Geisterteilchen neutrino research on TV

1. Nov 17, 2003

bigdowski_robert

I saw a series about neutrino research on TV and evrybody talked about 'Geisterteilchen' (ghost parts, literally translated)

As far as I understood there are 2 elementar pieces who change their spin in the same way though they might be at a great distance.

Evry try to measure the spin is vain as the spin changes depending on the way you wanna measure it. It's a tricky part.

It's confusing.

Can someone tell me about it. I feel so dumb

2. Nov 17, 2003

chroot

Staff Emeritus

It goes like this: you have two particles -- call them A and B. Two electrons, for example, will do nicely. You allow them to interact with each other (collide), and then send them off across the room (or across the universe) in different directions.

On one side of the room (or universe), there is a detector which can measure the spin of one of the electrons. This measurement will always give one of two values: +1/2, or -1/2. Spin, like all quantum numbers, cannot be measured absolutely -- all you can say is that the measurement has a particular probability of returning +1/2, and another particular probability of returning -1/2. It is critical to note that the particle does not really have a definite spin before you measure it. After you've measured it, however, repeating the measurement will always give the same result. This is known as "collapsing the wavefunction" of the measured particle: before the measurement, it is both +1/2 and -1/2 at the same time. The ability of a particle to simultaneously be in two different states is called "superposition," and is a basic feature of all quantum mechanical systems.

The tricky part is this: the two entangled particles must have opposite spins. If you measure one particle as +1/2, the other must be -1/2. When you measure the spin of one entangled particles, you collapse the wavefunctions of both at the exact same time -- even if the other particle is halfway across the Galaxy.

This would seem at first glance to violate relativity theory, which says that no information can propagate faster than light. This quantum-mechanical situation is called the Einstein-Podolsky-Rosen (EPR) paradox.

Does this make sense? My discussion is a little sloppy on purpose -- let me know if you would like some points clarified.

- Warren

3. Nov 18, 2003

rtharbaugh1

quantum entanglement of electrons

When you say that two electrons are made to collide, I wonder how this is done. How close together must the electrons be to collide? Does an electron have a radius?

Do we know what the spin of the electrons was before the collision? Does it make any difference if the electrons both have the same spin to start out with or if they start out with different spins?

Can spin be related to one of our three spatial dimensions? Is there any way to separate spin + electrons from spin- electrons? If I had an apparatus to measure the spin of a stream of spin+ electrons (assuming such a stream can be created) and I inverted the apparatus, would the apparatus indicate that the electrons were now spin-?

How is the spin of an electron measured? Does the measurement process affect the spin state?

I know this is a lot of questions. I have been wondering about these things since I first read that paired electrons in an atomic shell must have opposite spin. Does this mean that a chemical bond will not form between, say, Na+ and Cl-, unless the two atoms have electrons of opposite spin? Wouldn't this mean that two such atoms brought sufficiently close together would only form a bond half the time? Can we manipulate single atoms of sodium and chlorine to test this idea? Has it been done?

Thanks for any thoughts on these questions.

4. Nov 18, 2003

lethe

Re: quantum entanglement of electrons

in principle, any electrons can interact, although in practice they have to be very close to have a noticable effect.

classically, you know that the electric field from the point particle is just E=e2/r2. this means that the electric field fills all space.

this formula neglects quantum effects, so its not valid for high energy electrons, but the point is that "collide" just means get close enough to repel each other electrically.

as far as we can tell, the electron has no radius.

usually the electron beam is unpolarized, meaning it is an equal mixture of all spin states.

in that case, we have a formula for the interaction that depends on the spin, and we average over all spin states.

yes, it makes a difference. but as i said above, usually the beams are unpolarized, and we average over spin states.

in a sense. certainly, spin is a 3 vector, which means that it points in some spatial direction.

but i am referring here to the spin operator, which is not the same thing as the "value of the spin" of the electron in question. since the various components of spin are noncommuting observables, it doesn t make sense to talk about the spin of the electron having a direction in 3 dimensional space. the best you can do is specify one component of that vector. that is why we refer to them as spin up and spin down. the up and down refer to one component of the spin, and the other components of the spin are not in an eigenstate.

sure: the Stern-Gerlach apparatus. this is, in fact, how spin was first discovered. basically, just run the electrons through a magnetic field. since magnetic field couples to spin, it will interact differently with spin up and spin down, and seperate them into two seperate beams.

in this way, you can turn an unpolarized beam into a polarized one.

yes. all you have done is change coordinates, really.

by its interaction with the magnetic field, that s one way.

and yes, it does affect the spin. before the measurement, the electrons were not in an eigenstate, and afterwards, they are.

hmm... it s a little more complicated than that. the electron in the Cl ion and the electron in the Na atom both have wavefunctions. when you put the two atoms together, you get a few possible combinations of wavefunctions, one which is symmetric, and one which is antisymmetric. Pauli s exclusion principle allows the two electrons to have the same spin if they are in the antisymmetric combination of wavefunctions, and if they have opposite spins, they must go into the symmetric wavefuntion.

one of the combinations will have lower energy than the other, and the system can combine in whichever way is allowed, and then decay to the lower energy state.

in the end, no matter what the spin of the two atoms is, you can always make the bond.

but your idea that the reaction will only go forward half the time is not completely wrong. i would say that the reaction is slightly more favorable half the time (when the spins are aligned correctly). however, the energy difference between the spin states is so small compared to the energy released by the reaction, that in either case, the reaction will procede, and probably the difference in rates would be completely unmeasurable

5. Nov 18, 2003

chroot

Staff Emeritus
Re: quantum entanglement of electrons

No worries. We'll see what we can do!
It is true that "collision" is a loaded word. In our models, electrons are point particles. The electrons will never actually touch -- they will just get close enough to exchange enough virtual photons (the carriers of the electromagnetic force) to push each other away. As long as no real photons are generated in the scattering, the two electrons emerge in an entangled superposition of states.

The very definition of "touch" gets rocky in the subatomic domain. When you touch a wall, none of your body's atoms are actually touching any of the wall's -- the sensation of touch is actually due to electromagnetic repulsion.
The critical feature of spin measurement is that you can only measure it along one axis! In other words, if you measure spin in the "vertical" direction, you'll get either +1/2 or -1/2, randomly. If you then measure it in the "horizontal" direction, you'll lose all information about the "vertical" direction. If you measure the spin again in the "vertical" direction, you'll find it's again random, and not dependent upon the previous "vertical" measurement.
Well, as I've said, spin is a tricky thing to measure, and you can really only talk about spin along one axis. Either way, it doesn't make any difference what the spins were before the entanglement.
Yes, you can measure spin along any axis in three-dimensional space.
The apparatus to separate them is the same as the apparatus to measure them. It's none other than our good friend, the magnetic field. The +1/2 electrons get steered one way in the field, the -1/2 electrons get steered a slightly different way. The Stern-Gerlach apparatus which demonstrated the quantization of angular momentum works this way (google it!).
Yup.
Off the top of my head, I don't think electron spin will affect chemical bonding at all. Maybe a chemist can give some deeper insight?

edit: lethe's more accurate

- Warren

6. Nov 18, 2003

chroot

Staff Emeritus
7. Nov 18, 2003

Some great answers and points above guys - you have really helped clarify many things I have wondered about too.

One thing that does still puzzle me though and that is WHY entanglement takes place. Is there a simple answer to this, or is it another one of those 'thats just the way the Universe is' kind of questions?

8. Nov 18, 2003

chroot

Staff Emeritus
"Entanglement" is just the evocative name given to the condition where two particles are part of one quantum-mechanical system.

You see, people mostly treat the situations where the system is just one particle experiencing some potential, with the goal of determining the wavefunction and thus the energies allowed in the system. The wavefunction really describes the system (particle + potential), but people often get sloppy and refer to it as the particle's wavefunction.

When you have two particles involved in the system, as in an entangled pair, the wavefunction describes both particles, not just one in isolation. The evolution of that wavefunction -- for example, due to some measurement -- affects the entire system. When you measure a system, you leave it in an eigenstate of the observable -- this is sometimes known as "collapsing the wavefunction." You can't just measure part of the system and collapse part of its wavefunction -- it's an all or nothing deal. A measurement of either particle constitutes a measurement of the entire system, and therefore a collapse of the entire system's wavefunction -- leaving the entire system in an eigenstate of the observable (one electron spin-up, the other spin-down, for example).

- Warren

9. Nov 18, 2003

Once again, something complicated is explained in simple language very well... Thank you.

(Now if you could just explain life, the universe and everything....)

10. Nov 18, 2003

chroot

Staff Emeritus
*cracks knuckles*

The explanation of life, the universe, and everything is:

$$42$$

- Warren

11. Nov 20, 2003

turin

This interpretation of relativity has always made me uneasy, but it invariably seems to be relativity's response to the issue of entanglement. I need to put my misgivings to rest once and for all. Can you cite a reference for this interpretation?

12. Nov 21, 2003

rtharbaugh1

If I make two observations of a quantum system, do I collapse the wavefunction twice?

Warren, you said
"When you have two particles involved in the system, as in an entangled pair, the wavefunction describes both particles, not just one in isolation. The evolution of that wavefunction -- for example, due to some measurement -- affects the entire system. When you measure a system, you leave it in an eigenstate of the observable -- this is sometimes known as "collapsing the wavefunction." You can't just measure part of the system and collapse part of its wavefunction -- it's an all or nothing deal. A measurement of either particle constitutes a measurement of the entire system, and therefore a collapse of the entire system's wavefunction -- leaving the entire system in an eigenstate of the observable (one electron spin-up, the other spin-down, for example)."

If two spatially remote and isolated observers are in possession of entangled elements of a quantum system, and one of them collapses the wave function, can the other then detect any change in his possession which will enable a conclusion that the wavefunction has been collapsed? (I guess no, this would be ftl communication.)

If you collapse a wavefunction of a quantum system by an observation, and then make another observation, does the wavefunction collapse again? Does anything in the wavefunction tell you if the wavefunction has collapsed before? Does the wavefunction carry a history?

Is the wavefunction, which is spoken of here as collapseing, a property of the quantum system, a property of the observer, or a property of some intermediate which necessarily includes both the observer and the system?

I guess these questions are to the meaning of wavefunction. If I understand current discussion, I'd guess that there is no way, when observing a system, to know if the system had already been observed, that is, exists already in a collapsed state.

Thanks,

Richard T. Harbaugh