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**Physics, Astronomy & Cosmology / The TWINE Paradox**

« **on:**25/08/2006 23:02:59 »

Another relativity paradox, but don’t worry, it’s not the “Twin Paradox” again, it’s different.

Take a length of string (or twine, as I prefer to call it – cos then I can call this the “TWINE Paradox” – geddit?!)

Tie a knot in it every metre, then tie the two ends together so that it forms a loop. Say the loop is 100m long.

Now fit the loop onto two small pulleys which are 50m apart. So you can see two lengths of twine between the pulleys – the top one has 50 knots in it, and the bottom one has 50 knots in it.

Now start the pulleys spinning (at the same speed) very fast.

According to relativity, because the twine is moving (relative to me), the length of the twine will become contracted, so that the distance between each knot will now be LESS than 1m.

But the pulleys are in my “stationary” frame of reference, so they remain 50m apart.

So there must now be MORE than 50 knots between the two pulleys along the top edge of the loop (at any given point in time), and also MORE than 50 knots along the bottom edge.

To me, that seems like a paradox.

How do I resolve it?

Take a length of string (or twine, as I prefer to call it – cos then I can call this the “TWINE Paradox” – geddit?!)

Tie a knot in it every metre, then tie the two ends together so that it forms a loop. Say the loop is 100m long.

Now fit the loop onto two small pulleys which are 50m apart. So you can see two lengths of twine between the pulleys – the top one has 50 knots in it, and the bottom one has 50 knots in it.

Now start the pulleys spinning (at the same speed) very fast.

According to relativity, because the twine is moving (relative to me), the length of the twine will become contracted, so that the distance between each knot will now be LESS than 1m.

But the pulleys are in my “stationary” frame of reference, so they remain 50m apart.

So there must now be MORE than 50 knots between the two pulleys along the top edge of the loop (at any given point in time), and also MORE than 50 knots along the bottom edge.

To me, that seems like a paradox.

How do I resolve it?