Talk:Spin (physics)

Template:Onlinesource2004

OK, the operators describing spin observables do form an operator valued vector space defined by <math>[J_i,J_j]=i\epsilon_{ijk}\hbar J_k<math>. Why did you revert? And how about the part on SO(3) representations and Clebsch-Gordon coefficients?

• When one talks about an observable such as spin or energy, one is talking about the eigenvalue/eigenstate, not the corresponding operator(s). Spin does not transform like a vector, i.e. like the coordinates, under rotations. For example, if you have a spin-1/2 particle with a spin "up" in the x direction (i.e. it is an eigenstate of <math>\sigma_x<math> with eigenvalue +1, if you rotate your coordinate system by 360 degrees, you do not get back the same state; rather, it picks up a π phase shift. Alternatively, if you rotate your measurement apparatus by 90 degrees to measure spin along the y direction, you do not measure zero, you get a 50% chance of spin up or down. It is only as the angular momentum becomes large that you asymptotically recover the classical behavior.
  • (Of course, strictly speaking, angular momentum is not a vector either; it is a pseudovector.)
  • You are correct that the operators (<math>\sigma_1<math>,<math>\sigma_2<math>,<math>\sigma_3<math>) for spin-1/2, or J's for higher spins, do form the basis of a 3-vector space. i.e. for the operator <math>\sigma = v_1 \sigma_1 + v_2 \sigma_2 + v_3 \sigma_3<math>, the quantities <math>(v_1,v_2,v_3)<math> transform like a 3-vector (or maybe a pseudovector?) as the coordinate system is rotated. This is just a reflection of the fact that these operators are defined relative to the coordinate system, and not on the transformation properties of the underlying observable quantity.
  • (Also, please do not confuse 3-vectors with general abstract vector spaces, which of course include all quantum states.)

—Steven G. Johnson

An alternative calculation of spin

We have all noticed that spin is described as being a multiple of hbar/2. I thought that it would be better to set this value to a constant giving,

hdot = hbar/2 = 5.2728584118222738157569629987­554e-35 J.s

But now the equations for spin did not work with hdot, so I had to correct them.

Here are the corrected equations,

|sv| = sqrt(s(s + 2)) * hdot

and

Sz = ms.hdot

where,

sv is the quantized spin vector,

|sv| is the norm of the spin vector,

s is the spin quantum number, which can be any non negative integer,

Sz is the spin z projection,

ms is the secondary spin quantum number, ranging from -s to +s in steps of two integers

For spin 1 particles this gives:

|sv| = sqrt(3).hdot and Sz = -hdot, +hdot

For spin 2 particles this gives:

|sv| = sqrt(8).hdot and Sz = -hdot, 0, +hdot

Now that the spin equations have been corrected, the definitions for fermions and bosons are incorrect, and must be redefined as follows.

Fermions are particles that that have an odd integer spin.

Bosons are particles that have an even integer spin.

Would these redefinitions have any other effects on the Standard Model?

Can these redefinitions explain any currently unexplained phenomena?

Are there any experiments that could confirm or refute these claims?

I would like eveyone to have a good think about this, and give me your objections to it, or even data to support it.

spin

i think it would be really good if someone actually explains what is spin. fact is i dont know what it is