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

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Discussion Overview

The discussion revolves around the calculation of proper time along varying worldlines in the context of special relativity (SR). Participants explore the implications of straight versus curved worldlines, particularly in relation to acceleration and the behavior of moving clocks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that the longest proper time is indicated by a clock following a straight worldline, suggesting a relationship between worldline shape and proper time.
  • Another participant introduces the concept of curved worldlines due to acceleration and questions how proper time can be calculated in such scenarios.
  • There is a discussion about the meaning of proper time and worldlines, with one participant seeking clarification on how to calculate proper time when velocity is not constant.
  • Participants express varying levels of familiarity with the concepts, with one asking for a more detailed explanation of the calculation process.

Areas of Agreement / Disagreement

Participants generally agree on the basic principles of proper time and worldlines, but there is no consensus on the specific calculations involved for varying velocities along a curved worldline. The discussion remains unresolved regarding the methods for calculating proper time in these cases.

Contextual Notes

Some participants express uncertainty about the mathematical concepts involved, particularly in relation to calculus and the definitions of proper time and worldlines. There are indications of missing assumptions and varying levels of understanding among participants.

Who May Find This Useful

This discussion may be useful for individuals interested in special relativity, particularly those exploring the implications of worldlines and proper time in different contexts, including students and enthusiasts of physics and mathematics.

ehasan
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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
 
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welcome to pf!

hi ehasan! welcome to pf! :wink:

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


tiny-tim said:
hi ehasan! welcome to pf! :wink:

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


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

that's right :smile:
… 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? :wink:
 
tiny-tim said:
that's right :smile:


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? :wink:

I am sorry but could u please explain your point in a bit more detail. I couldn't get your point completely. :confused:
thanks
 
what don't you understand? :confused:
 
tiny-tim said:
what don't you understand? :confused:


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? ]
 
ehasan said:
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?
 
ehasan said:
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?
 
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