Can proper time be calculated for varying velocity along a worldline?

[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]

welcome to pf!

hi ehasan! welcome to pf!

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

 

[ehasan]

hi ehasan! welcome to pf!

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

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]

...I think straight worldline in space-time diagram represents linear motion with constant speed. and moving clocks run slow

that's right

… 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.

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]

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?

I am sorry but could u please explain your point in a bit more detail. I couldn't get your point completely.
thanks

 

[tiny-tim]

what don't you understand?

 

[ehasan]

what don't you understand?

I couldn't get the sense 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]

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

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]

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

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?