"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!
 A: Because of time dilation. If I have to go from A to B in a given coordinate time and I do so by zigzagging all over the place, on average my speed will be pretty high. As seen from an inertial frame, this means that my clock will run slow, and I will measure a shorter time. By going in a straight line at constant speed from A to B, I keep my average speed as low as possible, thus making my clock run as fast as possible, which will make me measure a longer time.
A: 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.
There are some subtleties in the math about what a geodesic is, but for flat spacetime straight (timelike) lines representing massive objects are ones which maximize dt^2 and minimize the other terms.
