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Particle theory concerns very small particles and relates only indirectly to large objects such as snow skis. Although it is perfectly true that both the snow, and the snow skis are composed of large numbers of tiny particles, those particles create electromagnetic fields, and the merged fields act like continuous surfaces. The solidity of solid matter is the result of electrons repelling each other, and nothing more than that. Since electrons are on the outside of atoms, and protons are on the inside, when you get close enough to any atom the negative charge predominates, hence, at a sufficiently close range, atomic matter repels other atomic matter (like charges repel, so negative charges repel other negative charges), hence, solid matter does not interpenetrate other solid matter, which is why it is solid.

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