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Suppose you touch a cube. There would still be a Plank length between your hand and the cube. Does this mean that it is impossible for anything to touch anything, specifically because there is always an infinitesimal distance between two objects? I don't think this would work (since there can be no distance smaller than a Plank length and that if you are a Plank length apart, you are "touching" something, but I want to make sure that this idea is void before I discard it).

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    You said “There would still be a Plank length between your hand and the cube.” There is no theoretical or experimental support for this claim. – Dale Nov 03 '21 at 16:20
  • It's just not clear how you come to that conclusion. Perhaps edit your question to clarify. – jng224 Nov 03 '21 at 16:23
  • It is not scientific. It has no basis in either experiment or any experimentally confirmed theory. I doubt it is even supported by a purely speculative published theory. – Dale Nov 03 '21 at 16:27
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    Possible duplicates: https://physics.stackexchange.com/q/23797/2451 , https://physics.stackexchange.com/q/1077/2451 and links therein. – Qmechanic Nov 03 '21 at 16:55
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    This is not a theory. So there is nothing to scrap. – nasu Nov 03 '21 at 16:59

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The reason your hand doesn't quite touch the cube is that the electrons around the atoms in your hand are repelling the electrons around the atoms in the cube. Specifically, photons exchanged between those electrons mediate the electromagnetic repulsion. The actual distance depends a lot on how hard you press, and even if you press really really hard, the closest you can get is many orders of magnitude larger than a Planck length.

So it's true that nothing touches anything else, but it's usually for a different reason. Except maybe in extremes like atomic nuclei and neutron stars where fermions are crowded right next to each other and Pauli exclusion effects start to become the reason. But those particles are themselves much larger (like $10^{20}$ times) than the Planck length, so it's even then hard to define what it means to say they're touching.

Gert
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Bob Wildfong
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    So what would you expect "touching" to mean? In practice, when the atoms are close enough to feel the repulsion it's touching. – nasu Nov 03 '21 at 17:01
  • Sure, maybe two things are "touching" when the repulsive electromagnetic force equals the force moving them together, so they stop getting closer. Or maybe it means there's no space in between them (so it never happens)? I don't know, it's a poorly defined term microscopically but we use it all the time macroscopically. – Bob Wildfong Nov 04 '21 at 01:59