What is electron? Is it a perfect point? What does it mean?

Electron is usually imagined as a simple point charge, but in fact it is a very complex entity:

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- being electric charge itself means singular(-like?) configuration of electric field - E behaves like 1/r^2,
- it is also magnetic dipole moment - singular(-like?) configuration of magnetic field - B behaves like 1/r^3,
- it acts like a tiny gyroscope: attaching a force leads to response orthogonal to this force and to direction of gyroscopic moment, for example in Larmor precession,
- it has some internal oscillations - seen as zitterbewegung in Dirac theory, or as de Broglie's clock (E = mc^2 = hbar*omega), which can be directly observed (e.g. http://link.springer.com/article/10.1007/s10701-008-9225-1 ).

These properties suggest that electron is quite a complex entity - how to fit them into a perfect point? (physics doesn't like discontinuities as they would have infinite energy)
The electric field itself says that a single electron would affect the entire universe ... we could even say that this singular field defines the charge (can't we?), that electron is a configuration of the fields (what more is it?) - that it is a soliton of, among others, electromagnetic field.

So what does the popular claim that electron is a point means?
I understand it that the central singularity is perfect E ~ 1/r^2 ... however, calculating energy of such point singularity we get integrate of E^2*r^2 ~ 1/r^2, what is divergent in r = 0.
In other words - point charge would require infinite energy of electric field only - what is a nonsense as we know that 2 x 511keVs is sufficient to create electron-positron pair.

Another argument against point charge is running coupling - from https://en.wikipedia.org/wiki/Coupling_constant#Running_coupling
"In particular, at low energies, α ≈ 1/137, whereas at the scale of the Z boson, about 90 GeV, one measures α ≈ 1/127."
So alpha ~ charge^2 decreases for high energy collisions - the effective charge is reduced while particles are very close together.
Doesn't it suggest that the E ~ 1/r^2 is weakened very close to the center - additionally allowing to repair the problem with infinite energy.

Why electron is believed to be a point? What does it mean?
What would be expected if it wouldn't be?
Doesn't running coupling and infinite energy of point charge suggest that E ~ 1/r^2 is weakened for very small r?

 

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The electron is less complicated than you think. Combine the electric field with the magnetic field like this to depict the electromagnetic field:

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You now start to get the idea of the electron being a "spinor". There's a rotation in the centre. Note though that the magnetic field is a dipole, and the electron is a three dimensional spin ½ entity. To depict the rotation in more detail, start with the Wikipedia spinor depiction:

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Then you inflate and animate to turn it into a torus:

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Image credit Adrian Rossiter


Then you keep on inflating until you achieve a spherical symmetry:

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Image credit Adrian Rossiter
This now resembles the s-orbital:

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Note though that this isn't the whole electron, because "the electron's field is what it is". It's just the central region, something like the eye of a hurricane.

You can't. The electron is not a point-particle. Note that in atomic orbitals "electrons exist as standing waves". Standing wave, standing field. You can diffract electrons. Electrons have a wave nature. It's quantum field theory, not quantum point-particle theory. The electron is said to be an excitation of the electron field. How that allows for anybody to claim the electron is a point-particle beats me.

Yes, that sounds about right.

Nothing. The electron isn't a point.

Yes, it's nonsense. Electron magnetic moment says it's nonsense, as does the Einstein-de Haas effect. Take a look at the Poynting vector for a static field , and this image.

Yes.

Note that ZapperZ's assertion that the electron should exhibit an electric dipole moment is a non-sequitur. The electron clearly has a spin ½ structure.

 

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In string theory it's a tiny string with physical extent. What they call the string length. It's > the Planck Length.

 

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If you had read and understood the Wikipedia entry, you would understand that the arrow is the artist's depiction of the spinor, not the Möbius strip; The Möbius strip is the result of showing that a 360° rotation of the green arrow results in the red arrow which is now pointed the opposite direction or negative of the green arrow. Thus a 720° rotation is needed to return the green arrow to its original orientation. There are classroom models of such behavior, but all are imperfect analogies. What's actually used in Quantum Electrodynamics and the Standard Model descriptions of the electron are the mathematics of spinors which are used to precisely calculation the behavior of electrons as they are modeled in those physical theories and where the success of those theories is judged on how close the behavior of electrons corresponds with those precise predictions.

What is clear is that there is no such Möbius strip associated with spinors as a Möbius strip is a rigid geometric shape embedded in three dimensions and which therefore returns to its original orientation over a rotation of just 360°. Thus there is nothing to “inflate and animate.” Your animated torii also don't share that property of spinors.

But really, you are just trying to recycle diagrams and pseudophysics from earlier posts.

Your use of both vortex and spinor are as meaningless as a diploma-mill degree upon the wall. It's not enough to spell words correctly, you must use those words as they are conventionally understood or your writing just becomes a shambles of unconnected baseless assertions. You model no vortices and you calculate with no spinors, so you have only empty-headed drivel, regardless of the illustriousness of your abused sources.​

I wrote that for a 2015-01-24 post in a thread where the paucity of your understanding of electrodynamics was exposed.

It's unclear if your lesser claims in this thread is a result of summarization or partial backtracking, but the correct thing to do is throw out all your diagrams as unhelpful and all pretensions to insight as delusional and either stay silent on the nature of the electron or first actually learn something reliable.

 

Farsight, by inflated torus you probably mean Hopf fibration: https://en.wikipedia.org/wiki/Hopf_fibration
But this is a very complex structure and it doesn't have E ~ 1/r^2 topological charge - it might correspond to neutrino(?)
Electron is basically a charge - we need mechanism for charge quatization, then the simplest nonzero charges should be leptons - and they are required to also enforce magnetic dipole moment/spin.
Probably the only reasonable mechanism for charge quantization is as topological charge (?), Gauss-Bonnet theorem is topological analogue of Gauss law (curvature of the field acts as electric field) ...
see lecture of prof. Faber: http://www.emqm13.org/abstracts/presentation-videos/video-manfried-faber/
It doesn't have magnetic dipole moment, it has only one family of leptons ... my way to repair it is using a field of ellipsoids of preferred shape: emphasized three orthogonal axes in each point of spacetime, vacuum dynamics is SO(3):
- we can perform three types of topological charge - leptons (hedgdehog of one of 3 axes - because of living in 3D),
- while performing hedgehog by one axis, we need to align the second axis on a sphere - hairy ball theorem says it cannot be done - the simplest charge requires also magnetic type of singularities - spin...
slides: https://dl.dropboxusercontent.com/u/12405967/soliton.pdf
"essay": http://fqxi.org/community/forum/topic/1416

However, this thread was supposed to understand mainstream physics - is electron really a perfect point there?
Some counterarguments:
- infinite energy of electric field of point charge, while we know that 2 x 511keV is sufficient to create electron+positron pair from nothing (energy),
- we know from experiments that alpha ~ charge^2 is decreasing for high energy collisions (running coupling) - suggesting that effective charge is reduced very close to particle,
- ultraviolet divergence in QFT - bounding maximal frequency and so minimal length,
- series in QFT are usually divergent (asymptotic) - we need to cut the summation of Feynman diagrams/scenarios, what kind of means that there is not enough space for too complex scenarios - that particles take some space ...
What are other counterarguments for electron as a perfect point?
How to understand above assuming a perfect point particle?

Not being a perfect point doesn't require anything exotic like electric dipole moment - only for example what is suggested by running coupling: that maybe e.g. E ~ q(r) / r^2, where q(r) effective charge is practically constant for r>r0, but drops to zero for r -> 0 to prevent infinite energy.
A similar effect is vacuum polarization in mainstream physics.
In soliton particle models (e.g. Faber's), this effective charge q(r) is reduced due to activation of Higgs-like potential (preferring unitary vectors): to prevent infinite energy, electromagnetism is "deformed" into other interactions (weak/strong).

 

goofy bullshit even for you. Extremal goofy.

 

With respect James, this isn't nonsense. That first picture is based on one by Maxwell:

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And check out Dirac's belt on Mathspages : "In this sense a Mobius strip is reminiscent of spin ½ particles in quantum mechanics, since such particles must be rotated through two complete rotations in order to be restored to their original state." It's the Dirac wave equation, not the Dirac point-particle equation. What Jarek is referring to relates to The Infinity Puzzle by Frank Close. Please don't allow trolls and quacks to get in the way of an interesting physics discussion.

 

Which is why he asked you to go to the alternative or pseudo section.

 

Not really. There's some resemblance, and in electromagnetism people talk about the curvature of a fibre bundle, but there are no actual fibres in any real sense. All we're dealing with is field.

No. It resembles the electron, not the neutrino, but it isn't a very good resemblance. As for topological charge, it's there once you know how to see it: you apply a chiral "winding" to a field variation to end up with a standing field. Gamma-gamma pair production isn't magic.

Yes, see electron magnetic moment on Wiki. The electron "behaves like a tiny bar magnet". A bar magnet is like a solenoid. A solenoid is like a current loop. Look at the Poynting vector for a static field:

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"While the circulating energy flow may seem nonsensical or paradoxical, it is necessary to maintain conservation of momentum. Momentum density is proportional to energy flow density, so the circulating flow of energy contains an angular momentum".

This is why the Einstein-de Haas effect demonstrates "that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics".

Yes, it's topological. Google on electromagnetc geometry.

That doesn't sound right. The electron has an electromagnetic field.

Again, that doesn't sound right.

It can be done with a hairy torus.

No it isn't. You can diffract electrons. A whole wealth of scientific evidence says the electron is not a point-particle. And it's quantum field theory, not quantum point-particle theory. The notion that the electron is a point particle is pseudoscience trash.

All points noted.

The electron's field is what it is. It isn't some speck that has a field, it is field. That's why you cannot separate the electron from its field. Saying the electron is a point particle is like hanging out of a helicopter probing a whirlpool with a bargepole and saying "I can't feel the billiard ball, it must be very very small".

That doesn't sound right either. IMHO you should try to avoid wandering away from hard scientific evidence. Bringing up some guy's speculative theory is a distraction from the wave nature of matter.

 

Farsight, your pictures are similar to of topological charge, like in 2D:

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They are used for example for quantization of magnetic field in supreconductor (fluxon/Abrikosov vortex) - there are also 3D analogues which dynamics is very similar to of electric charge, including 1/r^2 Coulomb attraction (see Faber's papers).

However, let us please focus here on the question: accodingly to mainstream physics, is electron a perfect point?

 

Jarek: no.

Mainstream physics says you can diffract electrons. Mainstream physics tells you about quantum field theory and field excitations and Compton wavelengths and the wave nature of matter. Not about quantum point-particle theory and the point-particle nature of matter.

The people who do, are cargo-cult quacks who will also tell you about SUSY and branes and the fabulous amplitudehedron. Which is why they have lost the respect of the public and politicians, and other physicists too. And that's why in the USA, particle physics is history.

 

That is of course exactly wrong except where Farsight tries to claim that there is a mainstream quantum field theory of the electron.

The simplest mainstream quantum field theory of the electron is called quantum electrodynamics, QED for short. It assumes there is a four-component massive electron-positron field \(\psi\) and a massless photon field which can be represented by its vector potential \(A\).
The equation governing the mechanics of just electrons is \(\mathcal{L}_e = i \bar\psi \gamma^\mu \partial_\mu \psi -m \bar{\psi} \psi \) tells us electrons are spin-1/2 and obey Pauli's exclusion principle. The equation governing the photon field is \( \mathcal{L}_p = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\) where \(F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \) just like in classical electromagnetism. In this formalism, an electron or a photon is just a disturbance in the respective fields that carries energy and momentum.

Finally there is an interaction between the two fields proportional to the charge of the electron: \(\mathcal{L}_i = - e\bar{\psi}\gamma_\mu A^\mu \psi \). This term says that at a specific place and time — a point in four-space — the energy and momentum of the photon field is coupled that of the electron-positron field. There is no non-locality, no size term. The magnetic moment of the electron comes only from its intrinsic spin and that term, not from any extra elements.

The whole of quantum electrodynamics is the treatment of the Lagrangian of the coupled fields: \(\mathcal{L} =\mathcal{L}_e + \mathcal{L}_p + \mathcal{L}_i\). There is no size term for photons or electrons. What phenomena Farsight raises (but does not argue) as evidence of non-pointlike electrons are only evidence of a finite value of Planck's constant.

So in ignorance of the true nature of the electron, current mainstream physics makes the most natural assumption of the size of the electron consistent with observation: the electron is point-like. The theory is one of fields — but fields interacting at points.

 

Rpenner: how on Earth can that be "the most natural asumption" when we're talking of field excitations, and when the E=hc/λ photon has a wavelength? And when you can make electrons out of photons and diffract electrons? The phenomena I referred to aren't only evidence of a finite h. They are clear unequivocal evidence of the wave nature of matter. So your "natural assumption" isn't a natural asumption at all. It's perverse. It flies in the face of the hard scientific evidence. The lack of a size term in the QED mathematics does not make the electron magnetic moment go away. And that magnetic moment doesn't come from some mathematical term, it comes from some physics reality. And as you said yourself, a quantum bound state is a little like a high-dimensional knot of quantum field configurations. That's not a point particle, now is it?

 

I feel like rpenner, PhysBang, and I spent a good long while poking holes in this model over in this thread. As far as I know, it's still a standing challenge to produce a concrete description of your model beyond some pictures and concepts that are "like the model in some respects, but different in others."

 

It isn't "my model". I'm not some my-theory guy. I didn't invent Dirac's belt and the Dirac wave equation. Or spin ½ and electron magnetic moment. Or the Einstein-de Haas effect and the Poynting vector. Or electron diffraction and spherical harmonics. Or toroidal harmonics. What I've done here is pointed to the hard scientific evidence, and whilst you might dislike the way I combine that pictorially above, you surely cannot be denying the indisputable proof for the wave nature of matter. The holes are poked in the cargo-cult notion that the electron is some mystical point particle somehow spitting out photons. As if hydrogen atoms twinkle, and magnets shine.

 

I've only just seen your pictures. They don't look right to me I'm afraid. Heaviside developed the gravitomagnetic field as an analogy of the electromagnetic field. Try asking around for depictions of the electromagnetic field. What's interesting is that there's virtually none out there.

 

Because from the full Lagrangian we can compute to various orders of approximation the perturbation expansion of the collision of two electrons in well-defined momentum-spin states (Møller scattering), we can theoretically distinguish the scattering of electrons off point-like theoretical particles versus the scattering of electrons off things with finite distributions of electric charge density. The method goes back to Rutherford's 1911 studies of the deflection of alpha and beta particles off gold nuclei.
http://www.tandfonline.com/doi/abs/10.1080/14786440508637080 ( showing that the Gold nucleus has a charge radius of not more than 34 fm, later experiments would place it closer to 7.5 fm)
http://arxiv.org/abs/nucl-ex/0310008 (modern paper on the charge radius of the proton, covering some of the details of model sensitivity to the shape (and not just size) of the charge distribution and extrapolation to the \(q^2=0\) approximation of finite size and no shape information)
http://journals.aps.org/prc/abstract/10.1103/PhysRevC.90.015206 (2014 article on e-p measurement of the proton charge radius)
Since the electron gives no such finite size effect, within current experimental limits, the knowledge of the electron's charge radius is somewhere in the range \(\left( \, 10^{-22} \, \textrm{m}, \; 0 \, \right]\). As there is no experiment which gives a lower bound on the charge radius of the electron and therefore we don't even have an order of magnitude estimate, the most sensible model-independent approximation of human knowledge of the electron's charge radius as a single number is 0.
http://iopscience.iop.org/article/10.1088/0031-8949/1988/T22/016/meta (1988 article explaining how finite size effects can be ruled out above \(10^{-20} \, \textrm{cm}\).)

You can't just arithmetically average the experimental upper bound with the theoretical lower bound of zero because that is averaging ignorance with knowledge and the resulting number of \(5 \times 10^{-23} \, \textrm{m}\) is sensitive only to the ignorance, not the knowledge. Alternately, the geometric average of a finite number and zero is zero. The precise statement of giving the empirical knowledge as bounds is preferred, but if you need to pick a single number there is no empirical justification to select a number distinct from the QED assumption of 0.

All photons are excitation of the same field, therefore if the photon is said to have a radius then that same radius must apply to radio waves and gamma rays equally. Thus the momentum-dependent wavelength (which in turn is dependent on a choice of a standard of rest) cannot be equated with some hypothetical co-variant radius of the photon.

You can't "make electrons out of photons" in the same sense that you can make a sandwich out of bread, butter (I'm meeting you half-way, you British self-promoter), and meat. QED says the electron and photon fields are distinct except for the interaction term in the Lagrangian. To claim that the best summary of human knowledge is that electrons are formed from photons requires production of a mathematical model for predicting the behavior of free and bound photons which does at least as well at predicting the behavior of photons and electrons as QED. Since the Standard Model improves on QED, it represents a higher bar to meet.

The QED predictions related to the empirically observed electromagnetic pair-production are calculated from the interaction term without assuming that electrons are made of photons or that either has finite size.

This is a phenomena related to the probabilistic nature of finding a point-like electron as controlled by the QED-described Dirac field. It's not a classical effect and cannot be related to a specific finite size of the electron.

Finite h and the wave nature of particles (not just matter) are the same damn thing. Planck's constant quantizes the action (in units of Joule-seconds) and requires that position and momentum probability distributions be related by Fourier transforms just like the frequency-time Fourier transforms relate two descriptions of the same time series.

These are empty claims. Now is the time when you should be making formal arguments for your position based on the evidence rather than just nakedly asserting your untutored opinions represent the state of human knowledge.

1) there is a physical reality, 2) physical electrons have a well-measured physical magnetic moment 3) Quantum Field Theory assumes particle fields are relativistically co-variant which means that Wigner's classification of the Poincaré group associates mass eigenvalues with well-defined spin states 4) thus a theory of electrons as spin-1/2 massive Dirac spinors in QED is theoretically permissible based on QFT's underpinnings 5) QED's only coupling between the electron field and the electromagnetic field is via a term proportional only to the electron's charge, not an independent measurement of its magnetic field. 6) Therefore the precise agreement between the measured electron magnetic moment of \(2.0023193043617(15) \, \frac{e h}{4 \pi m}\) and the theoretical expansion in the perturbation expansion \( \left( 2 + \frac{e^2}{ 2 \pi \varepsilon_0 h c} + \dots \right) \, \frac{e h}{4 \pi m}\) is a rigorous test of the mathematical assumptions underlying QED.

https://en.wikipedia.org/wiki/Precision_tests_of_QED
http://lmgtfy.com/?q=(electron charge)^2 / ( 2 pi * electric constant * planck's constant * c)

Electrons in QED are not bound states. Your citation of authority (me) is inapposite (incorrectly used).

 

Yes, there is an entire page related to an imperfect analogy of a spinor, but no actual spinor math.

http://www.mathpages.com/home/kmath619/kmath619.htm

That's not Maxwell's illustration of the electromagnetic field. That's Maxwell's illustration of vector fields with non-zero divergence and non-zero curl from the near the end of
J.C. Maxwell, “Remarks on the mathematical classification of physical quantities” Proceedings of the London Mathematical Society, Volume 3. London Mathematical Society, 1871. pp. 224-232
https://books.google.com/books?id=lekKAAAAYAAJ&pg=PA231
http://www.clerkmaxwellfoundation.org/MathematicalClassificationofPhysicalQuantities_Maxwell.pdf

You have cropped the images to remove their original captions. You have failed to cite the specific paper to deprive them of their original context.

 

This is at odds with pair production, Compton wavelength, magnetic moment, etc, and it's the wrong inference. Like I said above, it's like hanging out of a helicopter probing a whirlpool with a bargepole and saying "I can't feel the billiard ball, it must be very very small".

That isn't sensible at all. There no known finite size effect, that's all. You don't know the size is zero. You might just as well throw rocks at an elastic band and declare that because there's no tripartite pattern to the way they bounce back, the length of the elastic band is zero.

Agreed. That would be stupid too.

Yes there is. Electron diffraction and the electron Compton wavelength.

Photons don't have a radius.

Pair production says you can make electrons (and positrons, which I won't mention again) out of photons. This is experimental fact.

No it doesn't. All I have to do is point to that experimental fact. Electrons are formed from photons.

It doesn't matter. You start with photons, you end up with electrons. Ergo electrons are formed from photons, quod erat demonstrandum. That's QED for short.

No it isn't. Electron diffraction refers to the wave nature of electrons. It's an aspect of electron optics. You know, like Ehrenberg and Siday's 1949 paper? The one that predicted Aharonov-Bohm effect? It was called The Refractive Index in Electron Optics and the Principles of Dynamics. Electrons shown as plane waves going past the solenoid are retarded on one side and advanced on the other, see figure 2, so the interference fringes shift as per figure 3:

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And when you do an optical Fourier transform you see something pointlike, but the plane wave is not some point-particle.

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These claims are based on scientific evidence and bona-fide physics. They aren't "untutored opinions".

Only the interpretation is deficient, and photons couple to each other. Pair production does not occur because pair production occurred.

So we can't rely upon your authority, so you've just hoisted yourself with your own petard again! Take this from me repenner, it isn't authoritative, but I think it will be: electrons in reality are bound states. The electron field is a "bound state" of the photon field. There is no magic. One excitation doesn't magically pop out of existence whilst the other one pops in.

Now if you don't mind this is Jarek's thread, so I'll take a back seat for a while. If you want to talk about this stuff in details please start a separate thread.