# Spin of Quantum Particles

1. Nov 3, 2014

### Jimmy87

Hi pf. From what I have read, when measured, a particles spin can only be in one direction. So either 100% spinning up or 100% spinning down and not in between. So, you can't have a spin that is in between (tilted) - it must be one or the other. But I recently learnt that when we place a particle in an external magnetic field it precesses like a spinning top. Surely this contradicts what I originally said because if it is precessing then surely it has a component of its spin which is not in the up-down plane? Could someone please clarify, thanks.

Also, please could someone clarify if quantum mechanics is as spectacular and weird as it sounds. I have been briefly taught about things like entanglement, tunneling etc which sound fascinating but from reading on other forums some people suggest that there is nothing amazing about them and these quantum aspects are nothing more than mathematical correlations. For instance check this physics forum out (http://physics.stackexchange.com/questions/15282/quantum-entanglement-faster-than-speed-of-light) which argues that if quantum mechanics sounds great and strange then it has been explained wrong? Is that right?

2. Nov 3, 2014

### HomogenousCow

The spin angular momentum vector can be in any direction. The statement you quoted is probably referring to certain eigenstates. It is actually the magnitude of spin that is absolute and intrinsic to the particle.

Actually, when I mean the "spin angular momentum vector", I really just mean the expectation value for it. (The mean)

3. Nov 3, 2014

### jeffery_winkle

Julian Schwinger said, "We borrow only names from classical physics". The quantum-mechanical property of a particle that we refer to as "spin", is not the same thing as the physical rotation of a macroscopic object, like a top.

In physics, if you understand a subject, it is completely intuitive. It only appear counter intuitive if you don't understand it. The goal of a physics teacher lecturing in front of a classroom of students, or the writers of physics textbooks, is to make the students realize that the completely intuitive, and if you understand it, there is nothing counter intuitive about it. Unfortunately, that is the opposite of the goal of writers of articles in popular science magazines, such as Discovery magazine, or popular science tv shows, such as NOVA on PBS, or the Universe on the History Channel. The goal of popular science writers is to intentional stress the so-called counter-intuitive nature of the subject, because they are deliberately catering to a niche audience that enjoys enjoyed being freaked out by supposed "quantum weirdness", or other supposedly "mind blowing" concepts in advanced physics.

In other words, of course, there are all sorts of concepts in quantum physics, that don't exist in classical physics, such as entangled states, EPR steerable states, Bell non-local states, NOON states, etc. However, none of these concepts are "weird" or "spectacular", any more than if you talking about Newtonian dynamics, you would refer to Keplerian orbits as "weird" or "spectacular".

4. Nov 4, 2014

### Staff: Mentor

What you say is correct, but you have to remember that we are classical beings, used to the world around us having a classical behaviour. We need some kind of "suspension of disbelief" when diving into the quantum world.

5. Nov 4, 2014

### Staff: Mentor

This all boils down to the measuement problem. Before you make any measurement, the system will be in a defined quantum states, and theoretically you can calculate a series of observables, such as the expectation value of the projection of the spin along different axes, $\langle \hat{S}_x \rangle$, $\langle \hat{S}_y \rangle$ , $\langle \hat{S}_z \rangle$. In some cases, these can be seen as precessing, as if the spin was a classical vector. But once you make a mesurement, you will only be able to measure the system in one specific eigenstate (collapse of the wave function in the Copenhagen interpretation), so you will for instance measure $\hat{S}_x$ to be $\hbar/2$ or $-\hbar/2$ (for a spin-1/2 particle), but no other value, regardless of what $\langle \hat{S}_x \rangle$ was.

6. Nov 4, 2014

### HomogenousCow

But the important thing is that you measured along a given axis, you could have measured along any other direction.
Some sources often mis-phrase this and give the impression that somehow there is a universal z direction.

7. Nov 4, 2014

### Staff: Mentor

Indeed. That's why I chose to use x in my example instead of z.

8. Nov 5, 2014

### Jimmy87

This is what I'm getting mixed messages about. The original link to stack exchange I sent said that quantum mechanical aspects are just mathematical correlations and if anything in quantum mechanics sounds great then it is just hype. However, from what I have read, things like quantum entanglement have enabled physicists to teleport particles and they reckon that in a few decades scientists will be able to teleport molecules and maybe even viruses. Going back many decades teleportation was something of science fiction that has become science fact. Other things like quantum tunneling mean that particles can tunnel through solid objects. How can that not be weird and spectacular? This video () which I think is from NOVA is hugely hyped and goes on (in quite a dramatic way) about all the amazing things of the quantum world yet all the people speaking in it are leading physicists and some even Nobel laureates. I just want to know whether these things are really mind blowing or whether there is some false premise somewhere?

9. Nov 6, 2014

### nikkkom

You remember it wrong.
When measured *along any axis*:
spin of a "1/2 spin" particle is always +1/2 or -1/2 in Planck units. Here + and - denote rotating clockwise or counterclockwise along a chosen axis.
spin of a "1 spin" particle is always +1, 0, or -1.
spin of a "3/2 spin" particle is always +3/2, +1/2, -1/2 or -3/2.
spin of a "2 spin" particle is always +2, +1, 0, -1 or -2.

(We didn't discover any elementary particles with spins >1. Gravitons, if they exist, must have spin 2. Spins >2 are problematic from theoretical standpoint).

There are two peculiarities here.

The bigger one is that spin *along any axis* is discrete, no cos(alpha) multiplier appear when you measure it along another, tilted axis. A "classical" rotation doesn't work like that!
The smaller one is that spin is *discrete*, but by now we seem to be getting used to it. You know, the physics is called "quantum" for this exact reason ;)

10. Nov 6, 2014

### Khashishi

There's a distinction between the state of a particle and the outcome of a measurement on the particle. The state of the particle can have the spin pointed in any direction. But any measurement of the particle can only give discrete values of the spin projection. The state influences the probability of the resulting value of the measurement. (After the measurement, the state "collapses" based on the result of the measurement.)

You might have heard the allegory of Schrodinger's cat. The state of the cat can be partially dead and partially alive, but once you check on the cat, it is one or the other.

11. Nov 7, 2014

### jeffery_winkle

UUGH!!! NO!!! Using your misunderstanding of the word "teleportation", they have never "teleported" a particle, molecule, virus, or anything else. That is silly nonsense. This is a tragic unfortunate coincidence of language. In the 1920's, when the early quantum physicists invented the phrase "quantum teleportation", which refers to something you obviously never heard of, nobody at that time ever could have imagined that 40 years later, in the 1960's, Gene Roddenberry, who never heard of quantum teleportation, since he had zero scientific background, would independently invent the phrase "teleportation" to mean something totally different, moving an object from one place to another place, which is apparently how you are using the word.

In 1966, when they were first making the original Star Trek, they didn't have enough money to afford the special effects of sending a shuttle down to the surface every time the characters went to a planet, so Gene Roddenberry thought up the idea of instantly zapping the characters to the surface of the planet, just to save money on production cost, and he called this made up thing "teleportation". Today, when most people who are not scientists, hear the word "teleportation", they immediately think of an object disappearing and reappearing somewhere else.

This has absolutely nothing whatsoever to do with what physicists refer to as quantum teleportation. Let's say you have the creation of an electron-positron pair. If you measure the spin of the electron to be z+, that means the spin of the positron must be z-. It is random whether the spin of the electron is z+ or z-. However, once you measure the spin of the electron, you then know the spin of the positron. In a sense, the act of measuring the spin of the electron instantly affected the positron, even if it was far away. This does not violate special relativity because you have no control over whether the electron has spin z+ or z-, so it is not possible to send a message faster than light. This is what Einstein called "spooky action at a distance". This is what physicists call "quantum teleportation".

This has absolutely nothing to do with any physical object disappearing and reappearing somewhere else. Using your misunderstanding of the word "teleportation", they have never "teleported" a particle, molecule, virus, or anything else. Nothing similar to that will ever be possible. That is just silly nonsense. I'm worried that you are getting your information from people who are either intentionally misleading the audience, or don't have the slightest clue what they are talking about.

Mathematics is the language of physics. If you know the mathematics, you can understand the physics. However, you have to know the mathematics in order to be able to understand the physics. For quantum mechanics, you have to know the bra-ket notation, linear operators, inner products, and that sort of thing. What is your educational background?

12. Nov 7, 2014

### nikkkom

I don't think physicists call the process you described "quantum teleportation".

"Teleportation" means duplication of quantum state of a system. E.g. you have an isolated electron with unknown spin state. If you have means to make another, remote electron to acquire exactly the same spin state, then you have "electron spin teleporter". (BTW, due to no-cloning theorem, doing this _must_ destroy the initial electron's spin state).

If we will ever be able to do this to a big, macroscopic systems (such as humans), it will indeed work very similar to sci-fi teleportation. We are very far away from doing that. IIRC, currently the best we can do is "teleporting" a single atom.

13. Nov 7, 2014

### jeffery_winkle

Even what you describe does not involve any physical matter, not even a single electron, disappearing at one location and reappearing at a different location, but instead is just information being transferred, in your example, the information of what spin the electron should have is transferred, but the electron itself is not transferred. Both what you're describing, and what I described, which was a different process, involved a transfer of information, not physical matter, not even a single electron. You are transferring the information of what spin the electron should have, but not the electron itself. You are placing a different electron in the same spin state as the first.

14. Nov 8, 2014

### nikkkom

You can't label electrons. E.g. if you have two electrons simultaneously interfere in two-slit experiment and you get two blips on the screen, you don't know which electron ended up where. This question does not make sense. Electrons are indistinguishable.

If you would perfectly transfer a quantum state of a system of several (~10^23) electrons, neutrons and protons which constitute a human body, for all practical purposes it is equivalent to transfer of this human body. Whether it is "really" a transfer of the body or of "only information" is a philosophical question. It doesn't matter how you call it, the observable effects are the same.

15. Nov 8, 2014

### Jimmy87

Thanks for the information. My educational background is senior high school physics (pre-university). I have studied quantum physics but not in any real depth. I am just interested in it and this was after watching a video put together by the people that "teleported" the first particle in Hawaii. Yes, I do understand that only the quantum state is copied but to me that is still really amazing because couldn't you still use this process to re-create a molecule across a vast distance? I know the original molecule has not just disappeared and reappeared but you have effectively re-created a molecule over a vast distance? Or have I understood this wrong