Oops: did previous post with no preview and something filtered out my less-than symbols - "x y" should be "x less than y" and "y x" should be "y less than x"
Yes, we're in agreement that there seems to be no net effect - I'm merely trying to discover *where* Mayer might have gone wrong.
Unless I'm mistaken your argument is exactly the same as saying that both x y and y x can't be true, so that if A and B exchange information on the times showing on their clocks (once they're back in the inertial frame) they can't both be less that the other, which is what Mayer claims, by a symmetry argument?
As noted in more general ways in other posts, at least two relativistic effects are not dealt with in the crucial thought experiment.
Consider a pulse train from A to B: - There will be difference in time contraction from when the pulses are sent from A to when the are received at B; since the frame is accelerated it's traveling faster when reception at B occurs, so time is slowed as compared with the time when the pulses were sent from A, resulting in an INCREASE in the apparent pulse frequency of reception. - Length contraction may also play a role: as shown in the diagrams, even though the pulses are sent orthogonal to the direction of motion, they also have some travel in the direction of motion, and there is a difference in the amount of such contraction between the time they're sent and received, again due to the accelerated frame. THis will also INCREASE the apparent frequency. My suspicion is that these effects cancel out completely the RTR effect, but it's clear they should at least be considered in the thought experiment.
Slashdot Mirror
Oops: did previous post with no preview and something filtered out my less-than symbols - "x y" should be "x less than y" and "y x" should be "y less than x"
Yes, we're in agreement that there seems to be no net effect - I'm merely trying to discover *where* Mayer might have gone wrong.
Unless I'm mistaken your argument is exactly the same as saying that both x y and y x can't be true, so that if A and B exchange information on the times showing on their clocks (once they're back in the inertial frame) they can't both be less that the other, which is what Mayer claims, by a symmetry argument?
As noted in more general ways in other posts, at least two relativistic effects are not dealt with in the crucial thought experiment.
Consider a pulse train from A to B:
- There will be difference in time contraction from when the pulses are sent from A to when the are received at B; since the frame is accelerated it's traveling faster when reception at B occurs, so time is slowed as compared with the time when the pulses were sent from A, resulting in an INCREASE in the apparent pulse frequency of reception.
- Length contraction may also play a role: as shown in the diagrams, even though the pulses are sent orthogonal to the direction of motion, they also have some travel in the direction of motion, and there is a difference in the amount of such contraction between the time they're sent and received, again due to the accelerated frame. THis will also INCREASE the apparent frequency.
My suspicion is that these effects cancel out completely the RTR effect, but it's clear they should at least be considered in the thought experiment.