## Experimental boundaries for size of electron?

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

### Experimental boundaries for size of electron?

There is some confidence that fundamental particles are perfect points e.g. to simplify QFT calculations - what experimental evidence do we have, especially for electron?

Electron Wikipedia article only points argument based on g-factor being close to 2:Dehmelt's 1988 paper extrapolating (by fitting parabola to two points!) from proton and triton behavior that RMS (root mean square) radius for particles composed of 3 fermions should be ≈ g−2:

Another argument for point nature of electron might be tiny cross-section, so let's look at it for electron-positron collisions for GeV scale:

As we are are interested in size of resting electron (no Lorentz contraction), we should extrapolate the flat line sigma ~ 1/E^2 to resting electron, getting sigma ~ 100mb corresponding to ~2fm radius.

From the other side we know that two EM photons having 2 x 511keV energy can create electron-positron pair, hence energy conservation doesn't allow electric field of electron to exceed 511keV energy, what requires some its deformation in femtometer scale from E ~ 1/r^2: $\int_{1.4fm}^\infty \frac{1}{2} |E|^2 4\pi r^2 dr\approx 511keV$

Can we bound size of electron from above: g-factor or scattering experiments?
Is there other experimental evidence?
Jarek

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Joined: Tue Dec 08, 2015 12:57 am

### Re: Experimental boundaries for size of electron?

All experimental evidence for an electron past the screening effects of the quantum vacuum near Compton wavelength points that it has no constituent parts. We find theoretically that its "size" is very near to Planck length.

https://arxiv.org/abs/1705.06036

Not a point particle but very close to it.
FrediFizzx
Independent Physics Researcher

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### Re: Experimental boundaries for size of electron?

Compton wavelength of electron is relatively huge: 2.4pm, electron-positron scattering (and energy of electric field) suggests thousand times smaller fm-scale radius ...
Also baryon size is fm-scale, electron shouldn't be thousand times larger.
With pm-scale electron radius interaction with nucleus should be frequent, but it is relatively rare: https://en.wikipedia.org/wiki/Electron_capture https://en.wikipedia.org/wiki/Internal_conversion
Jarek

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Joined: Tue Dec 08, 2015 12:57 am

### Re: Experimental boundaries for size of electron?

Well..., effectively an electron has two "sizes". At low energy-momentum, they scatter off each other as if their size was of order of about the Compton wavelength. That is due to the screening effects. At high energy they scatter as if they are point-like. Experiments have shown that an electron must be smaller than 10^{-22} meters. We find that they are possibly of order of 10^{-34} meters very near to Planck length due to gravitational torsion.
FrediFizzx
Independent Physics Researcher

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Joined: Tue Mar 19, 2013 6:12 pm
Location: California, USA

### Re: Experimental boundaries for size of electron?

I am asking for objective size of resting electron - energy dependence (Lorentz contraction) should be removed by Lorentz transform to resting electron.
Sure, definition of particle's radius is nontrivial - they use root-mean square for composite particles: weighted average of squares of distances (e.g. negative for neutron due to positive charge being closer to center).

For non-composite particle like electron, we could define energy profile: E(r) as energy inside radius r sphere around electron.
We know that E(r) ~ 511keV for large r.
Increasing r, we need to add energy of EM field, so E(r) should be increasing.
One question is r->0 behavior, assuming electron being perfect point we would have E(r) -> - infinity.
To get E(r) -> 0 for r -> 0, we need to modify electric field of perfect point in femtometer scale.
Generally, we could define e.g. median radius: such that E(r) = 511/2 keV.

Experiments have shown that an electron must be smaller than 10^{-22} meters.

Great - this is exactly what I am asking for - could you point these experiments?
Are you referring to arguments based on g-factor: using Dehmelt's fitting parabola to two points (no kidding - top plot) ?
Jarek

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Joined: Tue Dec 08, 2015 12:57 am