What does not change

My clock

A clock that moves with me records ticks at a rate: that’s my time. At the most personal level, it records how I age. As physics is the same for everyone, even if Bob is moving past me, Bob can figure out how the clock is ticking for me. He might think I’m recording different times and different distances from those he records, but he could figure out the passage of time as I record it. With both different durations and different distances being recorded because of relative motions, look for something that does not change. Physicists often seek invariants. My time, the number ticks of a clock along my worldline is an invariant: the space-time interval.

If Bob is moving past me, he’ll record some of this interval as distance and some as time because of that movement, but he’ll be able to figure out what my clock says. It records the elapsed ticks between two happenings on my worldline (for example, lunch and dinner): the space-time interval. Charlie will agree on this interval, although if moving at a different speed from Bob, there will be differences in the times and distances. Any watcher agrees on the witnesses measured durations.

Maximal ageing

Alice, Bob or Charlie record clocks moving past them, ticking at a lower rate (going slow). No one else’s clock ticks as fast as the one that accompanies me on my worldline. When the spacetime interval is all time, time is maximised. The clock that travels in a straight line up the worldline shows the longest time.

Time and space are not interchangeable in spacetime. Straight lines measured purely as a distance are always the shortest – the distance is minimised. That’s completely different from straight lines in time, which maximise duration.