4 ms·

Even if the clocks are stationary with respect to each other (within some tolerance), it's impossible to guarantee completely synchronized clocks among the syst

Even if the clocks are stationary with respect to each other (within some tolerance), it's impossible to guarantee completely synchronized clocks among the systems. This follows trivially from the impossibility of instantaneous communication due to the second postulate of special relativity.

AnimalMuppet 11y ago
If two clocks are stationary with respect to each other, then there is no ambiguity about where the midpoint between them is. Then you just do something like, when your clock hits noon, fire a projectile at a fixed speed toward the other clock. If the projectiles meet at the halfway point, then the clocks are synchronized. And there is no relativistic funny business involved, because the clocks are stationary with respect to each other. There's no difference of viewpoint as to whether the projectiles met at the halfway point, or where the halfway point was, or even how far off from the halfway point they met (and therefore how far off the clocks are from each other). This is the argument used in my relativity class to show that you can synchronize clocks that are stationary with respect to each other. (You have to be able to do that to construct an inertial frame of reference, that is, to be able to determine what time coordinate some event occurs at, no matter what spatial location it occurred at.)
- chetanahuja 11y ago
  "If the projectiles meet at the halfway point, then the clocks are synchronized." And how would either end-point know this exactly?
  - AnimalMuppet 11y ago
    That's the point of using physical projectiles, not light beams. You watch. That's how you know. "Watch" may mean using something like a phased-array radar to measure it more precisely, if you wish...
bagels 11y ago
If you move the clocks together physically, and synchronize them, this removes a large degree of the concern about instantaneous communication (this probably makes communication faster than your tolerances)

AnimalMuppet 11y ago

If two clocks are stationary with respect to each other, then there is no ambiguity about where the midpoint between them is. Then you just do something like, when your clock hits noon, fire a projectile at a fixed speed toward the other clock. If the projectiles meet at the halfway point, then the clocks are synchronized. And there is no relativistic funny business involved, because the clocks are stationary with respect to each other. There's no difference of viewpoint as to whether the projectiles met at the halfway point, or where the halfway point was, or even how far off from the halfway point they met (and therefore how far off the clocks are from each other). This is the argument used in my relativity class to show that you can synchronize clocks that are stationary with respect to each other. (You have to be able to do that to construct an inertial frame of reference, that is, to be able to determine what time coordinate some event occurs at, no matter what spatial location it occurred at.)

chetanahuja 11y ago
"If the projectiles meet at the halfway point, then the clocks are synchronized." And how would either end-point know this exactly?
- AnimalMuppet 11y ago
  That's the point of using physical projectiles, not light beams. You watch. That's how you know. "Watch" may mean using something like a phased-array radar to measure it more precisely, if you wish...

bagels 11y ago

If you move the clocks together physically, and synchronize them, this removes a large degree of the concern about instantaneous communication (this probably makes communication faster than your tolerances)