Welcome, RJ. Hopefully in the course of this week your paper will also provide stimulus to flush some rarely seen members out of the woodwork for contributing to that constructive commentary.
I don’t understand your reason for rejecting relative velocity as the cause of time dilation.
(Sep 26, 2016 04:18 PM)Secular Sanity Wrote: [ -> ]I don’t understand your reason for rejecting relative velocity as the cause of time dilation.
OK, from a dimensional analysis perspective:
v = m/s
v^2 = m^2/s^2
and
a = m/s^2
d = m
therefore if we have a value for velocity squared we can just as easily consider it to be an acceleration multiplied by a distance.
gamma = sqrt(1-v^2/c^2) = sqrt(1-(a*d)/c^2)
The reason for wanting to do this is because velocity plays no role in gravitational time dilation, but acceleration and distance (i.e. a gravity well) do. It elevates the equivalence principle to being a physical identity.
(Sep 28, 2016 01:12 PM)Secular Sanity Wrote: [ -> ]What?
Hi SS, I'm afraid I need more information about what is confusing. The wiki excerpt seems to support my contention that SR time dilation is considered to be a consequence of velocity, and I claim that it is in fact a consequence of acceleration and distance. Did you read the section on the twin paradox?
(Sep 28, 2016 03:30 PM)rjbeery Wrote: [ -> ]Hi SS, I'm afraid I need more information about what is confusing. The wiki excerpt seems to support my contention that SR time dilation is considered to be a consequence of velocity, and I claim that it is in fact a consequence of acceleration and distance. Did you read the section on the twin paradox?
Acceleration is defined as the rate at which an object changes its velocity. If it’s not changing its velocity, then it’s not accelerating.
(Sep 28, 2016 05:47 PM)Secular Sanity Wrote: [ -> ] (Sep 28, 2016 03:30 PM)rjbeery Wrote: [ -> ]Hi SS, I'm afraid I need more information about what is confusing. The wiki excerpt seems to support my contention that SR time dilation is considered to be a consequence of velocity, and I claim that it is in fact a consequence of acceleration and distance. Did you read the section on the twin paradox?
Acceleration is defined as the rate at which an object changes its velocity. If it’s not changing its velocity, then it’s not accelerating.
Of course, but that breaks down in GR. I first show that we can reframe time dilation as a function of acceleration and distance, and then extend that to gravitational time dilation if we consider acceleration to be asymmetric forces on an object rather than the second derivative of position with respect to time.
(Sep 28, 2016 06:04 PM)rjbeery Wrote: [ -> ] (Sep 28, 2016 05:47 PM)Secular Sanity Wrote: [ -> ]Acceleration is defined as the rate at which an object changes its velocity. If it’s not changing its velocity, then it’s not accelerating.
Of course, but that breaks down in GR. I first show that we can reframe time dilation as a function of acceleration and distance, and then extend that to gravitational time dilation if we consider acceleration to be asymmetric forces on an object rather than the second derivative of position with respect to time.
But I’m still confused because…
"One difference between general and special relativity is that in the general theory all frames of reference, including spinning and accelerating frames, are treated on an equal footing. In special relativity accelerating frames are different to inertial frames. Velocities are relative but acceleration is treated as absolute. In general relativity all motion is relative. To accommodate this change, general relativity has to use curved space-time. In special relativity space-time is always flat."