electron g-factor

[zenakuten]

I've never really understood particle spin. Everything I read seems to be ambiguous. Macroscopic evidence of particle spin can be seen in the Einstein-de Hass effect, which is quite cool.

Particles with spin have angular momentum, yet particles are dimensionless according to QM, which is a paradox. No matter how fast you rotate something around an axis, the axis itself never rotates, therefore a dimensionless particle cannot rotate. There is nothing *to* rotate. So how can it have angular momentum? The standard model states spin is an intrinsic property, which IMO is kind of a big hand wave over the underlying mechanism.

Upon researching spin, I came across the electron g-factor, which is related to the gyromagnetic ratio of an electron.

"Consider a charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment and an angular momentum on account of its rotation. It can be shown that as long as its charge and mass are distributed identically (e.g., both distributed uniformly), its gyromagnetic ratio is"

Y= (q/2m)

but for the electron it is
Ye = (q/2m) g

g = 2.0023193043617

g is a correction factor that does not have a classical correlation.

My complaint about the gyromagnetic ratio equation for the electron is it assumes 360 symmetry. The electron has spin 1/2 suggesting 180 symmetry. In that case, the (q/2m) portion of the equation is wrong. It represents a spherical charge and mass, but that's not true of 180 symmetry.

If the electron is not spherical, but instead oblong or some other shape, then g could equal 1 in the electron equation as would be expected in the classical sense, depending on the shape of the charge/mass (not (q/2m)). I know it's heresy to talk of particle shapes, but it seems like there is something very wrong about the electron g-factor.

[MSimon]

Maybe string theory explains it. Then you might have something like the electron g string value. ;-)

In any case you might want to put your question to Lubos Motl at the Reference Frame blog. Tell him I sent you. Also mention you are a Polywell fan. He ran Roger Fox's video about a year back.

[BenTC]

I read this on wikipedia:

While an electron-positron virtual pair is in existence, the coulomb force from the ambient electric field surrounding an electron causes a created positron to be attracted to the original electron, while a created electron experiences a repulsion. This causes the two charged virtual particles to physically separate for a brief period before merging back together, and during this period they behave like an electric dipole. The combined effect of many such pair creations is to partially shield the charge of the electron, in a process called vacuum polarization. Thus the effective charge of an electron is actually smaller than its true value, and the charge decreases with increasing distance from the electron.[75][76] This polarization was confirmed experimentally in 1997 using the Japanese TRISTAN particle accelerator.[77]

So...
a. Is it generally accepted to work like that?

b. Do the virtual particles have mass?

c. Would these virtual particles cause the charge to be offset from the mass?

d. At relativistic speeds, would this offset be stretched out?

e. What is the orbital speed of an electron?
http://www.newton.dep.anl.gov/askasci/c ... m03980.htm[/quote]

[KitemanSA]

BenTC,

Given enough eyeballs, all bugs look kind of gross!

[zenakuten]

I think you are right about string theory explaining it. I will check out the Reference frame blog.

This always seems to happen to me. Just when I think I've thought of something new, I find it's been thoroughly debated and mathematically proven/dis-proven hundreds of years ago. Yesterday I was thinking about an alternate configuration of the original cyclotron, then discovered I just re-invented the synchrotron. Sigh.

e. What is the orbital speed of an electron?

I recall my high school physics teacher mentioning the lowest orbital electron in an atom orbits the nucleus at about 1/3 the speed of light, but without an actual reference for me to give you I'd take that with a grain of salt.

[D Tibbets]

...
I recall my high school physics teacher mentioning the lowest orbital electron in an atom orbits the nucleus at about 1/3 the speed of light, but without an actual reference for me to give you I'd take that with a grain of salt.

With a Google search I found an orbital speed of an electron in the lowest orbital of a hydrogen atom to be ~ 2 million meters/ sec. in a simple Bohr model.

Compare this with the reported 10 million meters/ sec. speed of an electron in a 10KeV potential well like that of WB6 (Bussard mentioned this, though I do not know if it represented the speed of the electron after the initial 10,000 volt acceleration or if it is the average speed of the electron as it travels back and forth within the Wiffleball).

Dan Tibbets

D Tibbets

[chrismb]

I'd just be guessing, but wouldn't the speed [kinetic energy] of an electron in its lowest orbit about a proton be 13.6eV?

So that'd be (assuming non-relativistic 2E=mv^2); v=SQRT(2x13eV/9.1E-31kg) = 2186km/s .

That same 13.6eV can be drawn equivalently to a frequency of E/h = 3.28E15 Hz, which defines its orbit as a radius of 1E-10m .

[BenTC]

BenTC, Given enough eyeballs, all bugs look kind of gross!

Quite true biologically. Perhaps the context is too obscure and its time for a new sig.
I meant it like this: The Cathedral and the Bazaar, Eric S Raymond (see point 8)

[gblaze42]

I've never really understood particle spin. Everything I read seems to be ambiguous. Macroscopic evidence of particle spin can be seen in the Einstein-de Hass effect, which is quite cool.

Particles with spin have angular momentum, yet particles are dimensionless according to QM, which is a paradox. No matter how fast you rotate something around an axis, the axis itself never rotates, therefore a dimensionless particle cannot rotate. There is nothing *to* rotate. So how can it have angular momentum? The standard model states spin is an intrinsic property, which IMO is kind of a big hand wave over the underlying mechanism.

Upon researching spin, I came across the electron g-factor, which is related to the gyromagnetic ratio of an electron.

"Consider a charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment and an angular momentum on account of its rotation. It can be shown that as long as its charge and mass are distributed identically (e.g., both distributed uniformly), its gyromagnetic ratio is"

Y= (q/2m)

but for the electron it is
Ye = (q/2m) g

g = 2.0023193043617

g is a correction factor that does not have a classical correlation.

My complaint about the gyromagnetic ratio equation for the electron is it assumes 360 symmetry. The electron has spin 1/2 suggesting 180 symmetry. In that case, the (q/2m) portion of the equation is wrong. It represents a spherical charge and mass, but that's not true of 180 symmetry.

If the electron is not spherical, but instead oblong or some other shape, then g could equal 1 in the electron equation as would be expected in the classical sense, depending on the shape of the charge/mass (not (q/2m)). I know it's heresy to talk of particle shapes, but it seems like there is something very wrong about the electron g-factor.

Ok I've always thought an electron was a point source as it is considered a 1 dimensional object and in this case, spin is a intrinsic property that only is written like angular momentum, emphasis on "like"!

[flying_eagle]

Consider General Relativity. Electrons are not a point with zero or infinitely small dimension. They have a finite size in space (they occupy space) because of normal mass and they curve space due to that mass. They do not live below their schwartzschild radius. These are not infinite densities of mass and are not black holes with singularities. Since electrons occupy physical space, electrons do not physically spin as that would require it to rotate faster than the speed of light for it's size and angular momentum. BTW, Spin (of 1) angular momentum is also carried by photons of zero rest mass. I'm still studying how this object and that of the photon truly do exist in space with wave and particle properties. I for one agree with the big handwaving of QM on many of its issues. Like what happens between when a photon or electron is emitted and detected (unknowable, I think not!) QM has problems still, although few believe so. Additionally, they look for relief in strings and quantum theories but to date they still don't reconcile well with GR and its predictions with most of them already confirmed. Yet, until we find better, it is hard to replace QM since it works so well. You may find interesting the implications of this experiment called a delayed choice quantum eraser: http://arxiv.org/PS_cache/quant-ph/pdf/ ... 3047v1.pdf

[MirariNefas]

Ok I've always thought an electron was a point source as it is considered a 1 dimensional object and in this case, spin is a intrinsic property that only is written like angular momentum, emphasis on "like"!

This is my understanding. The way I learned it, electrons can be described by several quantum numbers. One of those numbers can have two different values even when an electron has the same energy, and allows two of these electrons to occupy a given position/energy level in an atomic orbit. They called one number up and the other down because it was easier to remember that way. Thus we have spin up, and spin down.

As far as I know, they could have called it heads and tails.

[gblaze42]

Ok I've always thought an electron was a point source as it is considered a 1 dimensional object and in this case, spin is a intrinsic property that only is written like angular momentum, emphasis on "like"!

This is my understanding. The way I learned it, electrons can be described by several quantum numbers. One of those numbers can have two different values even when an electron has the same energy, and allows two of these electrons to occupy a given position/energy level in an atomic orbit. They called one number up and the other down because it was easier to remember that way. Thus we have spin up, and spin down.

As far as I know, they could have called it heads and tails.

Agreed, though my chemistry is weak after all these years. I do remember some S-orbital's and P- orbitals, vaguely.
What causes more confusion is when you have an aggregate of free space electrons that are "spin polarized".