## Thursday, July 8, 2021

### Electrons do Spin

There is a new PBS TV video on Electrons DO NOT Spin.

This guy is usually pretty reliable, but he is way off base here. Of course electorns spin.

His main argument is that if you conceptualize an electron as a particle, then it is hard to see how the charge distribution and angular velocity could result in the observed magnetic moment.

Okay, electrons are not classical particles. If you conceptualize an electron as a classical particle, you will have trouble with position, momentum, and everything else.

Spin is the intrinsic angular momentum, quantized.

Update: I found this explanation:

WHAT IS SPIN?

Spin is an inherent property possessed by the electron. However, it does not rotate. In quantum mechanics, we speak of an en electron as having an intrinsic angular momentum called spin. The reason we use this term is that electrons possess an angular momentum & a magnetic moment just like a rotating charged body.

DO ELECTRONS SPIN SIMILAR TO PLANETS?

IT IS MISLEADING TO IMAGINE AN ELECTRON AS A SMALL SPINNING OBJECT DUE TO THE FOLLOWING:

An electron’s spin is quantified. It has only two possible orientations, spin up and down, unlike a tossed ball.
To regard an electron as spinning, it must rotate with a speed greater than light to have the correct angular momentum[Griffiths, 2005, problem 4.25].
Similarly, the electron’s charge would have to rotate faster than the speed of light to generate the correct magnetic moment[Rohrlich, 2007, Pg 127].
Unlike a tossed ball, the spin of an electron never changes. It has only two possible orientations: spin up and down.

These arguments are just wrong.

The 1st and 4th are not true. An electron spin can be in any direction, not just up and down. If you put it in a suitable magnetic field, then it will be just up or down, but the same is true about a classical spinning charged ball.

I don't have those textbooks, but they presumably do a computation assuming an electron is a charged particle with extremely small size. But an electron is not a classical particle. While it looks like a point particle in some experiments, it also looks like a wave of concentrated fields. That wave/field is spinning.

#### 6 comments:

1. I agree with your "If you conceptualize an electron as a classical particle, you will have trouble with position, momentum, and everything else." I can't make as much contact as I'd like with your next statement, however, "Spin is the intrinsic angular momentum, quantized", although, fair enough, it makes sense to me as a fairly conventional statement about Lorentz symmetry properties of field equations in quantum field theory.

I associate spin 0, spin 1/2 and spin 1 with different classes of field equations, in which "intrinsic" spin is identifiably different from angular momentum, but there's an interplay between them that I've never found a way to think about that I've been entirely happy with. So to me it feels kinda both right and wrong to say "electrons do not spin".

1. David Hestenes has advocated for quantum realism using geometric algebra to reveal properties of spin: "A long‐standing debate over the interpretation of quantum mechanics has centered on the meaning of Schrodinger's wave function Ψ for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school (led by Bohr, Heisenberg and Pauli) holds that Ψ provides a complete description of a single electron state; hence the probability interpretation of ΨΨ* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school (led by Einstein, de Broglie, Bohm and Jaynes) holds that Ψ represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung (first noticed by Schrodinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in Ψ. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school."
https://aip.scitation.org/doi/abs/10.1063/1.3275605

"...complex numbers in the Dirac equation have a kinematical interpretation, with the unit imaginary identified as the generator of rotations in a spacelike plane representing the direction of electron spin. Thus, spin and complex numbers are shown to be inextricably related in the Dirac Theory. This leads to a new version of the zitterbewegung, wherein local circular motion of the electron is directly associated with the phase factor of the wave function. In consequence, the electron spin and magnetic moment can be attributed to the zitterbewegung, and many other features of quantum mechanics can be explained as zitterbewegung resonances."
http://geocalc.clas.asu.edu/pdf/SnarkPaper.pp.pdf

2. I do not agree that wave function (complex) phase has anything to do with spin, or that there is anything realist about the above approach.

3. Your approach isn't about science but mysticism, motivated by religious convictions about free will. I see right through you.

2. If I reductio ad absurdum ANYTHING into a number, Lo and Behold it becomes an abstraction without physicality, to the point where you are told 'Silly human, you just can't conceptualize it', which is actually true. You can't turn a number back into anything, just like you can't take a crappy MP3 sound file and turn it back into the entirety of the original sound it was sampled from. I can't tell you how human anatomy works if you just provide me with the number representing the height of the person.

This is an incredibly useful feature of numerical abstraction, with it you can turn even an entire human being into a digit which you can then easily manipulate mathematically with any disregard you wish, you can turn the largest genocide into a considerable number, Or a woman into a single notch on a bedpost, all without any inconvenient regard or moral concern.

Problem with such abstraction is, once you easily forget (and you will) that your 'number' isn't actually a number at all, you have next to no hope of understanding the actuality, context, and mechanical structure behind where the hell your numbers come from.

Galaxies spin. Galaxies spin around each other, even clusters of galaxies spin around other clusters of galaxies, All stars we have observed spin. Observed planets have spin. Atoms spin. LOOK at the goddamn picture of the Bubble chamber tracks in the lower right hand corner of the screen. Hell of a lot of spin and circular like motion going on, ya think? and now the electrons... Nope, they don't spin because that would be... inconvenient to the math and present atomic theory which is so comprehensive it still can't account for gravity or mass without a great deal of hand waving.

And still... No one is asking, bizarrely.. what makes it spin from macro to micro? What makes it go?

Mainstream Physics is just like a bunch of clown cars that drive around forever without a drop of gas, and no one asks questions for fear of smug reprimands.

3. Dear Roger, and all,

Am happy to share a *very* valuable link:

See the online and free-to-download textbook: "Motion Mountain", vol. 4 (on QM), by Christoph Schiller.

See the chapter 6, which is on rotations and the QM spin. Right in the first paragraph, the text notes a back-link which goes to p. 104 in the same volume. *Take* it! The description on p. 105 is absolutely outstanding. Then, return to chapter 6 / other topics.

I can't contain my happiness!

I have known this text for a long time, but I hadn't checked it out in years now, may be for a decade+. And even back then, when I had browsed through it, I had not checked the angular momentum related topics in it. ... Indeed, the book seems to have undergone a sea change (for the better) since I checked it last.

The ideas for the QM spin which I had come to develop independently, were *similar* to what Schiller mentions. But my ideas seem to be less developed.

Reason I didn't join this discussion earlier:

My notes on the mainstream QM have not been completed, and I didn't want to get into a blog discussion (like the present one) without having put out something concrete to which a reference can be made. The issues are, otherwise, too complex to discuss. In fact, ideally, I wanted to discuss spin only after my document on the new approach was ready. ... That's why, I had refrained from making a comment to this post.

Clarification: I have just downloaded this book, barely 1 hour ago. I have to go through the contents before I am ready to comment as to which ideas I had already (independently) developed and which ideas I now find to be extra, or new, or better presented, in Dr. Schiller's book. (Also, where, if anywhere, I disagree with him.) ... May be I will write a post at my own blog some time later, say a week or so later.

BTW, feel free to click on the animations contained in the PDF too! (Looks like animations are a part of the PDF itself, without a second trip to the servers.)

OK. Let me sign off. ... Hope the cited resource helps.

Best,
--Ajit