From: *Jason Resch* <[email protected]>
On Thu, Jun 21, 2018 at 12:56 AM, Bruce Kellett
<[email protected]> wrote:
There are only two photons, but each has two possible
polarizations. When you measure the polarization, you split into
two branches, one for each possible result. The partner photon
reaches the other person on each of your branches, but if
everything is purely local, the photon that is remotely measured
cannot know which result you obtained (it cannot know which of
your branches it is actually on), so it has indeterminate
polarization, and when measured, there is necessarily equal
probability for either result.
I think this is the heart of our disagreement. You are seeing the
entangled photons are still distinct objects without a correlation.
The entangled photons are a non-separable unity. But if everything is
local, the measurements by Alice and Bob, being space-like separated,
must be equivalent. If Alice splits into two branches, so must Bob. The
correlation arises because the entangled pair is not a local object --
it has no purely local description.
There are two events where some human experimenter gets entangled with
a photon (you could saw under MWI that two splits occur). Now I think
you ask why does the second measurement know to "split the right way",
but it doesn't, and doesn't need to. Both experimenters contagiously
contract the superposition of the photon they measure (entangle
themselves with).
What on earth does that mean? "contagiously contract the superposition".
It can only mean that the superposition is non-local, and that you are
actually making use of this non-locality without being aware of it.
This means that the photon that is on the branch in which your
photon passed the polarizer can either pass the remote polarizer,
or be absorbed, with 50% probability for each. Similarly for the
photon that is on the branch in which your photon was absorbed.
The outcome by considering both branches is four possible worlds,
one for each combination of 'pass' and 'absorb' results. Two of
these worlds violate angular momentum conservation. How do you
rule out these worlds with only local interactions?
The photon pair was created at one point in space time, it traveled
only at light speed to two locations, where its superpositional state
became entangled with the local environment at its point(s) of
measurement.
To say there are 4 possible worlds here, I think is to assume
measuring the same photon twice using the same polarization angle, can
produce inconsistent results.
You are confusing measurements on the entangled pair with repeated
measurement of the same single photon. The entangled state is a unity,
but it is not the same as a single photon.
Look at it this way. The two measurements are made at space-like
separation. If everything is local, the measurements must be
independent.
There is where I disagree. The actions are independent, but the
results are not.
Then there must be a non-local effect! If the measurements are made
independently at a space-like separation, there can be no correlation
without either a common cause or non-locality. Common cause is ruled out
by the statistics of repeated measurements of such entangled pairs at
different angles.
If the measurements are independent they cannot be correlated --
that is one possible operational definition of independence.
But when measuring an entangled photon pair, they must be correlated.
Exactly. So how did this correlation arise?
Since the measurement results are known to be correlated, they
cannot be independent. Since there can be no sub-luminal
interaction between the two measurements, this correlation can
only be a non-local effect. In the case that I have been
discussing, quantum mechanics predicts 100% correlation. There is
no way this can be achieved locally because the singlet you are
measuring is rotationally symmetric and has no intrinsic
polarization state that can be carried subluminally between the
experimenters.
In other words, the structure of the singlet state rules out a
common cause explanation for the 100% correlation. Bell's theorem
then rules out any /local/ hidden variable explanation.
Look, the singlet state is:
|psi> = (|+>|-> + |->|+>).
When Alice makes her measurement she effectively splits this state
into the |+>|-> state on one branch, and the |->|+> state on the
other branch.
I would not say she splits the state, I would say she splits herself,
by now becoming part of the state. The super position never goes away
so you get two Alices: (Alice * |+>|->) + (Alice |->|+>)
The "(Alice * |+>|->)" knows that Bob she will hear from who performs
the same measurement of the photon of the entangled pair will be the
Bob that sees the - photon, and "(Alice |->|+>)" knows the that the
Bob she will hear from who performs the same measurement of the photon
of the entangled pair will be the Bob who sees the + photon.
How does she know this? And why can't the Alice who sees the |+> not
hear from the Bob who sees the |+>. Both must exist if everything is
purely local, you know.
But if everything is purely local, this split does not happen for
Bob before he makes his measurement.
True Bob has not yet entangled himself. But you speak of splits as if
they are instantaneous things that create two whole universes
instantly. This is not what MWI predicts.
We are doing measurements with people and macro apparatus that is not
isolated from the environment. So the decoherence following the
measurement splits the world -- locally, of course, but that is all that
is required. Bob is at a space-like separation, so the split occasioned
by Alice's measurement has not encompassed him at the time he makes his
measurement. Is that so hard to grasp?
So he, too, measures the original entangled |psi> state, and he
also must have 50% probability of either result. However, quantum
mechanics says that when Alice measures |+>, Bob necessarily
measures only the |-> component of his photon; and when Alice
measures |->, Bob necessarily measures only the |+> component of
his photon.
Correct.
This is how the correlation comes about. But this is non-local --
the non-separable initial state is separated non-locally by the
measurements.
But they're measuring (entangling themselves with) the same
superpositional state: the entangled (mutually already measured)
photon pair.
What you say here makes no sense. Alice cannot entangle herself with
Bob's photon when she makes her measurement -- it is at a spacelike
separation. Or rather, any entanglement that does occur must be
non-local. The non-separability of the state means the correlations are
non-local in origin.
If I send a photon through a filter orientated at 0 degrees, and
it passes through, and goes all the way to Pluto where you
measure the filter at 0 degrees and it also passes, you would not
say this violates locality, would you?
No, because its passage to Pluto is at the speed of light.
Same as with the traversal of the photons in the photon pair, is it not?
If you think these cases are equivalent, then I am sorry, but there is
nothing more I can say that will ever convince you of your error.
One obvious problem with your attempt to equate the measurements on the
entangled pair with repeated measurements of a single photon is that in
neither case do you make any use of many-worlds to explain the EPR-type
correlations.There is no violation of counterfactual definiteness, no
use is made of measurements that could have been performed, but were
not. So what, exactly, is MWI giving you in your purported explanation
of EPR that is not already available in a collapse model?
Bruce
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