The diagram will likely get scrambled by the server. I include an
attachment.
From: RBZannelli@AOL.COM
Reply-to: avoid-l@hawaii.edu
To: avoid-l@hawaii.edu
Sent: 2/27/2008 1:56:46 P.M. Eastern Standard Time
Subj: INVERSE EPR AND RETRO CAUSATION ( CORRECTION)
INVERSE EPR AND RETRO CAUSATION
)))))))))))))))))))))))))))))))
d_1 d_2
I I
I I
BS
I I
I I
Z(-) Z(+) Z(-) Z(+)
I I
E_1 E_2
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Perhaps no experiment better illustrates the weirdness inherent in Quantum
Mechanics and the reason why some physicists insist that retro causation is at
work in the quantum world than the inverse EPR experiment devised by
Zeilinger and others. I will go through this step by step in order to attempt to
clearly describe this experiment. It’s not very difficult to understand.
We start with two photon detectors d_1, d_2 and two photon sources E_1 and
E_2. We set the photon sources to a very low intensity so that they each emit
one photon at a time with a very low probability that they will ever emit
photons at the same time.
We set up the emitters and the detectors so that the photons pass cross on
the way to the detectors (like the letter A). E_1 directed at d_2 and E_2
directed at d_1.
This gives us two possible paths which we will represent in ket form. [12>
and [21>
This gives us a purely classical result. If d_1 fires we know we had a
photon emitted from E_2 and from E_1 if d_2 fires. This set up gives us perfect
which way information because there is no interference between the two paths.
Next we add a beam splitter at the point that the two paths [12> and [21>
cross. The beam splitter will generate interference between the two paths
destroying our which way information. Now we have four possible paths for a single
photon. [12>, [21>, [11> and [22>. The path lengths are such that at d_2
we get destructive interference and and d_1 constructive interference. So with
the beam splitter in place only d_1 ever fires. With this set up we have no
way of knowing which path the photon traveled. We can write this superposition
state as
Psi(path) = (1/2)* { [ 12> + [ 21> + [11> + [ 22> }
Now we leave this experiment to create the next part of the inverse EPR set
up. We prepare two spin ½ atoms in a X (+) spin state so we get;
[X (+) > = (1/sqrt [2])* {[Z (+) + Z (-)}
In the Z axis basis.
We then split the atom’s state using a non uniform magnetic field into the Z
axis spin components and place them into two boxes. Z (+) and Z (-). It’s
important to understand that we aren’t splitting the atom and that the only
reason we have the atoms apparently in two boxes is that we take care not to
measure their actual spin for the Z axis. Were we to do this the atoms wave
function would collapse and we would find an atom in only one of the boxes.
Now we do this for a series of atom pairs and measure the spin of each pair
at two distant measurement devices. These measurement devices can rotate
their magnetic field independently which affect the probability of which
measurement result will occur. This gives us a record of measurement events for each
atom in the series of pairs.
When both measurement devices are at the same angle of rotation the
measurement
records are virtually identical for each atom of the pair. If we rotate the
measurement devices to different angles from each other we see that the
records of each atom diverge.
Every time a measurement event is different between the two atoms of the
pair we will call an error. By simple logic we see that the following
mathematical relationship must hold.
E( 2*theta) = < 2*E(theta)
This means that twice the errors at angle theta is equal to or less than the
errors recorded when the difference in angle is two times theta. The “less
than relationship” accounts for double errors which are recorded as no error.
This is called Bell’s inequality after the Physicist who first proposed it.
This mathematical relationship is bases on the premises that any event on
one measurement device has no effect at the other. And in the example described
here we find that this mathematical relation is upheld. This makes sense
since we have kept the atom pairs completely independent of each other.
Now we take the two set of boxes and place them in each path of the photons
described at the beginning of this. We place box Z (+) for the first atom in
the path for the photon from E_1 and the Z (-) box for the second atom in the
path for the photon emitted from E_2.
In 50 percent of the cases the one of the atoms will choose to reside in the
box which lies in the photon’s path. When this happens the photon will be
absorbed and there will no detection event. But in 25 percent of the cases the
photon will choose the other path where no atom is available to absorb the
photon. The possibilities are
1) Both atoms in both photon paths. Photon absorbed no detection.
2) Atom in path from E_1 and photon emits from E_1 Photon absorbed no
detection.
3) Atom in path from E_1 but photon emits from E_2 Detection by d_1 or d_2,
atoms are in an entangled state in this case.
4) Atom in path from E_2 and photon emits from E_2. Photon absorbed no
detection.
5) Atom in path from E_2 and photon emits from path E_1. Detection in either
d_1 or d_2. Again atoms are entangled in this case.
6) Neither atom in photon path, detection by d_1 only, no entanglement of
the atoms.
Note that only in cases 3 and 5 are the atoms entangled. But in all cased
where a detection event takes place for d_ 2 we have entangled atoms.
However, while we know that a detection event means a particular
relationship between the states of the atoms we do not know which path the photon took.
Our ignorance of the photon’s path is not merely epistemological but
ontological. Therefore we end up with the product state
Psi = (1/sqrt[2])*{ [ 12 > [ Z_1(+) Z_2(+) > - [ 22> [ Z_1(-) Z_2(-) > }
Now based on quantum theory when we measure the spin states of the atom
pairs we expect that
E= N* sin^2 [theta]
Where theta is the difference in angle between the two measurement devices
and N is the number of measurement events.
Therefore we can see that
E( 2*theta) = < 2*E(theta)
Does not hold.
This is a pretty astounding result. This means that the entanglement of the
photon paths has caused the atom pairs to also be entangled even though the
entanglement of the photon paths takes place AFTER THE PHOTON’S INTERACTION
WITH THE ATOM. An event occurring at a given point in time has affected an
event at an earlier point in time.
This I think illustrates very clearly why some physicists insist that retro
causation is at work at the quantum level.
Bob Zannelli