Spacetime Interval
Observers can disagree about spatial distance and elapsed coordinate time while agreeing on one deeper quantity: the spacetime interval between the same two events.
If observers disagree about space and time, what can they still agree on?
Lorentz transformations reshuffle the spatial and temporal parts of an event separation. The interval stays invariant, giving every inertial observer the same causal classification of the pair.
The lab uses , so time is measured in seconds and distance in light-seconds.
Move the second event, then boost the observer.
A slower-than-light causal influence can connect the events. Some frame places both events at the same position.
Only a light-speed signal connects the events. Every inertial observer keeps them on the light cone.
No subluminal causal signal can connect the events. Different frames may disagree about their time order.
Change the frame speed. Δt′ and Δx′ move, but their Minkowski combination stays the same apart from numerical rounding.
Timelike, lightlike, and spacelike are not observer opinions. The interval fixes the causal class for every inertial frame.
For this timelike pair, the proper-time magnitude is 1.95 s.