Wikipedia:Reference desk/Archives/Science/2013 June 5

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June 5

Sodium in softened water

I've been told that home water softeners that don't use reverse osmosis replace the calcium, iron, and magnesium in the water with sodium. (1) is that correct? (2) if that is true, does that put so much sodium in the water that you shouldn't use it for drinking water? Bubba73 ^{You talkin' to me?} 21:01, 5 June 2013 (UTC)

briefly covered in Water softening#Effects of sodium --Digrpat (talk) 22:15, 5 June 2013 (UTC)

Resolved

Thank you - that's what I wanted to know. Bubba73 ^{You talkin' to me?} 22:30, 5 June 2013 (UTC)

Spin in the classical context

I have seen classical fields being referred to as having a spin number, the classical electromagnetic field among them. As far as I can tell, this corresponds to the reciprocal of the period (in full cycles) of the effect of rotation on the field. The electromagnetic field is retored by a rotation of 2π (spin-1), and a gravitational field is restored by a rotation of π (spin-2). This seems to hold, extrapolated to QM fermion fields: a rotation of 4π (spin-1/2). Can anyone point me to the background of this concept in a classical setting? — Quondum 23:02, 5 June 2013 (UTC)

This is certainly true, and certainly classical, but I don't know what reference to point you to. You may want to ask at the math desk.

I'm not sure you were asking about this, but Dirac's equation is the spin−½ massive analog of Maxwell's equations and GR. It's typically given in a form like $i\hbar {\partial \!\!\!{\big /}}\psi -m\psi =0$; to get a classical form without ħ you need to substitute m/ħ = 2π/λ where λ is the Compton wavelength of the field. The QED field equations in Quantum electrodynamics#Mathematics work as a classical theory as well after a similar trick (in which you also need the fine structure constant), and you can even do it to the full Standard Model.

Spin can be interpreted classically in terms of angular momentum as well. E.g. quantum mechanically the angular momentum of a plane wave in the direction of motion is bounded by |L_z| ≤ σnħ where σ is the spin as a half-integer and n is the particle count. If you use another identity like p = nħk to eliminate nħ, you get an inequality that doesn't contain ħ and holds classically. -- BenRG 07:18, 6 June 2013 (UTC)

Thanks, though this approach seems to be trying to squeeze as much classical meaning out of the idea of quantum spin as possible, rather than just finding a classical definition, which various comments I've read (mostly on WP talk pages) led me to suspect existed. I guess I'll have to work through an example of the angular momentum bound of waves satisfying each type of equation. The idea of extending classical elements to the full Standard Model seems intriguing. — Quondum 16:06, 6 June 2013 (UTC)

You can probably just count the spin indices and divide by two, like counting the tensor indices in integer-spin field equations. Bargmann–Wigner equations may be relevant. I still think the math desk regulars might be able to give you a better answer. -- BenRG 08:10, 8 June 2013 (UTC)

Okay, thanks for the connection on index count; this is a pretty solid starting point. I'll take it further at the math refdesk if I need once I gain a feel for this connection. — Quondum 14:37, 8 June 2013 (UTC)