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Figure 01 EPR Paradox [view large image] |
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the pi meson into an electron-positron pair (Figure 02). Since the spin for the pi meson is 0, the spin for the electron-positron pair must be opposite according to the conservation of angular momentum. Therefore, no matter how far apart are the members of this pair, if the spin is flipped for one of the member, the spin for the other member will also be flipped to the opposite at precisely the same moment. This non-local influence (objects can influence each other only locally according to classical physics) occur instantaneously, as if some form of communication, which Einstein called a "spooky action at a distance", operates not just faster than the speed of light, but infinitely fast. |
Figure 02 Entanglement [view large image] |
Figure 02 demonstrates the origin of entanglement and its final collapse by measurement. The observers in the names of Alice and Bob are modern inventions. |
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![]() ![]() P++( ![]() ![]() ![]() P+-( ![]() ![]() ![]() |
Figure 03 Bell's Inequality Test, Single Channel [view large image] |
where ![]() ![]() |
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EEPR( ![]() ![]() ![]() Figure 04 compares the difference between EQM and EEPR. It is always small, and there are agreements at ![]() ![]() ![]() ![]() ![]() |
Figure 04 Correlation Coefficient |
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S(a,a',b,b') = E(a ![]() ![]() ![]() ![]() It can be shown (in that paper again) that for the case of hidden variable, the values of S are restricted to a range : |
Figure 05 2-channel Bell Test |
-2 ![]() ![]() ![]() In practice, the angles between the analyers are chosen to be 0o, 45o, 22.5o, and 67.5o. |
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SQM = 2(2)1/2 = 2.8284 ----- (8) which is clearly outside the range defined by SEPR in Eq.(7). Figure 06 shows the variation of SQM over a range of ![]() |
Figure 06 Bell's Inequality |
The Aspect experiment obtains Sexp = 2.697 ![]() |
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The Bell's inequality for this case is : -1 ![]() ![]() ![]() which just reiterates the fact that events would not be recorded if the signal is not faster than the speed of light. |
Figure 07 Non-locality Experiment [view large image] |
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An equilvalent form of the Bell's inequality asserts that if EPR were correct, the results found by two widely separated detectors measuring certain properties of 2 entangled particles would have to agree (match) more than 50% of the time. Figure 08 provides a very specific example to illustrate how underlying pre-arrangement (hidden variables) can bump up the chance of QM ramdon match. |
Figure 08 Bell's Theorem for Dummies [view large image] |
This is Brian Greene's analogy also known as "Bell's Theorem for Dummies". |
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experiment at Delft University solves both problems as shown in Figure 09. It produces entanglement of two electrons inside two diamonds respectively (separated by 1.3 km - enough to close the communication loophole and with no lost of entangled qbits) via the entanglement of the photons emitted by each. The occurrence is not very often - just a few per hour. Eventually, 245 measurements were taken to show that the standard quantum view is valid. Difficulty of the experiment produced a p-value of only 4% - a statistical significance just passes the usual 5% and is much shorter than the 1/106 standard for experiment in physics. Anyway, this experiment also guarantees the security in "quantum cryptography", which may be hacked through the loopholes. |
Figure 09 Bell Test, 2015 |
See more detail in "Quantum 'spookiness' passes toughest test yet". |