How did Einstein see that Entanglement lead to Connectedness

[LoveQM]

I am studying the history of Quantum Mechanics and was reading about particle entanglement. What I would like to know is how did Einstein see that particle Entanglement meant that particles would be affected by spooky action at a distance. I guess that spooky action at a distance may also be associated to mean a form of connectedness. I would like to understand what led him to this conclusion? Put another way what is it in the formulations of QM that suggested that this particular phenomenon would occur? I am an avid reader of physics books and magazines so please feel free to give as much detail as you like.

 

[DrChinese]

What I would like to know is how did Einstein see that particle Entanglement meant that particles would be affected by spooky action at a distance. I guess that spooky action at a distance may also be associated to mean a form of connectedness. I would like to understand what led him to this conclusion?

Einstein did not believe in "spooky action at a distance (FTL influences)." There were (and are) others who do. Certainly, entanglement of distant objects - as predicted by QM - would be a strong motivation for that view.

 

[LoveQM]

Einstein did not believe in "spooky action at a distance (FTL influences)." There were (and are) others who do. Certainly, entanglement of distant objects - as predicted by QM - would be a strong motivation for that view.

Okay, yes I agree he did not believe in spooky action at a distance. What exactly is it within QM that predicts this phenomenon? He must have seen or invented a particular equation that suggested EPR paradox. I think that there must be a particular equation that predicts it. So I guess I would like to know what that equation is and have it broken down and interpreted to the point where I can see for myself how this interpretation was discovered. I am looking for that specific detail.

 

[Nugatory]

Okay, yes I agree he did not believe in spooky action at a distance. What exactly is it within QM that predicts this phenomenon? He must have seen or invented a particular equation that suggested EPR paradox. I think that there must be a particular equation that predicts it. So I guess I would like to know what that equation is and have it broken down and interpreted to the point where I can see for myself how this interpretation was discovered. I am looking for that specific detail.

You will want to start with Louisa Gilder's excellent but layman-accessible history "The age of entanglement". That will give you enough context to make sense of what you find when you dig deeper into specific areas. You should then read Giancarlo Ghiardi's "Sneaking a look at God's cards" for the breakdown and interpretation that you're looking for.

 

[bhobba]

What exactly is it within QM that predicts this phenomenon?

Its a simple deduction from the principle of superposition.

Its a common, but incorrect, misconception that Einstein thought QM incorrect and didn't really understand it. Both are wrong. He believed QM correct, but incomplete. He carried a copy of Dirac's Principles of QM at all times saying it was the most perfect development. Dirac based his treatment on the principle of superposition so its hardly surprising he cottoned onto the implications of entanglement. Even Bohr was very impressed with EPR realizing it was very deep and subtle. Many scientists responded quite quickly to the EPR paper. Bohr was much more circumspect, taking a long time to publish his take.

Thanks
Bill

 

[LoveQM]

@Nugatory I ordered the book Giancarlo Ghiardi's "Sneaking a look at God's cards. Catch name. I have read other books on the topic but this one detail evades me.
@bhobba I got excited for a moment to hear Dirac connection, I did not know Einstein like Dirac's Principles of QM so much. I have read a lot about Einstein. I began to think about Superposition and I could not make the connection between Superposition and EPR entanglement. So at this point Einstein's realization about EPR is still hidden from me. Perhaps you could elaborate more on that angle.
There must exist an equation that has the proper elements that describes the entanglement process. To me entanglement means that some how twin particles are actually physically tied together just like two separate shoe strings. I know that this is most likely a naive assumption but what else could two particles be that are entangled. Somehow they become one single system and remain a locally contacted single element even though they are separating. I think the equation does not have a term that includes distance, time or velocity. Those elements would then bring a time interval into play and supposedly no time passes when one particle is measured and the other is affected.

 

[bhobba]

I began to think about Superposition and I could not make the connection between Superposition and EPR entanglement.

Suppose a particle can be in two states |a> and |b>. If particle 1 is in state |a> and particle 2 in state |b> then that is written as |a>|b>. Similarly if particle 1 is in state |b> and particle 2 in state |a> that is written as |b>|a>. Now the principle of superposition says if a system can be in two states |1> and |2> then c1*|1> + c2*|2> where c1 and c2 are complex numbers is another possible state. Applying this to state |a>|b> and |b>|a> means that c1*|a>|b> + c2*|b>|a> is also a possible state. Such states are called entangled which is something peculator allowed by QM. The particles are not in state |a> or |b> - they are in some weird sort of combination.

Just as an aside the latest research points to entanglement being the rock bottom essence of QM:
https://arxiv.org/abs/0911.0695

But that is bye the bye.

Now a typical state used in Bell type discussions is where c1 = 1/√2 and c2 = 1/√2 so we have the state 1/√2 |a>|b> + 1/√2 |b>|a>. Suppose we observe particle 1. If we find it is in state |a> then since the state with particle 1 in state |a> is |a>|b> particle 2 must be in state |b>. Similarly if we find it is in state |b> then since the state with particle 1 in state |b> is |b>|a> particle 2 must be in state |a>. While pretty intuitive it can be made totally rigorous using the rules of QM. That's all that going on. Because of superposition if you know the state of one particle you automatically know the other.

It was the genius of Einstein to see into the heart of this as a big issue for QM. The resolution came with Bell and his theorem:
http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

Thanks
Bill

 

[LoveQM]

@bhobba
Ah okay I got it. EPR is just a rule if A is in this state then the B has to be in the other. Okay now just for my own sanity sake then in order for EPR to become magical. They must have done an experiments that forced A into a particular state using some sort of polarizing filter and then somehow B changed to the appropriate state instantly. Do I have that part right? For my understanding I need to know that is what they actually did in the experiment. Thanks for your help the fog is starting to clear now.

 

[bhobba]

@bhobbaFor my understanding I need to know that is what they actually did in the experiment.

Its easy when you think in terms of spins:
http://plato.stanford.edu/entries/qt-epr/#3

See the section spin and the Bohm version.

Thanks
Bill