Understanding Electron Spin: The Mystery Behind a Fundamental Property

[THE HARLEQUIN]

okay , this question might look a little silly .. But i have been wondering about this for a while ..
i know electrons move around the orbit because of the electrostatic force between electron and proton ..
But what what makes an electron rotate about its axis ?
i believe even without the spin motion the orbital motion is possible because they are independent of each other ... so why can't an electron moving around the atom have no spin at all ?
and what makes them spin ?

thank you ..

 

[Orodruin]

Spin is not due to the electron spinning, it is an intrinsic property of an electron.

 

[THE HARLEQUIN]

Spin is not due to the electron spinning, it is an intrinsic property of an electron.

define this " intrinsic property " ... so are you saying that spin isn't due to the angular momentum w.r.t. the axis passing through the electron itself ?

 

[Orodruin]

Yes it is the angular momentum, but the electron is not a rotating object per se. The angular momentum of the electron is intrinsic, it is simply a property that electrons have, like their mass or electric charge. Asking for a deeper explanation within QFT is not a physics question but a philosophical one.

 

[THE HARLEQUIN]

Yes it is the angular momentum, but the electron is not a rotating object per se. The angular momentum of the electron is intrinsic, it is simply a property that electrons have, like their mass or electric charge. Asking for a deeper explanation within QFT is not a physics question but a philosophical one.

so this basically means that .. electron around an atom can't exist without this angular momentum.. right ?
what if a magnetic field is introduced which only affects the "spin angular momentum " of the electron and forces it to stop spinning , won't the electron still continue to rotate around the atom like it would before (as the orbital motion is independent of its spin motion)?
basically , u can't vanish mass like this but for the case of angular momentum u can .
so just because this angular momentum is intrinsic , i can't get why its origin should be a mystery or something .. or something that should be related to philosophy rather than physics..

 

[ChrisVer]

so this basically means that .. electron around an atom can't exist without this angular momentum.. right ?

The electron has that property whether it is in "orbit" around an atom or not... even the word "orbit" is not intuitively correct when you go in QuantumMechanics.
The spin is in fact the "angular momentum" the electron would have if you went to a frame where the electron is seen at rest...(check relativistic angular momenta).
So you cannot stop it from spinning because it does not spin. There is no way to define a classical spin (rotate around its own axis) for something that is considered pointlike in the first place...because there is no way to define such an axis (in fact you have infinite such axis).

 

[jtbell]

You cannot remove an electron's intrinsic angular momentum ("spin"), just like you cannot remove its mass or charge.

 

[my2cts]

"it does not spin"
There is no model of an electron that explains its intrinsic angular momentum.
We can in this sense not say that it spins, but without such a model it makes even less sense to state that it does not.
There is also no model of hydrogen in a 2P state in which the electron rotates about the proton,
yet it seems fair to say that it does.

 

[my2cts]

"There is no way to define a classical spin (rotate around its own axis) for something that is considered pointlike in the first place"
YJust take the limit to a point of a rotating sphere (for example). Since J=mr^2w=h and m are constant , w has to be taken to infinity.
I do not see that as a problem as the mass density is infinite as well for a massive point particle.

 

[ChrisVer]

"There is no way to define a classical spin (rotate around its own axis) for something that is considered pointlike in the first place"
YJust take the limit to a point of a rotating sphere (for example). Since J=mr^2w=h and m are constant , w has to be taken to infinity.
I do not see that as a problem as the mass density is infinite as well for a massive point particle.

That limit would be 0... I don't understand why you'd let w reach infinity...and how is the mass density->infinite connected to w?
But nevertheless... even in that case I don't see how this can help you (you have already taken J= non zero const).

 

[ChrisVer]

There is also no model of hydrogen in a 2P state in which the electron rotates about the proton,

The electron does not "rotate" around the proton... The states, where the electron exists in when it's bound to an atom, are stationary... as a result, the average momentum of the electrons are zero.
Since the average quantities of quantum mechanics show a classical behavior, you cannot make the classical picture of an electron going around the nucleus.

Also the well known example of that a rotating charged particle should radiate energy...

 

[my2cts]

"does not "rotate""
Please state the model leading to this conclusion.
"the average momentum of the electrons are zero"
The orbital momentum of for example a 2P(3/2) state is 2h, not zero.
"a rotating charged particle should radiate energy"
Are you arguing that no energy is radiated because the charges do not move?
I do not claim to know why no energy is radiated, but I do not subscribe to that.

 

[my2cts]

That limit would be 0... I don't understand why you'd let w reach infinity...and how is the mass density->infinite connected to w?
But nevertheless... even in that case I don't see how this can help you (you have already taken J= non zero const).

J=Iw. J=h. I=mr^2.
Letting r go to zero, at fixed J, requires letting w go to infinity.
Just like letting r go to zero, at fixed mass, requires letting the mass density going to infinity.

 

[ChrisVer]

Please state the model leading to this conclusion.

It's called Quantum mechanics...As I already noted it is wrong to picture the rotation classically... and the only thing I used is a fact for most (if not all) stationary states...

The orbital momentum of for example a 2P(3/2) state is 2h, not zero.

First of all I spoke about momentum...and not angular momentum.
Even that "orbital" angular momentum has little to do with an orbit...

Are you arguing that no energy is radiated because the charges do not move?

Because the charges are not accelerated as would be the case for a rotating charged particle.
I don't care if you subscribe to that- it is plain logic... if energy would be radiated, then the electron would classically fall into the nucleus...
These and many other examples were the problems of what is known as semi-classical quantum mechanics, the QM of the time when we started approaching the QM accuracy in our experiments.

 

[ChrisVer]

J=Iw. J=h. I=mr^2.
Letting r go to zero, at fixed J, requires letting w go to infinity.
Just like letting r go to zero, at fixed mass, requires letting the mass density going to infinity.

So far so good... but the J that you've written does not apply for r->0.
How would you compute the moment of inertia I (and what would that even mean) for a point particle (and not a solid extended object)?
And in what way did you choose its value mr^2?
In fact, through such a logic, any kind of a weird geometrical structure could be sent equivalently to a "point"...changing the I that you were using.

 

[my2cts]

"it's call QM"
That is wrong. You are confusing QM with some interpretation of QM that you adhere to.
QM says that atomic states can have orbital and total angular momentum.

the average momentum of the electrons are zero.

I interpreted this as meaning _orbital_ momentum.
Since you actually mean linear momentum, you are trivially right.

As I already noted it is wrong to picture the rotation classically

It is also wrong to picture it in any other way. All we know is that there can be non-zero angular momentum.

 

[my2cts]

So far so good... but the J that you've written does not apply for r->0.
How would you compute the moment of inertia I (and what would that even mean) for a point particle (and not a solid extended object)?
And in what way did you choose its value mr^2?
In fact, through such a logic, any kind of a weird geometrical structure could be sent equivalently to a "point"...changing the I that you were using.

It is a mathematical technique called "taking the limit". You can take r to zero if you take w to infinity, taking care that J=mr^2w remains equal to h.
I am surprised that I have to explain this.

 

[ChrisVer]

That is wrong. You are confusing QM with some interpretation of QM that you adhere to.

Nope... but there's not point in extending this here...

Since you actually mean linear momentum, you are trivially right.

Is the classical momentum of an object that orbits around a center equal to zero?

It is also wrong to picture it in any other way. All we know is that there can be non-zero angular momentum.

Why are you mixing in your head the angular momentum with some orbital motion?

 

[ChrisVer]

It is a mathematical technique called "taking the limit". You can take r to zero if you take w to infinity, taking care that J=mr^2w remains equal to h.
I am surprised that I have to explain this.

You cannot take the limit to zero... What's the angular momentum when you are at point zero around which you rotate?
$L \propto r \times p$

 

[THE HARLEQUIN]

Are you arguing that no energy is radiated because the charges do not move?
I do not claim to know why no energy is radiated, but I do not subscribe to that.

even if we choose classical model , it can be explained why electron doesn't radiate energy .. if the the path the electron chooses to rotate is taken as it has same potential (v) everywhere then the net work for movin an electron will be ( w = dvxI = 0xi=0 ) so therefore no energy is lost ..

So you cannot stop it from spinning because it does not spin. There is no way to define a classical spin (rotate around its own axis) for something that is considered pointlike in the first place...because there is no way to define such an axis (in fact you have infinite such axis).

so we can stop the angular momentum about its own axis( if not the 'spin') ?

 

[my2cts]

"nope"
That is a infantile way to argue. I expect a little more depth here.
From QM you cannot draw the conclusion that the electron does not rotate.
It only tells you that it may have angular (orbital, spin) momentum.

Is the classical momentum of an object that orbits around a center equal to zero?

On average, yes. I am surprised again to have to explain trivialities here. Please crank up the level.
Note that the operator p locally gives a nonzero result when operated on an atomic orbital. It is the integral over the volume that ends up to be zero.
The average is zero, just as in the classical case but the local value is not.

 

[THE HARLEQUIN]

if we put aside the spin ( that is the net vector because of the forces acting on the electron ) , and work with the " spin angular momentum"
, now what actually makes it spin ? and is this spin also intrinsic ? ( i mean even if electron is stopped does it keep spinning ?
like a cathode ray burst into a powerful magnetic field construct that makes the net vector of the velocity of electron 0 )

 

[my2cts]

You cannot take the limit to zero... What's the angular momentum when you are at point zero around which you rotate?
$L \propto r \times p$

Of course I can. This is getting silly.

 

[ChrisVer]

so we can stop the angular momentum about its own axis( if not the 'spin') ?

Have a look here:
https://en.wikipedia.org/wiki/Relat..._total_angular_momentum_in_special_relativity...

even if we choose classical model , it can be explained why electron doesn't radiate energy .. if the the path the electron chooses to rotate is taken as it has same potential (v) everywhere then the net work for movin an electron will be ( w = dvxI = 0xi=0 ) so therefore no energy is lost ..

The radiation comes about because you have an accelerating charged particle (if you want it to keep orbiting you have to keep it accelerating)...
Then it's just Larmor's formula.

 

[ChrisVer]

The average is zero, just as in the classical case but the local value is not.

In the classical case the momentum should at least be "periodic"...

Of course I can. This is getting silly.

OK, keep dreaming...

 

[ChrisVer]

if we put aside the spin ( that is the net vector because of the forces acting on the electron ) , and work with the " spin angular momentum"
, now what actually makes it spin ? and is this spin also intrinsic ? ( i mean even if electron is stopped does it keep spinning ? )

I am confused by this question...
let's see, in general you can have orbital + spin angular momentum, alright so far?

The orbital is somehow connected to a "rotation" of the electron around the nucleus...in reality it just reflects the fact that the energies can be altered by the orbiting (-->it affects the potential).
The spin is totally different. It's an intrinsic property of the electron, and so doesn't come from some "spinning". That means that even if your electron did not rotate, it would still have that spin...it doesn't come by any spinning or so what...

Sometimes we call "spin" the combination of orbital and spin momentum (so the total angular momentum), but that's another thing...

 

[THE HARLEQUIN]

The spin is totally different. It's an intrinsic property of the electron, and so doesn't come from some "spinning". That means that even if your electron did not rotate, it would still have that spin...it doesn't come by any spinning or so what...

ok .. i agree with that ..
but won't the electron magnetic moment be zero if the electron stops rotating ? or am i wrong ? or can't we do the reverse ( like by forcing the magnetic moment to be zero can't we stop the rotation ?) ?

 

[my2cts]

@ChrisVer
Additional note: In the limit r must remain larger than the compton wavelength.

 

[ChrisVer]

but won't the electron magnetic moment be zero if the electron stops rotating ? or am i wrong ? or can't we do the reverse ( like by forcing the magnetic moment to be zero can't we stop the rotation ?) ?

it won't... there will be some magnetic moment left due to its spin...
https://en.wikipedia.org/wiki/Spin_magnetic_moment

 

[THE HARLEQUIN]

it won't... there will be some magnetic moment left due to its spin...
https://en.wikipedia.org/wiki/Spin_magnetic_moment

have read this article several times .. it doesn't say why ... and moreover how can we visualize something to have magnetic moment which is not rotating at all .. ?

 

[my2cts]

even if your electron did not rotate, it would still have that spin

Just like a classical spin. If the Earth was stopped from orbiting about the sun somehow, it could still be spinning about its own axis.

 

[THE HARLEQUIN]

Just like a classical spin. If the Earth was stopped from orbiting about the sun somehow, it could still be spinning about its own axis.

actually Chrisver meant that even if the electron doesn't have " rotation about its own axis " it ll still have spin...

 

[ChrisVer]

have read this article several times .. it doesn't say why ... and moreover how can we visualize something to have magnetic moment which is not rotating at all .. ?

If you want you cannot call it "magnetic moment", or even better generalize your conception of what spinning is: without having to resort in imagining a spinning ball or anything like that, but seeing it as an intrinsic quantum property...However it still brings some interaction with the magnetic field...
You will have to do that in many cases of Quantum mechanics where visualization is not going to help you in any way...

Just like a classical spin. If the Earth was stopped from orbiting about the sun somehow, it could still be spinning about its own axis.

I think that if there is friction you can stop the Earth from rotating as happens with a spinning top...

 

[ChrisVer]

actually Chrisver meant that even if the electron doesn't have " rotation about its own axis " it ll still have spin...

That's exactly what I have been saying... and what anyone said when they mentioned intrinsic property...
Now if you are looking for a general reason "why have spin if not rotating", I am not sure you can find it within the context of physics...

 

[my2cts]

That's exactly what I have been saying... and what anyone said when they mentioned intrinsic property...
Now if you are looking for a general reason "why have spin if not rotating", I am not sure you can find it within the context of physics...

So you are saying that if an electron were to rotate about itself that would not constitute spin.
That will allow you to conclude that the electron does not spin precisely because it has spin.
That is just confusion.
An electron has spin and there is no mechanical explanation for it.