Understanding Spin: What is it & How is it Measured?

[PhysicsDad]

This may be a basic question, but it's something I'm having a hard time understanding. The Wikipedia article I am reading about spin http://en.wikipedia.org/wiki/Particle_spin seems to be saying that spin isn't really what we think of on the macroscopic scale (ie: spinning on an axis like a planet). So my question is, what exactly IS spin, and how is it measured? Any help in understanding this would be great.

Thank you all.

 

[tiny-tim]

Hi PhysicsDad!

The Wikipedia article I am reading about spin http://en.wikipedia.org/wiki/Particle_spin seems to be saying that spin isn't really what we think of on the macroscopic scale (ie: spinning on an axis like a planet). So my question is, what exactly IS spin, and how is it measured?

In the first sentence, it says spin is a form of angular momentum.

ok, it doesn't have an exact counterpart in classical mechanics, but I've never seen anything wrong in thinking of it as a spinning ball, at least for eg electrons.

You measure the spin by measuring the angular momentum, by seeing how it affects the angular momentum of other things.

 

[Bill_K]

ok, it doesn't have an exact counterpart in classical mechanics, but I've never seen anything wrong in thinking of it as a spinning ball, at least for eg electrons.

Okay! I'll add "Electrons are little spinning balls" to the Doublethink List - things we like to believe in, even though deep down inside we know they're false! This will make it easier when we have to unlearn them. Meanwhile, in order to complete the entry, I just have a few questions:

How big is the ball? What is it made of? Is the surface moving faster than the speed of light? Does the rapid rotation make the electron oblate? What overcomes the Coulomb repulsion and holds it together? Can it vibrate - is this what a muon is?

What about photons - are they little spinning balls too? If not, does that mean that photon spin is something basically different from electron spin?

Is spin a vector of length √s(s+1), inclined and precessing about the z axis?

 

[tiny-tim]

Hello Bill!

How big is the ball?

it is a point, like the singularity of a naked black hole

it has mass and angular momentum, like the singularity of a naked black hole

What is it made of?

it is made of what it is made of (obviously! ) …

same answer as i'd give to "what is an electron made of?" "what is a singularity made of?"

Is the surface moving faster than the speed of light?

what surface?

Does the rapid rotation make the electron oblate?

please define what you mean by "oblate" for a point object

What overcomes the Coulomb repulsion and holds it together?

the Coulomb repulsion between what and what?

Can it vibrate - is this what a muon is?

please define what you mean by "vibrate" for a point object

What about photons - are they little spinning balls too? If not, does that mean that photon spin is something basically different from electron spin?

you mean, are they like little spinning balls too?

as much as electrons are, but with spin 0 instead of spin 1/2

Is spin a vector of length √s(s+1), inclined and precessing about the z axis?

what z axis?

anyway, for electrons and photons there's no intrinsic (as opposed to orbital) precession, there's only spin-up and spin-down

in conclusion … there is no classical analogue to spin

moreover thinking of a particle as a particle is misleading anyway!

but if you insist on such an unnatural interpretation of the universe, you got to admit that the particle is rotating ​

 

[haael]

Spin is a swirl. Imagine a fluid in a round vessel. Imagine that the fluid rotates. This is a non-laminar motion. The outermost layer has some speed and some radius of rotation. Now imagine that all layers have the same angular momentum. Since they have different radiuses, they have to have different speeds. In the very center you have a degenerated layer being a single point. It has zero radius and hence zero speed. What it has is spin.

Spin in relation to orbital angular momentum are somewhat conceptually analogous to the relation of rest mass and relativistic mass.

Imagine any compound particle, say a meson. It has some rest mass. When we try do break it up, it comes out that a fraction of the meson's mass comes from the rest mass of its quarks, but most of it comes from their kinetic energy. That means - rest mass of a compound particle may be explained in terms of its components movement. We may ask - does it mean that all truly elementary particles are massless and all massive particles are just composed of moving parts? The answer is no - elementary particles do have rest mass that can't be explained as a movement of their components.

Now imagine our meson again. It has some intrinsic angular momentum. When we split it up, we see that part of the angular momentum comes from the intrinsic angular momentum of its quarks, but most of it come from their orbital movement. We may ask - are all truly elementary particles spinless and all intrinsic angular momentum may be explained in terms of their components movement? The answer is no - elementary particles do have intrinsic spin that can't be explained this way.

 

[Naty1]

So my question is, what exactly IS spin...

So by now you can probably tell there is no simple answer except maybe something like
'it's a characteristic of fermions and bosons that we have noticed and measured...' as Wikipedia describes.

Spin is an inherent characteristic of particles. If an electron did not have
its spin it would not be an electron, just as if it had no charge it would not be. You can't change the spin of a particle as you can change the spin of, say, a top.

And spin is quantized...it takes on only certain values. That's equally 'weird' and has no macroscopic counterpart...for example, you can 'spin' a baseball in many different ways and it remains a baseball...but note that such spin may change the characteristic trajectory of the ball. Spin, whatever it is, does have physical [observable] effects. Like 'charge'...nobody knows exactly what that is, either...but we observe it and how it interacts and describe it in mathematical models reflecting those observations.

It's not like spin pops out of some first principles and is required. But we know it IS required
for this universe because we observe it here. A number of things in quantum theory have no clear and unambiguous macroscopic counterpart: for example, that quantum theory is a causal but indeterministic theory. States, or observables, take a statistical range of values rather than an exact value. Particles exhibits both wave and particle characteristics...and spin! Quantum mechanics requires us to think in some new ways

 

[strangerep]

Okay! I'll add "Electrons are little spinning balls" to the Doublethink List - things we like to believe in, even though deep down inside we know they're false!

Geez Bill, take it easy. Did you forget to add this icon: ?

For the benefit of other readers:

Spin (aka intrinsic angular momentum) does have a classical meaning.
See earlier discussion: https://www.physicsforums.com/showthread.php?p=4004609

(Quantization of angular momentum is of course a quantum phenomenon, however.)

It's not like spin pops out of some first principles [...]

Actually, it kinda does -- if one regards the relativity principle (physical laws are the same for all inertial observers) as a more fundamental starting point.

 

[NegativeDept]

This may be a basic question, but it's something I'm having a hard time understanding. The Wikipedia article I am reading about spin http://en.wikipedia.org/wiki/Particle_spin seems to be saying that spin isn't really what we think of on the macroscopic scale (ie: spinning on an axis like a planet). So my question is, what exactly IS spin, and how is it measured?

This is a basic question, but it's something physicists have had a very hard time understanding for decades!

If you grab 10 quantum mechanics textbooks, I'd bet you'll find at least 5 different explanations of spin. That said, all of them will probably agree that 0) it's got units of angular momentum and 1) the change-of-coordinate rules for transforming spin states look a whole lot like the rules for transforming the classical angular momentum of a rigid spinning object.

If any of those textbooks are intended for graduate students, part 1) will probably include a bunch of stuff about Lie algebra isomorphisms to generators of angular momentum and maybe also a reference to Noether's theorem. Unfortunately, this will mostly look like mystical numerology nonsense.

 

[vanhees71]

Spin is a pretty abstract thing, not having a really good analogue in classical physics. The best way to establish the quantum-mechanical rules are symmetry principles, and the very first symmetry principles to be used to build a concrete quantum theoretical model for, e.g., elementary particles, are those arising from the symmetry of the underlying space-time model.

In non-relativistic (Newtonian) or special-relativistic physics space is represented by a three-dimensional Eucildean affine manifold and thus is homogeneous and isotropic. Thus translations and rotations are symmetries of space and thus must be represented in quantum theory. In addition there's also the time-translation and boost symmetry. Due to a famous analysis by Wigner this symmetry group of classical physics must be represented by a unitary ray representation of this group on Hilbert space. Since the group is continuous (more precisely that's the case for the proper orthochronous Galilei transformations and the proper orthochronous Poincare transformations), this is equivalent to a unitary representation of a central extension of the universal covering group.

In non-relativistic physics the central extension is given by the Galilei group with the rotation group SO(3) substituted with its covering group SU(2) and the mass operator as central charge. The spatial translation subgroup gives rise to momentum $\vec{p}$ as an observable and any momenum-eigenstate can be reached from the zero-momentum eigenstate by a Galilei boost, represented by the corresponding unitary operator. Thus one has only to deal with the subgroup which leaves the zero-momentum eigenstate invariant to get all possible representations. The group which leaves the zero-momentum eigenstate invariant obviously is the rotation group, represented by SU(2).

This means that the intrinsic structure of a quantum system with vanishing momentum is characterized by its mass (i.e., the value of the central charge of the representation) and the representation of SU(2) according to which the zero-momentum states are transforming under rotations. The unitary representations of SU(2) are well-known and derived in any good textbook of quantum theory, leading to the representations of angular momentum, which are nothing else than the generators for rotations. Thus "spin" tells us, how the zero-momentum eigenstates of the system transform under rotations.

In non-relativistic physics one can uniquely separate the total angular momentum in a spin and an orbital angular momentum part, because the boosts, which generate any momentum eigenstate out of the zero-momentum eigenstates built an Abelian subgroup of the Galilei group, not mixing with the rotations.

In relativistic physics the Poincare group is somwhat simpler than the Galilei group, and all ray representations are simply induced by unitary representations of the covering group, which substitutes the special orthochronous Lorentz group $\mathrm{SO}(1,3)^{\uparrow}$ by $\mathrm{SL}(2,\mathbb{C})$. The very same analysis of these representations leads to very similar notions for massive states (mass is given as the Casimir operator of four-momentum $p^2=m^2$, i.e., it's not a central charge as in Newtonian physics). Only it's not possible to uniquely split the total angular momentum into spin and orbital part, because the boosts themselves build no subgroup but only boosts together with rotations. For massless states it's a bit more complicated: There you have helicity instead of spin as the corresponding intrinsic quantum number of the system.

For details, see my qft manuscript

http://fias.uni-frankfurt.de/~hees/publ/hqm.pdf

or Weinberg, Quantum Theory of Fields, Volume 1.

So, spin is a rather abstract notion. The idea of imaging elementary particles with spin as rotating little bullets is dangerous. This picture is even dangerous for spinless particles since it's only a classical approximation which holds not true if quantum theory is really important. The best picture we have about them is quantum field theory and nothing else. We have to live with this rather abstract picture since our senses are simply not trained for the microscopic world, where quantum theory has to be applied. Except the fact that the matter among us is pretty stable, we don't experience much quantum-theoretical behavior of the macroscopic objects we deal with, so that we cannot have intuitive notions about it from everyday experience.

 

[chill_factor]

as much as electrons are, but with spin 0 instead of spin 1/2

photons are spin 1. that is why they can cause rotational transitions in molecules and carry off molecular angular momentum.

 

[tiny-tim]

oops!

 

[PuckNorris]

A point cannot spin on its axis because axis is a line which is an object made up of many points. The point do not have any sense of direction. Spin looks much like angular momentum for classical object but its very hard to imagine what it really is.
Trying to imagine what spin is as hard as trying to immagine what the electron is or what the photon is.
We much often use to describe particles as little tiny balls that have certain positions in space just to get some visual intuition but we know that this is not true.

When I think of particle spin I really avoid to imagine spinning balls(spinning dots?) and think of it like a fundamental proparty that just happens to look like a quantum version of angular momentum and does not need any explanation at this point.

 

[bahamagreen]

Does spin change when one rotates the object within which the particle is located?
For example, when I turn my coffee cup handle from the left side to the right, what happens to the spin of the particles that comprise the cup? With respect to what is spin measured?

 

[vanhees71]

It's always good to imagine what's observable when discussing a physical quantity. In connection with spin, two things come to mind. One is that the thermodynamic potential of an ideal gas of particles with spin has a degeneracy factor $2s+1$, which means that there are intrinsic degrees of freedom. Each momentum eigenspace is $2s+1$ dimensional (for massive particles).

Another is that with spin usually the particle also has a mangnetic moment, which can be used to measure the quantized spin-magnetic quantum numbers (i.e., $\sigma_z \in \{\pm s, \pm(s-1),\ldots \}$) in a Stern-Gerlach experiment.

This together with the abstract analysis of the spin phenomenon in terms of the representation theory of the space-time symmetries gives a picture about the meaning of spin as a quantum phenomenon for which there is no good classical analogy.

 

[epenguin]

Hello Bill!


it is a point, like the singularity of a naked black hole

it has mass and angular momentum, like the singularity of a naked black hole


it is made

Another physics outsider's crude question but...
I've often heard that the electron is a point.
Do they really mean, do they really think that?
Or do they mean 'as far as anyone knows' or 'there is nothing to probe it with that can reveal any extension like a blob' or something like that?
Does the concept have any operational significance, would anything observable change if it had some extension however small?
It always struck me that a point was contrary to the spirit of quantum mechanics where nothing can be totally defined in space. So I wondered if thisis not the cause of the problems I know you have?
And anyway our electrons in chemistry are not points they are fuzzy blobs. I know they are just probabilities of this point which is in principle everywhere, but is mostly somewhere because a force has kept it mostly there, they are called charge clouds, I suppose they are mass clouds too, (should we just call them property clouds?). Compressible blobs.
What pointlike property does it have actually?

 

[tiny-tim]

hi epenguin!

I've often heard that the electron is a point.
Do they really mean, do they really think that?
…
It always struck me that a point was contrary to the spirit of quantum mechanics where nothing can be totally defined in space. So I wondered if thisis not the cause of the problems I know you have?

in quantum mechanics, even thinking of a particle as a particle is unrealistic

intuitively, it can be helpful to regard an electron or photon as a point mass rotating on an axis

it is helpful for some purpose but not for others

as you say, they are also like fuzzy blobs!

there is no classical analogue to the spin of an electron or photon​

 

[Bill_K]

I've often heard that the electron is a point.
Do they really mean, do they really think that?
Or do they mean 'as far as anyone knows' or 'there is nothing to probe it with that can reveal any extension like a blob' or something like that?
Does the concept have any operational significance, would anything observable change if it had some extension however small?

Yes, we really, really do think that! I hope it was apparent that my earlier post to this thread was entirely tongue-in-cheek.

The correct term is point-like, meaning smaller than anything we've been able to measure. To the best of our knowledge and belief, all elementary particles are point-like. Only composite particles like neutrons and protons have an extended size. The small size limit corresponds to the high energy limit, presently multi-TeV, which is oh about 10^-16 to 10^-17 cm.

The point-like property of elementary particles is an absolutely essential cornerstone of the highly successful Standard Model, which is based on local QFT.

It always struck me that a point was contrary to the spirit of quantum mechanics where nothing can be totally defined in space.

This is a misconception. Schrödinger quantum mechanics too is a theory of a point particle. The "cloud" you refer to describes the probability of the particle's location, but wherever that particle is, it IS a point, and interactions between particles are understood to always occur at points.

 

[haael]

The "cloud" you refer to describes the probability of the particle's location, but wherever that particle is, it IS a point, and interactions between particles are understood to always occur at points.

It's just the Copenhagen interpretation. But it's not the only valid one.

I personally prefer to think of particles as fields. That means: the fields are fundamental objects and actual particles are their excitations. In this picture electron is not point-like, despite it yields exactly the same predictions as Copenhagen and any other interpretation.

Think of it: if all particles were literally points, they could not collide at all! The probability of a zero-sized point hitting other zero-sized point is exactly zero. Even in your picture you have to somewhat relax the notion of a point-like particle. You may introduce a field that surrounds it or some other thing i.e. to guide photons directly to the electron. You can not defend the picture of an elementary particle as a pure mathematical point.

 

[Bill_K]

Think of it: if all particles were literally points, they could not collide at all! The probability of a zero-sized point hitting other zero-sized point is exactly zero. Even in your picture you have to somewhat relax the notion of a point-like particle. You may introduce a field that surrounds it or some other thing i.e. to guide photons directly to the electron. You can not defend the picture of an elementary particle as a pure mathematical point.

Nonsense. Complete and utter nonsense.