Download EPR, reuscitate cat

PH 401
Dr. Cecilia Vogel
Review
Spin
spin angular momentum
not really spinning
simultaneous eigenstates and
measurement
Schrödinger's cat
Outline
Resuscitating Schrödinger's cat
Pauli Exclusion Principle
EPR Paradox
Review Schrödinger's Cat
http://en.wikipedia.org/wiki/Schroedinger's_cat#The
_thought_experiment
Set Up Analogue
Let’s pretend that a cat could really be considered a
quantum system. Its liveness is a two-eigenvalue
system, like an electron’s spin.
Let’s draw an analogy (that should not be taken
seriously!)
ELECTRON SYSTEM
CAT SYSTEM
Operator = Sz
eigenvalues:
spin-up (+/2)
spin-down (-/2)
Initial state = 50-50
superposition of spin-up
and spin-down
Operator = liveness
eigenvalues:
alive
dead
Initial state = 50-50
superposition of alive
and dead
Poor Cat is Dead
Initially (t=0), the
electron is in 50-50
superposition of spinup and -down
Suppose we measure
Sz and find spin-down
at t= t1, the
electron is no longer
in superposition
state
at t1, the state is
100% spin-down
Initially (t=0), the cat
is in 50-50
superposition of alive
and dead
Suppose we
measure liveness and
find the cat is dead
at t= t1, the cat is
no longer in
superposition state
at t1, the state is
100% dead
There is Hope
At t1, the state is 100%
spin-down
Now we measure Sx,
finding spin-right (or
left)
at t= t2, the electron
is no longer in spindown state
it is in a spin-right
(or left) state
which is a
superposition of spinup and spin-down
At t1, the state is 100%
dead 
Now we measure B, an
operator incompatible
with liveness
that places the cat in
an eigenstate of B
It can’t at the same
time be in an eigenstate
of liveness,
so its state is a
superposition of alive
and dead!
Resuscitating the Cat
At t= t2, the electron is
back in a superposition
of spin-up and spindown (as it was at t=0)
Again we measure Sz,
and find either
spin-up, and quit
or spin-down, in
which case we repeat
the Sx measurement
and go thru the loop
repeatedly until we
get spin-up
At t= t2, the cat is back
in a superposition of
alive and dead (as it was
at t=0)
Again we measure
liveness, and find either
ALIVE, yay 
or dead, in which
case we repeat the B
measurement and go
thru the loop
repeatedly until we
get a cat that is alive
Good Luck
The ability to resuscitate the cat
hinges on determining an operator B
that is incompatible with the liveness operator
[liveness, B] ≠ 0
I have no idea how you would express “liveness”
as a quantum operator,
much less how you would find a measurable
quantity, B, that is incompatible with it.
Classical observables do not behave this way –
incompatibility applies to the quantum realm only.
Why? *shrugs*
Pauli Exclusion Principle
In chemistry we learn that no two electrons in an
atom can have the same set of quantum numbers.
The Pauli Exclusion Principle is even more
general:
No two identical fermions can occupy the same
quantum state.
What is a fermion? Any particle with half-integer
spin, like electrons, protons, neutrons, muons,…
in contrast to bosons, which have integer spin,
like the photon, gluon, …
All electrons are identical – you can’t tell one from
another.
Quantum Entanglement
The Pauli Exclusion Principle gives us one way to
create entangled particles.
Suppose we have two electrons in the ground
state of a He atom.
They cannot be in the same state, so if one is spin-up, the
other is spin-down,
even if both are in states of superposition of spin-up and
spin-down.
These electrons are entangled, because a
measurement of the spin-state of one determines the
spin-state of the other.
If one is found to be spin-up, the other must be spindown.
EPR Paradox
So if we make an Sz measurement on one of those
electrons, we collapse its wavefunction.
If we find spin-up, then its state is no longer a
superposition, but rather 100% spin-up.
ALSO… the other electron is no longer in a
superposition state, but rather 100% spin-down.
We have collapsed its wavefunction without interacting
directly with it!
This violates separable local realism…
Either the two electrons cannot be treated separately
or there is an instantaneous interaction between them,
which violates causality in relativity
or reality doesn’t exist 
EPR Paradox
If we just have the simple system with simple Sz
measurements described above,
then we can’t prove that the electrons were
ever in a superposition state
maybe they were just 100% spin-up and 100%
spin down all along
like classical statistics.
We need a more complicated system to prove that
this doesn’t work, and that is our PAL
If you want to read more, look up EPR or Bell’s
inequality (the inequality that fails in the PAL)
EPR PAL