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Right. At least at Cornell (David Muller's quantum class) we were basically taught that wave-particle duality was the uncertainty principle from our earliest un
by drostie 12y ago
Right. At least at Cornell (David Muller's quantum class) we were basically taught that wave-particle duality was the uncertainty principle from our earliest undergraduate experience.
Basically, the very meaning of de Broglie's law (a particle with momentum p has a wavelength L = h / p) specifies a "particle wavelength", but that wavelength can only exist within that particle's position-uncertainty. Shrink that uncertainty and you necessarily have a small L to fit within there, which means a very high p, which means that little fluctuations e.g. in the direction of p translate to large uncertainties about p. About a quarter-way into the course it is revealed that de Broglie's law essentially identifies p-space with k-space (that is, the Fourier conjugate to x-space), and you then prove that all Fourier conjugate pairs have an uncertainty principle, quite independent of quantum mechanics. So the earliest statement of wave-particle duality already implies the uncertainty principle and this has been known for a long time.