Spin

[Anonymous No.9744131]

Spin still confuses the fuck out of me.

Try to explain spin in your own words, or ask questions about spin. I'm not looking for handwavy explanations. I want to understand the abstract algebra and Lie underpinnings.

[Anonymous No.9744135]

>>9744131
angular momentum, like that of the earth

[Anonymous No.9744141]

You want to understand SU(2)? Or the physics of spin?

[Anonymous No.9744148]

>>9744131
i specifically didnt join a lab that had a PI i loved because i would have to learn the intricacies and theory behind NMR.

[Anonymous No.9744156]

>>9744131
Imagine the atomic nucleus bathed in a sea of atomic plasma. As the nucleus oscillates, it also forms double layers of electric charge. This is known as the electron "cloud". Our Sun works similarly as its core (composed of heavy elements such as iron, silicon and nickel) distributes energy into its electric plasma layered atmosphere.

Electron spin is spinning plasma but at the quantum level.

[Anonymous No.9744187]

>>9744148
that was a mistake NMR is very useful

[Anonymous No.9744255]

>>9744141
Spin seems to be partially a consequence of space having rotational symmetry describable by a Lie algebra, and partially due to relativistic effects (mysteriously enough). It somehow results in quantized spin groups. I have heard of many of the pieces, but never put it all together. I guess I'm trying to sort it all out from step one (or if the relativity part is to complicated, from axioms).

[Anonymous No.9744258]

>>9744187
Oh i know, i just didnt really want to specialize in it, not passionate about it at all.

[Anonymous No.9744286]

>>9744255
Spin one of the examples of quantum object with no analogue, and it seems to be a fundamental component of particles. It cannot be derived from no where because it's a experimental fact. It's connection to "classical" orbital angular momentum cannot be ignored, but the later can be taken from passing from angular momentum in classical mechanics to the analogous case with equivalent operators. It's as empirical aa the fact that matter has charge

[Anonymous No.9744564]

>>9744131
de elegdron rodades around an agsis

[Anonymous No.9744610]

>>9744255
It is easier if you first learn about vector spin -- spin 1 -- before looking at spinors i.e spin 1/2.
Spin groups only enter when you discuss spinors, with vectors you just need to understand the representations of the special orthogonal groups, which have the obvious interpretation of rotations; Spin(n) is the double cover of SO(n), so when you understand spin 1, spin 1/2 comes naturally.

[Anonymous No.9744679]

>>9744148
the theory behind nmr should be within your grasp quite easily. Just the fourier transform nonsense for getting nice peaks ruins the gig

[Anonymous No.9744688]

>>9744564
Post of the century.

[Anonymous No.9744736]

I always think of electron spin as the angular momentum stored in the electron's intrinsic magnetic field.

I know this isn't really a generally applicable approach (doesn't quite work for photons), but it helps you detach a bit from the "spinning ball" image.

[Anonymous No.9744770]

Sometimes a pictures says more than a thousand words.

pic related

[Anonymous No.9744783]

>>9744135
The earth isn't spinning.

[Anonymous No.9744791]

>>9744783
Is this some flat earther reference I'm not getting?

[Anonymous No.9744795]

spin isn't physical property

[Anonymous No.9744832]

>>9744791
OMG you people have been brainwashed by the ESTABLISHMENT! !!
DON'T YOU SE HOW RETARDED YOU SOUND? NASA SHILL!!

THE EARTH IS FLAT THERE IS NO SPACE!! YOU CAN'T PUSH AGAINST NOTHING. BECAUSE NOTHING DOESN'T EXIST!! THE FIRMAMENT IS FLAT!!

THE EARTH IS FLAT, FUCKING FLAT!D
FLAT FLAT FLAT FLAT FLAT FLAT FLAT FLAT!!
THE EARTH IS FLAT!! I DON'T CARE ABOUT YOUR "PROFS" THE EARTH IS FLAT FLAT FLAT FUCKING FLAT!!
I SEE NO PROF, I DONT BELIEBE IN IT EVEN IF JESUS CHRIST DESENDED FROM EVEN AND SAID THE EARTH IS ROUND ITS STILL FLAT FLAT FLAT FLAT!D
EVEN IF YOU WOULD TAKE ME TO SPACE AND SHOW ME A "ROUND" EARTH; YOU KNOW WHAT? ITS A FUCKING HOLOGRAM!!! AND FLAT!!
EVEN IF GOD THE MIGHTY, THE CREATOR OF ALL THINGS, EA HIMSELF SHOWED ITSELF TO ME AND SHARED HIS GODHOOD AND KNOWLEDGE OF HOW THINGS ARE THE NATURE OF THE UNIVERSE AND HOW "ROUNF" EARTH IS. I REJECT ALL!!
YOU KNOW WHAT? ITS STILL FLAT!!
THE EARTH IS FLAT FLAT FLAT FUCKING FLAT FLAT FLAT FLAT FLAT!!
AHHHHHHHHHHHHHHHJJJJJHHHJJDKSKAKFJDKAKDMDKSJAJAEMSDKSKAKAKSJFJKAKAKSKDKJAKAKAKAKDD
FLAT.

[Anonymous No.9744848]

>>9744832
I bet you do drugs

[Anonymous No.9744851]

>>9744770
Not this time
Faggot

[Anonymous No.9744855]

First ask yourself, what is the difference between rotation and spin

[Anonymous No.9744856]

>>9744770
these are many repeating pictures

[Anonymous No.9744978]

>>9744131
It's a property that acts like angular momentum

[Anonymous No.9745347]

>>9744791
Flat or round the earth ain't fucking spinnin'.

[Anonymous No.9745384]

>>9744156
>Imagine the atomic nucleus bathed in a sea of atomic plasma.
>>9744156
>As the nucleus oscillates, it also forms double layers of electric charge.
Why does this give me an erection?

[Anonymous No.9745395]

>>9744770

[Anonymous No.9745624]

>>9745395

[Anonymous No.9745648]

>>9745624
>>9745395
>>9744770
Yeah, the only belt trick I learned was from Goofy.

How does the group of rotational symmetries relate to spin? How do you describe this group with Lie algebra in terms of infinitesimal rotations?

[Anonymous No.9745653]

>>9745347
>yfw you can't prove the entire universe isn't spinning around the earth

[Anonymous No.9745705]

>>9745653
coriolis forces, nigga

[Anonymous No.9745812]

>>9744131
It's a number used to classify particles.

[Anonymous No.9745868]

>>9744131
Rotational symmetry by SO(3) induces a unitary representation in the Hilbert space. The infinitesimal generators of each unitary transformation can have i factored out to obtain a set of antisymmetric Hermitian operators J_ij. The generators satisfy the same commutation relations as what they generate, so we can obtain a commutator relation between arbitrary vectors and the J_ij. The J_ij transform under the representation as 2-tensors in the original 3 dimensional Euclidean space. Thus we can contract them with the Levi-Civita tensor to obtain J_k. The commutation relations of the J_k with each other satisfies the one mentioned above for vectors, thus the J_k are vector components. The commutators also reduce to the same ones that orbital angular momentum defined by L = X x P satisfy. We define total angular momentum as the vector J. Now since L is a vector as well, we use the first commutator once again to see that the commutator relations between the L_k is equal to the commutator relations between L and J. Finally we define S = J - L so that J = L + S. S obviously commutes with L, and it's commutator relations with itself is again the same as orbital angular momentum. We call S spin .As you can see it is independent of orbital angular momentum, but still part of the total angular momentum. Thus even when the orbital angular momentum dependent on spatial momentum P is zero, there is still spin angular momentum.

[Anonymous No.9745870]

>>9744131
>>9745868
Spin is essentially just a label for the unitary representation of the rotation group SO(3). The dimension of the representation is 2s+1. Thus spin 0 particles transform trivially. Spin 1 particles transform just like vectors do in SO(3), the cosine and sine matrices which rotate basis vectors. Spin 1/2 particles transform like spinors do, whose transformations are 2x2 unitary matrices acting on two component spinors. There's no obvious way to represent these in 3 dimensions anymore. Lie algebras are not necessary here, but they are in higher dimensions seen in relativistic quantum mechanics. The Pauli matrices are the key here, which form a basis for the Clifford algebra of R3, and i times them form a basis for the lie algebra su(2). By taking the outer product of the spinor with its Hermitian adjoint we obtain a traceless Hermitian matrix that transforms like a Heisenberg operator under SU(2). Now from the position vector r we can construct a traceless Hermitian matrix which transforms the same, just by considering r as a representation of the Clifford algebra, consider the Pauli matrices as a vector and dot it with r as a vector to obtain a matrix. Note as well that the determinant remains the same which in this case means that x^2+y^2+z^2 is invariant. Thus in this sense the SU(2) transformation on the spinor induces a O(3) transformation on a position vector, allowing us to identify the spinor in some spatial sense. The spin operators now just give the components of the rotated vector induced by the unitary transformation.

[Anonymous No.9745882]

>>9744783
Yes it does, it spins with a characteristics similar to bosons, it has the same state after a 2 pi rotation.

[Anonymous No.9745907]

>>9745653
i think he meant what if all matter starts to spin in sync around one single point, the entire universe would be spinning with no outside reference point, then it makes no sense to assume a coriolis effect?

[Anonymous No.9745918]

Help a nigger out.
>>9745829

[Anonymous No.9745929]

>>9744156
>Electron spin is spinning plasma but at the quantum level.
this is the most inaccurate brainlet popsci explanation Ive ever heard

[Anonymous No.9746148]

>>9745907
Wait, does the universe have spin?

Can anyone studying this branch of physics give some in depth analysis on this question.

[Anonymous No.9746224]

>>9745868
>>9745870
This is the kind of answer I am looking for. It will take me some time to digest it and ask questions.

[Anonymous No.9746374]

The easiest way to explain spin is in the context of the stern gerlach experiment.

[Anonymous No.9747434]

>>9744131
Stop thinking about spin as rotation, think about spin as it was charge or mass.
It is just another property of particle that cannot be described by more underlying properties.

[Anonymous No.9747439]

>>9747434
That's not a very good analogy. You can make an electron change the sign of its spin (analogous to making a Newtonian object spin in a different direction), but you cannot change its (rest) mass or charge.

[Anonymous No.9747523]

>>9747434

This is pretty awful. Spin arises as a representation of the Lorentz group (specifically, it tells you how the particle transforms under rotation). So, actually, you can't think of spin as anything except for in the context of rotation.

I kind of like these notes:
http://hitoshi.berkeley.edu/221a/spin.pdf

[Anonymous No.9747669]

>>9747523
is spin rotational potential?

[Anonymous No.9747677]

>>9747439
>>9747523

In QM you can classify all particles as ireducible representations of Poincare group. Poincare group has two Cassimir operators that give two numbers for clasification, one of these numbers is particles mass and other is its spin. In combination to these numbers you can classify further particles with internal symmeties.
Charge comes from internal, for example Dirac qft is invariant to U(1) and this gives electron its charge.
So mass,spin,charge,color.. are fundamental properties of particles that can't be further simpified, they don't have to be the same and they aren't. They don't even transform in same way.

>You can make an electron change the sign of its spin (analogous to making a Newtonian object spin in a different direction), but you cannot change its (rest) mass or charge
You can't change mass or charge but you can change color throu gluons. Every quantum number has something unique to it.

[Anonymous No.9747686]

>>9747669
No, spin is irreducible representation of Poincare group. It arises from square of Pauli-Lubanski vector.

[Anonymous No.9747687]

>>9747677
>color
im a layman, how does color work in this context

[Anonymous No.9747733]

>>9747687
Color just like spin is some intrinsic property of particle but unlike spin people don't try to describe it with some classical concept. Both of these properties come from some symmetry of nature, both describe particle and both can change in some way.
Problem with spin is that when it was first discowered it was assumed that is some kind of rotation that originated from electrons internal structure. This is wrong since elecrron doesnt have any internal structure but people still try to understand it in this way. While it is true that spin has some properties that make it similar to classical angular momentum it shouldnt be thought this way. You should think about spin same way as you think about charge, that is you cant describe charge of particle as some other property.