Quantum mechanics

KazetNagorra has said he could answer a few questions in quantum mechanics. so here goes:
1. Can you describe electron spin. Does it have a specific direction in space? Can any electron point in any given direction?
2. Is it related to the polarity of photons? Does polarity have a specific direction for any given photon?

Originally posted by twhitehead
KazetNagorra has said he could answer a few questions in quantum mechanics. so here goes:
1. Can you describe electron spin. Does it have a specific direction in space? Can any electron point in any given direction?
2. Is it related to the polarity of photons? Does polarity have a specific direction for any given photon?

I think the attribute we call spin is more like the north and south of a magnetic field than an actual physical spin. I don't think it involves an actual magnetic field but Kaz can probably shed more light on that subject. No pun intended

This is a bit of a painful question, because the answer is so abstract. In classical physics the spin of a planet, say, is really just orbital angular momentum of the material in the planet about its axis of rotation. In quantum mechanics even elementary particles, such as electrons, which should be point-like and therefore not be able to spin possess some intrinsic angular momentum. This was detected in an experiment they describe better on Wikipedia than I would here called Stern-Gerlach. The reason for this is that electrons are described by what are called spinor representations of the Lorentz group (See spin (physics) and spinor on Wikipedia, they are not easy pages). So yes there is a spin vector and spin is jointly conserved with orbital angular momentum. It does not point in a well defined direction because it's a quantum system, but if you choose a z-axis and try measuring the spin then the component in that direction will have a half integer value. Because the electron is charged and has spin it has a magnetic moment, which is what is detected in Stern-Gerlach. A wierd facet is that it doesn't matter what axis you choose to measure the spin along the answer will always be 1/2 or -1/2.

Circular polarization of a single photon is due to it's intrinsic spin. Linear polarization is a linear superposition of two spin states (the wiki page on this is somewhat technical see photon polarization). To see the polarization vector get two bits of polaroid and have fun looking through them and twisting one relative to the other by 90 degrees.

Your first question is difficult because the answer is abstract and involves complex vector spaces and some group theory concepts. Kazet may have a simpler picture.

Originally posted by DeepThought
This is a bit of a painful question, because the answer is so abstract. In classical physics the spin of a planet, say, is really just orbital angular momentum of the material in the planet about its axis of rotation. In quantum mechanics even elementary particles, such as electrons, which should be point-like and therefore not be able to spin possess ...[text shortened]... lves complex vector spaces and some group theory concepts. Kazet may have a simpler picture.

I don't really have a simple analogy for spin. Mostly it's just an intrinsic property of matter that manifests itself in certain measurable ways.

Originally posted by KazetNagorra
I don't really have a simple analogy for spin. Mostly it's just an intrinsic property of matter that manifests itself in certain measurable ways.

I don't necessarily need a specific analogy, I just want to know some of its properties.
Does it point in a specific direction?
Does it change over time?
Is it related to the fact that only two electrons can share a given part of the electron shells?
Is magnetism related? Why is iron magnetic and almost nothing else?

Originally posted by twhitehead
I don't necessarily need a specific analogy, I just want to know some of its properties.
Does it point in a specific direction?
Does it change over time?
Is it related to the fact that only two electrons can share a given part of the electron shells?
Is magnetism related? Why is iron magnetic and almost nothing else?

Does it point in a specific direction?
Does it change over time?

Spin is described by a matrix, which can depend on time. It has a "direction" in some sense, but not in a classical sense. If you, for instance, measure the spin of an electron with respect to some direction, you will get +1/2 with some probability, and -1/2 with some other probability, depending on the system and the direction of measurement.

Is it related to the fact that only two electrons can share a given part of the electron shells?

Yes. This is a property of fermions (not just electrons) known as the Pauli exclusion principle, which is related to spin as well as quantum statistics.

Is magnetism related? Why is iron magnetic and almost nothing else?

Almost everything is "magnetic" in some sense; what you refer to is ferromagnetism. This is actually a very poorly understood phenomenon, wouldn't be able to tell you much about it.

Originally posted by KazetNagorra
Spin is described by a matrix, which can depend on time.

So an electrons spin may change over time? I believe people have come up with storage based on spin. Is this storage using single electrons or large groups? Does it manipulate the spin, or separate out those with a given spin? I know these might be outside your field being engineering rather than pure quantum mechanics.

Can the spin be manipulated?

If you, for instance, measure the spin of an electron with respect to some direction, you will get +1/2 with some probability, and -1/2 with some other probability, depending on the system and the direction of measurement.
So what does +1/2 mean? No units?

I have read somewhere that exchange of odd-integer spin bosons will make a pair of identical fermions repel one another, while the exchange of even-integer spin bosons will make a pair of identical fermions attract one another. What sort of mathematical reasoning demonstrates that it has to work this way?

If you have a wavefunction describing two (or more, but for the sake of argument consider two) indistinguishable particles, the probability distribution must be unaffected if you interchange the two particles (this is not true if the particles are distinguishable). So you have (in loose notation):

|psi_1 psi_2|^2 = |psi_2 psi_1|^2

But the interchange might still introduce factors that leave the square unchanged. As it happens, the factor is +1 for bosons and -1 for fermions, which is AFAIK a fact of nature and is not derived from more basic axioms in conventional quantum theory. In principle you could also introduce a factor of exp(i*phi), where phi is some phase. Such particles with phi != 0 and phi != pi (those are the bosons and fermions respectively) are called anyons.

Originally posted by KazetNagorra
If you have a wavefunction describing two (or more, but for the sake of argument consider two) indistinguishable particles, the probability distribution must be unaffected if you interchange the two particles...

Yes, the Pauli exclusion principle for fermions is a very important feature of the world.

But my question above does not have anything to do with that (at least not in any obvious way).

A pair of electrons repel one another through a field of spin-1 virtual photons. But they also attract one another (to a far, far lesser degree, granted) through a field of spin-2 virtual gravitons.

This is said to be a general thing. A spin-1 field has to create repulsion between two identical particles that couple to that field, while spin-0 and spin-2 fields have to create attraction between identical particles that couple to either of those fields. I have never come across the mathematics that make it clear why it has to be that way.

Originally posted by Paul Dirac II
Yes, the Pauli exclusion principle for fermions is a very important feature of the world.

But my question above does not have anything to do with that (at least not in any obvious way).

A pair of electrons repel one another through a field of spin-1 virtual photons. But they also attract one another (to a far, far lesser degree, granted) through ...[text shortened]... e fields. I have never come across the mathematics that make it clear why it has to be that way.

This is another question with a painfully abstract answer. Essentially it's because of the mathematical structure of the theory. Swapping an electron for a positron changes the order of some terms in the corresponding matrix element, and this changes the sign of the effective potential, depending on the structure of the bosonic propagator. Sorry really can't do better there, this is Quantum Field Theory, and some of the results are just plain mathematical.

Originally posted by twhitehead
KazetNagorra has said he could answer a few questions in quantum mechanics. so here goes:
1. Can you describe electron spin. Does it have a specific direction in space? Can any electron point in any given direction?
2. Is it related to the polarity of photons? Does polarity have a specific direction for any given photon?

Electron spin has a given orientation in space - only once you force it to assume a given orientation by measuring it, according to quantum mechanics. Until then, the wave function just makes it assume a superposition of all possible orientations...

Similarly for the polarisation of photons... a photon only has a given polarisation once you force it to assume one by measuring it

At least that is one interpretation of quantum mechanics....


And maybe if you measured them any tiny fraction of a second later they might have a totally different orientation or polarisation...

Originally posted by ptobler
Electron spin has a given orientation in space - only once you force it to assume a given orientation by measuring it, according to quantum mechanics. Until then, the wave function just makes it assume a superposition of all possible orientations...

Similarly for the polarisation of photons... a photon only has a given polarisation once you force it to as ...[text shortened]... ny fraction of a second later they might have a totally different orientation or polarisation...

That depends on how "tiny" the fraction is.

http://en.wikipedia.org/wiki/Quantum_zeno_effect

The 'Extreme Physics' special issue of 'Scientific American' says:

"Physicists know only that at least two neutrino species have nonzero masses."

The same issue has on page 23 a graph of species (aka flavor) percentage as a function of distance traveled, showing that if a neutrino is 100% muon species, it is down to 0% muon species at 250 kilometers.

Should we view the speed of a neutrino to be varying with position in space as it oscillates through different species having different masses, in order to conserve energy and linear momentum?

Sorry for not following up on this thread. I genuinely want to understand more about electron spin and photon polarity. However, the responses convinced me I need to do some reading first before asking questions or I won't understand the responses. (and my questions won't be very good).
I am in the middle of watching a Yale course on evolution, so when I am done with that, I will look at quantum mechanics again and when I finally
have reasonable questions, I will come back.
If anyone knows of a good a laymans course on the subject similar to Richard Feynman's lectures I would be interested. I want to understand the concepts without learning all the complicated mathematics or having to work out any problems. I want to be told how it works, and what results it gives and what interesting effects there are etc, and if possible, I would like the history kept to a minimum. I find Physics especially has a culture of spending 90% of the time giving history lessons, and 1% on the actual meat of what we know, then 9% on what we don't yet know. What I liked about Feinman is he pushed the 1% up to 90%.