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Fig. 15.15. Experiments with quan-
tum entanglement were carried out
using optical fibers running under Lake
Geneva in Switzerland by Nicolas Gisin
from the University of Geneva.
pion has zero spin, and because angular momentum must be the same before
and after the decay, the spins of the electron-positron pair must be in opposite
directions for conservation of angular momentum. If we also start with the
pion sitting at rest, conservation of linear momentum dictates that the elec-
tron and positron must fly off in opposite directions ( Fig. 15.16 ). If we just focus
on the spin state of the two particles, there is probability ½ for the positron to
be in the spin up state ↑ with the electron going in the opposite direction in
the spin down state ↓. Similarly there is probability ½ for the positron to be in
the spin down state ↓ and the electron in the spin up state ↑. What this means
is that if we measure the spin of the positron to be spin up ↑ even though the
particles may be widely separated in space, we know instantly that the spin of
the electron traveling in the opposite direction must be spin down ↓. Similarly,
if the positron is measured to be spin down ↓, we know instantly that the elec-
tron is spin up ↑. The spin information is shared - “entangled” - between the
two particles.
It was the physicist Erwin Schrödinger who came up with the wave
equation that determines how quantum probability waves evolve with time.
Schrödinger was familiar with superposition and the physics of waves from
classical physics. From the earliest days of quantum mechanics, he used the
term entangled to describe such two-particle states and said of this entangle-
ment property:
I would not call that one but rather the characteristic trait of quantum
mechanics, the one that enforces its entire departure from classical lines
of thought. By the interaction the two representatives (or ψ-functions) have
become entangled. 15
We can now do experiments to verify these spin measurement predictions
in situations where the information about the measurement of the first spin
could not have influenced the second measurement on its separated partner -
unless the information traveled faster than the speed of light. Albert Einstein
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