How does entanglement work for spin states?

[JustinHolmik]

Hello, I am a 40 year old Computer Scientist by education and profession. Education in general is my hobby. I am currently listening to a lecture on quantum mechanics: The Teaching Company's Quantum Mechanics Physics of the Microscopic World. Very good. So please excuse my nievity and ignorance in advance. I have not her taken a formal course in physics in high school or college but I have listened to many lectures.

Finally, my questions:
Particle entanglement: first: how is the relationship between two entangled particles formed initally? How is that relationship maintained even over very large distances. The second and more pressing question is regarding the spin states of particles: there is four spin states for two entangled particles: A, B, C and D. My question is how does a single particle have two spin states? How can a particle spin both south and north at the same time? Wouldn't that be like the Earth spinning both east and north at the same time?

Thanks in advance to anyone that answers my stupid questions. I again apologize for my ignorance but we all have to start someplace.

PS: (To admin, if any viewing) posting from mobile phone and mobile sites page entirely shifts left when subject line is longer than two words...thus the incomplete subject description. Which then made posting impossible. And when I tried pasting from my notepad it only pasted three words?

 

[StevieTNZ]

I am currently listening to a lecture on quantum mechanics: The Teaching Company's Quantum Mechanics Physics of the Microscopic World.

I have seen that series, it is very good.

Particle entanglement: first: how is the relationship between two entangled particles formed initally?

There are multiple ways. I'll give one example: two photons hitting a beam splitter and the output being unable to distinguish what photon came in from the left, and which came from the right.

The second and more pressing question is regarding the spin states of particles: there is four spin states for two entangled particles: A, B, C and D. My question is how does a single particle have two spin states? How can a particle spin both south and north at the same time? Wouldn't that be like the Earth spinning both east and north at the same time?

You are thinking of quantum superposition in terms of classical reality. When someone says a particle's spin is both up and down at the same time, they mean it is in a superposition of those two which has no classical analogue. Some call the two states the system can take on (spin up OR spin down) as potentialities, where only one occurs when 'measurement occurs'. However, when does the particle take on the definite spin? That's the crux of the measurement problem.

 

[JustinHolmik]

Thanks StevieTNZ for your response.

Definitely, The Teaching Companies series is very good. That and Modern Scholars Series. I have been listening to both, daily, for about 8 years now. My college education pales in comparison to that which I learned listening to the audio lectures by some of the best professors in the world. The only limitation is that a lot of it is introductory though it is thorough. To my great dissapointment listening to mathematical courses is often moot because one cannot see the equations on the board. I listened to a course on linear equations and barely muddled through it.

I had to look up the term superpostion and found a good explanation here: www.physics.org/article-questions.asp?id=124 . If I understand superposition correctly meshed with your explanation only two spins are probable but at time of measurement only one spin is observed. The article suggests that a particle has all potentialities until measured which must be wrong because all my education and yourself say there are two probabilities regarding the spin state?

There are multiple ways. I'll give one example: two photons hitting a beam splitter and the output being unable to distinguish what photon came in from the left, and which came from the right.

I am sorry StevieTNZ, and forgive me for I am slow, but I am still not understanding how the relationship is formed but if I'm understanding the entanglement relationship if I measure one photon of an entangled pair and find it to be rotating clockwise then the other photon of the entangled pair "knows" this and will be rotating counterclockwise? Though, I guess, what is at the heart of my relationship query is if I were able to not only measure but actually change the rotation of photon A from clockwise to counterclockwise would then photon B automatically change from rotation counterclockwise to clockwise without any direct action being put against photon B due to its entangled property with photon A and regardless of distance? And if so how does photon B know what happens to photon A?

Quantum entanglement fascinates me due to its endless computing applications. :)

 

[StevieTNZ]

I had to look up the term superpostion and found a good explanation here: www.physics.org/article-questions.asp?id=124 . If I understand superposition correctly meshed with your explanation only two spins are probable but at time of measurement only one spin is observed. The article suggests that a particle has all potentialities until measured which must be wrong because all my education and yourself say there are two probabilities regarding the spin state?

Yes, a quantum system has the potential to take on any state predicted by the fundamental Schrodinger equation. In terms of spin, up and down are the only possibilities.

if I measure one photon of an entangled pair and find it to be rotating clockwise then the other photon of the entangled pair "knows" this and will be rotating counterclockwise? Though, I guess, what is at the heart of my relationship query is if I were able to not only measure but actually change the rotation of photon A from clockwise to counterclockwise would then photon B automatically change from rotation counterclockwise to clockwise without any direct action being put against photon B due to its entangled property with photon A and regardless of distance? And if so how does photon B know what happens to photon A?

Let us use two photons entangled in this bell-state (there are four bell-states): |H>|V> - |V>|H>
If I measure photon 1 and it is found to be horizontally polarized (|H>), then I know if I measure photon 2 (or someone else does), they will get vertical polarization (V>).
Another bell-state: |H>|H> + |V>|V>
If photon 1 is measured to be vertical polarized, then measurement on 2 means photon 2 will also be vertically polarized.

However, in saying the above, we aren't sure if upon measuring one photon, the other photon takes on the state at the same time (we can't find out by measuring it whether it collapses at that point, or it collapsed at the measurement of photon 1 and we are simply detecting the state the photon took on a while back).

It seems entanglement between two photons will exist no matter the distance.

I don't think anyone has a definite answer as to why photon 2 knows what result we get from measuring photon 1. If it is communication between them, it needs to be faster than light -- http://www.unige.ch/gap/quantum/research:nonlocality_and_entanglement:experiment (scroll down to Testing the speed of quantum entanglement). In fact, a good book you could acquire is written by Nicolas Gisin: https://www.amazon.com/dp/3319054724/?tag=pfamazon01-20