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How can I stand on the ground? EM or/and Pauli?

It probably seems like a silly question to a physicist, but I'm from a pure maths background and don't know an awful lot about the real world. So what kind of force is it?

It can't be gravitational because that attracts matter together. And it's not like the atoms in your hand are physically colliding with the atoms in the door, because there's mostly empty space and your hand might as well go straight through the door. I guess it's fallen out of fashion to think of things as made of 'particles' these days anyway, at these small scales I hear more about fields and coupling between fields.

I'm doubtful it's anything related to strong or weak nuclear force. I've heard of van der Waals force, but didn't understand what it meant. So I guess that leaves.. an electric force or magnetic force? But my hand and the door aren't magnets. And we don't have much of a net charge, otherwise maybe I could push the door from a distance.

What does it actually mean to 'touch' the door, push, and exert a force on it?

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wim
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It is the electromagnetic force which allows you to push a door closed, or to touch anything. Electromagnetism isn't just about magnets. It includes the common idea of like charges repel and opposite charges attract as well. Our hand is comprised of atoms, which are surrounded by electrons. Similarly for the door. As our hand gets closer and closer to the door, the electrons in the door's atoms and the electrons hand's atoms too get closer, and the repulsion force between the two increases significantly. This is what stops us from putting our hand through the door, and also what allows us to push the door open.

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