How does the EPR paradox work?

[EduardoToledo]

Hi, I've heard about the EPR paradox as follows: Leave two entangled particles A and B carried by scientists A' and B', with a pair of incompatible properties (eg spin up/down and left/right) in possible Green/Yellow and Blue/Red states. If one measures Yellow state (eg, particle B in spin up and A in spin down), then the other must measure Yellow as well. If any of them measure the Blue/Red property, the next Green/Yellow measurement would be unpredictable.

Now suppose that the scientists combine the following: B' would only measure the Green/Yellow properties at a regular known interval. If A' wants to send the code "1", they should measure Blue/Red, then Green/Yellow, then Blue/Red, then Green/Yellow... until the Green/Yellow property changes randomly. If A' wants to send the code "0", they just don't do anything until B' measures the same Green/Yellow property a lot of times (say... 256), concluding that it's bad luck that A' couldn't change the property so many times (there is an image to help with visualization)

This thought experiment would allow you to communicate faster than the speed of light, so it must be wrong. I want to ask which misunderstanding I've made. Thanks in advance.

 

[DrChinese]

All any individual observer EVER sees is a series of 1's and 0's which are completely RANDOM. You get a 1 or a 0 (you can label them anything you like - U/D, H/T, 1/0) regardless of the spin property you measure (which you call G/Y and B/R).

The point is, there isn't much information to be found in a random sequence. You can match up the results of each trial to obtain the predicted correlations, but that requires classical communication (which cannot exceed c). So... no FTL signals to be obtained using this method.

Keep in mind that you need a new pair of entangled particles A & B to measure each iteration. Once they are measured, the entanglement disappears. Each pair of entangled particles is completely independent of all other pairs, assuming they are maximally entangled (which is your example).

 

[EduardoToledo]

Thank you! I didn't know that the entangled desappears, that's the misunderstanding I was looking for. In this case, how could we know that two particles were entangled. If we measure a property from one, how can we compare with the other? Wouldn't the entanglement disappear prior to the second measurement?

 

[Nugatory]

Thank you! I didn't know that the entangled desappears, that's the misunderstanding I was looking for. In this case, how could we know that two particles were entangled. If we measure a property from one, how can we compare with the other? Wouldn't the entanglement disappear prior to the second measurement?

We need large number of pairs. Say we have a particle source that periodically spits out pairs of particles, send one to you and one to me. We both measure our particles' spin at the same angle (we'e agreed about what that angle will be ahead of time) and note the results. We then get together and compare notes.

If we just consider one pair we haven't learned anything: they will mismatch (mine up and yours down, or vice versa) half the time just by random chance. But if we've done 10,000 pairs and every single time your measurement is the opposite of mine it's a pretty safe bet that our source is generating entangled pairs (only one chance in $2^{10000}$ that that could happen if the pairs are not entangled).

 

[DrChinese]

Wouldn't the entanglement disappear prior to the second measurement?

This is an interesting question, and cannot be answered experimentally. Let's assume that A is measured before B (this can be done). The system of A & B acts as if the following occurs:

i. A takes on a random value relative to the measurement performed on A. Its entanglement ends.

ii. B takes on a property value exactly matching (or anti-matching, as the case may be) the outcome of the measurement on A. It is as if B somehow "knows" what happened to A, regardless of the distance between A & B.Note that the above is silent on "when" B's entanglement ends. Also note that the above explanation holds regardless of the order of measuring A & B. The statistical results do not change when the ordering is changed.

Important: The above is a guide to understanding what the statistical outcomes will be, but should not be considered an actual description of what happens. For that, you must refer to the quantum interpretations. Those are not discussed in this forum, they are discussed and debated in their own subforum.