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Here is the shortest way I can describe the difference between old-school (Newtonian) spacetime and modern, relativistic (Minkowskian) spacetime:  in the old view, time was something separate and distinct from space:

S³ × T

Now, in the modern view, time is another kind of thing that’s just like space.

S⁴

Read on if that doesn’t say it all.

You know how left-right and forward-back are only relative to some axis system?  Like if you turn to the left, then left-right are different.  Also if you lie down, then up-down are different.  Well, sooner-later is the same kind of thing as left-right.  If you go really fast (like 10% of the speed of light) then you notice this.

Going this fast relative to me, your time will be slower than my time — your watch will literally run slower.  Just like, if we were facing the same direction, and I turned 10 degrees to the left, then our “forwards” would be different.  Which means, walking at the same speed I would achieve less “forward” than you, according to your “forward”.

SOURCE: Sean Carroll

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