Question

Which statement is a correct description of an interval of proper time?

A. An interval of proper-time between two events, Δτ, is calculated in the inertial reference frame where the events are simultaneous, and ∣Δτ∣<∣Δt∣ where Δt is calculated in some other inertial reference frame.
B. An interval of proper-time between two events, Δτ, is calculated only with the requirement that both events are observed in the same inertial reference frame.
C. An interval of proper-time between two events, Δτ, is calculated in the inertial reference frame where the events are simultaneous, and ∣Δτ∣>∣Δt∣ where Δt is calculated in some other inertial reference frame.
D. An interval of proper-time between two events, Δτ, is calculated in the inertial reference frame where both events occur at the same spatial coordinates, and ∣Δτ∣>∣Δt∣ where Δt is calculated in some other inertial reference frame.
E. An interval of proper-time between two events, Δτ, is calculated in the inertial reference frame where both events occur at the same spatial coordinates, and ∣Δτ∣<∣Δt∣ where Δt is calculated in some other inertial reference frame.

Answer 1

The correct statement describing the interval of proper time is D, which signifies that proper time is measured in the inertial reference frame where events occur at the same location, and it is the shortest measured time between those two events.

Step-by-step explanation:

The correct description of an interval of proper time, Δτ, is given by statement D: An interval of proper-time between two events, Δτ, is calculated in the inertial reference frame where both events occur at the same spatial coordinates, and |Δτ| < |Δt| where Δt is calculated in some other inertial reference frame. This is because proper time is the time interval measured by an observer for whom both events occur at the same location, and in the theory of relativity, it is the shortest time interval between two events. Thus, in any other inertial frame where the events are not at the same location, time appears to be dilated, and the measured time interval Δt is longer than the proper time Δτ.