What is dTau? The Role of dTau in Measuring Time on a Worldline

[sqljunkey]

I heard dTau measures time for the person traveling on a worldline. If the person traveling on that world line chalked marks on the world line every 1 minute, would those intervals be the same distance from each other?

 

[Dale]

Yes, they would each be 1 light-minute apart.

 

[PeterDonis]

If the person traveling on that world line chalked marks on the world line every 1 minute

The worldline is not a path through space; it's a path through spacetime. The person traveling on it already "chalks a mark" on the worldline every minute--all he has to do is watch the minute hand on his clock change. Each change of the minute hand is an event on the worldline--a "mark"--and these events are 1 minute apart.

 

[Ibix]

If the person traveling on that world line chalked marks on the world line every 1 minute, would those intervals be the same distance from each other?

As Peter says,you can't really do this because you can't "chalk a mark" on spacetime. But the proper time along your worldline while you wait for the second hand of your watch sweep out one minute is one minute, yes.

Note that this is the distance along your worldline. Your twin racing up and down the room at some fraction of $c$ has a different worldline and will experience less than a minute. This is the Minkowski spacetime equivalent of the mundane fact that the distance between two points depends on the route taken.