# I Classical v. quantum dynamics: Is spin the key difference?

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1. Mar 23, 2017

### N88

I'm interested in understanding the key physical differences between classical and quantum dynamics.

I understand that spin (intrinsic angular momentum) is one major physical difference.* So I wonder whether all else flows from this?

Or are there other major (unrelated) physical differences? Thanks.

* Like: blame Max; he started it with his aitch?

2. Mar 23, 2017

### Staff: Mentor

The key difference is QM depends on this thing called the State and the Born Rule.

The dynamics, and that includes spin, for both classical and quantum physics follows from symmetry considerations.

To understand the whole thing better get the following books and read them in this order (assuming you have done at least first year level university physics and math):
1, https://www.amazon.com/Mechanics-Third-Course-Theoretical-Physics/dp/0750628960
2 https://www.amazon.com/Quantum-Mechanics-Demystified-David-McMahon/dp/0071765638
4. https://www.amazon.com/Quantum-Mechanics-Modern-Development-2nd/dp/9814578584

Unfortunately, while very very beautiful. profound, and deep it does require some study to appreciate. Just a note, one part is the beautiful Noether's theorem. One professor who posts here tells how when he teaches it to his students they sit there in stunned silence while its importance sinks in. The books I gave cover all that and much more, of which what spin is and it's importance is just one part.

This is the deepest discovery of modern physics IMHO. Enough said.

Thanks
Bill

Last edited by a moderator: May 8, 2017
3. Mar 24, 2017

### N88

Thanks Bill, this detail is nice, and appreciated.

I'm reading #1,2,4. The book in #3 looks good.

Since 'state of information' has classical connections, as does symmetry: it is 'spin' -- that intrinsic angular momentum (not angular momentum in general) -- that remains the major difference for me.*

* PS: On this subject, I see spin as OK! But maybe you can help here. I'd like to be sure that I'm not confused by the following: In QM, there appears to be a widely accepted colloquialism that the spin (ie, the intrinsic angular momentum) of an electron is $\hbar/2$. This (it seems to me) is the z-component (the accepted standard direction for spin projection).

See this next, which I suggest supports my point; for "the fixed, unchangeable value which (like the mass) is the same for all particles of a given type," e.g. for electrons with spin-half, the (intrinsic) spin is $\frac {\sqrt 3} 2 \hbar$. It is not $\hbar/2$. Am I misinterpreting the colloquialism? SOS please!

Last edited by a moderator: May 8, 2017
4. Mar 24, 2017

### Staff: Mentor

Yes, if someone says something like "spin $\hbar/2$" with respect to an electron, it either refers to $S_z$, the "z-component" of intrinsic angular momentum, or else it's (at best) loose language or (at worst) an outright error. You have to interpret it in its context if necessary.

5. Mar 25, 2017

### N88

Many thanks! So, to be accurate and unless corrected, I should say:
(i) the spin (ie, the intrinsic angular momentum) of a spin-half particle) is $\frac {\sqrt 3} 2 \hbar$.
(ii) We typically identify particles by the z-component of spin; for spin-half particles this is $\hbar/2$.
QED.

6. Mar 25, 2017

### Staff: Mentor

I think it's more common to use simply the quantum number: 1/2 when referring to the magnitude; or +1/2 or -1/2 when referring specifically to "spin up" or "spin down" states.

7. Mar 25, 2017

### Staff: Mentor

Spin is actually deeper and more significant than you think. It cant be explained here - but the book physics from symmetry explains it in full detail.

Please, please read it. The only thing 'wrong' with that book IMHO is he can simplify a lot of what he says and certain things will stand out making you say - why didn't he do that. One example is the Klein-Gordon equation. He give a beautiful derivation of it, its the most general field equation you can write for a single valued complex or real field. But doesn't follow up directly the consequences which are surprising:
https://arxiv.org/ftp/quant-ph/papers/0604/0604169.pdf

But it must be said stuff you nut out for yourself you understand a lot better.

Thanks
Bill