Oops, Sorry Bruce, that following mail might have been resent a second
tie by error. May be you can check, my server seems to have a queer
behavior.
Bruno
On 09 May 2016, at 14:14, Bruno Marchal wrote:
On 30 Apr 2016, at 02:32, Bruce Kellett wrote:
On 29/04/2016 9:09 pm, Bruno Marchal wrote:
On 28 Apr 2016, at 03:33, Bruce Kellett wrote:
On 27/04/2016 4:57 pm, Bruno Marchal wrote:
On 27 Apr 2016, at 06:49, Bruce Kellett wrote:
On 27/04/2016 1:51 pm, Brent Meeker wrote:
That's pretty much the many-universes model that Bruno
proposes. But it's non-local in the sense that the "matching
scheme" must take account of which measurements are
compatible, i.e. it "knows" the results even while they are
spacelike separated.
Exactly, the model assumes the results it is trying to get. It
is not a local physical model because the statistics do not
originate locally.
The statistic did originate locally. Alice and Bob did prepare
the singlet state locally, and then travel away.
That is not strictly correct. The singlet state is conventionally
prepared centrally between A and B so that the measurements can
be made at spacelike separation. That would not be possible if A
and B jointly prepare the state then move away.
The measurement? OK. Not the preparation.
They are in infinitely many worlds, and in each with opposite
spin.
There are only two possible spin states for each -- so there are
really only two distinct possible worlds. Multiplying copies of
these two does not seem to accomplish much.
There is an infinity of possible states for each. There is an
infinity of possible distinct possible worlds. In each one A's and
B's particle spin are opposite/correlated, but neither Alice nor
Bob can know which one.
I think you are getting confused by the basis problem again.
I think you misinterpret the MWI? It might be related with your
problem with the first person indeterminacy in self-multiplication,
and your abstraction from the fact that the singlet state has
basically the same form in all base. Once Bob is in a separate light
cone, it is isolated from Alice, but the singlet state justifies why
the infinitely many Alices it describes will be correlated with the
Bob they are arble to talk with.
The cos^2(theta) is given by the math of the 1/sqrt(2)AB(I+>I->
- I->I+>)) = 1/sqrt(2)ABI+>I-> - 1/sqrt(2)ABI->I+>. With your
explanation to Jesse, I keep the feeling that you talk like if
Alice or Bob reduce the wave after their measurement, but they
just localize themselves in the relative branches.
Certainly, the cos^2(theta/2) comes from applying the standard
quantum rules to the singlet state
|psi> = (|+>|-> - |->|+>)/sqrt(2) (adding AB to this state adds
nothing).
We need them to get all the statistics correct.
I think it would be instructive to actually go through the usual
quantum derivation of the correlations because what you call
"reducing the wave after the measurement" is actually the result
of applying the standard quantum rules. It has nothing to do with
so-called 'collapse' interpretations: it is simply in the theory.
Well, either the meaurement give specific outcome, or, if there is
no physical collapse it is only an entanglement between A (or B)
with the singlet state. That is why A and B are needed in the
derivation.
A measurement results in an entanglement between the state and the
observer. But in order for the observer to see only one result (and
not a superposition) you need the projection postulate. That is
decoherence, not a rejection of many worlds.
You need only to look at the first person views of the relative
persons in the superposition states, they are infinite in a relative
proportion given by the Born rules.
Quantum rules for measurement say that the initial state can be
expanded in the basis corresponding to the particular measurement
in question (contextuality). That is what the state |psi> above
is -- the quantum expansion of the singlet state in the basis in
which say Alice is doing her measurement.
OK, but that state does not represent two possible worlds. It
looks like that for Alice because she has decided to make the
measurement "in that base", but, as we know, the correlation does
not depend on the choice of Alice's measurement. She will just
entangled herself with the singlet state, whatever the base or
measuring apparatus is.
Quantum rules then say that the result of the measurement (after
decoherence has fully operated)
Decoherence is only the contagion of the superposition to the
observer and/or his/her environment. It does not lead to a
classical universe. That is only what the infinitely many Alice
will phenomenologivally realize.
Decoherence is the basis for the (apparent) emergence of the
classical from the quantum. Decoherence allows coarse-graining,
partial tracing over environmental variables, and the other things
that enable us to get definite experimental results.
But is only relative first person plural views. No classical
universe needs to ever be infinitely singularize? Neither with QM
(without collapse) nor with Digital Mechanism (made mathematical by
Church Turing thesis, even arithmetical).
is one of the eigenstates in the expansion, and the measurement
result is the corresponding eigenvalue. In our case, there are
two possibilities for Alice after her measurement is complete:
result '+', with corresponding eigenstate |+>|->, or '-', with
corresponding eigenstate |->|+>. There are no other
possibilities, and Alice has a 50% chance of obtaining either
result, or of being in the corresponding branch of the evolved
wave function.
That is correct phenomenologically. But QM-without collapse just
say that we get a new Ipsi> equal to A(|+>|-> - |->|+>)/sqrt(2) =
(A|+>|-> - A|->|+>)/sqrt(2). At no moment is Alice in front of
only |+>|-> or |->|+>. The singlet state never disappear.
That is the basis of your confusion. What you are saying, in
effect, is that the state is not reduced to the eigenvector
corresponding to the obtained eigenvalue after measurement.
Yes.
That contradicts the results of almost every quantum experiment.
Not one.
If we denote measurement (with outcome) on particle 1 by M1(+) or
M1(-) in the spinor case, we can write the measurement on particle
1 of entangled pair (by Alice, say) in the following way:
M1|psi> = (M1(+)|+>|-> - M1(-)|->|+>)/sqrt(2).
If Alice's result is M1(+), but no projection on to the
corresponding eigenvector takes place, then a subsequent
measurement of particle 1 by Alice would be represented by:
M1*M1|psi> = M1(+)*(M1(+)|+>|-> - M1(-)|->|+>)/sqrt(2).
In other words, Alice could see the sequence '++' OR the sequence
'+-'.
You do have a problem with the FPI!
If Alice measure +, to see what the Alices who saw + will get, you
have to take into account that by linearity of the schroedinger time
evolution, the superposed state are evolves independently.
That is already well explained in Everett which justifies a similar
apparent contradiction. From the first person point of view, things
looks like the wave would have collapsed, and the indeterminacy is
only due to the incoming non predictible information you get when
you duplicate yourself in the proportion given by the amplitudes of
the term of the relative wave.
You interpret the non collapse like if the observer did not entangle
itself, in flesh and bones, with the state of the particle.
At least I realize that you genuinely do not understand the FPI. The
guy which open the WM duplication box and see Moscow will also have
a feeling that a third person description has collapsed abruptly and
asymmetrically, where for the external observer all things have been
has smooth and 3p predictible as an amoeba division. You must put
yourself in the mind of the amoeba.
Measurement results would not be stable under repeated measurement,
That is simply wrong. Once Alice has found (+) she will always found
(+), has she is the one having learn that she is the branch where a
particle has been measure +. That objection is already well debunked
by Everett himself. Only if she forget her result, and clean a
little bit her environment of any trace of the result (not easy),
will she be able again to get a different result, as she will be
again indeterminated relatively to the state, and thus her state can
be factor again, and then your argument go through.
contrary to all the experimental evidence. If your suggestion were
correct, it would mean that in Schrödinger's cat experiment, we
could open the box once, and find the cat to be dead. But we could
then open it again sometime later and find the cat now to be alive.
If we open the box and see the cat dead, as long as we memorize that
fact, we can open the bow again and again, we will see in dead again
and again. But if we wait some time, and forget about the state of
the cat, then indeed we can see the cat alive some time later. It is
the quantum erasure procedure, it is easier to explain in Everett (+
Comp FPI) than in the collapse theory, imo.
This is contrary to sense as well as to all the evidence.
Decoherence is very effective at reducing the quantum state to a
series of separate disjoint worlds -- this process is essentially
irreversible, so we cannot get contradictory results from repeated
experiments.
It is in principle reversible, by unitarity, and is irreversible
only due to the gigantic number involved and classical probability
theory, + FPI in the self-superposition when we look around.
The question now arises as to how the formalism describes Bob's
measurement, assuming that it follows that of Alice (there will
always be a Lorentz frame in which that is true for spacelike
separations. For timelike separations, it is either true, or we
reverse the A/B labels so that it is true.) Since the description
of the state does not depend on the separation between A and B,
after A gets '+' and her eigenstate is |+>|->, Bob must measure
the state |-> in the direction of his magnet. To get the relative
probabilities for his results, we must rotate the eigenfunction
from Alice's basis to the basis appropriate for Bob's
measurement. This is the standard rotation of a spinor, given by
|-> = sin(theta/2)|+'> -i cos(theta/2)|-'>
Applying the standard quantum rules to this state, Bob has a
probability of sin^2(theta/2) of obtaining a '+' result, and a
probability of cos^2(theta/2) of obtaining a '-' result.
Using test values for the relative orientation, theta, we get the
usual results. For theta = 0º, Bob has probability 0 of obtaining
'+', and probability 1 of obtaining '-'. For 90º orientation, the
probabilities for '+' and '-' are both 0.5. For a relative
orientation of 120º, Bob's probability of getting '+' is 0.75 and
the probability of getting '-' is 0.25. And so on for the
familiar results.
This is not controversial, and the result depends only on the
standard rules of quantum mechanics. The problem of
interpretation, of course, is that since Alice and Bob are at
different locations, and the state they are measuring is
independent of separation, there is an intrinsic non-locality
implied by the standard calculation.
Right, but it does not involve any action at a distance, once you
distribute the persons involved on the singlet state. Indeed, it
multiplies your formal calculation above for *all* couples above.
This is well explained by Price and Maudlin.
There is a widely cited paper by Tipler (arxiv:quant-ph/0003146v1)
that claims to show the MWI does away with non-locality. It is
instructive to go through his argument, and to see how he has
managed to deceive himself. We start with the singlet state:
|psi> = (|+>|-> - |->|+>)/sqrt(2)
and then expand the state for the second particle in a different
basis (at relative angle theta):
|+>_2 = cos(theta/2)*|+'> + sin(theta/2)*|-'>,
|->_2 = -sin(theta/2)*|+'> + cos(theta/2)*|-'>.
Substituting this into the singlet state above, we get
|psi> = -[ sin(theta/2)*|+>|+'> - cos(theta/2)*|+>|-'> + cos(theta/
2)*|->|+'> + sin(theta/2)*|->+'>]/sqrt(2),
which exactly represents the requisite four worlds, corresponding
to the (+,+'), (+,-'), (-,+'), and (-,-') possibilities for joint
results, each world weighted by the required probability. Tipler
claims that this shows how the standard statistics come about by
local measurements splitting the universe into distinct worlds.
He is, of course, deluding himself, because the above calculation
is not local. It is, in fact, nothing more that the standard
quantum calculations (with the projection postulate evident) that I
gave above for the possible (+) and (-) results for Alice, combined
in the one equation. It still uses the fact that Alice's
measurement of particle 1 affects the quantum state for particle 2
(which is, by then, a large spacelike distance away). Tipler
utilizes the no-local nature of this change to extract theta, the
relative orientation of magnets -- a relative orientation that can
only be known by comparing orientations at A and B directly. So
Tipler's derivation is every bit as much local or non-local as the
conventional calculation -- he has not eliminated non-locality by
his trivial reworking of the derivation.
Sorry, I think Tipler is right, and justify why Alice and Bob will
always find themselves in the right universe, violating the Bell's
inequality, but just because at the start we have all all Alices and
Bobs correlating their particles in some local way, and departing,
without ever knowing the spin of the particles. Tipler just use the
intuitive FPI of the relative self-superpositions.
If you take out the quantum rule that the result of a measurement
is, after decoherence, reduction to an eigenstate with the
corresponding eigenvalue, you take away an essential ingredient
of the quantum derivation, and leave Bob's measurement as being
completely independent of that of Alice, so the only possible
results for Bob are '+' and '-' with equal probability, whatever
the orientation of his magnet.
Once Bob is space-like separated, its measurement needs not to be
correlated with the previous Alice *that you have fixed for your
purpose*. But the "decoherence/entanglement" will propagate at the
speed of light or below, so that each Alice and Bob can only meet
them in the realities where the spin are correlated. That follows
from applying the quantum standard rule, again it seems to me that
is clear from Price.
Yes, of course, they can only compare results and actually see the
correlations when their light cones later overlap and they meet, by
the actual results have decohered into definite separate worlds by
then.
OK. But The MWI allows all that to be explained without any physical
action at a distance.
Any account that deviates from this is no longer a standard
quantum account because it would not conform to the above rules.
And these rules are among the best-tested rules in all of
physics. They are the basis for the whole of the phenomenal
success of this theory over nearly a hundred years and in every
field in which it has been applied. You abandon these principles
only at extreme peril.
I don't abandon them at all. I only apply them to the *whole*
system. But this necessitates to take into account all Alice and
Bob. The non locality is apparent only. Bernard d'Espagnat also
made that clear and suggest the term "inseparability" to reserve
"non-locality" for "action at a distance".
That is a semantic matter. There is a problem if one insists that
"non-local" means the propagation of a real physical influence
(particle of wave) faster-than-light. But "non-locality" in
standard quantum usage means the above -- the entangled state acts
as a single physical unit even when its components are widely
separated.
But only because it describes macroscopic superposition. The point
is that by keeping all branches, or the whole phase space, we see
that there is no mysterious action at a distance, no physical
influence at all, and a fortiori no information sending.
Bell's theorem rules out the possibility that such "non-locality"
can be explained by local physical "hidden variables" or influences
travelling sub-luminally.
Right. But assuming that a measurement gives a definite result, when
in Everett, it does not, it only entangle and superpose the observer
with the components of the wave. It is that point, and the correct
use of the FPI which makes possible to Everett to make QM a local
theory and a determinist, reversible even, theory.
Call this "inseparability" if you wish -- there are reasons why
this might be preferable terminology -- but it is only a
terminological issue.
As long as you don't invoke mysterious spooky action at a distance,
which does not really make sense to me, especially with already only
special relativity. Your error is that you factor out Alice memory
from the picture, instead of putting yourself at the place of the
Alice having seen +, she just cannot be factored out. For her things
have decohered, but that is only her *appearances*.
We might need to come back on the classical "simple" (non quantum)
self-duplication and its associated phenomenologies.
Bruno
Bruce
Like Jesse said: no "matching" between copies of measurement-
outcomes at different locations takes place at any location in
space-time that doesn't lie in the future light cone of both
measurements. Only if a reduction of the wave occur would a
genuine action at a distance have to take place to keep up the
cos^2(theta). In the MWI, we keep it intact because 1/sqrt(2)ABI
+>I-> - 1/sqrt(2)ABI->I+> describes a global state of the
multiverse. There is a form on non separability, but it does not
use non local action. It uses only the fact that the many Alice
and Bob are in the same branches and remains in the same
branches when travelling away of each other in each branch, but
they both cannot know in which branch they are, and what is the
spin of their respective particles. They do know that they are
correlated by 1/sqrt(2)ABI+>I-> - 1/sqrt(2)ABI->I+>, but that is
all they can know.
Frankly, I do not know what this means. I think that you will
have to work through the details more explicitly.
I think you get the MWI of the singet state wrong. You fix Alice,
like if she was unique. She is not.
You have to show where the standard rules of quantum mechanics
cease to apply, and why.
I only apply the standard rule, but on the whole system.
And why they cease only for this entangled state, while remaining
intact elsewhere. There seem to be questions of consilience and
consistency at stake here.
No, there is no problem. You can also look at the explanation in
Susskind and Friedman. My feeling is that you interpret the result
of measurement like it would change the density matrices of each
observer, but that does never happen. At no moment at all does the
singlet state describe a possible action of Alice having a
repercussion on what Bob can observe. It describes only the
realities in which both can belong, and compare. I am not even
sure that relativistic quantum field theory would make sense if a
measurement influence another at space-like separation. And I
don't see any trace of such a non-locality present in the singlet
state. Bell's theorem just shows that we have to take into account
the MWI if we want physical action remaining local. I took the
Aspect experience has a vindication of the MWI. I might reread
d'Espagnat on this, as I feel remembering that he did propose
different interpretation of the QM-without-collapse, and made
clear that in some of them, there is no action at a distance, your
own interpretation of non-collapse might be naïve, which would
explain why you think we can abstract from the presence of A and
B. To be continued ...
Bruno
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