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

[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?

 

[bhobba]

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/dp/0750628960/?tag=pfamazon01-20
2 https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20
3. https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20
4. https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

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

 

[N88]

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/dp/0750628960/?tag=pfamazon01-20
2 https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20
3. https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20
4. https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

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

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!

There are two separate but related quantum numbers associated with intrinsic angular momentum ("spin"). The first one, $s$, is associated with the magnitude of a particle's spin: $S = \sqrt{s(s+1)}\hbar$ which for an electron equals $\sqrt{\frac 1 2 \cdot \frac 3 2}\hbar = \frac {\sqrt 3} 2 \hbar \approx 9.14 \times 10^{-35}~\rm{kg \cdot m^2 / s}$. This is a fixed, unchangeable value which (like the mass) is the same for all particles of a given type, e.g. 1/2 for electrons.

The second one, $m_s$, is associated with the orientation (direction) of the spin, specifically with the component of the spin along any given direction, which we customarily call the "z-component" although it doesn't have to be actually along the z-direction: $S_z = m_s \hbar$.

$m_s$ can have one of the values ranging from $-s$ to $+s$ in integer intervals. For $s=\frac 1 2$ (e.g. for an electron) these values are $m_s = - \frac 1 2$ ("spin down") and $m_s = + \frac 1 2$ ("spin up"). For $s = 1$ they are $m_s = -1, 0, +1$, for $s=\frac 3 2$ they are $m_s = -\frac 3 2, -\frac 1 2, +\frac 1 2, +\frac 3 2$, and similarly for other values of $s$.

For an electron, $S_z = \pm \frac 1 2 \hbar \approx \pm 5.28 \times 10^{-35}~\rm{kg \cdot m^2 / s}$.

 

[jtbell]

there appears to be a widely accepted colloquialism that the spin (ie, the intrinsic angular momentum) of an electron is ℏ/2\hbar/2. This (it seems to me) is the z-component (the accepted standard direction for spin projection).

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.

 

[N88]

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.

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 $\hbar/2$.
(iii) Then add in your helpful remarks about precession (which I've yet to study).
QED.

 

[jtbell]

ii) We typically identify particles by the z-component of spin; for spin-half particles this is $\hbar/2$.

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.

 

[bhobba]

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.

Spin is actually deeper and more significant than you think. It can't 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