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enter image description here

Two particles fall side by side, towards the earth. The horizontal distance between them is 10m. As they advance nearer and nearer to the earth's surface, the horizontal distance decreases, from 10m to say 8m and the particles move closer and closer towards each other.

I understand that happens because spacetime curves inwards and so the particles move towards each other. What I dont understand is how the spacetime curvature effect the particle's velocity. How does spactime curvature induce acceleration?

A non-mathematical answer would be preferred.

Black Dagger
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1 Answers1

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The velocity vector of the particle actually has constant length $c$. Its apparent increasing relative velocity $v$ is due to parallel transporting the vector to the observer (or equivalently, transporting the observer's coordinate frame) through a curved spacetime:

lie

Note that the picture is something of a lie-to-children due to not taking the non-euclidean metric into account, but I failed to come up with a better visualization.

Christoph
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