EPR Paradox Confusion: Understanding the Violation of Locality and Uncertainty

[dsdsuster]

Hello,

I've read through several sources about the EPR Paradox but I'm not sure I'm understanding everything. I know that:
-the paradox in question seems to be due to a violation of the principle of locality
-there is no useful transferred faster than c regardless of which axes the two observers choose to measure along

My primary concern is:
-Why is the example where the two observer's measure along different axes introduced?

From my current understanding, this adds nothing new to the violation of the principle of locality when both observer's are measuring along the same axis. I've read several sources which mention a violation of the principle of uncertainty, with the implication that this is at the crux of the paradox. I don't see any point in the experiment where one can claim to know the spin along more than one axis.

All of this leads me to believe that I am missing a point.

Thank you

 

[.Scott]

"Why is the example where the two observer's measure along different axes introduced?"

Without reading the exact language your referring to, when discussing locality, two reference frames are often used to highlight the problem of assigning a causal relationship to two events in time/space that occur so close in time that a light signal could not cross the distance between them in that time. The point is to show that in such cases there is no objective agreement as to which occurred first - it depends on your frame of reference. Since there is no objective agreement on which occurred first, assigning a causal relationship is problematic - how can the first event cause the second event when either one could be seen as the "first".

"All of this leads me to believe that I am missing a point."

The crux of the paradox is better explained in the Bell Inequality. Bell described a specific experiment which, when data is collected on all or nearly all of the particles, QM predicts statistical results that cannot be created with hidden values.

 

[Nugatory]

Why is the example where the two observer's measure along different axes introduced?

If you only consider measurements on one axis, the results might still have a purely local explanation.

As an analogy, consider what happens if I take a pair of gloves, put each glove in its own box, and then mail them to two different people in two different parts of the world. When one recipient opens his box and finds a left-handed glove, he knows immediately that whenever the other person opens their box they'll find a right-handed glove. There's no quantum weirdness happening here, no wave function instantaneously collapsing everywhere when one of us opens a box, no non-locality, no way that my observing my glove has any influence whatsoever on the other glove in the other box. We just had a left-handed and a right-handed glove all along. This is basically the EPR argument - there's some underlying physics that we don't know yet that explains how one particle was spin-up and the other was spin-down all along, and the quantum mechanical randomness just reflects our incomplete understanding of the system.

However, it turns out that there is no way of setting up initial conditions so that any measurement on any axis will match the quantum mechanical predictions; the glove analogy only works for a single axis. Thus, we have to look at results on multiple axes to be sure that we're seeing quantum mechanical effects and not just some preexisting values of the particle states.

Google for "Bell's Theorem" for more information.

 

[DrChinese]

My primary concern is:
-Why is the example where the two observer's measure along different axes introduced?

From my current understanding, this adds nothing new to the violation of the principle of locality when both observer's are measuring along the same axis. I've read several sources which mention a violation of the principle of uncertainty, with the implication that this is at the crux of the paradox. I don't see any point in the experiment where one can claim to know the spin along more than one axis.

EPR was from 1935 and QM was still new. The authors believed a deeper theory might be possible, that QM was somehow incomplete. They postulated: since you could determine Alice's property P from measuring Bob's P without actually measuring Alice, that property must be predetermined. If you accept that as true, then you could measure Alice's non-commuting Q and then you would know P and Q about Alice. That would, in fact, violate the Heisenberg Uncertainty Principle.

The flaw in the argument is the idea that the decision to measure Bob's P does not in any way affect Alice. That flaw was not obvious until Bell came along and demonstrated the inconsistency in the EPR argument.