The spin of the the electron is known as h/2.
We are told that this is not the classical spin primarily because the speed of the electron would need to far exceed the speed of light.
What is the effective speed in multiples of the speed of light that the classical model actually predicts.
This is a very important question in the understanding th dynamics of the electron.
Thank you for your answer
Is the answer by any chance closer to 137 (alpha), and could you show me your workings
I have looked at tha maths and two things are clear the equations are non sequitur
if as the author stated uB =2/3.evr^2
where uB is the electron magnetic moment, e the electron charge,v the rotation per sec and r the radius.
And presuming velocity = 2pi. r.v
. ie varying the radius does not allow the equations to match the Bohr magneton and be consistant because in one case v is proportional to r^2, and in the other v is ptoportional to r.
Am I going wrong on this point ?
The radius is assumed to be the classical electron radius.
Is there another mathamatical proof you can send
Dear colleagues,
I criticise a bit the second approach, too. In equation (1.1) there should be “>”, because the rest energy could contain something else in addition to the electrostatic potential energy. In that case there should be “
Dear all,
Hi, how are you? I like the second method just because it is neat although dear Antti gives more suggestions. Here we have supposed that an electron is a sphere with a uniform density of charge. Other assumptions may lead to better numbers but can not change the ending story. Perhaps, the electron has an ellipsoidal distribution with an intrinsic symmetry broken, who knows? The first method follows this way and calculates the surface current with the surface density of charge. But the result, 970 times the speed of light, seems a little bit confusing. But the second one gives 137, which is connected to a famous constant. Done! Usually, a direct way to calculate the relations between classical and quantum is resorted to angular momentum (action) L=mvr=hbar/2. We don't care more about the geometric shape. So I like the second derivation although both are nice. Best wishes!
Dear Lin Zhang,
You cannot avoid taking a stand on the geometric shape of the electron, if you want to calculate the speed of the electron spin. The left side of equation (1.2) of the second method, mvr is actually the angular momentum of a point mass m at a distance r from the axis of rotation. So, the second method assumes that all the charge is at a fixed distance from the spin axis!
The electron is a fundamental particle. We don’t know its shape, volume or structure. If it has no structure, it is a point-like particle with a point charge and should have no intrinsic angular momentum and no intrinsic magnetic moment at all. Besides, according to quantum electrodynamics the electron is surrounded by a polarized cloud of virtual electron-positron pairs.
The only purpose of these discussions on the speed of the electron spin is to show that the spin of an elementary particle is beyond the classical perspective.
Best wishes
Antti
@Antti
A good answer is Elman's, because it shows that at the classical electron radius, the speed the electron has to go is 1/alpha to maintain a spin of h/2- which explains why alpha is alpha quite nicely and the formula for alpha at the same time.
As you say if the electron had no structure it should not have angular momentum and no magnetic moment and yet it does, so it has some structure, it is that we can't measure it because it is too small.
I am predicting that it will be somewhere around 10-25 m.
The "speed of the electron spin" is described in Section 1 of the webpage www.tachyonmodel.com
The electron does have the following internal structure: it consists of 100 minute spheres which themselves have no knowable (i.e. on the finite level of reality) structure, so these 100 "truly elementary particles" can be called 'ultimatons'. However, I am not aware of any rigorous mathematical treatment which utilises this "ready answer" to build a serious model that corresponds to what we know about electrons (and other leptons) from experiments, or at least goes over in some approximation into the existing frameworks, such as Dirac's equation for electron and positron. Thus, such "ready" (or "revealed") answers do not give us any unearned knowledge --- we still have to work out the real theory ourselves...
The electron's charge revolves it a Compton wavelength orbit at the speed of light. You can calculate the magnetic moment in three simple algebraic equations. You can also show that the angular momentum is h_bar / 2 in three simple equations. Or, if you don't want to calculate it yourself, it is done for you www.tachyonmodel.com. (No tachyons used here, it was a website that happened to be available.)
Tigran, Preston, and others: Do you have a web page showing your answers, numbers, or models? I provided a web page for you to look at. Did any of you look at it? The charge revolves at the speed of light in a Compton wavelength orbit. It takes 3 simple algebraic equations to show that the magnetic moment is the Bohr magnetic moment, identically. It takes three simple algebraic equations to provide h_bar/2 as the angular momentum. Show us you model or how you get your numbers.
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