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Comment by Schroedingersat | Hacker News Reader

It's very decidedly not an abstraction on linear momentum.

It's a conserved quantity just like any other. Light has angular momentum even when travelling in a straight line. Anything with spin does even when stopped.

In physics there is a concept known as symmetry. Any way you can swap around your variables without influencing the answers corresponds to a way in which the laws of physics are symmetric (or a way someone could change the time/position/orientation/etc of the region in which you did your experiment and you would get the same results as long as you stayed in the lab they moved).

Angular momentum is the conserved quantity from rotational symmetry and is just as primary as energy-momentum or charge.

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Is that the _same_ angular momentum, or just the same term used for something different? My understanding is that "spin" isn't really anything necessarily spinning and it's more just an analogy for a property of subatomic particles that doesn't exactly correspond to a concept at the macro level.

It has almost the same relationship to angular momentum (and tangentially magnetic fields) as charge on an electron has to charge in a capacitor or an electric fields.

> My understanding is that "spin" isn't really anything necessarily spinning

Yeah, this is kind of the point. A bunch of non-spinning things like particles, or more abstractly an EM field can have angular momentum. This is the same quantity that is conserved in things that are spinning.

> This is the same quantity that is conserved in things that are spinning.

In what sense is it the same? If we called them completely different names, what would be different or more complex?

To flip the spin of a particle from eg. +1/2 to -1/2 it must exchange some angular momentum with its environment, usually in the form of a spin 1 photon. Each unit of spin corresponds to a fundamental amount of angular momentum, and if you add up all of the angular momentum in a closed system the total does not change.

Spin falls out of qm equations as the quantized number associated with the angular momentum quantity that falls out of classical equations.

Much like you get energy-momentum from translating in time and space, and this falls out in a constrained quantum system where energy-momentum is quantized as an integer we call wave number.

IANAP, but it seems to me that right now we are able to make the statement: "Angular momentum is conserved."

If we were to give different names to different types of angular momentum, we could no longer say that. Instead we would have to say something like: "The sum of Type 1 Angular Momentum and Type 2 Angular Momentum is conserved."

Does that qualify as more complex?

Yes to your statement. I'm not quite sure what you're asking with the question, but will try.

I mean you're increasing the complexity of your explanation I guess, and if you don't draw the distinction quite right you might be doing so for no explanatory benefit and a net reduction in communication effectiveness. But there are other reasons quantized spin is important and relevant compared to, say, the net angular momentum you have around Detroit at the current time.

To clarify, my question was basically asking whether the author of the parent comment is satisfied by my comment.

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