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This is a very simple and stupid question but ever since I watched the first Harry Potter and saw Harry and his friends run through a wall at King's Cross Station I have wondered what keeps us from just running through objects or falling through the floor? Is there some fundamental physical law/concept that prevents us from doing this?

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Of course there is. A wall, or a floor, is some chemical construction and it is in the solid state of aggregation because of stiff bonds between an atom/molecule and its neighbors - look at this for instance, to see a crystal structure. The higher this energy is, the more difficult is to break the material. To penetrate the wall/floor you have to break this bond in a region, i.e. to invest a higher energy than that binding energy.

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