Special & General Relativity, time dilation, acceleration

[alviros]

Homework Statement

From https://www.physicsforums.com/library.php?do=view_item&itemid=166
Time dilation does not depend on the acceleration of the clock.
From https://www.physicsforums.com/archive/index.php/t-175886.html
jtbell
Jul12-07, 07:56 AM
If the two ships have the same "acceleration profiles" then yes, their clocks will show the same amount of elapsed time when they return to Earth.

Homework Equations

The Attempt at a Solution

I feel confused. Can somebody help ? Is true the sentence in bold ?
I don't want discuss again the old thread, but I thought acceleration and gravity were equivalent.

 

[tiny-tim]

Welcome to PF!

Hi alviros! Welcome to PF!

From https://www.physicsforums.com/library.php?do=view_item&itemid=166
Time dilation does not depend on the acceleration of the clock.
From https://www.physicsforums.com/archive/index.php/t-175886.html
jtbell
Jul12-07, 07:56 AM
If the two ships have the same "acceleration profiles" then yes, their clocks will show the same amount of elapsed time when they return to Earth.
…
I feel confused. Can somebody help ? Is true the sentence in bold ?
I don't want discuss again the old thread, but I thought acceleration and gravity were equivalent.

Time dilation, in the absence of gravity, depends only on velocity and not on acceleration.

However, if the velocity is changing, then the acceleration will be also, which I assume is what jtbell meant by the acceleration profiles being the same (or different).

But the instantaneous time dilation depends only on velocity.

And so the overall time dilation depends only on the velocity at each instant: √(1 - v²/c²).

 

[alviros]

Thank you.