From: *Jason Resch* <jasonre...@gmail.com <mailto:jasonre...@gmail.com>>
On Tue, Jun 19, 2018 at 12:03 AM, Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>> wrote:
I find Baylock's exposition of counterfactual indefiniteness as
applied in MWI quite opaque. He makes the argument needlessly
complicated by considering a sequence of experiments with
non-aligned filters. Then analyses these by comparing to an
arbitrary 0º and 90º pair of orientations. When he does his
general analysis he gets four possible worlds as he should, but he
does not calculate the probabilities for these individually.
Rather, he relates the results back to the 0º and 90º
orientations. And then says that because no measurements were
actually made at these angles the lack of counterfactual
definiteness rules out the worlds in which the results do not
agree with the quantum predictions. This is quite confused. There
is no need to consider sequences of measurements at different
angles, one need consider only one set of such measurments and
calculate the resulting probabilities for each of the four
possible sets of results. By doing something quite peculiar,
Baylock does nothing more than confuse himself into error.
What specifically, is the error?
Opacity. There is no need for reference to violations of counterfactual
definiteness, because no comparison with measurements that were
possible, but not made, is ever necessary. The account that I have given
only ever refers to measurements that are actually made.
We should concentrate on the simple case that I have presented,
where the polarizers are aligned by construction, and no reference
is made to measurements that are not made, but are assumed to have
definite outcomes (no violation of counterfactual defininteness
need be assumed). You have to be able to give a local account of
why certain combinations of results are not observed. You have
been unable to do this.
You agreed both photons are entangled to each other.
When you measure either of the photons, you too become entangled not
only with that photon, but also with its pair.
Entanglement with the partner photon is the non-local effect. The pair
is at a spacelike separation.
If someone measures it's partner photon, now you, the left photon, the
right photon, and that other person are now all entangled with each other.
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.
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?
(entanglement is nothing mysterious, it is equivalent to measurement).
Yes, but entanglement, being a local effect, can only spread at, or less
than, the velocity of light. You cannot be entangled with your remote
partner when he does his measurement, because you are space-like separated.
When nothing collapses, all you get are local effects, of information
(in the form of particles or fields) moving through space time at
light or sublight speeds.
That is the conclusion that you have not been able to establish. The
Bell-like correlations actually have nothing to do with collapse or
non-collapse. The entanglement is intrinsically non-local in either case.
You never observe the person who got the inconsistent measurement, nor
ever hear their radio signal because you are entangled with the person
who got the result consistent with your measurement.
But that entanglement is the non-local effect.
Look at it this way. The two measurements are made at space-like
separation. If everything is local, the measurements must be
independent. If the measurements are independent they cannot be
correlated -- that is one possible operational definition of
independence. 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. But if everything is purely local, this split does not happen
for Bob before he makes his measurement. 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. This is how the correlation comes about. But this is
non-local -- the non-separable initial state is separated non-locally by
the measurements.
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.
It is the same picture.
But it is not the same picture. In the case you mention, you send a
polarized photon to Pluto at the speed of light. In the case of the
entangled singlet state there are two separated photons that are
measured simultaneously (in one frame at least), so no one is sending a
photon of known polarization anywhere.
You might as rightly ask why are future measurements correlated
(entangled) with past measurements. I don't see anything in the theory
that suggests we should expect such inconsistencies in any two
successive measurements (be they of an entangled photon pair, or two
measurements of the same photon).
Because in one case information is transmitted at the speed of light and
in the other case the influence is non-local. The entangled state is
non-separable, whereas two measurements on the same photon are separable.
Can you elaborate on why you think the Schrodinger equation implies
such inconsistencies ought to arise?
It is not really something in the Schrödinger equation. It is in the
nature of the initial state. The Schrödinger equation describes the time
development of the wave function and it operates equally on the single
photon state and on the entangled two-photon state. In the latter case,
the time development (propagation) of the two photons is independent.
Besides, the Schrödinger equation describes multiparticle states in
configuration space, not ordinary 3-space.
There is no inconsistency since the two cases are quite different -- why
should you expect a single photon to behave in exactly the same way as
an entangled pair?
Bruce
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