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

Nothing referenced by Hermann Haus regarding electrons, or the size thereof? It would help, perhaps, if we considered the electron in two or three known environs when considering size, e.g. when bound in an atom or free-space environ ...

Added, also Haus, who was working on development of a “free electron” laser. One would think he had some insights in this matter.

Some work by Haus shown here: https://wikivisually.com/wiki/Nonradiation_condition
_Jim

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

Regarding nonradiation condition, this is a question for from the size of electron: ~10^-10m vs ~10^-15m.

But generally it is strongly connected with quantization condition - if electron is not exactly in one of orbitals, it should quickly get to a close orbital and release the abundant energy as EM radiation (photon) - time of such process should be in attosecond scale: http://science.sciencemag.org/content/328/5986/1658

The best intuitions for orbit quantization come from walking droplets experiments - allowing to get orbit quantization in a few different ways (slides 11-22 here).
Generally it comes from ("pilot") wave created by electron's internal clock (de Broglie's/zitterbewegung) - it will have the lowest energy if becoming a standing wave (described by stationary Schrodinger), which we will get if satisfying (Bohr-Sommerfeld like) quantization condition: the clock has to perform integer number of ticks during a single orbit.
Here are nice videos: http://www.pnas.org/content/pnas/suppl/ ... rgetid=SM1 from http://www.pnas.org/content/107/41/17515

Jarek

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

Q-reeus

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

Regarding problems with recreating interference, which is even further from the title: experimental boundaries for size of electron (maybe let's take it to dedicated: viewtopic.php?f=6&t=361 ), these are only (hydrodynamical) analogues - instead we need to use de Broglie-Bohm: obtained by substituting phi = sqrt(rho) * exp(iS) to Schrodinger equation, and confirmed experimentally e.g. while (weakly) measuring average trajectories of interfering photons: http://science.sciencemag.org/content/332/6034/1170
And instead of interference, we are talking here about intuitions for orbit quantization to prevent synchrotron radiation - orbit quantization was obtained in multiple ways for walking droplets by different groups - providing clear intuition: that to minimize energy of e.g. electron-proton system (they cannot join as neutron is much heavier), the coupled (pilot) wave needs to become a standing wave (described by stationary Schrodinger equation) - otherwise it would have additional energy in form of fluctuations.
Do you disagree with such intuition for nonradiation?

Regarding vacuum self-organizing into particles - localized stable energy configurations (formally called solitons), I generally agree.
The most crucial question there is explaining charge quantization (barely mentioned in the paper you have linked) - having that, e.g. electron is just the simplest (lightest) negative (quantized) charge.
Charge quantization is a restriction for Gauss law: that integrating electric field over a closed surface, the returned charge is not any real number like in standard EM, but an integer multiplicity of e (or e/3).
But there is also quantized version of Gauss law: topological Gauss-Bonnet theorem says that integrating curvature of a vector field over a closed surface, we get topological charge inside - which has to be integer.
Hence interpreting curvature of some deeper field as EM field, we get quantized (by topology) charges governed by electromagnetism (Faber's model of electron): https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf
Jarek

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

Jarek I have no pretensions to expertise in these difficult subjects. Regarding your first criticism - that Manasson's approach doesn't predict the absolute value of charge quantization (completely ab initio), well no-one can without assuming some relations a priori as brute facts. For instance, linking field strength to field energy density, one has to write in by hand given values for vacuum permittivity and permeability. But with few assumptions, his scheme seems to go very far in explaining (nearly) all of particle physics! But not Bell. For an ongoing discussion, see:

Regarding clear absence of double slit interference for Couder bouncing drops experiments, how is resorting to inherently non-local DBB theory going to leave other Couder results any more than interesting analogues to actual QP, but now shown to be without full correspondence?
Q-reeus

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

Once again, no one claims that hydrodnynamical analogues give perfect agreement - there are many differences, they only provide valuable intuitions ... especially for orbit quantization in many settings - including double quantization (of separately radius and angular momentum like in Bohr-Sommerfeld: https://www.nature.com/articles/ncomms4219 ) and Zeeman effect (using Coriolis force in place of Lorentz force: https://journals.aps.org/prl/abstract/1 ... 108.264503 ).
This is the only intuition for quantization, nonradiation I know: that coupled wave needs to become standing wave to minimize energy - do you have some objection to it or a different explanation?

Regarding "no-one can" for charge quantization, I disagree - mathematicians know well quantization of topological charges.
Take vector field v preferring unit lengths due to Higgs potential: V(v) = (1-|v|^2)^2.
It can get topologically nontrivial configuration, e.g. hedgehog: v(x) ~ x/|x|, there is Gauss(-Bonnet) law for them and they can only get quantized possibilities e.g.
Jarek

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

This may seem harsh but if an analog model predicts everything fine except for one crucial feature (say one-particle-at-a-time double slit interference pattern) then it fails, period. One either looks for another conceptual scheme that can explain it and the other aspects, or accept QP as primary in itself and without deeper explanation.

Re charge quantization - my point was that deriving the value, not necessarily the phenomena itself, has to presuppose one or more primitives ab initio. Planck constant, HUP, de Broglie relations, permittivity/permeability, or such. Manasson starts with such primitives in place and it will be likewise with your mentioned topological charge scheme(s). Maybe I misinterpreted your initial criticism of Manasson article.
Q-reeus

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

Regarding hydrodynamics, the real QM model is dBB pilot wave: substituting psi = sqrt(rho) exp(iS) to Schrodinger and looking at equations for density rho and action S: https://en.wikipedia.org/wiki/Pilot_wav ... e_particle
It gives interference in double-slit experiment as tested e.g. in http://science.sciencemag.org/content/332/6034/1170
Walking droplets is not the same but have some similarities - I don't understand how inability of some people to recreate interference says anything about its success in recreating charge quantization? Does somebody also claim inability to recreate these orbit quantization experiments?
Can you show that they are somehow equivalent?
That its quantization mechanism is incorrect: (described by stationary Schrodinger) standing wave as having the lowest energy? Do you know any other quantization mechanism?

Regarding charge quantization - you need any mechanism (e.g. topological), then just define/calibrate its lowest nonzero charge as 'e'.
I was looking for quantization mechanism in the paper you linked, but without success - could you briefly explain this mechanism?
Jarek

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

Jarek wrote:...Regarding charge quantization - you need any mechanism (e.g. topological), then just define/calibrate its lowest nonzero charge as 'e'.
I was looking for quantization mechanism in the paper you linked, but without success - could you briefly explain this mechanism?

He he. I suggest re-reading that article several times. The author builds an overall concept slowly and from numbers of subtle non-linear phenomena. Particle physics is very not my forte. Ditto for self-organizing dissipative structures. If it really interests, consider contacting him directly for expert clarification.
Q-reeus

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

Arnold Neumaier has responded on stack ( https://physics.stackexchange.com/quest ... f-electron ) - he has gathered many materials on this topic:
https://www.mat.univie.ac.at/~neum/phys ... tlike.html
But still no clear argument that electron is much smaller then femtometer (?)

Anyway, to better specify the problem, define E(r) as energy in a radius r ball around electron.
We know that E(r) ~ 511keVs for large r, for smaller it reduces e.g. by energy of electric field. Assuming perfect point charge, we would get E(r) -> -infinity for r->0 this way. Where does divergence from this assumption starts?
More specifically: for example where is maximum of E'(r) - in which distance there is maximal deposition of 511keVs energy?
Or median range: such that E(r) = 511/2 keVs.
It is not a question about the exact values, only their scale: ~femtometer or much lower?
Jarek

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

Jarek wrote:Arnold Neumaier has responded on stack ( https://physics.stackexchange.com/quest ... f-electron ) - he has gathered many materials on this topic:
https://www.mat.univie.ac.at/~neum/phys ... tlike.html
But still no clear argument that electron is much smaller then femtometer (?)

Anyway, to better specify the problem, define E(r) as energy in a radius r ball around electron.
We know that E(r) ~ 511keVs for large r, for smaller it reduces e.g. by energy of electric field. Assuming perfect point charge, we would get E(r) -> -infinity for r->0 this way. Where does divergence from this assumption starts?
More specifically: for example where is maximum of E'(r) - in which distance there is maximal deposition of 511keVs energy?
Or median range: such that E(r) = 511/2 keVs.
It is not a question about the exact values, only their scale: ~femtometer or much lower?

What about electric dipole moment of an electron?

http://www.doylegroup.harvard.edu/wiki/ ... ersion.pdf

Does this not indicate that the charge radius of an electron must be smaller than 4.3 x 10^-30 cm?
.
FrediFizzx
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### Re: Experimental boundaries for size of electron?

If you want to conclude from dipole moments, so what about magnetic dipole moment of electron?
It is ~1000x larger than of proton, does it mean that electron is 1000x larger?
Neutron has similar boundaries for EDM ( https://en.wikipedia.org/wiki/Neutron_e ... ole_moment ) - do you also conclude its size from it?
Jarek

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

Yeah, sorry EDM is just how much it deviates from a perfectly spherical shape. Nothing to do with size.
FrediFizzx
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### Re: Experimental boundaries for size of electron?

So neutron is perfectly spherically symmetric? ... built of 3 quarks ...

The "perfect ball" fairy tale is only to convince public that another experiment reducing boudary for EDM makes sense ...
Electron has huge magnetic dipole moment - is tiny magnet ... is at most cylindrically symmetric.
Zero EDM means only that ... e.g. + - + quadrupole has also zero EDM, but has nonzero radius and is not spherically symmetric.
Jarek

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

Jarek wrote:So neutron is perfectly spherically symmetric? ... built of 3 quarks ...

The "perfect ball" fairy tale is only to convince public that another experiment reducing boudary for EDM makes sense ...
Electron has huge magnetic dipole moment - is tiny magnet ... is at most cylindrically symmetric.
Zero EDM means only that ... e.g. + - + quadrupole has also zero EDM, but has nonzero radius and is not spherically symmetric.

Well, zero EDM means that the electron's electric charge radius is perfectly spherical. Of course its "magnetic charge" radius is not perfectly spherical.
FrediFizzx
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