Is it a real property of electrons or some mathematical variable? What property would be analogous to it on the macro level? Not actually spinning is it? Also, what is a spin network? Do photons have spin too? Please Register or Log in to view the hidden image!
It's a real property, in that electrons really behave as if they have it, as their magnetic moment testifies. But it does not behave exactly like the "classical" spin we are used to in the spin of the Earth for example. In general, the angular momentum of QM wave-particles, and the properties that derive from it, are modelled rather differently from the classical picture due to the apparent wave nature of QM reality. Photons also have spin, reflected in their circular polarisation, if I recall correctly. You can get an idea of how unlike this is to the classical picture from the following: http://en.wikipedia.org/wiki/Photon_polarization I don't know what a spin network is. Let's hope another reader can help with that.
So we can think of spin sort of like magnetic polarization--a sort of field that wraps around an axis of orientation?
A spin network is a theoretical structure related to quantum gravity. I don't think it has anything to do with spin of particles. Oh, wait, it does: --http://en.wikipedia.org/wiki/Spin_network
Spin is considered the defining property, by some, of quantum mechanics. This should be called quantum spin-phase space, perhaps; the "mechanics" isn't very mechanical, except for the experimental side. It's called what it's called for probably mostly historical reasons; recall that Einstein explained the "mechanics" of the photoelectric effect. Penrose explains spin in terms of the "Riemann sphere of states". The Riemann sphere isn't too scary, it's an extension of the complex plane, or, where you have one angle for a complex number in the plane, you have two in the sphere. The Bloch sphere can be considered an isomorphism of the Riemann sphere, with like, a choice of coordinates. A qubit is described by this spherical representation of the complex numbers.
I am often on the edge of things, but at least I know when I am treading that thin line between the consensus understanding of things and well.., speculation and fringe interpretations. Reiku while he was around here did not seem to understand the difference between how he imagined things to be and how they appear to be to most rational observers. I would not take anything he presents as a reasonable interpretation, of reality, even a reasonable speculation, about what might be real.., without significant credible supporting references.
I would rather think of it as a standing wave that circulates round an axis, since the key thing is the presence of angular momentum, in a entity which is partly like a particle and partly like a wave.
It's a big problem in modern physics, regarding the ability of the man in the street to see what it is all about.. So many of the models we now have require fairly advanced mathematics to comprehend them properly. I worked with chemical QM long enough for the maths to have given me an intuitive sense of what it "feels" like qualitatively, but with things such as as general relativity it's an uphill struggle.
Spin is, as I recall, a kind of symetry. It's how many times a thing looks like itself when you rotate it through 360°. A moebius strip has spin 1/2 - you need to pass it through two complete rotations before it looks the same again. A sphere or a point have spin 0 - they always look the same no matter how far or how little you spin them. A nine inch nail has spin 1 (in one direction anyway) - you need to rotate it through a full rotation before you regain the original image. A rectangle has spin 2 (and so on).
Could be. I never learnt much about spin - it was just given to us as an entity with angular momentum, magnetic moment (with charged particles) and of course a quantum number. With orbital angular momentum of a electron in an atom, there certainly is such a symmetry. A d orbital has 4 lobes and 2 units of angular momentum whereas a p orbital has 2 lobes and 1 unit, while an s orbital has one lobe (spherical symmetry) and zero units. So I can imagine something analogous applies to spin.
A couple of points (and don't take my word for any of this, because I'm nowhere near an expert). The Schrodinger equation does not describe spin. Pauli's exclusion principle explains why electrons are paired up in orbital states, or how it is that electrons "share" the same energy level. The two electrons only do this when they have opposite spins. Look at the Pauli matrices, there are three, the same number as the dimensions of ordinary space, and you can always map or 'fix' at least one of the Pauli operators to a single dimension, which is to say, assign say \( \sigma_x \) to an x direction; this might be the direction of a magnetic field. You really need to understand the connections between the Pauli operators and the complex numbers; say you need to explain why particles like fermions precess about the 'spin axis' in a strong enough field. The fact that electrons pair up when their spins are antiparallel was a surprise to Einstein and Besso, they did an experiment whose result was out by a factor of 2.
Yes Spin can be represented by a Lie group of continuous symmetries. As in your example, spin \(0\) has a representation as the group \(U(1)\), that of spin \(1\) as \(SO(3) \) and that of spin \(\frac{1}{2}\) as \(SU(2)\) In the last case it is interesting to note that the basis for the associated algebra \(su(2)\) is precisely the 3 Pauli spin matrices (up to an imaginary factor)
Cosmology (both microcosmology, e.g., quarks and leptons; and macrocosmology, e.g., no space-time continuum prior to the Big Bang) stopped making sense to laymen decades ago when it began to be largely counterintuitive. Perhaps it goes back to Einstein and relativity. I was smart enough to be admitted to a top university, but it took me a year to work my way through the theory. Needless to say, I transferred to a different school and studied accounting. Please Register or Log in to view the hidden image! The man in the street can't really understand more than the bonehead-basics of chemistry either. Science has vastly outpaced the ability of the average human brain to grasp it. But especially here. A large part of the problem is the dumbing-down of the U.S. education system. In most school districts, elementary-school students (grades K-8 although 7-8 are sometimes called "middle school") are promoted mechanically from one grade to the next without the language or mathematical skills they need to actually comprehend the material that will be presented to them in high school (grades 9-12 although 9 is sometimes grouped with middle school). By the time they enter a university, a gigantic percentage of them have to enroll in remedial English classes (and I'm talking about native speakers here!), and it's a struggle for them to pass just one year of dumbed-down quasi-university-level classes in math and biology. The majority of Americans never set foot in a university classroom, and a large percentage of those who do never graduate. And the ones who graduate? They take degrees in subjects like art history and political science. There's no way these people can understand early 20th-century physics, much less 21st-century cosmology. The average American is hopelessly innumerate. If he walks into a grocery store and sees a sign reading "canned beans: 3 for $4," then walks to the checkout counter with 5 cans, pleased with himself for spotting such a great bargain, and the clerk rings up a total of $7.50, he'll never know he was cheated. It's no wonder that our people are so easily convinced that terrorists, who have killed an average of fewer than 400 of us per year in this century, are a major threat, while gun owners, who have killed an average of 30,000 of us per year, are not. (Even the gun lobby admits to 3,000.) So you can give up all hope of teaching them to understand modern cosmology. In case you haven't guessed, Trippy is not an American. Please Register or Log in to view the hidden image!
Those are the same things, with electrons. As with electromagnetic wavelength, potential energy, field strength, and the myriad other properties and features of the world we can only perceive via mathematical extensions and additions to our mental sensory processing, the math is our central perception of the thing. What our sensory processing cannot put into context, we must use math to perceive. Not only "spin", but "particle" and "wave" (the things that are "spinning"), are metaphorical borrowings from a vocabulary developed to label what we need no math to perceive. The central difficulty here is not educational, but with the nature of common sense and human understanding. Cosmology trashed almost everyone's intuition when it postulated a spherical planet moving in orbit around an impossibly distant Sun (and the best educated were among the worst confused). Our intuition has caught up (one can now ->see<- the huge and darkening Earth rotate away from the Sun at sundown, and continue to turn majestically underneath a vast volume of space shot through with fantastically distant stars. That is now visible.) It might again - although one suspects the existence of a limit to comprehension itself when confronted with violations of Bell's Theorem. It is possible that we can perceive - "see" - mathematically what we can never "understand" in the ordinary sense of that word - can never place in context and interconnect with a larger world of meaning. But that remains to be seen. So when confronted with an "us/them" construction immediately contradicted by some invalid statistics (gun owners mostly kill themselves and each other, not "us"), do we blame the educational system for the innumeracy or the illiteracy visible?
You can think of electrons as acting like little bar magnets. The strength of the magnet and the direction that it is aligned are both related to the electron's spin. What's strange in the quantum description of the electron spin is that in an external magnetic field the electron is only "allowed" to align itself with one of two angles to the direction of the applied field, whereas in the case of a classical bar magnet any angle of alignment is possible.
Max Tegmark said on his book that in order for us to understand these concepts we have to learn a new language.. the language of Math.
