Prior to the emergence of quantum mechanics, fundamental physics was marked by a peculiar dualism. On the one hand, we had electric and magnetic fields, governed by Maxwell’s equations. The fields filled all of space and were continuous. On the other hand, we had atoms, governed by Newtonian mechanics. The atoms were spatially limited — indeed, quite small — discrete objects. At the heart of this dualism was the contrast of light and substance, a theme that has fascinated not only scientists but artists and mystics for many centuries.
One of the glories of quantum theory is that it has replaced that dualistic view of matter with a unified one. We learned to make fields from photons, and atoms from electrons (together with other elementary particles). Both photons and electrons are described using the same mathematical structure. They are particles, in the sense that they come in discrete units with definite, reproducible properties. But the new quantum-mechanical sort of “particle” cannot be associated with a definite location in space. Instead, the possible results of measuring its position are given by a probability distribution. And that distribution is given as the square of a space-filling field, its so-called wave function.
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