Time dilation means that

a) no two clocks at rest can ever read the same time.

b) time is unchanging regardless of the frame of reference.

c) the slowing of time in a moving frame of reference is only an illusion resulting from motion.

d) time really does pass more slowly in a frame of reference moving relative to a frame of reference at relative rest.

e) time really does pass more slowly in a rest frame of reference relative to a frame of reference that is moving

e) True. when the observer is in movement the time passes slower

Explanation:

Newton's mechanics clearly established that the laws of physics are the same in all inertial frames of reference, that is, they do not have acceleration.

In subsequent experiments it was discovered that the speed of light is a universal constant and does not depend on the relative speed of the reference system where it is being measured.

Special relativity takes these two principles and uses them to analyze how a phenomenon is seen from frames of reference with relative speed between them, since the information is propagated with a finite speed (finite time).

Based on this it follows that when an observer who does not move with respect to the phenomenon measures a time called proper time (τ) and when the observer is in motion with respect to the phenomenon, the change time was due to the time it takes for the light to carry the information, for this observer with relative speed the time is

t = τ / √ (1 - (v/c) ²)

where you can see that always t> τ,

let's analyze the statements given

a) False. If the clocks are at rest, they both measure their own time

b) False. Time changes due to the relative speed of the reference frames

c) False. It is a real fact because the information takes time to reach the observer

d) False. It's the opposite

e) True. It is in agreement with the superior equation of change of the time, when the observer is in movement the time passes slower