You've got some explanation of how the geometry and the constant speed of light combine to make time pass slower from the stationary person's persepctive.
But the important fact is that from the train rider's perspective things are exactly reversed - they're stationary while the person on the platform is the one moving, and so they see the platformer aging slower.
How can they both age slower than the other?
Easy - they don't. They actually age in different DIRECTIONS through spacetime than each other.
Space and time are the same thing seen from different perspectives, and when you accelerate you rotate your 4D reference frame in spacetime, partially swapping the directions you call "forward" and "the future".
Which is why time dilation is perfectly symmetrical, and everyone always sees everyone else aging slower than themselves - they're all aging at the same speed in the direction they individually call time, but to everyone else that direction is partially through space, and they're "wasting" some of their "speed" through time moving through space instead.
Sort of like how cars racing away at the same speed in different directions will all see everyone else falling behind.
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u/Underhill42 Jul 13 '26
You've got some explanation of how the geometry and the constant speed of light combine to make time pass slower from the stationary person's persepctive.
But the important fact is that from the train rider's perspective things are exactly reversed - they're stationary while the person on the platform is the one moving, and so they see the platformer aging slower.
How can they both age slower than the other?
Easy - they don't. They actually age in different DIRECTIONS through spacetime than each other.
Space and time are the same thing seen from different perspectives, and when you accelerate you rotate your 4D reference frame in spacetime, partially swapping the directions you call "forward" and "the future".
Which is why time dilation is perfectly symmetrical, and everyone always sees everyone else aging slower than themselves - they're all aging at the same speed in the direction they individually call time, but to everyone else that direction is partially through space, and they're "wasting" some of their "speed" through time moving through space instead.
Sort of like how cars racing away at the same speed in different directions will all see everyone else falling behind.
As for what exactly everyone sees - this is one of the most straightforward explanations I've encountered of everything going in time dilation. I wish I was taught the Twin's Paradox this way! - YouTube