3 ms·

the assumption that time dilation is identical for the same acceleration profiles is equivalent to an assumption of the 1 way speed of light. if you do the full

the assumption that time dilation is identical for the same acceleration profiles is equivalent to an assumption of the 1 way speed of light. if you do the full math with a non constant light speed, you find that degree of asymmetry in the 1 way speed of light directly cancels the difference in time dilation

AnimalMuppet 3y ago
How can that work? I can control both how hard I accelerate, and how far I go with constant velocity. So I can control how much of the clock skew is due to acceleration time dilation. That can't match the speed difference for all possible experimental setups. For experiment 1, say I accelerate the clocks at 0.1 g for 10 seconds, then drive with constant velocity for 1 hour, then decelerate at 0.1 g for 10 seconds. That acceleration time dilation exactly matches the change in propagation time due to the difference in c? Fine, I'll give you that. So for experiment 2, I drive at constant velocity for two hours. I've kept the acceleration time dilation the same as in experiment 1, but doubled the distance. If the change in propagation time matched in experiment 1, it can't match now. Or, for experiment 3, I accelerate at 0.1 g for five seconds, reaching 1/4 of the previous velocity, then drive for two hours. Now the propagation difference is the same as in experiment 1, but the acceleration time dilation is different. So how is this going to come out "you can't tell" in all three experiments?
- adgjlsfhk1 3y ago
  > then drive with constant velocity for 1 hour 1 hour according to who's clock? The point is that if the 1 way speed of light is different, the clocks traveling in opposite directs will measure the 1 hour passing at different speeds.
  - AnimalMuppet 3y ago
    The (non-GR) time dilation rate difference will be proportional to v^2/c^2 (neglecting 4th order terms and higher). The total time dilation difference will be that times the time in transit, which is d/v (with d being the distance traveled). So the total time dilation difference will be proportional to vd/c^2. By making the velocity small, I can make that term as small as I want. But what if I don't know what c is? Doesn't matter. I know it's much, much larger than the velocity I'm moving at. So I don't buy the "according to who's clock" argument. I can make it so that it doesn't matter, just by going slow enough.
    - adgjlsfhk1 3y ago
      the part you're missing is that during the acceleration phase, if the 1 way speed of light is different, the velocities achieved relative to a stationary observer by accelerating for t seconds relative to the clock that is doing the acceleration will be different depending on the direction of acceleration.
      - AnimalMuppet 3y ago
        To what order in v? I'd like to see your math, but I'm pretty sure I can still minimize that by going slow (relative to the speed of light in any direction).
        adgjlsfhk1 3y ago
        Wikipedia does the math for us here. https://en.wikipedia.org/wiki/One-way_speed_of_light#Slow_clock-transport https://en.wikipedia.org/wiki/One-way_speed_of_light#Slow_cl.... The TLDR is that the standard lorentz transform assumes the 1 way speed of light doesn't vary, so to do the math correctly you need generalized lorentz transformations https://en.wikipedia.org/wiki/One-way_speed_of_light#Generalizations_of_Lorentz_transformations_with_anisotropic_one-way_speeds https://en.wikipedia.org/wiki/One-way_speed_of_light#General...

AnimalMuppet 3y ago

How can that work? I can control both how hard I accelerate, and how far I go with constant velocity. So I can control how much of the clock skew is due to acceleration time dilation. That can't match the speed difference for all possible experimental setups. For experiment 1, say I accelerate the clocks at 0.1 g for 10 seconds, then drive with constant velocity for 1 hour, then decelerate at 0.1 g for 10 seconds. That acceleration time dilation exactly matches the change in propagation time due to the difference in c? Fine, I'll give you that. So for experiment 2, I drive at constant velocity for two hours. I've kept the acceleration time dilation the same as in experiment 1, but doubled the distance. If the change in propagation time matched in experiment 1, it can't match now. Or, for experiment 3, I accelerate at 0.1 g for five seconds, reaching 1/4 of the previous velocity, then drive for two hours. Now the propagation difference is the same as in experiment 1, but the acceleration time dilation is different. So how is this going to come out "you can't tell" in all three experiments?

adgjlsfhk1 3y ago
> then drive with constant velocity for 1 hour 1 hour according to who's clock? The point is that if the 1 way speed of light is different, the clocks traveling in opposite directs will measure the 1 hour passing at different speeds.
- AnimalMuppet 3y ago
  The (non-GR) time dilation rate difference will be proportional to v^2/c^2 (neglecting 4th order terms and higher). The total time dilation difference will be that times the time in transit, which is d/v (with d being the distance traveled). So the total time dilation difference will be proportional to vd/c^2. By making the velocity small, I can make that term as small as I want. But what if I don't know what c is? Doesn't matter. I know it's much, much larger than the velocity I'm moving at. So I don't buy the "according to who's clock" argument. I can make it so that it doesn't matter, just by going slow enough.
  - adgjlsfhk1 3y ago
    the part you're missing is that during the acceleration phase, if the 1 way speed of light is different, the velocities achieved relative to a stationary observer by accelerating for t seconds relative to the clock that is doing the acceleration will be different depending on the direction of acceleration.
    - AnimalMuppet 3y ago
      To what order in v? I'd like to see your math, but I'm pretty sure I can still minimize that by going slow (relative to the speed of light in any direction).
      - adgjlsfhk1 3y ago
        Wikipedia does the math for us here. https://en.wikipedia.org/wiki/One-way_speed_of_light#Slow_clock-transport https://en.wikipedia.org/wiki/One-way_speed_of_light#Slow_cl.... The TLDR is that the standard lorentz transform assumes the 1 way speed of light doesn't vary, so to do the math correctly you need generalized lorentz transformations https://en.wikipedia.org/wiki/One-way_speed_of_light#Generalizations_of_Lorentz_transformations_with_anisotropic_one-way_speeds https://en.wikipedia.org/wiki/One-way_speed_of_light#General...