Time Dilation and Relativity of Simultaneity
Time is not universal
Time dilation
A moving clock ticks more slowly according to a stationary observer. If the proper time interval is , then the observed interval is
Proper time
Proper time is the time measured in the frame where the two events occur at the same position. It is the shortest time interval between those events among inertial frames.
Relativity of simultaneity
Two events that are simultaneous in one inertial frame may not be simultaneous in another. This follows directly from the Lorentz time transformation, because depends on position .
Core idea
Moving clocks do not merely look slow because of signal delays; time itself is measured differently in different inertial frames.
If a moving clock has proper time interval and , what interval does a stationary observer measure?
Using , we get .
Correct answer: 20 s
What quantity is measured in the clock's rest frame?
Proper time is the interval between events measured where the events happen at the same location.
Correct answer: Proper time
Common relativity effects
| Effect | What changes |
|---|---|
| Time dilation | Observed time intervals increase for moving clocks |
| Relativity of simultaneity | Events can switch order of simultaneity between frames |
| Length contraction | Lengths along motion decrease in moving frames |