Chapter 37, Problem 65E

(a)

To determine

To show: The time interval $\Delta t\text{'}$ between the two events in the frame $S\text{'}$ is given by $\Delta t\text{'}=\sqrt{{\left(\Delta t\right)}^2-{\left(\frac{\Delta x}{c}\right)}^2}$ and for $\Delta x>c\Delta t$ there is no frame $S\text{'}$. Also determine if it is appropriate to call $\Delta t\text{'}$ proper time interval.

(b)

To determine

The distance between the two events in $S\text{'}$ frame and whether it is appropriate to call it a proper length.

(c)

To determine

The time interval between the events as measured in $S$.