# "In spacetime, a straight path yields the longest elapsed time between two events". Could someone explain this please?

I know this may appear to be a duplicate question but the other question Straight lines and longest distance doesn't seem to explain in laymans terms. So... I'm trying to understand this but have read loads of stuff about Minkowski space etc but it's still beyond my tiny brain to grasp.

So, would anyone like to tackle this in layman's terms for me please.

The quote I've seen and would like explaining is this..

In space, a straight line describes the shortest distance between two points. In spacetime, by contrast, a straight path yields the longest elapsed time between two events.

I just can't get my head around why the straight line is the longest time in spacetime!

• Possible duplicates: physics.stackexchange.com/q/303461/2451 and links therein. Nov 22, 2022 at 11:07
• It may not be obvious to OP why the linked question is (functionally) a duplicate. Only one of the answers really gets to the heart of the issue, which is that space and time have opposite signs in the (pseudo-)metric of spacetime $ds^2=-dt^2+dx^22+dy^2+dz^2$. Using that sign convention it becomes clear that one minimizes the length (value of the metric) by maximizing dt, which makes the length become more negative (hence smaller). Nov 22, 2022 at 13:17

As I mentioned in a comment: space and time have opposite signs in the spacetime (pseudo)metric. That means that in Minkowski space the "distance squared" $$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$ can become negative. So the "shortest distance" corresponds to the "longest time" in the same way that, say, -20 is smaller than +10 or even -10.