Question about proper time

In summary, in the frame where the two events occur at the same position, the proper time (\tau) is equal to the time interval (\Delta t) divided by the speed of light (c). This can be proven by plugging in these values into the spacetime invariant, which only works for events where the spacetime interval is greater than or equal to 0.
  • #1
nwdavis1
3
0

Homework Statement


If the spacetime interval (delta S)^2 > 0, show that delta t=deltaS/c is the proper time between the two events.


Homework Equations


Can anyone please explain to me how I should be approaching this problem. I have been working on it for a while with no success. I was able to do the problem before it easily, which was "use Lorentz' equations to prove that delta S is invariant", but this one is giving me trouble.


The Attempt at a Solution

 
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  • #2
I guess I worded the problem incorrectly. It should read "for ds^2 >0, show that tau=ds/c is the proper time".
 
  • #3
nwdavis1 said:

Homework Statement


If the spacetime interval (delta S)^2 > 0, show that delta t=deltaS/c is the proper time between the two events.


Homework Equations


Can anyone please explain to me how I should be approaching this problem. I have been working on it for a while with no success. I was able to do the problem before it easily, which was "use Lorentz' equations to prove that delta S is invariant", but this one is giving me trouble.


The Attempt at a Solution


By definition, th eproper time is the time between two events in the frame where the two events occur at the same position. So all you have to say is that when you are in the frame where [itex] \Delta x =0 [/itex] then [itex] \Delta t = \tau [/itex]. Plug that in the spacetime invariant and you get the answer. Note that this definition works only for events for which [itex] (\Delta s)^2 \geq 0 [/itex].
 

What is proper time?

Proper time is a concept in physics that refers to the time measured by an observer who is moving along with a clock. It is sometimes also referred to as the "clock time." Proper time is relative and can differ between different observers, depending on their relative motion.

How is proper time different from coordinate time?

Coordinate time is the time measured by a stationary observer, while proper time is the time measured by an observer who is moving along with the clock. Coordinate time is independent of an observer's relative motion, while proper time is not.

Why is proper time important?

Proper time is important in physics because it allows us to understand and describe the behavior of objects in motion. It helps us to understand how time is affected by an object's velocity and how time is relative to different observers.

What is the equation for calculating proper time?

The equation for calculating proper time is t = t0/√(1-v2/c2), where t is the proper time, t0 is the coordinate time, v is the velocity of the object, and c is the speed of light.

Can proper time be measured?

Yes, proper time can be measured using a clock that is moving along with the observer. However, it is important to note that proper time is relative and can differ between different observers, depending on their relative motion.

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