Transcript ENTANGLEMENT II by Robert Nemiroff Michigan

ENTANGLEMENT 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
ENTANGLEMENT:
ENTANGLED DOUBLE SLIT (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?
ENTANGLEMENT:
ENTANGLED DOUBLE SLIT (I)
1.
2.
3.
4.
An interference pattern. The photon enters a classic double slit
experiment and a classic interference pattern results.
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.
There is not enough information to tell.
Positronium explosions destroy the entire experiment.
ENTANGLEMENT:
ENTANGLED DOUBLE SLIT (I)
1. Interference pattern.
Comment: The entangled twin does not carry "which path" information,
therefore there is nothing that will destroy the interference pattern.
ENTANGLEMENT:
DOUBLE 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?
ENTANGLEMENT:
DOUBLE SLIT WITH AN ENTANGLED TWIN (I)
1.
2.
3.
4.
An interference pattern. The photon enters a classic double slit
experiment and a classic interference pattern results.
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.
There is not enough information to tell.
I've really stopped caring at this point.
ENTANGLEMENT:
DOUBLE 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.
ENTANGLEMENT:
COUNTERFACTUAL 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.
ENTANGLEMENT: BELL'S THEOREM
Hidden variable theories cannot explain the fundamental results of
quantum mechanics.
Written differently: quantum uncertainty is not based on a lack of past
knowledge.
ENTANGLEMENT: BELL'S THEOREM
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:
ENTANGLEMENT: BELL'S THEOREM
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.
ENTANGLEMENT: BELL'S THEOREM
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