Clock postulate and differential aging

[sylas]

The most common English translation of Einstein's first Special Relativity Postulate is:
"The laws of physics are the same in all inertial reference systems." The definition of an inertial system is that all motion is in Einstein's own words "in uniform translation " which indisputably disallows acceleration. That doesn't mean that time dilation that includes acceleration can't exist. it simply means you can't atribute that to Special Relativity.

DanRay... you can handle acceleration with special relativity just fine. Einstein did this too. An accelerated frame is not inertial, of course, but you can still describe accelerated motions from an inertial frame, and using SR you can find all the time dilations that apply for any motion you like... as long as there's no gravity involved. Accelerations are not a problem.

When Einstein developed general relativity, he did so by generalizing the consequences for an accelerated observer (which can be found using SR) to those of an observer in a gravitational field. He did not need GR to describe accelerated motions, or find the time dilation of accelerated motions.

bcrowell has given some helpful references if this seems confusing, but it is a mathematical fact that you can use special relativity to figure out all the time dilations for any motion you like. You just integrate the proper time c²dτ² = c²dt² - dx² - dy² - dz² along any path given using x,y,z,t co-ordinates in an inertial frame.

Cheers -- sylas

 

[Demystifier]

No.

I had already provided an example:
2 twin scenatio with identical acceleration, with the same distance where second twin is accelerated, but with 2 different "arms" - total travel distance where the accelerated twin is moving without acceleration

Based on your hypotesis, age difference will be the same in both cases (as acceleration is identical), while it is not (in a case with a longer arm there is more difference)

Dmitry is right. See e.g. Eq. (7) in
http://xxx.lanl.gov/abs/physics/0004024 [Found.Phys.Lett. 13 (2000) 595]

 

[ThomasT]

Dmitry is right. See e.g. Eq. (7) in
http://xxx.lanl.gov/abs/physics/0004024 [Found.Phys.Lett. 13 (2000) 595]

The person I was primarily asking (about whether or not we were in agreement) was DaleSpam, who replied that we are in agreement (since we agree on the math and the experimental results) and that the problem (that I was having) was just a semantic one.

OK (or no)?

 

[Al68]

The most common English translation of Einstein's first Special Relativity Postulate is:
"The laws of physics are the same in all inertial reference systems." The definition of an inertial system is that all motion is in Einstein's own words "in uniform translation " which indisputably disallows acceleration..

This just isn't true. An inertial frame means that the reference frame isn't accelerated. Objects may very well accelerate relative to an inertial frame in SR.

In other words, the only thing not allowed to accelerate in (1905) SR is the reference frame. Even that restriction was overcome (by Einstein) around 1907 by defining an accelerated frame by specifying its motion relative to a specified inertial frame.

 

[bcrowell]

This just isn't true. An inertial frame means that the reference frame isn't accelerated. Objects may very well accelerate relative to an inertial frame in SR.

Right.

In other words, the only thing not allowed to accelerate in (1905) SR is the reference frame. Even that restriction was overcome (by Einstein) around 1907 by defining an accelerated frame by specifying its motion relative to a specified inertial frame.

I think it's clear that people eventually worked out all the issues with treating accelerated frames in SR, and that most modern authors consider SR to be defined by flat spacetime, not unaccelerated frames. But does this really go back as far as Einstein in 1907? E.g., I have in front of me a translation of "The foundation of the general theory of relativity," A. Einstein, Annalen der Physik 49 , 1916. In the introduction:

The word "special" is meant to intimate that the principle is restricted to the case when K' has a motion of uniform translation relatively to K, but that the equivalence of K' and K does not extend to the case of nonuniform motion of K' relatively to K."

So it seems to me that as late as 1916, Einstein was defining SR in terms of unaccelerated frames, not flat spacetime.