From: *Jason Resch* <[email protected] <mailto:[email protected]>>
On Mon, Jun 18, 2018 at 7:26 PM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
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.
I see.
Could you explain the point of error in the following paper? I've
excerpted the relevant sections if it helps your search.
From: https://arxiv.org/pdf/0902.3827.pdf
<https://arxiv.org/pdf/0902.3827.pdf>
*According to quantum mechanics, whichever measurement is
performed first collapses the entangled twin state superposition
to a single polarization state that is identical for both photons.*
*
*
*[...]*
*
*
*If we wish to know what the probability is of getting the same
measurement for photon 1, we need only figure out what the
probability is for a photon with polarization along θ2 to pass
through a filter oriented along θ1. This probability is easily
calculated according to simple trigonometry. Any arbitrary linear
polarization can be thought of as a superposition of polarization
along the θ1 direction (which will pass through the filter) and
perpendicular to the θ1 direction (which will be absorbed by the
filter). For a wave polarized along the θ2 direction, the
amplitude component along the θ1 direction is given by cos(θ2 −
θ1), and the probability for transmission, given by the wave
amplitude squared, is cos2 (θ2 − θ1). That is the prediction of
quantum mechanics
*
*
*
*[...]*
*
*
*The key is to allow more than one possibility for the potential
result of a measurement. Orthodox quantum mechanics embraces this
notion of multiple possibilities whenever a quantum state is in a
superposition. In the absence of measurement (and collapse), there
is no single definite potential result. Instead, there are many
potential results represented by many components of the superposition.
*
*
*
*[...]*
*
*
*It is possible to violate Bell’s inequality using either
nonlocality or counterfactual indefiniteness alone, and there are
examples of each approach. To better understand the role of
counterfactual indefiniteness, it is instructive to examine an
interpretation of quantum mechanics that relies solely on
counterfactual indefiniteness to violate the inequality. One of
the most popular of these is the “many worlds” interpretation.
*
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 con sider only
one set of such measurments and calculate the resulting probabilities
for each of the four possib le sets of results. By doing something quite
peculiar, Baylock does nothing more than confuse himself into error.
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.
*
*
*[...]*
*
*
*We claim that the many-worlds interpretation passes the Bell test
by violating counterfactual definiteness, while still respecting
locality. First of all, we argue that after eliminating the
nonlocal collapse of orthodox quantum mechanics, the many-worlds
interpretation can be formulated as a local theory. In particular,
the correlated entangled states used in EPR-Bell experiments can
be produced via purely local processes. For instance, two photons
with entangled polarizations might be produced from the decay of a
parent particle. In this case the entangled state is produced at
one location, where the parent decays, and its immediate effects
are limited to that one spacetime point. Thereafter, the photons
may go their separate ways, and as they separate they carry the
correlation to separate locations. It is the original correlation
produced at a single location that guarantees measurements will
always match in any experiment in any branch where observers
compare notes. In this respect the spread of the correlation to
distant locations is akin to the delivery of newspapers, where a
common story is generated at a central location and disseminated
all over the neighborhood. In the many-worlds context, however,
different branches (which originally split at a common location)
carry different editions of the newspaper.
*
That begins to sound like the "Bertlmann's socks" fallacy. In fact, many
advocates of locality via MWI talk about correlations being a "common
cause effect". That is just Bertlmann's socks, and Bell explicitly rules
that out.
*
*
*[...]*
*
*
*Measurement induces local branching based on the local
measurement result, but it does not cause branching at any distant
location. As an example of this thinking, the many-worlds
explanation of Bell’s experiment36 argues that when measurements
are made on a pair of photons with θ1 = 30◦ for filter 1 and θ2 =
−30◦ for filter 2, the result is a superposition of four terms:
*
*
*
*At first glance it would seem that each experimenter has branched
into four versions – one branching as a result of the local
measurement of his/her own photon and another branching as a
result of the distant measurement of the other photon. However,
this view is mistaken, for only local branching has really
occurred. To illustrate the local nature of that branching, Eq.
(4) can be factored into two terms according to:
*
*
*
*After the two experimenters communicate their results to each
other, each experimenter is finally split into four distinct
branches corresponding to the four two-photon states:
*
*
*
*but this final splitting occurs only following a chain of local
communications at sublight speed. In this context we see that
entanglement and branching in the many-worlds interpretation are
local, point-like operations.
*
That does not explain why the invalid combinations cannot appear for the
case of aligned polarizers.
*
*
*[...]*
*
*
*One may not like the many-worlds interpretation for several
reasons (and this author might agree), but it does provide an
example in which locality can survive. The many-worlds
interpretation is thus realist (in the sense that superpositions
can be regarded as real entities and that every possible
measurement result exists in some branch), deterministic (the
superpositions evolve according to a deterministic wave equation),
and local (involving only point-like interactions), but
counterfactually indefinite. In this case the multiple
possibilities described by the superposition preclude a single
definite possibility, and thus provide the means for violating
counterfactual definiteness. The many-worlds interpretation is not
only counterfactually indefinite, it is factually indefinite as
well. Even when measurements are actually performed, many
different results can exist in a multitude of different branches.
A single definite result is not guaranteed.
*
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.
Is this comment addressed by the second-to-last paragraph I quoted (I
didn't attempt to paste the equations because the symbols did not
carry through) but they are in the paper. I would appreciate if you
could highlight the error in the equation of that paper. (equations 4,
5, and 6 on page 15).
No, that does not address the point I am making. Eqs 4, 5 and 6 of
Baylock give the four possible worlds corresponding to the different
combinations of results, but he does not calculate the probabilities for
each possible world. It is those probabilities that are important, not
particular sequences of results. So his appeal to the violation of
counterfactual defniteness by relating things back to aligned polarizers
is invalid.
Is your argument is that MWI works but is non-local due to the
immediacy of branch selection/determination?
What is wrong with the idea that the necessary information is
generated at the point the pair is created, and then travels at the
speed of light to each measurement location?
That is a local hidden variable account -- Bertlemann's socks. MWI does
not make this legitimate, as can be seen in my example.
Are you assuming that there are no "hidden multi variables" (for lack
of a better term) in the MWI? My understanding, (which may be in
error), is that hidden variables can work to explain Bell's inequality
if one gives up contra-factual definiteness.
This is indeed a mistaken view. Violations of counterfactual
definiteness do not actually help in MWI, as is seen in the simplest
examples which do not rely on counterfactual definiteness.
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.
I agree there are only two possible outcomes of the measurement
(absorbed or transmitted) but how does this related to your statement
that the polarization might be along any possible angle? Does the
math prevent us from viewing this as a superposition of the every
possible polarization angle?
Yes, quite definitely the rotational invariance of the singlet state
cannot be seen as a superpositionof all possible polarization angles.
See the simple expansions of the singlet state that I gave in a previous
post. QM does not countenance such superpositions.
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
They are ruled out for the same reason that we get consistent
measurements. When we measure the same property twice in a row we
always observe the same outcome. Measuring my Pluto photon, and
measuring your radio signal is an example of this measurement
consistency. Asking why "++" and "--" are ruled out is, in my view,
equivalent to asking why we observe either "spin down" and "spin down"
or "spin up" and "spin up" when we measure the spin of the same
electron twice in a row, and never measure "spin down" and "spin up"
or "spin up" and "spin down" when measuring the same electron's spin
twice in a row.
You are appealing to a "common cause effect", "Bertlmann's socks". That
local hidden variable is not available, even in MWI.
I refer you to the quote from Maudlin's book that I gave in an earlier post:
"And if some sense can be made of the existence of correlations [in
MWI], we have to understand how, In particular, if appeal is made to the
wave function to explicate the sense in which, say, the 'passed' outcome
on the right is paired with the 'absorbed' outcome on the left to form a
single 'world', then we have to recognize that this is not a /local/
account of the correclations since the wave function is not a local
object."(3rd edition, p. 252)
I think this is the mistake that you (and Baylock and many others) fall
into. You do not recognize that the wave function of the singlet state
is intrinsically non-local.
Bruce
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