Question

How does the elapsed time for a process seem to be longer, an observer moving with the

process or observer moving relative to the process? Which observer measures proper

time? Explain your answer

Answer 1

Explanation

• It has found that time is seen to be shorter at relativistic speeds: speeds very near the speed of light.
• This is distinguishable only at relativistic speeds hence in day-to-day activities this is not experienced.
• This relationship is expressed in the equation,

$\qquad\qquad \begin{aligned} \small T&= \small \gamma\cdot \tau=\frac{1}{\sqrt {1-\frac{v^2}{c^2}}}\cdot\tau\\ \end{aligned}$

• T is the time measured by the observer moving relative to the process.
• $\small \tau$ is that measured by the observer moving with the process.
• $\gamma$ is called the Lorentz factor which values larger numbers when the speed of the moving frame gets near the speed of light.

• Proper time is measured by the observer moving with the process whereas the observer moving relative to that measures some extended time.