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M1L7g.txt
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M1L7g.txt
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#
# File: content-mit-8422-1x-captions/M1L7g.txt
#
# Captions for 8.422x module
#
# This file has 88 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
So now what are we doing quantum mechanically?
We want to prove that quantum mechanics cannot be reduced
to this classical reasoning.
So we want to show that this inequality is violated.
We have a source of entangled photons.
We've talked about how we can entangle photons.
And now we measure the quantities Q, R, S, and T.
And just to give you an example about the many possible
choices, Q can be a linear polarizer,
and R can be a circular polarizer.
S can be a linear polarizer at 45 degree.
And T can be a quarter-wave plate
followed by a linear polarizer at 45 degrees.
Well, that sounds like many trig functions,
but we're not going into it.
You have to choose your polarizations.
There's a certain scheme, that linear polarization is not
orthogonal to circular polarization.
So there's a certain theme behind it.
And if you would work it out by just looking
at entangled photons, the entangled photons
are in a state, let's say, hv plus vh.
They are correlated in polarization
or spin up, spin down, [? because ?] the down spin--
up it's a singlet state.
And you can just work out what is the polarization when
you detect it.
And what happens is that a simple but tedious calculation
says that all those quantities, QS, RS, and RT, are equal.
Here we have a minus sign, and they are all 1 over square root
2.
And that means that instead of the classical inequality,
that this quantity is smaller than 2,
we find that this is 2 times square root 2.
And the fact that this is larger than 2
has been experimentally confirmed
with larger and larger precision.
Actually, the person who gave the CUA seminar a week ago,
Jean Dalibard, was part of the team with Alain Aspect, who
did one of the very, very first measurements-- violations
of Bell's inequality in the '80s, some 30 years ago.
So I mean, this happened rather recently.
So the math is trivial.
The result seems trivial.
It just shows that the world is quantum mechanically and not
classical.
And a lot of papers have been written
and discussions have been had about,
what does it really mean?
What does it mean about the world?
What does it tell us about the world?
So the implication from the established--
from the violation of Bell's inequality and the CHSH
inequality is that when we assumed that the state has
definite values of Q, R, S, T before observation,
we have to give up that.
Or we have to give up that a measurement performed by Alice
does not influence Bob's experiment, Bob's measurement.
So in other words, what I have formulated here is the locality
principle, that what happens in one location cannot influence
what happens in the other location.
Well, you can say maybe there's some secret channel sending
signals with speed of light.
But people have been to great lengths
to put the detectors so far away that even
a signal at the speed of light could not have influenced
the other measurement.
So after the first Bell's inequality experiment,
there have been a series of experiments
to avoid all those loopholes that there
is some unknown secret communication between the two
detectors.
The first one is the principle of--
and that's sometimes I think a more philosophical world
than physical world reality, that those quantities are real,
and they should exist before we measure them.
So the outcome of Bell's inequality is--
the violation of Bell's inequality is at least one
of them--
at least one of these principles, reality--
at least one of these principles does not hold in nature.
So either reality or locality are violated.