Do entangled electrons still turn 720 degrees?

[Faradave]

I'm an outsider with only casual reading of QM. I have read that with respect to spin, electrons must complete eight 90 degree turns to summersault back to their original state (while you and I require only four such turns). Has this been verified to be the case with entangled electrons as well? (I was thinking they might act more like us when entangled, rotating completely through only 360 degrees.)

 

[Faradave]

In the absence of an answer or reference, advice on a search strategy (recommended keywords) or your considered opinion is appreciated.

 

[Academic]

If an electron is entangled, its spin is still 1/2.

 

[Faradave]

OK. But how many times can we flip it by 90 degrees until it returns to its original state?

 

[Klockan3]

If an electron is entangled, its spin is still 1/2.

Actually an electron pair with opposite spin and in the same state effectively have spin 0 and when turned around 360 degrees you get exactly the same state unlike spin 1/2 particles. If there were any force to keep them together they would even act as bosons like helium 4 atoms do.

 

[0xDEADBEEF]

If you look at a single electron, then it will usually not matter if it was entangled. The theory for this goes much deeper, and in a way it has been verified also for multi electron and entangled systems.

The main thing that happens with multiple electrons, is, that two electrons can occupy the same place, except for a 360 degree rotation, so if you take two, then turning the electron pair will not change it at all. (That is the spin 0 state).

Taking even more electrons you can add them with various degrees of rotation, but there may never be more then two in the same place.This leads to systems that have very funky behavior under rotations. If you add two electrons to form a spin 1 system, then it will behave in space like an arrow, so it will behave "more normal" under rotations.

All of this is governed by group theory and all quantum theory relies on it.

 

[my_wan]

I liked the way 0xDEADBEEF put it. To expand, the Pauli exclusion principle, which does not allow 2 electrons to occupy the same place at the same time, is oversimplified. It really means that no two electrons can have the same quantum numbers. When entangled, the exclusion principle only requires that the spin states can't be the same, when they are effectively in the same place. This, taking both electrons as a single entity with the same location, washes out the physical effects of rotation, even though individually they still maintain a spin of 1/2.

 

[Faradave]

Thanks folks. I presume you all had a chance to view the super image of electron spin effects at http://www.sciencedaily.com/releases/2010/04/100426151638.htm but it's worth a second look (It illustrates 6 of the 8 possible spin states).

Here's another question very similar to my op. Suppose I give you a dozen electrons, a Stern-Gerlach type device for detecting their spins and another device for flipping their spins. Could you, using those devices, identify the one electron in the group which is entangled with a remote electron?

I understand that entangled electrons are in a total spin zero state. But if you only had access to only one of a pair, would it be apparent? I'm curious as to whether there is another quality more like a product than a sum (a sum giving total spin = 0). A product of negative spins might cancel (like multiplying two negative numbers), cutting in half the number of unique spin states for each in the pair.

If that was the case, the one entangled electron in the dozen given would be identifiable by the fact that it returns to its original spin state in only four, 90 degree flips while the others all require eight.

That's what I was getting at with the op. Has anyone counted the number of unique spin states of a single electron in an entangled pair? I apologize if this is nonsense.

 

[0xDEADBEEF]

Entanglement tells you something about your knowledge of the system, not about the electron. You cannot pick up a random electron and check if it is entangled. If you measure one electron another will be forced to be in a certain state, your measurement is not affected at all.
To repeat myself, entanglement is never the property of a single particle. Any electron in existence is in some way entangled with the rest of the universe, for a certain type of observer.
If we use the picture of the astronauts with the socks it might help (although some mathematical details are wrong...) Imagine that you know an astronaut has only two pairs of socks. Red ones and green ones. He never mixes them.
He is flying to the moon, and you are ensured that he is wearing socks, but nobody tells you the color. If it was a quantum system, the socks that are left in the drawer at home could be called entangled to the socks of the astronaut on the moon. When you open the drawer at home and find red socks you instantly know that the color of the socks on the moon is green. (Quantum systems are a bit different, and one can show that the socks on the moon don't know their color before you open the drawer.) But the bottom line remains, nothing you do with the socks that you find in the drawer will do anything to the socks on the moon.

 

[Faradave]

But the bottom line remains, nothing you do with the socks that you find in the drawer will do anything to the socks on the moon.

Thanks for taking the time to share that helpful explanation. This is much the understanding I had been given before. A QM outsider, like myself, can be easily mislead by statements such as the following from (http://www.sciencedaily.com/releases/2009/06/090603131429.htm ) reporting on an actual experiment:

Mechanical oscillators like two pendulum-based clocks have previously been synchronized, but their vibrations can still be independent, so that changes in one have no effect on the other. Quantum entanglement-"spooky action at a distance," in Einstein's words-is a far more counterintuitive process: If two objects are entangled, then manipulating one instantaneously affects the other, no matter how far away it is. Entangled objects do not necessarily have identical properties, just properties that are linked in predictable ways.

One gets the clear impression that acting on one of the entangled pair causes a mirror action on the other one, regardless of distance. This is not the first time I have had to be set straight after reading such descriptions. Do you think its just the reporter not understanding the subject? Thanks.

 

[0xDEADBEEF]

The reporter is unfortunately right, and I was imprecise. But it is very hard to put into words.
Quantum mechanics has this peculiar behavior to look as everything is normal when you actually take a look. (i.e. when you do a measurement) In between the measurements the wave functions do funky things and when you look again quantum mechanics will give you another picture. Which one depends on chance. But again it will look "normal".
If we have two electrons in a spin 0 system then we know that they have opposing spins. The spins are entangled. When the spins are not measured, the spins don't know which way they are pointing, and this can be proved! There are deep philosophical problems connected to this, also called the Einstein Podolski Rosen paradox. It is complicated but definitely true, people have done the math.
But when you actually check the spin then it is just like the socks. It will look as if one spin has always been up and the other one has always been down. You also couldn't tell if someone else has already measured the spin and made the wave function "collapse" before you did it.
So if we use a certain interpretation, we can say that your measurement makes the wave function collapse and forces the other particle to collapse too - what the reporter mentioned. But the wrong intuition that people get from it, is that this will make a difference on the other end. If one electron is on the moon, no one there can prove that it is entangled or watch how the wave function collapses. Nothing noticeable or measurable happens to that electron. The only thing that nature guarantees, is that when an observer comes back from the moon he will have a consistent result with yours. So if he measured up you measured down, no matter who measured first.

Maybe this helps, and maybe you get an idea why quantum mechanics shattered our ideas about reality.

 

[Faradave]

...it is very hard to put into words...Maybe this helps...

It does. Thanks for taking the time to make that clarification.

As to my OP, it would appear that while entangled, the pair spin oppositely no matter how often either one is turned. However, the moment someone measures the spin of either one (as I would to count the number of turns to complete a rotation), the entangled state collapses. The total number of turns thus, appears inaccessible.

 

[0xDEADBEEF]

That is almost right. Except that the spins don't move while they are not being observed. In fact they don't exist according to our present theory.
When you measure it will look as if they kept opposite directions after the entanglement and before the measurement. But they didn't need to keep anything because they didn't exist.

If you force a turn on one spin which has not been measured yet, the other spin will not follow. For example, if you start with a spin 0 state to entangle two spins to be opposing, and then flip one spin, which is possible without looking at it. When you measure afterwards, you will always find both spins looking in the same direction, but you don't know which.

But again: in between measurements quantum particles are in some kind of probabilistic wave state, that can be manipulated according to certain rules, they don't have a position or a speed, and most properties are somehow smeared out. Just when we measure nature will make sure that certain rules are kept. No energy is created, no momentum, and a couple of other ones. As I said: afterwards - at the measurement - is the time, when nature makes things look normal.

I cannot explain any more without serious math, if you are really interested you should get a quantum mechanics intro book.

 

[DevilsAvocado]

... then flip one spin, which is possible without looking at it.

Very interesting! How is this 'trick' performed!?

 

[0xDEADBEEF]

Very interesting! How is this 'trick' performed!?

Well I am not sure if it is practically possible in 3D. Maybe through some entanglement trick and then you probably have to get lucky. (Just use the cases where a measurement yields the right result...)

But I think you can do it in 2D like this: If you start with a S_z=0 state you can do a pi/2 pulse to rotate it in the xy-plane by 180° then the x and y components should flip signs. Similar to spin echo http://en.wikipedia.org/wiki/Spin_echo

 

[DevilsAvocado]

But I think you can do it in 2D like this

Well yes... but I’m a little 'skeptical'... those little "bastards" seems to be very sensitive for "exposure"...

If you compare with e.g. the http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser" they definitely don’t want to play...

Are you sure it can ever work...?


P.S. You really got me with your user name! Spent quite awhile wondering what 3,735,928,559 could "mean"...? ∏√0xDEADBEEF = 1 ?? Nice 'trick' DeadBeef! (I must be completely stupid...)

 

[0xDEADBEEF]

In that experiment they look especially robust, as they keep their coherence even though you do all that parametric down conversion stuff.

Considering that you can even run quantum algorithms in NMR, I am sure that you can do that spin flip too.