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I've been working on de Broglie's thesis (English PDF, Original French PDF) for a course, and I've found something that's been bothering me. My training is in Physics, and so I'm not particularly aware of a lot of the history of this subject, so I'd appreciate any insight!

The thesis makes a large number of assumptions, some of which we now know to be untrue. However, many others were quite ahead of their time. One of these assumptions that he makes very early on in the document is the following:

An electron is for us the archetype of isolated parcel of energy, which we believe, perhaps incorrectly, to know well; but, by received wisdom, the energy of an electron is spread over all space with a strong concentration in a very small region, but otherwise whose properties are very poorly known. That which makes an electron an atom of energy is not its small volume that it occupies in space, I repeat: it occupies all space, but the fact that it is undividable, that it constitutes a unit.

It would appear -- in his description of the electron as being "spread over all space" -- that de Broglie is hinting at it being a sort of wave packet. Indeed, this statement is often used to show how de Broglie was aware of the electron's wave nature. However, this statement is made very early in the paper, before he describes phase and group velocities, or even tries to associate a phase-wave to a massive particle. So was it really "received wisdom" that the electron was spread over in space?

There is some debate in our class as to whether or not this is an important assumption for his thesis. For example, one could argue that stating that the electron's energy is spread over space is just a way of saying it isn't a point particle. Perhaps this is so, but de Broglie's argument, in particular the phrase below (emphasis mine), seems to be a much stronger claim since he says:

[...] I repeat: it occupies all space [...]

Furthermore, one page later he uses a "crude" mechanical comparison that "speaks to the intuition" to describe a parcel of energy as a set of masses and springs that are spread out over all space, and oscillating synchronously in the particle's rest frame (see here for an animation). He then goes on to say that the central point is that there is a "dephasing" of the motion of the weights, which forms a wave-like phenomenon that he envisions to be the phase-wave. Thus it would appear that the electron not being a point particle is quite important to his argument.

So I suppose my questions would be:

  1. What exactly was de Broglie's justification was for making the assumption that the electron was spread over all space?
  2. Was this a common assumption for people to make at the time, or was he being very imaginative?
  3. Were there any preexisting theories that supported this idea that the electron was delocalised?
  4. Or is there some evidence to show that de Broglie realised that a delocalised electron was essential for his argument to work, and introduced it post facto?

(I should note that I am most interested in the historical ideas that lead to his thesis being consistent, rather than correct.)

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I am not knowledgeable in the history of the subject either, so the following may be wrong, but I would suspect that what de Broglie had in mind was that electron's Coulomb field (and, therefore, the energy of this field) "is spread over all space". This was common knowledge then, I believe.

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    $\begingroup$ Oh, that's interesting! I didn't think about that! Perhaps the fact that the electron's Coulomb field extended over all space, and Einstein's equivalence of mass and energy might have led to him assuming the mass of the electron was spread all over space too. Hmm. $\endgroup$
    – Philip
    Mar 8, 2022 at 14:43

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