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Comment by pontus | Hacker News Reader

The distance between two points is basically just the Pythagorean theorem: x^2 + y^2 + z^2. If you have extra dimensions, you just add more terms to this. Now, if you know that e.g. x is very large then that puts a lower bound on the distance:

Distance^2 = x^2 + y^2 + z^2 + ... > x^2.

In other words, if x is large there's no way that the two particles are still somehow close together.

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Put two iron pellets on a very thin, flexible fabric. Underneath the fabric, put a magnet so each pellet is stuck to one pole of the magnet through the fabric. Tug the magnet "down" in the third dimension, which will fold the fabric and move the pellets so that from their perspective (stuck to the 2D surface of the fabric) they're moving far away from each other. They also maintain a constant and very short distance in the third dimension, but they can't take advantage of it because I forgot to mention the fabric is impervious to them.

This is only true for cartesian spaces. If the low-dimensional manifold is "folded" or "crinkly" inside a higher-dimensional space then you can indeed have particles that look far apart on the manifold but which are actually close together in the higher-dimensional space.

(My terminology here is largely wrong; this is not my field. Perhaps an expert can correct me.)

ER=EPR entanglement could be realized as a non-local distance mapping

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