# What is spin up and spin down?

• davidong3000

#### davidong3000

I tried to find this on google but could not find any solid answers. What is spin up and spin down? I know its something only applying to spin 1/2 particles. Does spin up mean a right hand rule spin with the magnetic north pole of the particle parallel in the direction of the thumb? Or does it mean that when u look at a particle in a certain direction it appears to be rotating anti clockwise along that direction?

As far as I know we have limitations on how we can measure spin due to the Heisenberg uncertainty. In practice this means it is only possible to measure the magnitude of the spin vector and the magnitude of one component. If I remember correctly this axis is usually labelled $$S_z$$ and since the z-axis is usually tied to up and down directions I would guess that $$S_z$$ < 0 is spin down and $$S_z$$ > 0 is spin up.

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Jheriko said:
As far as I know we have limitations on how we can measure spin due to the Heisenberg uncertainty. In practice this means it is only possible to measure the magnitude of the spin vector and the magnitude of one component. If I remember correctly this axis is usually labelled $$S_z$$ and since the z-axis is usually tied to up and down directions I would guess that $$S_z$$ < 0 is spin down and $$S_z$$ > 0 is spin up.

I have seen that link and was reading it long time before u sent this message :(

I still don't get it... when they talk about measuring the particle from z direction is z direction any agreed upon angle? And when the particle is up does this mean the north pole of the particle is facing toward the viewer or instrument along that angle?

some 1 please help, there seems to be zero proper definition of spin up or down on the internet...

Dave

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davidong3000 said:
I still don't get it... when they talk about measuring the particle from z direction is z direction any agreed upon angle? And when the particle is up does this mean the north pole of the particle is facing toward the viewer or instrument along that angle?

The observer picks a line, any line, and orients his apparatus along it (in Stern-Gerlach, for example, this would be the orientation of the magnetic field). This then divides the incoming particle stream into three, one of the outer ones of which is labeled spin up and the other spin down, while the middle stream is regarded as having spin component zero along that line. The important point here is that spins along different lines do not commute, and are subject to an uncertainty relation in consequence.

AFAIK the z is just an arbitrary label for a direction.

Also after looking in Wikipedia more thoroughly myself there is a little bit defining spin up and spin down. It also reminds me that I neglected to mention the importance of spin-1/2, afaik the spin up and spin down labels only apply to these particles, presumably because other spins have more eigenstates (I am not sure, I am a quantum noob myself).

http://en.wikipedia.org/wiki/Spin-1/2

Found It!

The observer picks a line, any line, and orients his apparatus along it (in Stern-Gerlach, for example, this would be the orientation of the magnetic field). This then divides the incoming particle stream into three, one of the outer ones of which is labeled spin up and the other spin down, while the middle stream is regarded as having spin component zero along that line. The important point here is that spins along different lines do not commute, and are subject to an uncertainty relation in consequence.

Check this out

http://www.ncsu.edu/felder-public/kenny/papers/bell.html#FOOTNOTE_9

and scroll down to "Appendix II. What's Being Measured"

According to this link, what ever angle u choose to look at a particle it's magnetic south pole with either point directly toward or away from you. If toward : spin up, if away : spin down.

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davidong3000 said:
I tried to find this on google but could not find any solid answers. What is spin up and spin down? I know its something only applying to spin 1/2 particles. Does spin up mean a right hand rule spin with the magnetic north pole of the particle parallel in the direction of the thumb? Or does it mean that when u look at a particle in a certain direction it appears to be rotating anti clockwise along that direction?

There's no such thing as "magnetic north pole of the particle"...Nor "south pole", nor any pole. These terms apply only to macroscopic spherical objects which have an internal structure as to give them magnetic properties: planet Earth is a good example (it's a revolution ellipsoid really, but nvm).

Besides, particles in quantum mechanics are point particles...

Daniel.

^ And in addition with this one has to remember that spin is not rotation (quite evident for point like objects). The particles just happen to have a property, whose observables are the generators of SU(2).

Los Bobos said:
^ And in addition with this one has to remember that spin is not rotation (quite evident for point like objects). The particles just happen to have a property, whose observables are the generators of SU(2).

As a physicist, it's not easy to accept the fact that "particles JUST HAPPEN to have a property, whose observables are the generators of SU(2)." In the case of spin 1/2 particles such as the electron, the concept of their spin really comes out of the dirac equation, and the fact that in completing the square of the Klein-Gordon equation, in order to factorize it, and allow space and time to be on the same footing, in the form of them both having a first derivative, one must resort to the use of 4X4 matrices and 4 component spinors. These 4-d spinors can be decomposed into 2-d spinors which form the familiar spin up and spin down particles we all know about. Bringing group theory into this before tackling what I talked about makes very little sense, unless you're a pure mathematician.

dextercioby said:
There's no such thing as "magnetic north pole of the particle"...Nor "south pole", nor any pole. These terms apply only to macroscopic spherical objects which have an internal structure as to give them magnetic properties: planet Earth is a good example (it's a revolution ellipsoid really, but nvm).

Besides, particles in quantum mechanics are point particles...

Daniel.

Then this literature below must be wrong then?

http://www.ncsu.edu/felder-public/kenny/papers/bell.html#FOOTNOTE_9
Apendix II
" If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole. The direction of the spin can be identified as the direction of the south pole of the magnet."

Dave

Gza said:
As a physicist, it's not easy to accept the fact that "particles JUST HAPPEN to have a property, whose observables are the generators of SU(2)." In the case of spin 1/2 particles such as the electron, the concept of their spin really comes out of the dirac equation, and the fact that in completing the square of the Klein-Gordon equation, in order to factorize it, and allow space and time to be on the same footing, in the form of them both having a first derivative, one must resort to the use of 4X4 matrices and 4 component spinors. These 4-d spinors can be decomposed into 2-d spinors which form the familiar spin up and spin down particles we all know about. Bringing group theory into this before tackling what I talked about makes very little sense, unless you're a pure mathematician.

Mind you that spin comes into play in QM not necessarily in connection with the Dirac equation, which is a relativistic one, but in connection with the representation theory of the Galilei group, which is the symmetry group of nonrelativistic classical mechanics. The only reason that equations invariant under the Galilei group are not used in a QM description of the electron and other spin 1/2 particles is the appearence of the Special Theory of Relativity which forbids using the Galilei group as the fundamental symmetry group of flat spacetime, but rather the Poincare' group.

So the concept of spin really comes out of nonrelativistic physics.

Daniel.

davidong3000 said:
Then this literature below must be wrong then?

http://www.ncsu.edu/felder-public/kenny/papers/bell.html#FOOTNOTE_9
Apendix II
" If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole. The direction of the spin can be identified as the direction of the south pole of the magnet."

Dave

The exact formulation "If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole." has the advantage of using the expression "simplest way to think about spin". However, as the author implies, this view is incorrect(oversimplified, if you prefer) and a full understanding of the concept of spin cannot be done without group theory.

Daniel.

davidong3000 said:
Then this literature below must be wrong then?

http://www.ncsu.edu/felder-public/kenny/papers/bell.html#FOOTNOTE_9
Apendix II
" If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole. The direction of the spin can be identified as the direction of the south pole of the magnet."

Dave

I bolded the most important part of your quote. He obviously presupposes a laymans perspective in his description of spin, so in a sense he's only right to a certain degree. If you aren't familiar with the intracacies of the dynamics of spin in quantum mechanics, I guess it's okay to think about the magnetic field generated by a "spinning" electron (cringe,) since that's the only way to connect with the concept of spin in a classical sense(electrons really don't have any extended structure, so speaking about their "spinning", along with the magnetic field generated by this "spinning" makes little sense at the scale described by quantum mechanics). In fact, you can use this classical picture of spin to generate a hamiltonian(basically a quantum mechanical operator that represents the total energy of a system) that describes the interaction of a spin 1/2 particle with a magnetic field in a quantum mechanical context (but please don't take your author's picture of spin too literally).

dextercioby said:
Mind you that spin comes into play in QM not necessarily in connection with the Dirac equation, which is a relativistic one, but in connection with the representation theory of the Galilei group, which is the symmetry group of nonrelativistic classical mechanics. The only reason that equations invariant under the Galilei group are not used in a QM description of the electron and other spin 1/2 particles is the appearence of the Special Theory of Relativity which forbids using the Galilei group as the fundamental symmetry group of flat spacetime, but rather the Poincare' group.

So the concept of spin really comes out of nonrelativistic physics.

Daniel.

Very interesting viewpoint dex; thank you.

Gza said:
As a physicist, it's not easy to accept the fact that "particles JUST HAPPEN to have a property, whose observables are the generators of SU(2)." In the case of spin 1/2 particles such as the electron, the concept of their spin really comes out of the dirac equation, and the fact that in completing the square of the Klein-Gordon equation, in order to factorize it, and allow space and time to be on the same footing, in the form of them both having a first derivative, one must resort to the use of 4X4 matrices and 4 component spinors. These 4-d spinors can be decomposed into 2-d spinors which form the familiar spin up and spin down particles we all know about. Bringing group theory into this before tackling what I talked about makes very little sense, unless you're a pure mathematician.

You completely misundestood my point. I tried to say, that the reason why we called it spin is that this internal property happens to have almost the same group structure as the 3-D rotations.

Gza said:
I bolded the most important part of your quote. He obviously presupposes a laymans perspective in his description of spin, so in a sense he's only right to a certain degree. If you aren't familiar with the intracacies of the dynamics of spin in quantum mechanics, I guess it's okay to think about the magnetic field generated by a "spinning" electron (cringe,) since that's the only way to connect with the concept of spin in a classical sense(electrons really don't have any extended structure, so speaking about their "spinning", along with the magnetic field generated by this "spinning" makes little sense at the scale described by quantum mechanics). In fact, you can use this classical picture of spin to generate a hamiltonian(basically a quantum mechanical operator that represents the total energy of a system) that describes the interaction of a spin 1/2 particle with a magnetic field in a quantum mechanical context (but please don't take your author's picture of spin too literally).
Yes. I just would like to express my personal opinion that this image of a "spinning particle" or of a "little magnet" has made more damage than benefit.

dextercioby said:
The exact formulation "If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole." has the advantage of using the expression "simplest way to think about spin". However, as the author implies, this view is incorrect(oversimplified, if you prefer) and a full understanding of the concept of spin cannot be done without group theory.

Daniel.

I know that the electron is a point particle and does not have a rotating physical volume, that's not what I am debating here. But surely it has a north magnetic and south magnetic pole? Otherwise how do natural magnets have north and south magnetic poles too? What's their source?

Dave

davidong3000 said:
I know that the electron is a point particle and does not have a rotating physical volume, that's not what I am debating here. But surely it has a north magnetic and south magnetic pole? Otherwise how do natural magnets have north and south magnetic poles too? What's their source?

Dave

If I remember correctly, natural magnets aren't fully understood, but to a close enough degree, you can think of the north and south poles of magnetized material as arising from the charged electron being in "orbit" around the nucleus, of an atom in the material, thus giving rise to a north or south pole as a consequence of the charge being seen as a "current" generating the field. (once again, don't take this classical picture as the end-all of what happens sub-atomically)

interesting. I always thought that this was basically an interesting property describing the sign of the wavefunction. I guess I learn something new each day.

Gza said:
If I remember correctly, natural magnets aren't fully understood, but to a close enough degree, you can think of the north and south poles of magnetized material as arising from the charged electron being in "orbit" around the nucleus, of an atom in the material, thus giving rise to a north or south pole as a consequence of the charge being seen as a "current" generating the field. (once again, don't take this classical picture as the end-all of what happens sub-atomically)

Actualy most of the internet literature indicate that although the electron's orbit does generate part of the magnetic field, a majority of the magnetic field is generated from the electron's spin not it's orbit.

http://en.wikipedia.org/wiki/Magnetism
"This can arise either from movement of electrons in an electric current, resulting in "electromagnetism", or from the quantum-mechanical spin and orbital motion of electrons, resulting in what are known as "permanent magnets". Electron spin is the dominant effect within atoms. The so-called 'orbital motion' of electrons around the nucleus is a secondary effect that slightly modifies the magnetic field created by spin."

Dave

Dear GZA,

why do you talk about time as though it is real as opposed to a concept?

time doesn't exist if there's no one there to observe it!

do you really believe in time as a fundamental structure, dimension of our universe or do you just use it as a convenient tool ?

A little confused!

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Dear GZA,

why do you talk about time as though it is real as opposed to a concept?

time doesn't exist if there's no one there to observe it!

do you really believe in time as a fundamental structure, dimension of our universe or do you just use it as a convenient tool ?

A little confused!

This is nonsense. Try removing "time" from Special Relativity and tell me that you could get the same result.

Zz.

Dear Daniel,

I have seen several replys you've given to other's questions and you seem to know what your talking about. I am just someone with an interest in QM and PP generally so am no expert at all.

So, with the above in mind could you please try to help me understand what particle spin is? - I have heard it described as being like AM - (but according to what I understand about AM) AM is something that is NOT intrinsic it is a measurement of angle based upon an external point axis. (or have I completely missurderstood AM?) So I really am a little confused here, I heard also that Spin is/was detected by Light spectra experiements though I cannot find anywhere on the net that explains, documents this. Do you know of a link to a good resource page?

I'd be very grateful if you'd have a bash at explaining "spin" to me and also if you don't mind I'd like to know how you visualise it to be.

Joanna

This is probably cringe-worthy, I'm not an expert, but I'm curious what more knowledgeable people might think.

I started thinking of 1/2 spin particles as hypercubes. If you have a two dimensional space and rotate a 'square' of it 180 degrees through a 3rd 'unseen' dimension its still a 2 dimensional square but the sides are now opposite to what they were. Rotate it again and it comes back to the same 'state', its sides back to where they originally were.

If the square is actually a cube however, as it rotates through a 2 dimensional space it takes twice as long, two turns to get to the 'opposing' side and two more to return to the original configuration.

If 1/2 spin particles are hypercubes that interact with our 3 space dimensions... or something similar... then the angular momentum of a particle would be something like the energy it takes to 'turn' it.

Heheh... or something. Ok, maybe it just sounds good in my brain.

davidong3000,

I've already tried to determine what this is and got the same basic response you are getting. No one seems capable of explaining anything in QM in simple terms. It seems that more double talk goes on than actual explanations of any form. I'm not sure if its because most people talking don't really understand it themselves and therefore can't explain it, ( but don't want to admit it) or if its because they don't want anyone else to understand it.

The fact is, QM does an obviously good job mathematically of making predictions, however, I think philosophically speaking, its gone on a rampage of its own. There are more absolutely insane (in my opinion) interpretations of QM than anyone could count.

I believe that from what I've read, spin really isn't spin at all. Whoever decided that would be what they called it made a drastic mistake in language and no one has ever been able to get rid of it. I also don't believe magnetism has anything to do with it either, but again, I'm stuck where you're at as well.

There really is NO explanation of what is meant by spin. I gave up on this topic and am currently in another thread trying to determine what exactly entanglement is and how one goes about performing its art. So far, I seem to be destined as you, but I'm hopeful someone will pop up with an explanation that one can relate to.

Good luck with your question, I'm going to continue to watch it in hopes someone can offer a real answer.

glenn

davidong3000,

I've already tried to determine what this is and got the same basic response you are getting. No one seems capable of explaining anything in QM in simple terms. It seems that more double talk goes on than actual explanations of any form. I'm not sure if its because most people talking don't really understand it themselves and therefore can't explain it, ( but don't want to admit it) or if its because they don't want anyone else to understand it.

The fact is, QM does an obviously good job mathematically of making predictions, however, I think philosophically speaking, its gone on a rampage of its own. There are more absolutely insane (in my opinion) interpretations of QM than anyone could count.

I believe that from what I've read, spin really isn't spin at all. Whoever decided that would be what they called it made a drastic mistake in language and no one has ever been able to get rid of it. I also don't believe magnetism has anything to do with it either, but again, I'm stuck where you're at as well.

There really is NO explanation of what is meant by spin. I gave up on this topic and am currently in another thread trying to determine what exactly entanglement is and how one goes about performing its art. So far, I seem to be destined as you, but I'm hopeful someone will pop up with an explanation that one can relate to.

Good luck with your question, I'm going to continue to watch it in hopes someone can offer a real answer.

glenn

Glenn, I think you are right.
Here it is my very subjective point of view, using a metaphore:
1. you observe an Alexandrite's crystal at daylight and you notice it's green;
2. you observe it under an incandescence lamp and it's red.

Question: is Alexandrite's colour an intrinsic property of that crystal?

I would say that colour is not an intrinsic property of objects; put apart how we perceive them, I would say an object's colour also depends on the kind of light we use to see it;
in the same way, I would say spin is not a property of the particle alone but of the particle and of the measurement device too (a sort of an unbreakable "entanglement" between the two).

Glenn, I think you are right.
Here it is my very subjective point of view, using a metaphore:
1. you observe an Alexandrite's crystal at daylight and you notice it's green;
2. you observe it under an incandescence lamp and it's red.

Question: is Alexandrite's colour an intrinsic property of that crystal?

I would say that colour is not an intrinsic property of objects; put apart how we perceive them, I would say an object's colour also depends on the kind of light we use to see it;
in the same way, I would say spin is not a property of the particle alone but of the particle and of the measurement device too (a sort of an unbreakable "entanglement" between the two).

But think some more and what you just described is NOT just applicable to spin. In fact, I could say the same with everything that you observe. So why pick on the spin property?

Furthermore, if you have studied QM rather carefully, you'll notice that "spin" is an intrinsic property of the particle that isn't a subject to be negotiated. You are confusing the spin quantum number versus the projection spin quantum number that allows for various components to be measured, i.e. $s$ versus $m_s$. Those two are not identical!

Anyone who does not think that spin has anything to do with magnetism should not use their computers or hard drives, and heaven forbid if you have a need to use MRI to diagnose your sickness.

Zz.

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Dear Daniel,

I have seen several replys you've given to other's questions and you seem to know what your talking about. I am just someone with an interest in QM and PP generally so am no expert at all.

So, with the above in mind could you please try to help me understand what particle spin is? - I have heard it described as being like AM - (but according to what I understand about AM) AM is something that is NOT intrinsic it is a measurement of angle based upon an external point axis. (or have I completely missurderstood AM?) So I really am a little confused here, I heard also that Spin is/was detected by Light spectra experiements though I cannot find anywhere on the net that explains, documents this. Do you know of a link to a good resource page?

I'd be very grateful if you'd have a bash at explaining "spin" to me and also if you don't mind I'd like to know how you visualise it to be.

Joanna
In very simplistic terms:
Spin is a magnetic moment of a particle that doesn't depend on the particle's position, as a magnet bar. It's called "intrinsic" for this reason.

If you put a magnetic bar inside a magnetic field, you find that the bar's energy now have an additional term, which depends on the bar's orientation with respect to the field (max energy if the two magnetic fields, that of the bar and the external, are aligned and opposites, min energy if aligned and the same versus).

Electrons in an atom behaves quite the same: their energies depends also on the magnetic field there is in that exact location of space, which also depends on how all the other electrons are moving (moving charged particles generate magnetic fields).

I believe that from what I've read, spin really isn't spin at all. Whoever decided that would be what they called it made a drastic mistake in language and no one has ever been able to get rid of it.

Yes, what we call the "spin" of an electron or other fundamental particle cannot be thought of as the angular momentum of a little spinning ball or something similar. But we're stuck with the name because of historical reasons and because it's a lot shorter than "intrinsic angular momentum."

But it is angular momentum, and it contributes to the total macroscopic angular momentum of an object, as observed in the Einstein - de Haas effect.

But think some more and what you just described is NOT just applicable to spin. In fact, I could say the same with everything that you observe. So why pick on the spin property?
It's "easier" for me to understand the situation.
Furthermore, if you have studied QM rather carefully, you'll notice that "spin" is an intrinsic property of the particle that isn't a subject to be negotiated. You are confusing the spin quantum number versus the projection spin quantum number that allows for various components to be measured, i.e. $s$ versus $m_s$. Those two are not identical!
Yes, you are right; I intended to talk about the spin components. These interest me more, since they are measurable.
Anyone who does not think that spin has anything to do with magnetism should not use their computers or hard drives, and heaven forbid if you have a need to use MRI to diagnose your sickness.
I intended to agree with Glenn about his diffuculties on understandind QM and spin, but I didn't intend to agree with him when he says:
"I also don't believe magnetism has anything to do with it".
Sorry I didn't specify this.

History, once again, gives the answers. Go back and study the Stern-Gerlach experiment.

Regards,
Reilly Atkinson

History, once again, gives the answers. Go back and study the Stern-Gerlach experiment.

Regards,
Reilly Atkinson
You were answering to my post?

History, once again, gives the answers. Go back and study the Stern-Gerlach experiment.

Regards,
Reilly Atkinson

Thanks reilly. Reading it now and it seems to be written where even I can understand it... :-)

Thanks,

glenn

History, once again, gives the answers. Go back and study the Stern-Gerlach experiment.

Regards,
Reilly Atkinson

I've erased my previous question as I think I figured it out on my own. I'll post again if I think of something else.

Thanks,

glenn

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lightarrow -- There are two main reasons why QM is difficult, odd, weird, and contrary to normal common sense.

First, QM was developed to explain phenomena that could not be explained by classical physics: atomic spectra, electron diffraction; nuclear decay, spin, ...These are brain defying phenomena if you try to understand or describe them with classical physics. Can't be done.

Second: the natural language of QM involves fairly sophisticated math, PDE, Hilbert Spaces, and so on.

Thus it is difficult to get a good understanding of QM without several years of hard study. Sad but true. You can get an "OK" understanding from the literature for layfolks, but there will be many aspects of QM beyond your reach until you get to graduate level QM.

Regards,
Reilly Atkinson

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