what is spin? i have a vague idea but im not very sure about it; also how does it affect particles?
Often, spin is referred to as some "intrinsic" rotation of the particle.
So you have angular momentum, which is what a particle gets when it orbits around some center, and you have spin, which is like something the particle has because it rotates around an axis.
The advantage of this view is that it gives you a mental picture, and that mathematically (extrinsic) angular momentum and (intrinsic) spin are very much the same (basically, it's the same mathematics with a different interpretation).
Unfortunately, the picture is flawed in the sense that the particle is not really "rotating around an axis" because that requires you to have a "classical" picture of the particle as a small sphere, for example, while spin is something manifestly quantum-mechanical in nature. So if you want to really have things right, you just have to think about spin as some property of a particle that allows us to explain why particles do what they do, in the same way as electric charge, quark color, lepton number, etc.
spin is an angular momentum. not the orbital angular momentum, but another one. some books try to explain it with a particle that is "spinning" around its own axis. but it really doesnt.
The best way to explain what it really is, I think is to treat spin like a property of a particle, like for example mass or charge. There are many effects that you can explain and understand using spin. Particles with spin do have spin-magnetic-momentum that gets affected by external magnetic field
Edit: CompuChip, you was faster than me ;)
ah ok i get it but how does it affect the particle? for instance i know that bosons have integer spins and fermions have half integer spins. what does this mean for the particle?
I think you know that a particle's state is expressed by ket vector on hilbert space.
before we study spin, we think only spatial state is considered
But when spin is considered , state is given by not just wave function of spatial part but also internal part called spin. That means just scalar wave function isn't enough to representate state of particle. Mathematiclly say, we use two state ket vector and direct product of two ket can be full state of particle. One is related to its spatial state and the other is relate to its internal state.
Electron has spin 1/2 and it means that need 2-D hilbert space in addition to express its state. There exist two electorns that have same spatial wave function psi(x,t). If psi can fully express of state, it dose'n make sense SG-experiment. Because we find that one electron move up meanwhile the other move down in SG-experiment even two electron have same spatial state. How do same state particles act differently in same condition? So We have to conclude that there is another factor to describe a particle's state so we made conception of spin as another degrees of freedom.
If you know spin state of particle, you may know about its internal state of particle. Its all meaning of spin.
It has profound implications. To begin with, the difference between Bose-Einstein and Fermi-Dirac statistics.
Consider the atom. The Pauli exclusion principle leads to the fact that only two electrons (with opposite spin) can occupy an electronic orbital. Which gives you these orbitals and shells and essentially the whole periodic table. If electrons were bosons, the bulk of them would just hang around in the lowest energy state(s). There would be no chemical bonding, no chemistry, and ultimately no biology - we couldn't exist to see it!
It's ok to develop a "simple minded" classical concept of what spin is (rotation about a particles own axis) so we can "visualize" it. But its a quantum concept, not a classical one. So there are severe limits.
Our usual notion of "spin" falls short when we think about the fact that particles are (quantum mechanical) waves not classical "solid" mass spinning. (now what is spinning??)Which is just as well because our classical intution about such things has most often proved to be illusory at best, often wrong.
The picture gets more hazy since "spin" is quantized (who ordered that???) and may have half integer quantum numbers (Oh my gosh!!!). That's just incompatible with classical reasoning. The electron spin is a key to the Pauli exclusion principle and I don't recall any classical interpretation for that either...
Did you ever heard people talking how particles in quantum regime - even in ground state - have energy? Well, spin is something like that - smallest amount of angular momentum that you can not take away from its owner =) Additional, as you probably know, spin is connected to symmetries that particle has.
People something use analogies with "spinning ball", but IMNSHO - it will do good to you not to think in such inadequate terms.
ooh ok i get ty guys you've helped a lot!
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