Question

3) An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats. What will observers in all other inertial reference frames measure for the time interval between her heartbeats? A) Δt B) more than Δt C) less than Δt D) The answer depends on whether they are moving toward her or away from her.

Answer 1

Observers in other inertial frames will measure a longer time interval between the astronaut's heartbeats due to time dilation.

Step-by-step explanation:

Observers in all other inertial reference frames will measure a greater time interval between the astronaut's heartbeats compared to the astronaut herself.

This is due to the phenomenon of time dilation, where time appears to move slower for objects in motion relative to an observer at rest. As the astronaut is moving, her heartbeats will appear slower to an observer at rest, resulting in a longer measured time interval.

The answer does not depend on whether the observers are moving toward or away from the astronaut.

Answer 2

Observers in all inertial frames other than that of the astronaut will measure the time interval between her heartbeats as more than Δt due to the effects of time dilation, which is independent of their direction of motion relative to the astronaut.

Step-by-step explanation:

The phenomenon affecting the measurement of time intervals in different inertial frames is known as time dilation, which is a consequence of the theory of special relativity. When an astronaut, in her own inertial frame, measures the time interval Δt between her heartbeats, this time interval is known as the proper time and is the shortest possible measurement of time for these two events (her heartbeats). However, for observers in all other inertial frames, particularly those who are moving relative to the astronaut, the time interval measured for her heartbeats will be longer than Δt due to time dilation. Therefore, observers in all other inertial frames (assuming none are at rest with respect to the astronaut) will measure the time interval to be more than Δt.

It's crucial to recognize that this effect doesn't depend on whether the observers are moving toward or away from the astronaut. Rather, it is purely a result of their relative motion; all inertial observers will agree that the moving clocks (including biological processes like heartbeats) are slower. Thus, the correct answer to the student's question is B) more than Δt.