Spin

[Schneibster]

Spin is an interesting topic.

It isn't "rotation" the way we normally think of it; but it obeys the same rules. The big difference between the degree of freedom we call "spin" or more properly "spin angular momentum" in quanta, and the ordinary angular momentum of macroscopic objects, is that quantum spin is subject to Heisenberg uncertainty. What that means is, if you positively determine the spin of a quantum on one axis, you cannot determine the spin on another. Unlike position and momentum, the most commonly cited conjugate variables under uncertainty, spin isn't more or less precisely determinable- you either know it all, or you know nothing. On a given axis, you determine the spin of a photon as "up" or "down." Those are the only possible values, and they are discrete, not continuous like position and momentum. So if you know the spin on one axis, you cannot know it about any other at the same time.

Polarization is basically spin-sorting. What you do is interpose a material, generally crystalline, that interacts differently with photons based on whether their spin is up or down based on the axis of optical activity in the material, into a beam of light. Photons either pass or are scattered. The ones that pass are the ones that are measured to have the spin the material selects for. A polarizing crystal actually creates two beams; one all spin up when measured in the optical axis of the material, the other spin down. These are called the "ordinary" and "extraordinary" rays. In polaroid film, the extraordinary ray is suppressed; so you get photons that have the same spin when measured in the optical axis of the polarizer. Note that because of uncertainty, this says nothing about their spin in other axes; however, it does affect the probability of what spin will be measured in other axes, such that it varies as the cosine of the angle between the two axes of measurement. In other words, at a right angle, the probability is zero that any photon will have the same spin as was previously measured; at an angle of zero or a full angle, two right angles, it is one.

Now, since angular momentum is conserved, if you then measure their spin in another axis, you'd think you'd know it in two axes. But that is not the case. In fact, finding it in a second axis removes the knowledge previously gained of the spin in the first. This can be demonstrated using three npolarizers, as follows:

Take two polarizers. Put them on an optical bench, with their axes of optical activity pointing in the same direction. Most of the light gets through. Now rotate one of them through a right angle. Most of the light is blocked. Now take a third polarizer, oriented at 45 degrees to both, and put it in the middle. Some of the light now makes it through. How did this happen? When the third polarizer was inserted, another measurement, in a different axis of spin, "threw out" the original measurement by the first polarizer; the probabilities are now recast, as the cosine of the angle from the second measurement, not the first. Now the photons' spin in the axis at a right angle to the axis of optical activity of the second polarizer no longer has a probability of zero- the probability is changed to the standard distribution by the presence of the third polarizer. This effect can only be explained by quantum mechanics. It has no classical physics analog.

Now, note that an object without mass moving at the speed of light can only have one kind of spin- longitudinal. It cannot have transverse spin, because if it did, one side would be going slower than the speed of light- impossible for a massless particle- and the other would be going faster- impossible for anything. So when we say the spin is "up" or "down," what we're really saying is that the side of the particle that we're measuring is going up- supposing that it is moving to the right, this indicates left-handed longitudinal spin- or down- indicating right-handed longitudinal spin. Where this gets weird is, if we look at the particle at one angle, we can find whether it is "up" or "down," but if we do we cannot say what we will find if we look at any other angle simultaneously. In fact, it is an axiom of quantum mechanics that we cannot successfully look at it from two different angles at once. And it's not even that it has a value that we can't see- the simple polarization experiment above shows that it doesn't have a value in any other viewing angle but the one we looked at. If we later measure it in another angle, we'll get the probability we'd expect of a random distribution.

Now, when we talk about matter particles, the case is far more complex. They, of course, can spin transversely to their direction of propagation, because they are not limited by having to move at lightspeed, no more, no less. Their spin is therefore far more complex. But it is subject to the same uncertainty relation.

Spin is an inherent property of all quanta. Spin zero is not "no spin." It is a bosonic (whole number) spin, and a quantum that possesses it is a boson, subject to the Laws of Spin and Statistics for bosons, which include an associative principle that is the opposite of the Pauli exclusion principle that makes fermions (half integer spin particles) "exclude" one another and form finite-sized aggregations we call "matter." Bosons can exhibit coherence, the opposite of exclusion, and the bosonic quanta are mostly massless, and mostly are the exchange particles of the forces; photons, gravitons, weak bosons, and gluons are all bosons. All but the weak bosons are massless and move at the speed of light at all times.

Spin angular momentum isn't spin; it's the quantum essence of angular momentum, and a particle doesn't rotate, it has spin. This is unaffected by time dilation. Both massless and massful particles have spin. But it was a good guess.

[maiforpeace]

[apophenia]

Cool. Thanks Schneibster. I don't care what 'Zilla says about you, you're alright in my book.



Seriously though, thank you. It is fascinating. Do you believe in the graviton, or, perhaps, that in order to bring gravity under the umbrella, a new framework that is neither relativistic or quantum mechanical will be required?

[Gawdzilla Sama]

I need a spin doctor. And apophenia needs a firecracker up her ass. Just sayin'.

[Schneibster]

Cool. Thanks Schneibster. I don't care what 'Zilla says about you, you're alright in my book.

Seriously though, thank you. It is fascinating.

You're welcome. You reminded me of it and I've gotten part of it; there are a few others out there, I'll grab them in time as I remember them.

Do you believe in the graviton, or, perhaps, that in order to bring gravity under the umbrella, a new framework that is neither relativistic or quantum mechanical will be required?

It's pretty clear that the exchange boson of gravity has to be spin-2 and massless. It's also pretty clear that an individual graviton has to be damn near indetectible. I favor direct outgrowths of relativity, like string physics or rather brane physics as some of them are calling it now, anyway that line of inquiry, over the others, though I would never say that research into alternatives should be abandoned until it has been milked dry. I think we all know the lessons of forgotten vistas of math suddenly becoming the most important thing in the world too well to say that. But I expect a stringy sort of answer to show up.

Such "new framework" stuff likely already has been found; what we're working on is a way to test it. And some better math to try to understand what it means and how to manipulate it.

[JimC]

In the classical representation of electromagnetic radiation, it was seen as a combination of orthogonal magnetic and electric fields, vibrating together as they moved through space as paired transverse waves. Maxwell's equations did a beautiful job of describing them as linked phenomena, with the speed of light emerging as a given. In terms of polarisation, it was the orientation of the electric field that was critical.

In quantum terms, the spin of a photon (up vs down) seems to be the equivalent of vertical vs horizontal orientation of the electric component of the classical wave model...

[devogue]

I have no fucking idea what this shit is about but I am horrendously sunburnt, enormously happy, and I feel like fucking a tight assholed favelo begotten Brazilian. (Lozzer say: ) . So fucking bravo to my favourite schneiby type thing.

[Schneibster]

In the classical representation of electromagnetic radiation, it was seen as a combination of orthogonal magnetic and electric fields, vibrating together as they moved through space as paired transverse waves. Maxwell's equations did a beautiful job of describing them as linked phenomena, with the speed of light emerging as a given. In terms of polarisation, it was the orientation of the electric field that was critical.

In quantum terms, the spin of a photon (up vs down) seems to be the equivalent of vertical vs horizontal orientation of the electric component of the classical wave model...

Magnetism is actually the relativistic correction for the electric force.

When you get to thinking about a moving charged particle passing another, motionless, "observer" particle, what happens is that the impulse of the electric field moves at the speed of light. This means that the vector of the force that the observer particle feels does not point toward (or away, if the charges are like) to the place where the moving particle is now, but where it was one lightspeed delay ago. If you think about the geometry as the particles move toward closest approach a second component will be introduced to the force from the observer particle's POV. This second component will point in the opposite direction of the movement of the moving particle, perpendicular to the direction of the main force vector on the observer particle and smaller in magnitude.

This force, opposite the motion and perpendicular to the electric force, is magnetism. Note that what was merely a correction for the speed-of-light delay of the electric force appears to have become a separate force; really, it's not though, it's just a correction to what we should expect the electric force to do if it were instantaneous. So physicists speak of the "electromagnetic force."

Now, both of these can interact through spin of the particle. Charged particles are a charge monopole; that is, a single charged particle has no "positive" and "negative" pole, it is one or the other. If this particle were to classically spin, then it would generate a magnetic field; think about the moving charges from the magnetism discussion above, then think about it spinning in a circle and you'll see why there has to be a magnetic field associated with it. Of course, these particles are quanta; so they can't have classical spin, they have to have quantum spin. Quantum spin means that on average over time, you can measure the particle having turned a certain amount per unit time. But if you keep measuring it again and again, you'll just get a random collection of turn amounts, without seeing a progression that you'd call "turning." It's a quantum; they don't do that. But it still averages out as if they had, and in fact we can and have measured the magnetic field that results from the speed-of-light correction to the electric force, emanating from charged particles.

That's how spin and electric charge combine to create a magnetic field around an electron to go with its electric field. If it had no spin, there would just be a pure electric field; no magnetism.

Finally, the sort of relation between classical spin and spin angular momentum also applies to the orbitals of electrons. And that is the source of classical magnetism; the same sort of "twist in space" that gets created because of the spin angular momentum, but this time it's closer to classical spin because it's the whole particle moving in an orbital rather than turning on its own axis. But it's still not a thing you can find by measuring the position in the orbital over and over again; you'll just get a random set of positions. But the magnetic field is there, and tells you that those positions average out over time to an orbit, sort of (orbitals are plane waves, which is more than I want to take on this evening), thus creating the situation that requires the correction, and thus creating a magnetic field to go with the electric one.

That's why we always say there's an electric field and motion associated with every magnetic field.