Subatomic spin, etc.?

[gonegahgah]

The transfer of energy between modes of rotation and vibration are quite well understood: the branch of thermodynamics deals with it at atomic levels, and the effect of tidal drag etc is how it happens at a planetary scale. A planet in four dimensions has two independent rotations, which would, for a fairly spherically symmetrical planet, settle down into a clifford-style rotation, where every point on the surface goes around the centre, since this equalises the energies in the different modes of rotation.

Hi Wendy. Just wondering if you able to help me with the subatomic world and its relation to spin? (The topic of spin really interests me).
You understand some very complex things so I'm guessing you would understand an impressive amount of today's physics (certainly against my understanding)?

I'm not sure I've been able to find an explanation for why electrons shooting across a magnetic pole deviate left or right (direction depending on whether the pole is south or north).
My understanding is that physics states that subatomic spin is just a property and is not related to actual spin? Or have I got that wrong?

Actual 'spin' would, to my current thinking, provide a simple explanation for why an electron moves left or right; instead of towards or away from a magnetic pole but, if not spin, is there some other explanation for the lateral, rather than direct, movement that occurs?

[wendy]

Electrons move to the left or right across a magnetic pole, largely because of fairly ordinary physics (F = qv×B). q = -1e (charge), v=velocity, and B is the magnetic flux, which reverses if you use a S pole, rather than a north pole. Spin has nothing to do with it.

A similar thing is the 'hall effect'. You can tell what kind of charge carries the current, because if you put a thin slice of conductor, like Al, and put a magnetic field across it, then F = qv×B still holds, but qv is the general current carrier and velocity, the current carrier will accumulate on a particular size, because if q is negative, v is negative, and if q is positive, v is positive. So whatever is carrying the current will accumulate on a given side.

In some metals, the current carrier is not 'electrons', but 'holes'. A hole can be thought of as a bubble in the sea of electrons, and effectively carries a positive charge (since an electron would fill it, has a negative charge).

Spin is a term used for subatomic particles, to determine whether they are bosons or fermions. These are terms relating to 'thermodynamics'.

A boson obeys 'Bose-Einstein' statistics and have integer spin. This is pretty much what you normally expect of gases for example, that you can have any number of particles at the same energy level. So at absolute zero, all of the bosons have stopped moving. Particles like the He^4 are bosons.

A fermion obeys 'Fermi-Dirac' statistics, and have integer-half spin. This means a gas would behave differently to what you normally expect, in that each particle of the gas must occupy a unique energy level. The layers in the electron shells of an atom, for example, are because electrons can only occupy unique states, and you get a +1/2 and -1/2 spin, in each possible orbital. The different orbitals are solutions to Schrodinger's wave equation, and the order of layers can be guessed at from the periodic table of elements.

Spin is not as you might concieve it, as a rapidly spinning particle. Instead, it has a density-2 solution. This means if you got an electron, and looked at it, and turned it around, you would have to turn it 720 degrees before you get back where you started from. It's weird.

[gonegahgah]

Thanks Wendy. The last bit does sound strange.

With the math, how does that relate to physical effect?
A magnetic field spreads away from one pole to the opposite pole in all directions out from the pole ends.
I'm not aware of the magnetic field having a left-ward-ness or a right-ward-ness.

So what physically causes an electron travelling toward a South pole to veer left; and if travelling toward a North pole to veer right.
Magnets tend to have pull towards or push away effect ordinarily for metals. I'm wondering why physically there is instead a cross stream effect in the electrons case?

[wendy]

Electrons veer to one direction in a magnetic field, because magnetism is a curl-force that acts on charge and velocity. If you feed positrons in there, they veer the opposite direction. The colorisus effect, which makes cyclones and hurricanes rotate in different directions, is a curl-force caused by the rotation of the world, the different directions are becasue cyclones are on the south end, and the hurricanes are on the north.

[Klitzing]

... The colorisus effect, which makes cyclones and hurricanes rotate in different directions, is a curl-force caused by the rotation of the world, the different directions are becasue cyclones are on the south end, and the hurricanes are on the north.

Haha, Wendy and the typos. - She meant "Coriolis" here. Cf. http://en.wikipedia.org/wiki/Coriolis_effect.

Btw. the Lorentz force you also would find in Wikipedia, cf. http://en.wikipedia.org/wiki/Lorentz_force.

The important ingrediant here is the cross-product, aka vector product. This is a relation which asigns to 2 vectors a third one, which is orthogonal to both original ones. (The orientation here depends on the sign of the charge.)

The angular momentum e.g. is such a quantity. Consider a spinning whirlgig. Being slightly slanted, the gravitational force would ask for a straight drop down. Instead its spinning axis would move to the side.

Most probably you were originally just mixing up "spin" with spinning. The former is a mere quantum mechanical quantum number. Cf. http://en.wikipedia.org/wiki/Spin_(physics).

--- rk

[wendy]

not typos, real mangles. Anyway, thanks.

I'm getting a novel by l.a. lorentz in to have a bit of a read about. It's supposed to be the first book to use the heaviside-lorentz units in pretty much their modern form, but apparently h. hertz used them too.

still trying to figure out what a math is. it's supposed to be a latex command to put maths into text documents or something.

[Klitzing]

sometimes it really boils down to that.
But then, what were mathematicians at all doing, before the aera of computers (and latex)?
--- rk

[gonegahgah]

Most probably you were originally just mixing up "spin" with spinning. The former is a mere quantum mechanical quantum number. Cf.

Thanks Klitzing, I most probably was; I never thought of it that way.

So rather then saying that an electron has spin; should I say instead that something has to be spinning (or some equivalent motion) to cause the electron to travel sideways; instead of towards/away?

Whether that's exclusively the magnet internals, (or as I proposed) the electron, can then be distinguised I guess?
Can electrons be considered to be spinning (or some equivalent motion - separate from the 'spin' property given by quantum theory)?

[wendy]

mathematicians were doing maths, i suppose.

Latex is horrible and does not like thorns (þ) too much without severe training. Still have to teach it about the long hundred. Did Knuth understand a hundred is really vi score? It does not handle dates correctly. You got to write some macros to fix that.

You fiddle these dates to match the desired punctuation, and then fiddle 'heute' (it's a german word for 'today'), to get today's date in the right format. If you want any general day, you just write eg \ukdate{23}{7}{1957}. I'm thinking of adding 0-date support to it.

Code: Select all

\newcommand{\ukdate}[3]{%
  #1\space\ifcase\number #2
  \or Janruary\or February \or March \or April \or May \or June \or July\or
  August\or September\or October\or November\or December\fi \space\ #3}
\newcommand{\heute}{\ukdate{\number\day}{\number\month}{\number\year}}