Does intrinsic (e.g., spin) imply elementary (irreducible)?

[nomadreid]

TL;DR

When one says that quantum spin is an intrinsic property of a particle, does this mean that it cannot be reduced to other properties?

Some time ago, before particles turned out to be mutable wave excitations (making Alchemist's dreams sound nicer, I guess :-) ) , to say that something was an "elementary particle" meant that it couldn't be broken down further. OK, that idea bit the dust, but now there are intrinsic properties of particles -- are these similar to being "elementary" in that they are irreducible, or are they also one convenient point of reference from which to start, but in reality one could reduce it to other properties?

[Moderator's note: Moved from Classical to Quantum Physics.]

 

[bob012345]

Please explain what you mean by "mutable wave excitations". Thanks.

 

[kuruman]

I always took it to mean that an electron has spin 1/2 just like it has mass 9.11x10^-31 kg and charge 1.6x10^-19 C. It's what makes an electron an electron.

 

[nomadreid]

Thanks for the replies, bob012345 and kuruman.

Please explain what you mean by "mutable wave excitations". Thanks.

I should have probably stated that as "excitation of fields" (an interesting point of view of this is in https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf); by "mutable" I mean that any particle can change into another particle , destroying the ancient idea of the immutability of "elementary particles".

I always took it to mean that an electron has spin 1/2 just like it has mass 9.11x10^-31 kg and charge 1.6x10^-19 C. It's what makes an electron an electron.

Very good answer. The question is whether one could reasonably substitute "spin 1/2" by a combination of other properties. (I have no idea what this might be: as a limit or quantization of a classical spinning point particle, whatever that might be, a representation in terms of other properties of the particle, some topological or matrix representation of space-time, I do not know: this is why I ask.)

 

[Vanadium 50]

I think your question is too vague to be answered. "Some topological or matrix representation of space-time" sounds like it has meaning, but when you look at it closely, not so much.

Specifically, why isn't "intrinsic orbital angular momentum" an answer to your question?

 

[nomadreid]

You are correct, Vanadium, my question is rather vague, so I will rephrase it. Basically, the description of spin as intrinsic orbital angular momentum is satisfactory, but:
(a) is it the fact that spin is quantized that guarantees that spin cannot be formulated as a classical property (at best having analogies to classical theory)? Or is there a deeper reason?
(b) Do I understand correctly that spin is an independent quantity in the sense that, if we could list all the other independent quantities of an electron (mass-energy, charge, position, etc.) , then spin could not be replaced by a function of these other quantities? (This is a straight yes/no question. Tie-in to my previous formulation: the independence would be the analogue of the ancient idea of entities which were "elementary" in not being composite or reducible. )

(I cannot justify the suggestions in my previous post, as they were not pointing to any specific representation, but merely asking if something more specific along these lines existed. From your reaction, I gather the answer is no.)

To put this another way (and to give the motivation behind the question): from Wikipedia https://en.wikipedia.org/wiki/Spin_(physics)
'Wolfgang Pauli in 1924 was the first to propose a doubling of the number of available electron states due to a two-valued non-classical "hidden rotation".'
I would guess that this meant that he was proposing an inner degree of freedom of the electron, which could not be described classically. What convinced him that this had to necessarily be purely quantum mechanical in nature? (This was before the correct interpretation of the Stern-Gerlach experiment, again according to Wikipedia.)

 

[vanhees71]

Why are you posting in the classical physics forum about spin? It's a quantum-theoretical concept and cannot be explained in terms of classical physics.

The spin of a particle is indeed one of several intrinsic properties characterizing the specific kind of a particle. The best theory we have today about particles is the standard model of elementary particle physics. To understand, how particles are classified you need the concept of symmetry groups and unitary group representations in quantum mechanics.

 

[nomadreid]

Why are you posting in the classical physics forum about spin?

Oops. No justification, merely an oversight. My apologies. Should I, can I, transfer this thread?

It's a quantum-theoretical concept and cannot be explained in terms of classical physics.

To understand, how particles are classified you need the concept of symmetry groups and unitary group representations in quantum mechanics.

I understand that spin is described in quantum-mechanical terms, and apparently that works very well, and no classical way to do it has been found. However, this is not the same (although it is a strong indication) as an impossibility (no-go) proof, of which there are lots in physics (ignoring trivial objections that physics is not as unchangeable as pure mathematics). There are no perpetual motion machines. Is there a corresponding no-go theorem for a classical representation of quantum spin?

 

[Vanadium 50]

(a) is it the fact that spin is quantized that guarantees that spin cannot be formulated as a classical property (at best having analogies to classical theory)?

Why are you picking on spin? The universe is fundamentally quantum mechanical.

(b) Do I understand correctly that spin is an independent quantity in the sense that, if we could list all the other independent quantities of an electron (mass-energy, charge, position, etc.) , then spin could not be replaced by a function of these other quantities?

I think the answer is "yes", but one could say if the mass is 511 keV and the charge is negative, I know the magnitude of the spin, because electrons are spin-1/2.

 

[bob012345]

Oops. No justification, merely an oversight. My apologies. Should I, can I, transfer this thread?

I understand that spin is described in quantum-mechanical terms, and apparently that works very well, and no classical way to do it has been found. However, this is not the same (although it is a strong indication) as an impossibility (no-go) proof, of which there are lots in physics (ignoring trivial objections that physics is not as unchangeable as pure mathematics). There are no perpetual motion machines. Is there a corresponding no-go theorem for a classical representation of quantum spin?

If spin is just intrinsic angular momentum, (a term I prefer to intrinsic orbital angular momentum since what is being orbited in an isolated electron?), then whether or not there could ever be a classical model of it depends on how you model the electron. If it's an infinitesimal mathematical point, as I was taught, a classical rotation doesn't work. If it were modeled as something else, maybe it would. As a point, mass and charge seem equally mysterious as how does an infinitesimal point carry a mass or charge at all with no size to speak of? Sometimes I think the boundary between what we call classical and what we call quantum has more to do with the history of scientific thought that meaningful boundaries.