3 ms·

> 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 wo

> 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?

Schroedingersat 4y ago
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.
hakuseki 4y ago
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?
- Schroedingersat 4y ago
  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.
  - hakuseki 4y ago
    To clarify, my question was basically asking whether the author of the parent comment is satisfied by my comment.

> 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?

Schroedingersat 4y ago

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.

hakuseki 4y ago

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?

Schroedingersat 4y ago
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.
- hakuseki 4y ago
  To clarify, my question was basically asking whether the author of the parent comment is satisfied by my comment.