# E NTANGLEMENT II by Robert Nemiroff Michigan Tech.

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E NTANGLEMENT II by Robert Nemiroff Michigan Tech

Physics X: About This Course Officially "Extraordinary Concepts in Physics" Being taught for credit at Michigan Tech o Light on math, heavy on concepts o Anyone anywhere is welcome No textbook required o Wikipedia, web links, and lectures only o Find all the lectures with Google at: "Starship Asterisk" then "Physics X" o http://bb.nightskylive.net/asterisk/viewforum.php?f=39

E NTANGLEMENT : E NTANGLED D OUBLE S LIT (I) Experiment: One positronium photon goes toward a classic double slit experiment, while its entangled twin goes toward a very near image screen. The very near image screen records only imprecisely. The entangled photon entering the double slit experiment still has the opposite momentum, but now this momentum could allow it to enter either slit. This identical situation is repeated numerous times. What will image screen behind the double slit experiment show?

E NTANGLEMENT E NTANGLEMENT : E NTANGLED D OUBLE S LIT (I) 1. An interference pattern. The photon enters a classic double slit experiment and a classic interference pattern results. 2. No interference pattern. The precision of the entangled twin's momentum determination is irrelevant. Since it COULD have been measured at high precision, "which-way" information could have existed, so that no interference pattern can occur. 3. There is not enough information to tell. 4. Positronium explosions destroy the entire experiment.

E NTANGLEMENT : E NTANGLED D OUBLE S LIT (I) 1. Interference pattern. Comment: The entangled twin does not carry "which path" information, therefore there is nothing that will destroy the interference pattern.

E NTANGLEMENT : D OUBLE SLIT WITH AN ENTANGLED TWIN (I) Experiment: One positronium photon goes toward a classic double slit experiment, while its entangled twin goes toward a very distant image screen. The very distant screen records very precisely the momentum that photon had when it was created. The entangled photon entering the double slit experiment must therefore have had the opposite momentum. This identical situation is repeated numerous times. What will the double slit experiment show?

E NTANGLEMENT : D OUBLE SLIT WITH AN ENTANGLED TWIN (I) 1. An interference pattern. The photon enters a classic double slit experiment and a classic interference pattern results. 2. No interference pattern. The entangled twin's momentum determination allows the determination of which slit its entangled twin will go through. This "which-way" information will destroy the interference pattern. 3. There is not enough information to tell. 4. I've really stopped caring at this point.

E NTANGLEMENT : D OUBLE SLIT WITH AN ENTANGLED TWIN (I) 1. Interference pattern. Even though the entangled twin carries precise position information, this information is not shared with high enough fidelity to allow "which path" information to exist. This is essentially the "Einstein Slit" experiment redone with photons. Since good enough "which-way" information does exist, the interference pattern will persist.

E NTANGLEMENT : C OUNTERFACTUAL DEFINITENESS C OUNTERFACTUAL DEFINITENESS The ability to know the result of a nonlocal experiment definitively given the result of a local experiment -- even if that local experiment did not measure anything. Example: A created photon must go somewhere. If half the photon's sky is made up of a shell, and the shell does not record that photon, then that photon must have gone in the direction of the other half of its sky. That piece of knowledge is an example of counterfactual definiteness.

E NTANGLEMENT : B ELL ' S T HEOREMB ELL ' S T HEOREM Hidden variable theories cannot explain the fundamental results of quantum mechanics. Written differently: quantum uncertainty is not based on a lack of past knowledge.

E NTANGLEMENT : B ELL ' S T HEOREMB ELL ' S T HEOREM Two entangled particles are created by a central source and sent to two observers, Alice and Bob, who can measure their vertical or horizontal spins:

E NTANGLEMENT : B ELL ' S T HEOREMB ELL ' S T HEOREM Now Bob and Alice can choose individually to measure each spin vertically or horizontally. If they both choose the same, they get opposite spins (angular momentum is conserved). If one chooses vertical and the other horizontal, they agree only 50% of the time. But let's say Alice and Bob choose a difference angle of, say, 22.5 degrees. How often do their spin measurements agree then? QM says one number, hidden variables says another (Bell first realized the discrepancy.) Results show QM is right.

E NTANGLEMENT : B ELL ' S T HEOREMB ELL ' S T HEOREM QM being right shows that "local realism" is wrong. Local realism assumes that: Objects have a definite state that determines all measurable properties (Hidden Variables) Effects of local actions cannot be transmitted faster than the speed of light. o does not necessarily mean that Alice and Bob can send messages to each other FTL