Experimental boundaries for size of electron?

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Experimental boundaries for size of electron?

Postby Jarek » Wed Feb 13, 2019 1:16 pm

As written, it concerns only first moment, not excluding e.g. quadrupole moment like plus - minus - plus.
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Re: Experimental boundaries for size of electron?

Postby JohnDuffield » Tue Mar 05, 2019 1:19 pm

Hi Jarek. I've looked into this. IMHO there's actually no evidence that the electron is small. Yes, the particle data group will tell you that electrons “are definitely smaller than 10ˉ¹⁸ meters”, but when you look for the supporting evidence, it just isn't there. See the 2002 paper limits on sizes of fundamental particles and on gravitational mass of a scalar by Irina Dymnikova, Juergen Ulbricht, and Jiawei Zhao. They talk about the QED reaction e+e− → γγ(γ) at energies between 91GeV and 202GeV. That’s high-energy electron-positron annihilation to gamma photons. They say the interaction proceeds via the exchange of a virtual or “excited” electron with a mass greater than 402 GeV, and the characteristic size of this is less than 1.17 x 10ˉ¹⁷cm. They also say that they assume that a fundamental particle must have a de Sitter vacuum core related to its mass, with a finite geometrical size defined by gravity. This de Sitter vacuum core is hypothetical. It cannot be employed to support a claim that relies upon a virtual electron exchange. Not when virtual particles "only exist in the mathematics of the model". There’s no evidence that a 402 GeV electron is exchanged between the electron and the positron, and there’s no evidence for the de-Sitter vacuum core. So there’s no evidence here that the electron is small.

On Wikipedia you can read that “observation of a single electron in a Penning trap shows the upper limit of the particle’s radius is 10ˉ²² meters”. But when you follow up on the references and read Hans Dehmelt’s 1989 Nobel lecture you realise that the upper limit is merely an extrapolation. It’s an extrapolation from a measured g value, which relies upon “a plausible relation given by Brodsky and Drell (1980) for the simplest composite theoretical model of the electron”. The extrapolation yields an electron radius R ≈ 10ˉ²⁰cm, but it isn’t a measurement. Especially when “the electron forms a 1 μm long wave packet, 30 nm in diameter”. When you track back to Brodsky and Dell you can read the anomalous magnetic moment and limits on fermion substructure. And what you read is this: “If the electron or muon is in fact a composite system, it is very different from the familiar picture of a bound state formed of elementary constituents since it must be simultaneously light in mass and small in spatial extension”. The conclusion is effectively this: if an electron is composite it must be small. But there’s no actual evidence that it’s composite. So it’s a non-sequitur to claim that the electron must be small. So again there’s no evidence here that the electron is small.

The electron isn't small. Its field is what it is. It isn't some billiard ball thing that has a field. It is field. It's got the Compton wavelength it's got because h is what it is.
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