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Take a particle, it has a position $(x, y, z)$ maybe it is $(0.231, 8.962, 10.567)$.

Is there a maximum precision to this? Is the space discrete or continuous? If it is discrete, how thin the measurement is between a point A and B in space?

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  • $\begingroup$ No one knows. You can, if you want to (and people have done this), enforce a minimum possible length in your theory. It also matters whether one can experimentally detect such small distances. Unfortunately, these correspond to very high (Planck scale) energies which are far from current technology's reach. $\endgroup$ – Avantgarde Jan 16 at 1:28
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/9720/2451 and links therein. $\endgroup$ – Qmechanic Jan 16 at 6:12
  • $\begingroup$ The smaller you go, the more space becomes blurred by the uncertainty principle, so the question about the nature of space loses its meaning. $\endgroup$ – safesphere Jan 16 at 6:15
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There is no experimental evidence that space is discrete, but there are theoretical reasons to think it might be.

https://en.wikipedia.org/wiki/Loop_quantum_gravity

If it is in fact discrete, the smallest length is expected to be on the order of the Planck length, $\sqrt{\hbar G/c^3}$, built out of Planck’s constant, Newton’s gravitational constant, and the speed of light. This distance is a minuscule $1.6\times 10^{-35}$ meters, so you can see why we haven’t detected any discreteness yet.

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