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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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  • I don't think there is a good non-mathematical way to understand this. If you willing to try a bit of maths look at the answer to this question, which calculates the acceleration from the metric. – John Rennie Jan 24 '14 at 17:58
  • Although you use the term "fall" in the question, it's important to note that the curved path of the particles isn't necessarily due to gravitational force acting on the particles, but rather gravity affecting the curvature of spacetime. The distinction means that the paths of even massless particles, such as photons, are affected by this curvature. – Edward Jan 24 '14 at 18:34

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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