From: *Jason Resch* <[email protected] <mailto:[email protected]>
On Mon, Jun 18, 2018 at 7:38 AM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
From: *Jason Resch* <[email protected]
<mailto:[email protected]>>
In the EPR experiment, a pair of photons is created. Each photon
is in a super position of every possible polarization, and
because it is created as a pair, it's dual in the superposed
state always has exactly the opposite polarization (rotated 180
degrees).
OK.
When you perform a measurement of your left-traveling photon on
Earth, you become entangled (correlated) with it, and all the
possible states of that photon, when measured, leak into the
room, starting with the measuring device, then your eyes, then
your brain, then your notebook, etc. until now everything is in
the room, and soon Earth is now in many states which contagiously
spread from that photon.
OK. Your result (and you) become entangled with your environment.
Also, because the photon you measured was entangled (correlated)
with its pair in the superposition, whatever result you measure
for the photon's polarization tells you immediately what the
polarization of its pair is (in your branch at least). So any
future communication you get from me on Pluto will necessarily
align with the result you measured.
This is where the mistake creeps in. My measurement tells me the
polarization of the entangled photon in the branch in which my
measurement was made. When you come to measure your entangled
photon on Pluto, how do you know what branch my measurement was
made in? You are at a spacelike separation from me, and completely
independent. So I ask again, how come you assume that your
measurement will be in the same branch as mine was?
Let's make it more concrete and say there are only 360 possible
polarizations, each having an equal probability.
That is not a very good way to look at it. The photon is not in a
superposition of all possible polarization states. You cannot write the
photon wave function as such a superposition:
|psi> = Sum_i a_i |i> for i running over all 360 possibilities in
the case you outline.
The most you can ever do is write the state as a superposition of the
two possible polarizations in any particular direction. Thus:
|psi> = (|+> + |->), ignoring normalization factors.
This can be written for |+> and |-> being the polarization eigenstates
in any chosen direction. But not all directions at once.
The photon pair is then in a superposition of 360 possible states.
The photon pair must be considered as a single object, because if your
photon is 240 degrees, mine is -240 (120 degrees), and so on. There
are only 360 possible values that could be obtained from measurement,
not (360 * 360).
There are only ever two possible polarization states, although these can
be defined in any of an infinity of possible directions. But once a
basis is chosen, that defines the total superposition.
When I measure my photon on Pluto, I am self-locating myself to a
branch (one of 360 possible branches of the wave function
corresponding to each of the 360 possible polarization of the photon
on Pluto). Once I have located myself to this branch, I may not know
which measurement angle you will set your filter at, I remain in a
super position of all possible measurement angles you might choose
(let's say there are 3 possible measurement angles).
After your measurement, you first transmit, not your result, but your
measurement angle. Once the photons from this radio signal reach me,
I have located myself to one of the 3 possibilities for the
measurement angle. At this moment, I have all the information I need
to be able to completely predict the statistics of your measurement
result, based on my measurement result and angle which I knew since
the time of measurement, and now with your measurement angle
information having reached me. When you transmit your measurement
result to me, I find it in agreement with my expectations for having
located myself to a branch that had (360 * 3) possibilities that were
unknown to me at the time prior to performing the experiment.
We can make it simpler than this. Even though the two measurements are
supposed to be independent -- at independent angles -- we can relax this
for the purposes of illustration and say that the two experimenters
agree to both measure at some particular angle. If you on Pluto make a
measurement at this angle, there are only two possible outcomes, the |+>
or |-> states in the notation I have used above. So you are in a
superposition of two possible worlds, one for each result. Because of
conservation of angular momentum, you know that if you got the |+>
result, then the other photon of the entangled pair would, if measured
at the same angle, give |->, and similarly if you are in the branch that
got a |-> result.
When I make my measurement at the same agreed angle, I also have two
possible results, |+> or |->. But I have no control over which result I
get. A long sequence of measurements will show that I get each result
with approximately 50% probability. In order for my result to be
determined by the result that you obtained on Pluto, somehow it must be
arranged that I get only the part of the entangled pair corresponding to
your result. In other words, I must already be in the branch
corresponding to your result. If I were not in that branch, then I would
get |+> or |-> with equal probability. Unless there is some non-local
effect which sets me on the branch corresponding the your result (be it
|+> or |->), then there is nothing to stop me getting |+> when you get
|+>, or |-> when you get |->, results that are in conflict with the
conservation of angular momentum and the definition of the entangled
singlet state.
You have confused your account by introducing branches for each possible
measurement angle, but this is never the case -- there are no such
branches in Everettian quantum mechanics. There are only ever two
branches corresponding to the two possible outcomes for your
polarization measurement. So given two independent experimenters making
independent polarization measurements, there are only ever 4 possible
branches -- the '++', '+-', '-+', and '--' branches. If the measurements
are made on the same singlet state, the '++' and '--' branches cannot
exist. You have not explained why these are possibilities are ruled out.
By assuming that they are, you have introduced an unrecognized
non-locality into your account
Bruce
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