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I am reading a textbook on quantum mechanics and came across the following, "... one of the reasons that the electron cannot be regarded as being literally a wave is that its wave function expands to macroscopic size quite rapidly, and it is quite certain that electrons are not macroscopic objects."

My question is why must an electron always be considered a microscopic object? I recognize in normal interactions electrons are part of atoms and thus microscopic from that context, but are there other frames of reference in which an electron could be viewed as existing in a macroscopic state? For example, as length contraction allows large scale relativistic objects to appear much smaller, is there an analogous but opposite effect at the subatomic level which scales up objects in that realm?

Alternatively, is it correct to describe an electron as a wavefunction representing a bundle of energy in the electromagnetic field - and if so why can't this bunched energy spread out (in specific contexts) to macroscopic size?

Adam
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    "Alternatively, is it correct to describe an electron as a wavefunction representing a bundle of energy in the electromagnetic field (...)?" No. The quanta of the EM field are photons, not electrons. In QFT electrons are excitations of the electron field. – Marius Ladegård Meyer Dec 14 '23 at 22:13
  • In mainstream physics electrons are point particles; they are not microscopic in the "can see them with a microscope" sense, they have zero spatial extension. The interpretation of the wave function is not that the electron itself spreads out; among other reasons, the wave function is complex, so cannot represent a real (extended) position. – Marius Ladegård Meyer Dec 14 '23 at 22:16
  • This may help - Does the collapse of the wave function happen immediately everywhere?. It is a different question, but in my answer I talk about how the size of an electron means something different from a classical size. – mmesser314 Dec 15 '23 at 01:09

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Experiments conducted at very high energies with electrons have failed to find evidence of an internal structure. Hence an electron appears to be a point object and that is about as microscopic as you can get. An electron's wave function, on the other hand, can grow to macroscopic size. Consider an electron in a Rydberg orbital for example. It is important here to distinguish between an electron (a truly elementary particle) and its wave function whose square modulus gives the probability of finding the electron at any given location at a specific time.

Lewis Miller
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