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.
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.
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.
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. That contradicts the results of
almost every quantum experiment. 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 '+-'.
Measurement results would not be stable under repeated measurement,
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. 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.
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.
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.
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. Bell's theorem rules out
the possibility that such "non-locality" can be explained by local
physical "hidden variables" or influences travelling sub-luminally. Call
this "inseparability" if you wish -- there are reasons why this might be
preferable terminology -- but it is only a terminological issue.
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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