How do you determine if the spin is up or down?

Question

Fundamental particles such as quarks and leptons can have a spin either up or down. These spins are (obviously) opposite of each other. But what differentiates them? Let's say you examine a pair of electrons and you find out they're opposite (one up and one down). How do you know which one is up and which one is down? Do all up-spinning-particles in the universe point to an established direction? If not, how can we know the difference between an up and a down spin?

One correction: fundamental particles which have half integer spins are called Fermions. There is another family of fundamental particles which has integer spins (including zero, for example, photon) which are called Bosons. I recommend you to read Stern–Gerlach experiment from your favourite physics-learning tool. — physicopath, Dec 10 '15 at 13:41
@linuxick yeah, I don't know much about quantum physics, I'm only 16. I probably said some wrong things. But is my answer valid? — Gabe12, Dec 10 '15 at 13:45
https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment — , Dec 10 '15 at 13:50
for non charged particles, such as a photon, see http://physics.stackexchange.com/questions/73942/how-do-we-know-photons-have-spin-1 — , Dec 10 '15 at 13:59
that's right, photon was an example for bosons not for spin zero particles — physicopath, Dec 10 '15 at 14:16

score 3 · Accepted Answer · answered Dec 10 '15 at 14:02

There's no universal notion of "up" or "down", just like there's no universal notion of "left" or "right" in the universe.

Speaking of "spin up" and "spin down" involves two completely arbitrary choices - a choice of axis and then a choice of "up" and "down" along that axis. You can swap the meanings of "up" and "down", and you can choose another axis to speak of "up" and "down" along. It's just a choice.

As to how to distinguish "up" and "down": For example, if you have a constant magnetic field in a direction and put an electron into it, the electron states with spin "up" along the axis of that field will have a different energy value from the states with spin "down", since the magnetic field essentially couples to the spin "direction" through the magnetic moment. Which one of these you call "up" or "down" is still somewhat arbitrary, but you can distinguish them.

I just wanted to add to the list of non-universal universals: the north and south poles of a magnet, positive and negative charges, matter and antimatter, "ordinary" energy and matter and dark energy and matter, clockwise and counter clockwise... I agree that in case of spins, up and down is pretty arbitrary but we should at least stick to some concepts being "universal". Right? (shall I say instead Left?) — physicopath, Dec 10 '15 at 14:23

score 0 · Answer 2 · answered Dec 10 '15 at 14:03

Let's say you examine a pair of electrons and you find out they're opposite (one up and one down). How do you know which one is up and which one is down?

There is no way of knowing, or more accurately, there is no answer to your question. The wave function of the state you describe is a super position of the two options. There is not even any way of distinguishing between the two (they don't have individual names).

How do you determine if the spin is up or down?

2 Answers2