# What exactly is an electron?

by CF.Gauss
Tags: electron
P: 4,663
 Quote by Fastman99 This question is similar to asking what is a photon? Photons and electrons and other elementary particles are not actually little billiard balls that are flying around high speeds. They are both quantum excitations of their respective fields. The entire universe is filled with a photon field, and it's mostly empty. You can think of it as an empty EM field as well. At every point in space there is a quantum harmonic oscillator for each possible spatial frequency, and thing about quantum harmonic oscillators is that only allowed energy levels come in steps of hw. The minimum energy of the oscillator is 3/2hw in 3 dimensions, and then it goes up to 5/2hw, then 7/2 hw, etc. One step above the zero-point level is considered one photon at that spatial frequency. The photon could have a range of frequencies, and be localized in some way, or be more spread out and less localized. Just think of it of a field as an infinite set of harmonic oscillators at every point in space, and think of the particles as quantum vibrations of this field. In a similar way, there is an electron field that fills of space with a zero-point energy, and it has certain linearly quantized energy levels above the zero level that indicate the number of electrons. This explains why every electron has exactly the same mass, charge, spin, and g-factor. Saying an electron is the same thing as saying a quantum vibration of the electron field, but the latter is too wordy. The electron vibration can be localized, as in a vibration around an atom, or more spread out like a free particle, or an electron in a double slit experiment. The big difference between the electron field and the photon field is that with electron vibrations, they can't stack directly on top each other. This is described as the Pauli Exclusion rule. The electron field is a fermion field, described by the Dirac equation. Two electron vibrations can be in almost the same state very close to each other, but they can never occupy the same exact state. I like to visual all quantum particles, whether they are photons or electrons, as 3 dimensional fuzz balls, and those fuzz balls oscillate and move around and sometimes disappear according the probabilistic laws of QFT. It's the sudden collapse of the fuzz balls that's most shocking to me, (wavefucntion collapse is mysterious).
Suppose we had a 50 or 100 GeV electron beam, like SLAC or the CERN LEP accelerator, and we shot it through this field of an infinite set of harmonic oscillators, or photons. What would happen?

In the normal Compton scattering, where the electron is at rest in the Lab, above a few MeV photon energy, an inelastic Compton scattering would begin to produce real electron-positron pairs, and we would see the extra positrons and electrons. The cross section for Compton (Klein-Nishina) scattering is ≈0.665 barns (6.65 x 10-25 cm2).

Now gamma shift into the reference frame where the electrons are 50 or 100 GeV, and we should see the electrons colliding with the infinite set of harmonic oscillators or photons in the vacuum (and even with the CMB). Shouldn't we see the inverse Compton effect, with high energy gammas, and possibly even positrons comming out of the vacuum chamber? Can't we use this test to put an upper limit on the density of photons or harmonic oscillators in the vacuum?
 Mentor P: 12,022 Most of these harmonic oscillators with significant energy levels are in their ground state, which means there is no photon to interact with. High-energetic charged particles in space can interact with the CMB without problems. For protons, this leads to effects like the GZK cutoff.
P: 4,663
 Quote by mfb Most of these harmonic oscillators with significant energy levels are in their ground state, which means there is no photon to interact with. High-energetic charged particles in space can interact with the CMB without problems. For protons, this leads to effects like the GZK cutoff.
Energetic electrons interact with the CMB (cosmic microwave background) via the SZ (Sunyaev–Zel'dovich) effect. See http://en.wikipedia.org/wiki/Sunyaev...7dovich_effect. Is your "field of photons" density less than the CMB?
 Mentor P: 12,022 If you consider a volume in some object cooler than 3K and without any sources except blackbody radiation, yes.
 P: 53 A comment by P. A. M. Dirac from Proceedings of the Royal Society of London (1962) may be helpful here. Title: Particles of finite size in the gravitational field. "So from the physical point of view, the possibility of having a point singularity in the Einstein field is ruled out. Each particle (electron) must have a finite size no smaller than the Schwarzschild radius. I tried for some time to work with a particle with radius equal to the Schwarzschild radius, but I found great difficulties, because the field at the Schwarzschild radius is so strongly singular, and it seems that a more profitable line of investigation is to take a particle bigger than the Schwarzschild radius and to try to construct a theory for such a particle interacting with the gravitational field." The next larger significant size (not so strongly singular) is the radius 3Gm/c squared. This size could provide gravitational confinement without gravitational collapse to infinite (or unknown) density. This size is too small to measure.
 P: 53 If we want to know, what exactly is an electron, we need to know how electrons (and positrons) are produced (materialized). So much has been learned about this process that it is difficult to keep up. First, we know electrons are produced from photons (produced from electromagnetic energy). We know an electron can absorb a photon. This absorption is a direct conversion of photon energy to mass. Energy added to the electron increases its mass. A photon consists of equal amounts of positive and negative electric field energy. And so, we cannot materialize an electron without also producing a positive charge particle. The electron has extremely high energy density with a radius less than 10 exp -18 meters while the photon with sufficient energy to produce an electron, positron pair has a wavelength that is large, with far less energy density than the electron. A photon, when absorbed by an existing (high density) particle will become a high energy density entity. This is the first step required to produce mass particles.
 P: 5,632 As noted, nobody knows 'exactly' what any of the fundamental particle are. The best we can do so far is to describe characteristics according to quantum mechanics...spin, mass, charge, etc, whatever is incorporated in the Standard Model of particle physics....A complementary and different perspective might be afforded via string theory and that is a nice approach since it relates all the elementary particles to one another....as energy vibrations.
 P: 5,632 as luck would have it, a related string discussion is underway: http://www.physicsforums.com/showthr...13#post3981113
 P: 53 Much has been learned, and we can now discuss a limitation on the smallness of things called a "cutoff". A quote from Leonard Susskind follows: "A cutoff sounds like a cop-out, but there is an excuse. Physicists have long speculated that the Planck length is the ultimate atom of space. Feynman diagrams, even those involving gravitons, make perfect sense as long as you cease adding structures smaller than the Planck length - or so the argument goes. This was the almost universal expectation about space-time -- that it would have an indivisable, voxelated structure at the Planck scale." This is from the book, The Black Hole War (page 335). If the electron radius is equal to the Planck length or 1.616x10^-35 meter, this is much larger than the electron Schwarzschild radius and so, (at first evaluation) we may find that the electron cannot collapse to its Schwarzschild radius, 2Gm/c^2 and it cannot collapse to the larger radius, 3Gm/c^2. Another quote from Leonard Susskind follows: "But extraordinary things are happening. In recent years, we have been accumulating evidence that the machinery in the interior of particles (electrons) is not mush bigger, nor is it much smaller than the Planck length." (page 214) When the electron radius value is reduced to the Planck length (or slightly larger) due to gravitational time dilation (blueshift) and an equal amount of gravitational length contraction then the size (close to) 2Gm/c^2 is attainable.
P: 612
 Quote by Naty1 The best we can do so far is to describe characteristics according to quantum mechanics...spin, mass, charge, etc, whatever is incorporated in the Standard Model of particle physics
With the knowledge we collectively have we can probably do a lot better than that. One of the best known fundamental prescriptions of QM, Dirac's "Principles of Quantum Mechanics" describes the motion of the charge of the electron that travels at the speed of light. Why it should do that and what it means in terms of the electron's structure and observable parameters is a not-so-well-known but arguably important Physics cottage industry and there is quite a bit of literature on the subject.
 P: 53 You are so correct, there is much literature on the subject of electron structure. With careful selection from available literature, we can do a lot better. Charge motion at speed of light is necessary to explain electron angular momentum (and magnetic moment). John A. Wheeler has suggested that the electron is the result of gravitational collapse. See page 1215 in the book, Gravitation. In the book, The Enigmatic Electron, author, Malcolm H. MacGregor writes, "One electromagnetic configuration --- is a current loop formed by a rotating point-like charge." In a (2008) paper titled, The Dirac-Kerr-Newman electron, theorist Alexander Burinskii writes, "Recall that the angular momentum J = h bar/2 for parameters of electron is so high that the black hole horizons disappear and the source of the Kerr-Newman spinning particle (electron) represents a naked singular ring." We can see (in this concept) the electron size cannot be as small as its Schwarzschild radius because charge velocity greater than c would be needed to obtain angular momentum (h bar/2). The minimum radius with the charge moving at the speed of light is (3Gm/ c^2). Malcolm MacGregor has said, "It remains to this day one of the most arcane subjects in particle physics." And later, "---the spin of the electron--is a mysterious internal angular momentum for which no concrete picture is available, and for which there is no classical analog." Can we put these pieces of the electron puzzle together to create an improved electron description? I will suggest that this can be accomplished.
 P: 612 To that I'll add that Martin Rivas' "Kinematical Theory of Spinning Particles: Classical and Quantum" gives quite a thorough and integrated review of very many approaches to modeling spin, especially in the electron. Unfortunately both MacGregor's and Rivas' books are out-of-print these days.
 P: 53 I will try to find a copy of the Martin Rivas book. I am saddened to learn that the MacGregor book out-of-print. His book is very readable. This quote (page 72) points out a significant requirement. "Thus we are forced from stability considerations alone, to introduce a non-electromagnetic force that holds the electron together. If we were to consider an extremely small size for the electron, -- then gravitational forces could be invoked to solve the stability problem." Though MacGregor does not pursue this solution, a number of theorists, including Brian Greene, John Wheeler and Alexander Burinskii expect that electrons have some properties very much like a micro black hole.
 P: 612 I should probably warn that the math comprehension requirements for Rivas' book are fairly steep. He kind of starts where Ballentine's QM textbook leaves off.
 P: 1 Even in classical electrodynamics one can describe the electron as an orbiting massless charge embedded in its synchrotron radiation and obtains the fundamental properties, also the mass and the de Broglie wave. The /size/ of the mass needs quantum mechanic considerations
 P: 53 In post # 47, a minimum electron radius value, (3Gm/c^2) was noted. From this radius, a fundamental mass value is defined, using a ring shape with the angular momentum (h/4pi). The charge spins at light velocity so that the effective mass times velocity times radius will equal angular momentum. m c (3Gm/c^2) = h/4pi (m)^2 = (h/4pi) (c/3G) m = (hc/12pi G)^1/2 m = (1/2) (2/3)^1/2 (Planck mass) I suggest this mass value is the fundamental value that has a specific relationship to the electron mass, the muon mass and the tau mass. The photon wavelength that has energy to produce two particles with each particle mass value equal to (hc/12pi G)^1/2 is (3pi hG/c^3)^1/2 meter. This wavelength is: wavelength = 2pi (3/2)^1/2 (Planck length) The ratio of this fundamental wavelength to the wavelength (h/2mc) is approximately 1.025x10^-22 to one. I will suggest that this is also equal to [h/(2pi)^2] divided by (2mc^2) where the m value is the electron mass. This ratio is 1.025028393x10^-22. If these ratio values are precisely correct then the true G value must be very close to 6.671745197x10^-11. Improved experiments will determine if this is correct.
 P: 7 First off I'm no physicist but an EE. So my question might seem odd, but in light of everything that was said until now, why has nobody (except for one guy I believe) proposed string theory to try to explain what elementary particles are (electron included)? Is this because it is still an "unproven" (untested) theory? String theory seems to be acknowledged by many recognized scientists, so perhaps it is a valid one at answering the initial question: what is an electron? Btw, what a great forum this is. Just recently found it. Since then I just can't help but try to read every single posts. Waaa, I'm going crazy :)
 P: 53 Hi kended, String Theory and Quantum Gravity are well covered in the book by Lee Smolin, titled Three Roads To Quantum Gravity. Much work is needed if string theory is to accomplish its objective. A quote from the book follows: "Modern physicists try -- to explain particles in terms of fields. But this does not eliminate all problems. Some of the most serious of these problems have to do with the fact that theory of fields is full of infinite quantities. They arize because the strength of the electric field around a charged particle increases as one gets closer to the particle. But a particle has no size, so one can get as close as one likes to it. The result is that the field approaches infinity as one appraches the particle. This is responsible for many of the infinite expressions that arize in the equations of modern physics." He suggests, we may deny that space is continuous and so it is impossible to get arbitrarily close to a particle. We may also replace particles by little loops or strings. String theory is interesting but it is not yet mature enough to explain specifics such as electron mass.

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