SR time dilation problem

ehasan

Ideal clocks are taken from event A to event B along various worldlines. then that the longest proper time for the trip is indicated by that clock whcih follows the straight worldline. How it can be showed. thanks

tiny-tim

hi ehasan! welcome to pf!

tell us what you think, and then we'll comment!

ehasan

thanks... actually i am novice to SR.
well ...I think straight worldline in space-time diagram represents linear motion with constant speed. and moving clocks run slow. but what happen when clocks are taken from event 1 to event 2 in a fashion that make curveved worldline? i.e. when clocks move with some acceleration.
thanks a lot

tiny-tim

that's right
yes, that's what you're supposed to work out …

how would you calculate the proper time along a world-line (t, x(t)) where dx/dt isn't constant?

ehasan

I am sorry but could u please explain your point in a bit more detail. I couldnt get your point completely.
thanks

tiny-tim

what don't you understand?

ehasan

I couldnt get the sence of this sentence.
[ how would you calculate the proper time along a world-line (t, x(t)) where dx/dt isn't constant? ]

tiny-tim

but that's the original question!

if a body is at position x(t) at each time t, with of course velocity v = dx/dt, what is the proper time τ(t) at each time t?

JesseM

you used the words "proper time" and "worldline" in your posts so you seem to know what those mean, (t, x(t)) is just a way of defining the coordinates of a worldline in some inertial frame (at any given t, x(t) is some function that tells you the x-coordinate of the object at that time), and dx/dt is just the velocity at any given t coordinate (the derivative of x(t)). How familiar are you with calculus?