Spin

[swansont]

you must know some clever 12 year olds... (jk).

 

OK, so if I understand correctly (unlikely), angular momentum in classical physics is rotational momentum, such that when you set some object spinning about its own axis, it tends to keep spinning unless some force acts upon it to slow it down or stop it.

 

In QM, it seems like spin is a measure of angular momentum of elementary particles but which can only hold specific values (quantised)? But elementary particles don't have an internal structure, so they don't actually rotate. Is that correct?

 

Can you point me in the right direction from here?

 

That's basically it.

[Blahah]

OK, but if elementary particles can't actually rotate on their own axis, what does angular momentum mean in a QM context? Or is it just an analogy?

[swansont]

OK, but if elementary particles can't actually rotate on their own axis, what does angular momentum mean in a QM context? Or is it just an analogy?

 

It's still angular momentum, and with the caveat of it being quantized, still behaves the same way as classical angular momentum. In fact, circularly polarized light, which also has spin, was used to make a physical glass plate spin just by passing light straight through it.

[Blahah]

It's still angular momentum, and with the caveat of it being quantized, still behaves the same way as classical angular momentum. In fact, circularly polarized light, which also has spin, was used to make a physical glass plate spin just by passing light straight through it.

 

That is extremely cool. Do you know a reference where I can read more about that, as I can't find it on google (the plate spinning, I have stuff to read on spin and circular polarized light).

[swansont]

That is extremely cool. Do you know a reference where I can read more about that, as I can't find it on google (the plate spinning, I have stuff to read on spin and circular polarized light).

Yeah, I meant to include a link. (I was just dealing with a power outage. Lost the internet there for a few minutes.)

 

http://scienceblogs.com/principles/2010/04/measuring_the_angular_momentum.php

 

In the Feynman video on the other thread, he mentions that iron atoms get magnetized because all the electrons are spinning together in the same direction. For some reason this led me to wonder if there was something special about iron. Then it occurred to me that iron is supposedly the cut off point for elements that can split and release rather than consume energy. Is it possible that these two attributes of iron are related? Should this question be posted as a new thread?

 

No, magnetism is an atomic effect and fission/fusion is nuclear, and there are other ferromagnetic elements. Iron behaves this way because of the unpaired electrons and because it has a metal lattice structure, so you can "freeze in" the alignments when the material is cool enough. (if it's too hot the thermal motion scrambles the alignment and there is no net field)

[lemur]

No, magnetism is an atomic effect and fission/fusion is nuclear, and there are other ferromagnetic elements. Iron behaves this way because of the unpaired electrons and because it has a metal lattice structure, so you can "freeze in" the alignments when the material is cool enough. (if it's too hot the thermal motion scrambles the alignment and there is no net field)

So the iron atom tends toward asymmetry (unpaired electrons) and the lattice-freezing prevents it from losing that symmetry once established? I think I read about this with the formation of natural magnets due to the Earth's magnetic field. I guess that raises the question of what magnetized Earth in the first place.

 

As for the atomic vs. nuclear issue, I sort of knew that but I thought there could possibly be some relationship between the electron structure of the atom and its nuclear dynamics, like maybe the unpaired-electron quality is related to some kind of fission/fusion neutrality in the nuclear force. I know this sounds like straw-grasping, and it is basically, but I also question whether the correlation should be so easily dismissed without further thought (nevermind the fact that I'll be thinking about it further one way or the other now).

 

 

[Mike Smith Cosmos]

Thank you Mr Shaken not stirred "swansont". For your succinct comment. Surely we are moving from one simple statement like "spin" to another like "angular momentum". Perhaps I need to go and do some homework on angular momentum. But I thought it had something to do with mass and velocity not in a straight line but in some form of curved path. Perhaps this curved movement is more of a partial arc rather than a complete circle. This would infer more of a vibration than a spin. Is this leaning more toward string theory? I am aware that residual spin is the result of the sum of all spins within the system. However I still struggle to visualise (fatal comment) what is being summed and whats going on.

Is that a gun that you are holding in your picture ? I suggest you use it on me while I am still sane !

 

Sorry! I did not realise there was a second page. Clearly this topic of spin, has a few persons with the sort of conceptual problems that I have. I must say I think it is a defeat if we give in to the oft quoted comment ." If you think you understand it , you have got it wrong" Feynman .

[Mike Smith Cosmos]

I have started to do literature search on "Angular Momentum ". This often leads back to spin , which is inevitable. However often circular orbits, having set circumference as a constrain for standing waves and hence leading to quantum mechanical ideas as supported by Bhor, are quoted as the classical angular momentum from orbitals. The angular momentum for electrons and other particles is said to be an additional element to the overall angular momentum of the system or atom. I am currently reading the Cambridge University Press book THE NEW QUANTUM UNIVERSE by Tony Hey and Patrick Walters which has some good explanations. The fact that the term angular momentum is applied directly to spin, still seems to infer that something ( even if it is ill defined by locality and non locality issues ) is generating a "force" be it by a principle of equivalence or some other mathematical transform. Can anyone share more ideas on the difference between classical angular rotation giving rise to standing waves, and Spin ( angular momentum) again in quantum terms of up and down spin?

[swansont]

Spin is angular momentum and behaves like angular momentum in interactions. A photon, which has one unit of angular momentum, can be absorbed an atom, but requires the atom change its angular momentum by one quantum ([math]\hbar[/math]). That can be by changing the orbital value by 1 or by flipping the spin from up to down vice versa.

[ajb]

Can anyone share more ideas on the difference between classical angular rotation giving rise to standing waves, and Spin ( angular momentum) again in quantum terms of up and down spin?

 

Well, let us consider the momentum of a massive particle in its rest frame. It is given by

 

[math]P^{\mu} = (m ,0,0,0)[/math]

 

(set the speed of light to 1). You see that rotations, can be thought of as being a subgroup of the Lorentz group, will preserve the momentum. In essence this is the origin of spin. So it does have something to do with rotations, but it is not as simple as considering the particle to be rotating about some axis.

 

To understand this properly you have to think about Casimir operators and the Pauli-lubanski pseudovector.

[steevey]

It's still angular momentum, and with the caveat of it being quantized, still behaves the same way as classical angular momentum. In fact, circularly polarized light, which also has spin, was used to make a physical glass plate spin just by passing light straight through it.

 

Do particles have angular momentum in the way that you can derive the shape of an electron using and angular momentum properties and some other properties in a 3D Cartesian grid? Like the shape of an electron is in sphere, so in a classical sense the electron is circularly traveling around the nucleus?

[swansont]

Do particles have angular momentum in the way that you can derive the shape of an electron using and angular momentum properties and some other properties in a 3D Cartesian grid? Like the shape of an electron is in sphere, so in a classical sense the electron is circularly traveling around the nucleus?

 

The shape of the electron or the shape of the orbital? The electron is, as best as we can measure, a point particle. As far as orbits, orbitals go, you can tell the shape if they have a large amount of angular momentum, in so-called Rydberg states. (n is 40 or 50 or so, and the electron has maximum angular momentum of [imath](n-1)\hbar[/imath] ) Then it starts behaving classically.

[steevey]

The shape of the electron or the shape of the orbital? The electron is, as best as we can measure, a point particle. As far as orbits, orbitals go, you can tell the shape if they have a large amount of angular momentum, in so-called Rydberg states. (n is 40 or 50 or so, and the electron has maximum angular momentum of [imath](n-1)\hbar[/imath] ) Then it starts behaving classically.

 

I still don't get why spin matters then if a particle in the atomic level acts nothing like we see in the classical level. Aren't they virtual particles there? How can they really even have angular momentum unless thats just another classical description that would make sense to describe its shape?

Edited February 21, 2011 by steevey

[swansont]

I still don't get why spin matters then if a particle in the atomic level acts nothing like we see in the classical level. Aren't they virtual particles there? How can they really even have angular momentum unless thats just another classical description that would make sense to describe its shape?

 

To say that it acts nothing like a classical system isn't accurate. It behaves like it has angular momentum, so angular momentum has to be conserved, and that all still holds. The source of the angular momentum isn't classical, and modeling it as such quickly leads to a failure of the model.

[mississippichem]

I still don't get why spin matters then if a particle in the atomic level acts nothing like we see in the classical level. Aren't they virtual particles there? How can they really even have angular momentum unless thats just another classical description that would make sense to describe its shape?

 

The angular momentum manifests itself as different orbital shapes:

 

 

The electrons have the angular momentum:[math] (n-1)\hbar [/math]

 

Also, the angular momentum quantum numbers that are allowed are all the whole number values from [imath] n-n [/imath] to [imath]n-1[/imath]. So for an [imath]n=2[/imath] orbital, values for *[imath]m_{\ell}[/imath] (angular momentum number) are [imath] n-2=0[/imath] (a sphere), and [math] n-1=1[/math] (two "dumbells").

 

One can loosely see, by inspection, that these orbitals are all in a series of harmonics and that angular momentum increases as we go up the harmonic series. One can also see that in the Rydberg atoms that swansont mentioned (where "n" is quite large) there are many available angular momentum states, which is getting more and more similar to the classical world we are familiar with.

 

EDIT: [math] \ell [/math] quantum number not [math]m_{\ell}[/math]

Edited February 22, 2011 by mississippichem

[lemur]

The angular momentum manifests itself as different orbital shapes:

 

 

The electrons have the angular momentum:[math] (n-1)\hbar [/math]

 

Also, the angular momentum quantum numbers that are allowed are all the whole number values from [imath] n-n [/imath] to [imath]n-1[/imath]. So for an [imath]n=2[/imath] orbital, values for [imath]m_{\ell}[/imath] (angular momentum number) are [imath] n-2=0[/imath] (a sphere), and [math] n-1=1[/math] (two "dumbells").

 

One can loosely see, by inspection, that these orbitals are all in a series of harmonics and that angular momentum increases as we go up the harmonic series. One can also see that in the Rydberg atoms that swansont mentioned (where "n" is quite large) there are many available angular momentum states, which is getting more and more similar to the classical world we are familiar with.

So these shapes are the wave distributions of electron-position as they orbit their nucleus? And the angular momentum of their "spin" as point-particles is what causes their wave-distributions to change into the above-depicted shapes? And then is it the case that the atoms behave as solid objects in these shapes? I.e. that they can move around and turn in various directions in a non-quantized way? Or are they still, at this level, bound by quantized states of motion?

[steevey]

The angular momentum manifests itself as different orbital shapes:

 

 

The electrons have the angular momentum:[math] (n-1)\hbar [/math]

 

Also, the angular momentum quantum numbers that are allowed are all the whole number values from [imath] n-n [/imath] to [imath]n-1[/imath]. So for an [imath]n=2[/imath] orbital, values for *[imath]m_{\ell}[/imath] (angular momentum number) are [imath] n-2=0[/imath] (a sphere), and [math] n-1=1[/math] (two "dumbells").

 

One can loosely see, by inspection, that these orbitals are all in a series of harmonics and that angular momentum increases as we go up the harmonic series. One can also see that in the Rydberg atoms that swansont mentioned (where "n" is quite large) there are many available angular momentum states, which is getting more and more similar to the classical world we are familiar with.

 

EDIT: [math] \ell [/math] quantum number not [math]m_{\ell}[/math]

 

So although an electron isn't just a single point, as a wave it sort of acts like its turning and moving in specific ways? Because that really doesn't seem like how virtual particles act at all.

Spin and angular momentum at this level seem more like an imaginary number, like Pi.

Edited February 22, 2011 by steevey

[swansont]

So although an electron isn't just a single point, as a wave it sort of acts like its turning and moving in specific ways? Because that really doesn't seem like how virtual particles act at all.

Spin and angular momentum at this level seem more like an imaginary number, like Pi.

 

Atomic electrons aren't virtual particles.

[imatfaal]

So although an electron isn't just a single point, as a wave it sort of acts like its turning and moving in specific ways? Because that really doesn't seem like how virtual particles act at all.

Spin and angular momentum at this level seem more like an imaginary number, like Pi.

 

And Pi isn't an imaginary number. An imaginary number has a square that is negative and are usually shown by using a multiple of i which is defined as the square root of minus one . Pi is an irrational (ie is not the ratio of two integers) and transcendental number (ie is not the root of any polynomial with rational coefficients)

Edited February 22, 2011 by imatfaal

[steevey]

And Pi isn't an imaginary number. An imaginary number has a square that is negative and are usually shown by using a multiple of i which is defined as the square root of minus one . Pi is an irrational (ie is not the ratio of two integers) and transcendental number (ie is not the root of any polynomial with rational coefficients)

 

It's still a number that isn't existent in reality but still helps you find the results in it which also happens to be the nature of squared negative numbers. It's only mathematically that a circumference has infinitesimal length because a, I could theoretically just cut it into a straight line proving its finite length, or b, it contains only a specific number of atoms.

Edited February 22, 2011 by steevey

[ajb]

It's still a number that isn't existent in reality but still helps you find the results in it which also happens to be the nature of squared negative numbers. It's only mathematically that a circumference has infinitesimal length because a, I could theoretically just cut it into a straight line proving its finite length, or b, it contains only a specific number of atoms.

 

 

The point is the term imaginary has a very specific meaning in mathematics. You will have to avoid using it for something else, otherwise we will all get very confused.

[imatfaal]

It's still a number that isn't existent in reality but still helps you find the results in it which also happens to be the nature of squared negative numbers. It's only mathematically that a circumference has infinitesimal length because a, I could theoretically just cut it into a straight line proving its finite length, or b, it contains only a specific number of atoms.

 

Steevey - I am trying to help here. Maths and physics use very precise definitions and getting them confused, conflating them, or using them wrongly will totally throw you.

 

As an example, you use the phrase above "squared negative numbers" - most people would say that a squared negative number is a positive number ( eg (-2)² = 4); the imaginary number is a 'square root of negative number' or alternatively a number whose square is negative.

[steevey]

The point is the term imaginary has a very specific meaning in mathematics. You will have to avoid using it for something else, otherwise we will all get very confused.

 

Point taken

 

Steevey - I am trying to help here. Maths and physics use very precise definitions and getting them confused, conflating them, or using them wrongly will totally throw you.

 

As an example, you use the phrase above "squared negative numbers" - most people would say that a squared negative number is a positive number ( eg (-2)² = 4); the imaginary number is a 'square root of negative number' or alternatively a number whose square is negative.

 

I know your trying to help me, but I don't just care about the tiny semantics right now as much as I care about people understanding the concept I'm asking about so that it can get my question answered.

Is spin an actual physical thing, or is it more like and imaginary number where the classical components of it can be mathematically used to describe the shape or positions but doesn't actually exist?

Edited February 23, 2011 by steevey

[mississippichem]

I know your trying to help me, but I don't just care about the tiny semantics right now as much as I care about people understanding the concept I'm asking about so that it can get my question answered. [/size][/font]

Is spin an actual physical thing, or is it more like and imaginary number where the classical components of it can be mathematically used to describe the shape or positions but doesn't actually exist?

 

I would hardly call the definition of imaginary numbers "tiny semantics". It is in fact very relevant to the quantum mechanics you seem so interested in.

 

But yes, spin physically exists. Don't think of it as a classically spinning object though, because it isn't. Just know that every electron can take on one of two spin values that are equal in magnitude and opposite. If you truly want to understand spin, you must take on the mathematics that are required for everyone else to understand it.

[steevey]

I would hardly call the definition of imaginary numbers "tiny semantics". It is in fact very relevant to the quantum mechanics you seem so interested in.

 

But yes, spin physically exists. Don't think of it as a classically spinning object though, because it isn't. Just know that every electron can take on one of two spin values that are equal in magnitude and opposite. If you truly want to understand spin, you must take on the mathematics that are required for everyone else to understand it.

 

 

Mathematics would help me see the patterns of spin, but it why would it help me see it as a physical thing.?I can see an electron as a wave of existence without considering any mathematics, yet math is crucial for determining the specifics of that. And I wasn't saying "tiny" in referring to the importance of its definition, but rather of its importance to my question.