Question regarding spin and magnetic field

[jimmylegss]

Does spin up mean which way the magnetic field is pointed in relation it's environment (so when do you know if it is up or down, or does that depend on the environment?)

So if it is spin up, it means the field lines go from up to down, and vice versa. So spin pretty much means where the poles are in relation to everything else?

Thanks in advance!

[mentor's note: The original post contained two unrelated questions. The second has been split out into its own thread]

 

[Nugatory]

Does spin up mean which way the magnetic field is pointed in relation it's environment (so when do you know if it is up or down, or does that depend on the environment?)

Do you mean the magnetic field of the particle (which is very weak) or the magnetic field that we apply to measure the direction of the spin?

When we say that a particle is spin-up or spin-down (to keep things simple, let's stick to the spin-1/2 particles for now so that up and down are the only two possibilities) we're making a statement about how that particle reacts to an external magnetic field that we've applied in a particular direction. If it acts as if it is aligned with the field it's up and and if it acts as if it's it's aligned against the field it's down.

There is no way to talk about what the direction of spin is until we've done something to measure it, such as applying that external magnetic field or otherwise interacting with the particle. The way we do that measurement (which direction do we choose for the external field, for example) determines the direction that we're measuring and hence the direction in which the particle will be up or down.

 

[Khashishi]

I think what you are trying to ask is, if a particle is "spin up" in one frame of reference, does it become "spin down" in a frame of reference where we rotated 180 so up is down?. The answer is yes. The physics will be more clear if we use more precise language to describe spin.

Spin has a magnitude and direction. For spin 1/2 particles (which includes all the fundamental fermions and protons and neutrons), spin is a special kind of vector called a spinor. It is different than a normal vector in that if you rotate it 360 degrees, the wavefunction changes sign, but otherwise is much like a vector. When we say a particle is "spin up", what this really means is that the projection of the spin vector along the vertical direction is upward. Clearly, if you rotate the vector 180, the projection becomes downward. Rotate 360, and it becomes upward again, but the wavefunction changes sign.

So far, pretty simple, but in quantum mechanics, the projection of the spin along any direction is quantized. That means a measurement of the spin projection along any direction is only allowed to take specific values. For a spin 1/2 particle, these values are +1/2 and -1/2. If the spin vector is pointed upward, then you will measure +1/2. If the spin vector is pointed sideways, you will measure either +1/2 or -1/2 with equal probabilities. For some diagonal spin vector, you get some probabilities weighted toward the side the vector is pointed at. If the spin vector was pointed sideways, and you randomly measure the spin projection along the vertical direction to be +1/2, then the spin vector will become pointed straight up. Any measurement causes the particle to collapse into that measured state.

 

[jimmylegss]

Sorry if this sounds stupid, but the reason Earth has a magnetic field is because there is a concentrated imbalance in which direction Earth's 'particles' are directed?

If they are all directed in a random direction (so I guess side ways? or just up and down evenly spread out?) then you will not have a magnetic field?

Secondly, is there some absolute (like light and other particles) that you compare the spin to? So what frame of reference determines wether it is up or down?

And finally what does it mean when you say it changes sign?

Thanks

 

[Khashishi]

No, Earth's magnetic field is believed to be due to the dynamo effect. http://en.wikipedia.org/wiki/Dynamo_theory

The frame of reference is arbitrary but is normally chosen to match some part of the experimental apparatus. In the Stern-Gerlach experiment, we choose "up" (or maybe "down") to be pointed in the direction of the gradient of the magnitude of the magnetic field.

If you don't know what the wavefunction is, there's no way to explain what it means for it to change sign. It is just a mathematical quantity, and you switch sign by multiplying it by -1. You can't directly observe either the sign of the wavefunction, but it affects the interference pattern and is responsible for Pauli's exclusion principle.