bad choice of words. I should have called them "clamps" or something.
These clamps (or hammers) snap shut and grip the twine so that it stops instantaneously.
So along the whole 50km (in my frame of reference) length of twine, we have a mechanism (50 million clamps) that causes every part of the twine to stop simultaneously (in my frame of reference).
In case it's of interest, the original thinking behind this paradox (i.e. why it was thought up in the first place) is as follows:
In the good old Twin Paradox, my (accelerating) twin experiences time dilation - i.e. she measures the "displacement in time" between two events as being different from what I would measure.
When she stops again, we both measure the same "displacement in time" from then on (i.e. our clocks tick at the same rate from then on).
But we can tell from our clocks that, during her journey, we must have measured different "displacements in time".
In the Twine paradox, my twin (or Albert in the above description), experiences length contraction - i.e. he measures the "displacement in space" (length) between two events as being different from what I would measure.
When he stops again, we both measure the same "displacement in space" from then on.
But is there a way to tell that, during his journey, we must have measured different "displacements in space"? Is there something that does the equivalent of a clock, but for indicating past dispacements in space rather than past displacements in time?
Hence the possibility that, after the twine has stopped, you'll see it as being 50,000,000 mm in length but it will contain 50,000,001 knots in it.
OK, maybe that's a really stupid idea and I'm just demonstrating my lack of understanding about relativity. But I just can't convince myself why it's wrong.
Paul.
These clamps (or hammers) snap shut and grip the twine so that it stops instantaneously.
So along the whole 50km (in my frame of reference) length of twine, we have a mechanism (50 million clamps) that causes every part of the twine to stop simultaneously (in my frame of reference).
In case it's of interest, the original thinking behind this paradox (i.e. why it was thought up in the first place) is as follows:
In the good old Twin Paradox, my (accelerating) twin experiences time dilation - i.e. she measures the "displacement in time" between two events as being different from what I would measure.
When she stops again, we both measure the same "displacement in time" from then on (i.e. our clocks tick at the same rate from then on).
But we can tell from our clocks that, during her journey, we must have measured different "displacements in time".
In the Twine paradox, my twin (or Albert in the above description), experiences length contraction - i.e. he measures the "displacement in space" (length) between two events as being different from what I would measure.
When he stops again, we both measure the same "displacement in space" from then on.
But is there a way to tell that, during his journey, we must have measured different "displacements in space"? Is there something that does the equivalent of a clock, but for indicating past dispacements in space rather than past displacements in time?
Hence the possibility that, after the twine has stopped, you'll see it as being 50,000,000 mm in length but it will contain 50,000,001 knots in it.
OK, maybe that's a really stupid idea and I'm just demonstrating my lack of understanding about relativity. But I just can't convince myself why it's wrong.
Paul.