"How do we know that electrons are point-like particles?"
...reminded me that I have never quite understood the necessity for particle-wave duality. De Broglie postulated that all matter has wave-like properties (and derived the relationship between mass and wavelength) and intuitively it makes no sense to think of matter as anything other than a wave function of some force in space. If two "travelling" waves intersect then at some point, we know experimentally that something clearly often “flips”. Given the exhibited quantum nature of matter, we may well expect some critical threshold to be reached when the wave changes - for example when an electron “orbiting” a nucleus loses enough energy to fall into a lower shell. The reason it simply doesn’t get progressively closer to the nucleus (ie in an analogue fashion), is because it is resonating and it has to have an integer period of oscillation - it is simply not in a stable state otherwise. However, even though it may be intrinsically impossible to measure it, the transition will happen in an analogue fashion. The point or particle-like behaviour does not, to me, indicate that an electron is itself is a particle, merely that some transition state has occured at some localised point in space and time and we could interpret this a point-like behaviour.
Why do we need any sort of duality?
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