The mathematics of QM

[Johnny5]

Who on earth actually understands what a magnetic field is? There has got to be some kind of interaction of something external with the electron.

 

Right off the bat, the magnetic force formula is totally strange, because its a cross product. What force in classical mechanics is like this?

 

F = q(v X B)

[Tom Mattson]

Who on earth actually understands what a magnetic field is?

 

Anyone who has studied classical EM theory understands what a magnetic field is.

 

There has got to be some kind of interaction of something external with the electron.

 

There is: A magnetic field.

 

Right off the bat' date=' the magnetic force formula is totally strange, because its a cross product. What force in classical mechanics is like this?

 

F = q(v X B)[/quote']

 

So what if it's a cross product?

 

Incidentally, it's not the force on the charge that is used to turn the electrons. It's the force on the magnetic moment. That's why (chargless) neutrons can be used.

[Johnny5]

Incidentally' date=' it's not the force on the charge that is used to turn the electrons. It's the force on the [i']magnetic moment[/i]. That's why (chargless) neutrons can be used.

 

Neutron interferometry?

 

How can a magnetic field rotate a neutrally charged object?

 

magnetic force = Q(vXB)

 

v = neutron speed

B= external magnetic field.

 

Both are nonzero so everything looks good but

 

q=0 for a neutron hence F=0

 

So where is my mistake?

 

I know you are going to say... force on magnetic moment.

 

But a magnetic moment can only arise from a current loop, so now what?

[Tom Mattson]

So where is my mistake?

 

I know you are going to say... force on magnetic moment.

 

You've just answered your own question.

 

But a magnetic moment can only arise from a current loop' date=' so now what?[/quote']

 

As it explains quite clearly in your Big Blue Book o' Quantum Physics, there are current loops inside the neutron. They're called "moving quarks". The charges cancel out, but the magnetic moments do not.

[Johnny5]

there are[/b'] current loops inside the neutron. They're called "moving quarks". The charges cancel out, but the magnetic moments do not.

 

Well that explains that... i suppose. i mean it does explain quark theory at least.

 

But I'm bothered by something. We don't know what a magnetic field is. I don't know what is being done to those little neutrons.

 

Are they being bombarded by magnetic particles?

 

The quick answer is no, because magnetic monopoles do not exist, since the divergence of a magnetic field is zero. But if magnetic monopoles do not exist, then what is a magnetic field. It can't be nothing.

[Tom Mattson]

But I'm bothered by something. We don't know what a magnetic field is.

 

Says who?

 

I don't know what is being done to those little neutrons.

 

Then consult an EM book. The interaction of a magnetic dipole moment mwith a uniform static B field is well-known. The torque is T=mXB.

 

Are they being bombarded by magnetic particles?

 

Not that it's necessary to invoke QED here' date=' but the magnetic force is just an aspect of the EM force, which is mediated by virtual photons. But as I said, there's no need to go to QED when looking at field strengths that are as large as those that are typically used in this sort of experiment.

 

The quick answer is no, because magnetic monopoles do not exist, since the divergence of a magnetic field is zero.

 

This is actually backwards. We set the divergence of the magnetic field equal to zero because no monopoles have been observed, not the other way around. If a monopole were found, a source term would be added to the RHS of that equation.

[Johnny5]

 

Then consult an EM book. The interaction of a magnetic dipole moment mwith a uniform static B field is well-known. The torque is T=mXB.

 

 

Yes I know this one, but you have a 'neutron' particle's dipole moment acting with a 'field.' Thats strange, certainly non-classical.

 

What is the B field composed of?

[Tom Mattson]

Yes I know this one, but you have a 'neutron' particle's dipole moment acting with a 'field.' Thats strange.

 

There's nothing strange about it. It's just another magnetic dipole.

[Johnny5]

There's nothing strange about it. It's just another magnetic dipole.

 

Review dipole for me if you don't mind. Griffith's EM book discussed them for atoms. Basically just a + somwhere and a - somewhere else. Di-pole... two poles.

 

Here

 

It still doesn't tell me what a B field is, just the field lines, due to the existence of a dipole.

 

You say that it's just another magnetic dipole.

 

I'm looking at this now.

 

Neutron electric dipole moment

 

and this

 

Neutron magnetic dipole moment

[Tom Mattson]

Review dipole for me if you don't mind. Griffith's EM book discussed them for atoms. Basically just a + somwhere and a - somewhere else. Di-pole... two poles.

 

You already said it: A dipole is 2 poles' date=' which we call north and south.

 

Here

 

It still doesn't tell me what a B field is, just the field lines, due to the existence of a dipole.

 

Well if you have Griffiths, then surely you can find out what a B field is with a minimum of trouble. Griffiths is the best book out there at the undergraduate level.

[Johnny5]

 

Well if you have Griffiths' date=' then surely you can find out what a B field is with a minimum of trouble. Griffiths is the best book out there at the undergraduate level.[/quote']

 

You can say that again. I think I even know the page numbers of things.

 

In all honesty though he admits he cannot tell you what a field is, E or B, just how to calculate with them. Actually just from memory, I think he admits that in chapter one. I think his exact words are "I can tell you what to do with them once you've got them(the fields)"

 

When it comes to B fields, all he really does is define B using Biot-Savart formula.

[Johnny5]

"moving quarks". The charges cancel out, but the magnetic moments do not.

 

Are quarks really particles, or is something else going on?