Spin 1/2 vs Spin 2: Does 360 Degrees Change?

In summary, the electron must turn twice to be back in its original position (so that its complex wave function is identically restore). Spin-1 particles look the same only if one turns it a 360 degrees, and spin-0 particles only exist in the trivial representation.
  • #1
alphachapmtl
81
1
As mentionned in the "A question about nonlocality" thread,
the electron (a spin 1/2 particle) must turn twice to be back in its original position (so that its complex wave function is identically restore).

Now my question is this:
If a spin 1/2 particle must turn 2*360 for it's wave function to be identical, can we say that a spin 2 particle must turn 360/2 for it's wave function to be identical ?
 
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  • #2
alphachapmtl said:
Now my question is this:
If a spin 1/2 particle must turn 2*360 for it's wave function to be identical, can we say that a spin 2 particle must turn 360/2 for it's wave function to be identical ?

Yes, it is like a two-headed arrow. And spin-1 particle looks the same only if one turns it a 360 degrees, it is like an arrow. Do you know how to represent a spin-0 particle?:cool:

sam
 
  • #3
Here is a related quote for those interested.
(but it's a bit more than what I can understand myself)
from http://math.ucr.edu/home/baez/week109.html >>

The spin-0 representation is the trivial representation. Physicists call vectors in this representation "scalars", since they are just complex numbers. Particles transforming in the spin-0 representation of SU(2) are also called scalars. Examples include pions and other mesons. The only fundamental scalar particle in the Standard Model is the Higgs boson - hypothesized but still not seen.

The spin-1/2 representation is the fundamental representation, in which SU(2) acts on C^2 in the obvious way. Physicists call vectors in this representation "spinors". Examples of spin-1/2 particles include electrons, protons, neutrons, and neutrinos. The fundamental spin-1/2 particles in the Standard Model are the leptons (electron, muon, tau and their corresponding neutrinos) and quarks.

The spin-1 representation comes from turning elements of SU(2) into 3x3 matrices using the double cover SU(2) → SO(3). This is therefore also called the "vector" representation. The spin-1 particles in the Standard Model are the gauge fields: the photon, the W and Z, and the gluons.

Though you can certainly make composite particles of higher spin, like hadrons and atomic nuclei, there are no fundamental particles of spin greater than 1 in the Standard Model. But the Standard Model doesn't cover gravity. In gravity, the spin-2 representation is very important. This comes from letting SO(3), and thus SU(2), act on symmetric traceless 3x3 matrices in the obvious way (by conjugation). In perturbative quantum gravity, gravitons are expected to be spin-2 particles
 
  • #4
No guys i think you are making something wrong...
Representations on wavefunctions by SU(2) is siglevalued on integers spin (s=1,2,3..)
and double valued on half integers (s=1/2,3/2..).
Thats the only motivation...


regards marco.
 

FAQ: Spin 1/2 vs Spin 2: Does 360 Degrees Change?

What is the difference between spin 1/2 and spin 2?

Spin is a quantum mechanical property of particles, and it refers to the intrinsic angular momentum of a particle. Spin 1/2 particles have a half-integer spin value, while spin 2 particles have an integer spin value. This means that spin 1/2 particles have a spin of either +1/2 or -1/2, while spin 2 particles have a spin of +2 or -2.

How do spin 1/2 and spin 2 particles behave differently?

Spin 1/2 particles, also known as fermions, follow the Pauli exclusion principle, which states that no two particles can occupy the same quantum state simultaneously. This leads to the phenomenon of spin pairing, where particles with opposite spins are able to occupy the same space. Spin 2 particles, also known as bosons, do not follow this principle and can occupy the same quantum state simultaneously.

How does spin affect the behavior of particles in a magnetic field?

Spin plays a crucial role in how particles interact with magnetic fields. Spin 1/2 particles, due to their half-integer spin value, behave like tiny magnets and can align either with or against an external magnetic field. This is known as spin alignment and is the basis for magnetic resonance imaging (MRI) technology. Spin 2 particles, with their integer spin value, have a more complex relationship with magnetic fields and can exhibit behaviors such as superconductivity.

Can particles change their spin value?

No, the spin value of a particle is an intrinsic property and cannot be changed. However, particles can change their spin orientation, meaning they can flip from spin up to spin down or vice versa.

How does a 360 degree rotation affect particles with different spin values?

A 360 degree rotation will result in a change of sign for spin 1/2 particles, meaning they will flip from spin up to spin down or vice versa. However, spin 2 particles will remain unchanged after a 360 degree rotation as their spin values are already integers. This is due to the mathematical property of rotation known as the spin-statistics theorem.

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