Saturday, May 4, 2013

Correlation Measurements in Flatland (EPR paradox)

I will follow the instructions very similar to what you can see here:(http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html)
We imagine a radioactive substance that emits a pair of flat electrons in each decay. These two electrons go in opposite directions, and are emitted nearly simultaneously. So we can have a sample emitting these pairs of flat electrons. Figure 1 shows such a sample and flat electron filters measuring the spin of each member of the pair:






Figure 1 Entangled flat electrons traveling through filters in opposite directions.

Continuing, for the radioactive substance we will be considering in Figure 1, one-half of the flat electrons incident on the up hand filter emerge and one-half do not. Similarly, one-half of the flat electrons incident on the down hand filter emerge and one-half do not.

But if we look at the correlation between these flat electrons in Figure 2, we find that if the up hand electron does pass through the filter, then its down hand companion does not pass its filter. The handedness of the coupled flat electrons at the center determined this correlation.




Figure 2 Example of a 0% correlation.


We say that each radioactive decay has a total spin of zero: if one electron is spin right its companion is spin left. Now, the case where the two filters have opposite emerged spin.






Figure 3 Example of a 100 % correlation


This time if a particular left hand flat electron passes its filter down Figure 3, then its companion right hand flat electron always passes its filter. It is obvious that the handedness of the flat electrons produced this correlation! 

Finally, if the two filters defined the same emerged flat electron are one perpendicular to the other. 



Figure 4. Correlation experiment with different magnetic field orientation.

One-half of the down hand flat electrons emerge from their filter. One-half of the up hand flat electrons emerge from their filter. If a particular down hand electron passes its filter, one-half of the time its companion up hand flat electron will emerge from its filter, one-half of the time it will not. Because this particular orientation produced the donut intersection and a 50:50 percent probability to have either structure again (see Figure 4).

Thus, Einstein was right! "Imagine that your friend had a pair of gloves and two boxes. He put one glove in each box, and then separated the boxes. Now imagine that you didn’t know which glove was in which box, and you were asked to open one of the boxes. Simple logic would tell you that there was a 50-percent chance of getting the right-handed glove and a 50-percent chance of getting the left-handed glove. And say you opened the box and saw the right-handed glove. You would automatically know which glove was in the other box, but there wouldn’t be any occult connection between the two gloves. Rather, each glove always had its handedness before the observation. "

The orientations of the filters in Figure 1, 2 and 3 were arbitrarily but consistently set to get the Space-Land experimental results.