# Entanglement and EPR

1. Apr 28, 2015

### underworld

The EPR paradox is often described this way: (from Wikipedia)

A common presentation of the paradox is as follows: two particles interact and fly off in opposite directions. Even when the particles are so far apart that any classical interaction would be impossible (see principle of locality), a measurement of one particle nonetheless determines the corresponding result of a measurement of the other.
My question is that when the particles "fly off in opposite directions", are they not already spinning opposite each other? Said differently, how do we know the difference between these two scenarios:

1) The particles each have unknowable and indeterminate spin until we measure one of the particles, and then we know the spin of the other.
2) The particles each have unknowable, but definite spin, and knowing one particle's spin can inform us about the other.

In the first case, we must invoke a nonlocal mechanism to ensure the integrity of the system. But in the second, the locality of the particles during the incident which sends them off in opposite directions is what actually caused the opposite spin. Measuring one of the particles doesn't create a "causation" of the second particle physically, it merely reveals the information which was previously unknowable.

I assume there is some experiment which rules out the second scenario?

2. Apr 28, 2015

### Staff: Mentor

QM is silent about what systems are doing when not observed ie it can have proprieties like position momentum spin etc (such a view is called realism) or not. The theory has no take one way or the other.

The key thing about EPR is it rules out local reality:
http://en.wikipedia.org/wiki/Principle_of_locality

That is you cant have both realism and locality. If you assume what you posted ie its simply revealing what's there then you don't get what QM and experiment tells us:
http://www.drchinese.com/Bells_Theorem.htm

This of course is a deep result but not quite as bad as one might think because in QM locality isn't what we usually think anyway - locality is replaced by the so called cluster decomposition property:
http://en.wikipedia.org/wiki/Cluster_decomposition_theorem

It doesn't apply to correlated systems and in EPR the spins are correlated.

Thanks
Bill

3. Apr 28, 2015

### stevendaryl

Staff Emeritus
Choice 2) is a type of hidden-variables model, which is ruled out by Bell's theorem.

What that choice amounts to is the assumption that
1. Each particle has a spin vector, $\vec{S}$.
2. The spin vectors of the two particles are in opposite directions
3. if you measure that particle's spin along an axis $\vec{A}$, you'll get spin-up if the angle between $\vec{A}$ and $\vec{S}$ is less than 90o, and you'll get spin-down if the angle is more than 90o.
This model correctly predicts the perfect anti-correlation between spin measurements (if Alice measures spin-up along axis $\vec{A}$, then Bob measures spin-down along axis $\vec{A}$), but it doesn't correctly predict the probabilities when the angle between Alice's axis, $\vec{A}$ and Bob's axis, $\vec{B}$ is some angle between 0o and 180o

4. Apr 28, 2015

### jfizzix

The idea in the EPR scenario is that if the effect of measurement cannot travel faster than light, then the measurement statistics of each particle are determined exclusively by any/all events in their past light cone. So, the only things that could influence the underlying statistics would be any influences traveling at or below the speed of light.

If the particle's statistics are determined by such local influences, we might say that the particles have well-defined, but unknown spins.

However, entangled pairs of particles separated by large distances still exhibit very strong measurement correlations. Strong enough even to rule out the possibility that each particle's statistics are determined just by their own local history. Experiments which show this come under the umbrella of violating Bell inequalities.

So, if you do violate a Bell inequality, you show that the correlations between a pair of particles are not determined by any/all information in their past light cones.
Beyond that is interpretation.
You could say that their statistics are determined, but not locally, or you could say that there simply isn't enough information to determine their statistics (being somehow fundamentally indeterminate), though I expect there are multiple other possible conclusions too.

5. Apr 28, 2015