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Question

How is the normal reaction force an electromagnetic force?

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Solution

The normal force is not really due to any of the four force of nature. The forces of nature are not all the forces in the macroscopic sense, they are just the fundamental bosonic particles in a modern quantum field theory description.

The normal force is due to the Pauli exclusion principle almost exclusively. This is because electrons have the property that two electrons cannot be in the same quantum state. Two electrons can't be at exactly the same point.

But you might be thinking, "two point particles in three dimensions can't ever be at the same point, it's infinitely improbable!" In quantum mechanics, the particles are spread out in a wavefunction, and the condition that they can't be at the same point means that wherever their spread-out-ness overlaps, the wavefunction is zero. The wavefunction is in 6 dimensions for 2 particles, so it is hard to visualize, but the zeros appear on the diagonal part, where the two positions for the particle coincide.

When you bring two objects to touch, the electron wavefunctions are squeezed together, and the average scale of variation increases slightly, because of the exclusion. The rate of change of the wavefunction is the momentum of the electron, and as you push them closer, it costs energy. This is the source of the normal force. It would not exist if electrons were elementary bosons.

​​​hope you understood


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