Comments by "Lepi Doptera" (@lepidoptera9337) on "Everything Vibrates. It Really Does." video.
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There are two sources of discreteness in quantum mechanics. One is the measurement process. A measurement is an irreversible change of field energy. By that we mean that no matter what happens in detail, there is a long term (more precisely infinitely long) change in the energy distribution between the system under measurement and the measuring system. The "result" of that change, per special relativity, is a change of energy and momentum, but it can also involve angular momentum/spin, electric charge and other conserved (or nearly conserved) quantities. Logic necessitates that such a one time change has to have a discrete (single value) property. That, of course, is merely the source of discrete measurements. It is not the source of quantization of the fields. For that we also need the quantization of angular momentum/spin. I don't have a really good fundamental reason for that, even though I know that theorists have tried to derive it from deeper principles. It may be due to symmetries of spacetime. It may have to do with the partition properties of physical systems that require a theory that obeys something like the law of conditional probabilities, which can be used to derive the linear structure of quantum mechanics. It may be the intersection of both or something physically deeper, still.
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