On 19 Apr 2016, at 02:08, Bruce Kellett wrote:
On 19/04/2016 12:17 am, Bruno Marchal wrote:
On 18 Apr 2016, at 09:45, Bruce Kellett wrote:
Let me reduce this to simple steps:
1) MWI is an interpretation of QM only. I.e., it reproduces all
the results of QM without adding any additional structure or
dynamics.
What do you mean by QM? I am not sure I agree with you. Everett did
not talk about a new intepretation of QM, but about a new
formulation of QM. And he is right in the sense of the logician.
Before Everett: QM was formulated roughly SWE + Collapse + an
implicit dualist theory of mind or of scale (mircro/macro).
Everett's QM is SWE, the abandon of collapse, + a mechanist theory
of mind, with the implicit use of the FPI.
No, you are confusing the mathematical theory of QM with its various
interpretations. The mathematical theory of quantum mechanics is the
theory that associates physical states with vectors in Hilbert
space; observables with Hermitian operators in that space; and
measurement results with the eigenvalues of the corresponding
operator. Supplemented with the Born rule, which states that the
probability for obtaining any particular eigenvalue as the result of
a measurement is given by the absolute square of the coefficient of
that eigenvalue in the superposition describing the state, we get
the standard mathematical theory of quantum mechanics.
OK.
Note that this says nothing about collapse or not, about one or many
worlds, or about any interpretational issues.
More or less OK? but then you take QM without collapse. Copenhague put
the collapse in the axioms. Everett withdrew it. That are two
different theories. Then, if you define a world by a set of events
close for intrecation: non collapse entails many worlds, independently
of the interpretations. It is a point where I geree with Deustch: QM
without collapse is a theory of many-worlds, or many (possibly
superposed) states.
Interpretational issues are overlaid on this basic theory of QM, and
it is central to the whole discussion that the predicted
experimental results depend only on the underlying theory and not on
the interpretational superstructure. All interpretations must give
the same predictions for experimental results or else they are
alternative theories and not interpretations of (standard) QM.
Bt the collapse theory is too fuzzy to make specific predictions, and
when they do, they are contradicted by the experiments. There are not
yet one evidence for the collapse of the wave, and without collapse,
we keep the superposition (many-worlds) intact.
For a logician, if QM (without collapse) is formalized, you get an
"Herbrand minimal model" which contains already all relative state
(like we get them already in the sigma_1 arithmetic with the
Mechanist Hypothesis in the Cognitive Science).
Given the linearity of the tensor product and the evolution, we can
only abstract away the self-superposition, although we would have
to take them into account if we get a quantum brain (and here the
SWE give non ambigous result where a collapse theory has to first
make more precise how the (non local) collapse is made physically.
I don't know what you are talking about. But you are still confusing
the theory with its interpretation.
Sorry, but in logic, such notion, like theories and interpretation is
the very subject of study.
In this case we have three theories:
1) SWE + collapse + dualist theory of measurement/mind (copenhagen)
2) SWE + Mechanism
3) Mechanism
The corresponding interpretations are
1) A unique physical reality (and a strange non local and magical
association with mind)
2) a multiverse
3) a multidream (which exists provably in arithmetic, if we assume
mechanism)
2) The QM state describing an entangled singlet pair does not
refer to, or depend on, the separation between the particles.
OK. But the singlet state describe an infinity of Bob and Alice
with their spin correlated, yet both of them see their own
particles with a random result, as none of them know in which
universe they are. They know only one thing for sure: their spin
are correlated, and remains so independently of the distance.
The only thing either of them knows for sure locally is that they
have 50% probability of getting |+> and 50% probability of getting |-
>. After the experiment is complete and completely decohered
locally, they have just one result.
Yes, but they have been multiplied. They each observe one result, like
their counterparts, but in their independent branches, the results are
correlated.
You might interpret this situation by claiming that there are two
local copies of each, one with |+> and one with |->, but that is an
interpretation, it is not the mathematical theory, which predicts
only the probabilities.
Then you are introducing a collapse, and are changing of theory. QM
without collapse justifies the probabilities by something quite
similar to the computationalist FPI. The theory gives the evolution of
the "big picture" (the wave, say), and the probabilities are given by
the Born rule and the FPI. You can't make disappear any superposition
(and thus the other terms of the wave), if only because that is not in
the formalism (unless you want some non locality at play).
3) The quantum calculation of the joint probabilities depends on
the relative orientation between the separate measurements on the
separated particles.
No problem.
4) This quantum calculation is the same for any physical
separation, since the singlet state itself does not depend on the
separation.
No problem.
5) The quantum calculation is, therefore, intrinsically non-local
because it does not depend on the separation, which can be
arbitrarily large.
This does not follow. It would be if the state |psi> = (|+>|-> - |-
>|+>) would be interpreted by We know that Alice has a particle in
state |+> or in state |-> and Bob the opposite. But the state (|+>|-
> - |->|+>) means eaxctly that neither Alice nor Bob know in which
universe they are. It could be one with |+'> or |-'> or whatever.
Again, you are confused by the basis issue. The singlet state can be
expanded in the above form in any basis whatsoever, sure, but you
are forgetting the crucial matter of contextuality. For Alice,
sitting there with her EPR particle, the basis in which the singlet
state is expanded is completely irrelevant -- there is only one
Alice at this stage. Once she chooses the setting for her magnet,
she needs to be able to calculate the probabilities for the possible
results that she can get. To calculate these probabilities she
chooses the basis that corresponds to the orientation of her magnet.
This is the effect of contextuality. She could, of course, choose to
make her calculations in any of the other infinite number of
possible bases. But then, in order to relate the results of her
calculation to the results of her experiment, she has to perform the
rotation to bring the theoretical and experimental bases into
alignment.
6) Since MWI does not add anything to standard QM, and standard QM
gives a non-local account of the probabilities we are considering,
any MWI account must also be intrinsically non-local.
Proof?
The above sequence of steps constitutes the proof.
Sorry but I don't see any proof. I don't see anything non local at play.
Don't invoke Bell's theorem, because it assumes Alice and Bob are
in the same reality, where without collapse, the measurement of Bob
and Alice propagate only locally from multiple Alice to mutiple
Bob, as describe by the superposition singlet state (in any base).
I don't have to invoke Bell's theorem. That is not relevant for what
I am saying above. Let me spell it out:
1) The QM singlet state |psi> = (|+>|-'> - |->|+'>) is intrinsically
non-local. This is universally agreed. If it were local, then QM
would be intrinsically local and we would not be having this
discussion.
Only in Copenhagen is |psi> intrinsically non-local. I don't see why
that should be in the many-worlds. (|+>|-'> - |->|+'>) describes a
multiverse with all orientation of spins being uniformally spreaded,
yet correlated in each branches. So I disagree with 1.
2) A hidden variable theory, which would be a "completion" of QM (in
Einstein's sense), would be a different theory, not standard QM. (It
would have a mechanism whereby the orientation at A was available
for the interpretation of the orientation at B. This is the
mechanism that Jesse was confusing with the mathematical theory for
calculating probabilities. QM is non-local because it provides no
such mechanism. Any local theory must provide such a mechanism, and
thus must be a different theory from conventional QM.)
Of course I disagree, due to already disagreeing with the 1 above.
3) What Bell's argument shows is that even if you "complete" QM by
adding hidden variables, the resulting theory is still inescapably
non-local.
OK. But the Many-worlds is not a hidden variable theory (unless we
extend the meaning of "hidden variable" to include the unknown
branch-"localization" of the observers).
4) Experiment irrefutable bears out the violation of the Bell
inequalities, so demonstrates that reality is non-local.
Not at all. It demonstrates only that reality is non local OR that the
superposition are "real", and that there is no collapse.
If I find some time, I might try to describe this with the density
matrix formalism, which I think can make this more obvious.
One physical reality, and/or hidden variables specifying unqiueness
of state + Violation of Bell's inequality entails non-locality.
That is shown by Bell's inequality violatin.
But without "collapsing" a wave at a distance, the apparent non-
locality comes only from Alice or Bob determining in which universe
they are. There are just no reason they found themsleves in the
same universe. If they can compare the results, it is only after
the contagion of their superposed state with each other, and in
that case, the statistics implies the Bell correlations, without
any physical action at a distance. You need to transform the pure
state in some mixture, before the measurement to get non-locality,
but such mixture are local and different for each Alice and Bob in
the superposition state, so you cannot take them as definite like
if Alice or Bob could know that in advance.
What can I say? There are only two local possibilities for both
Alice and Bob: they get either |+> or |->, relative to their own
context as defined by the orientation of their respective magnets.
So there can only ever be four distinct worlds.
Which Alice? and Which Bob? If you take them as inhabiting the same
universe, which they cannot know, and is not statistically plausible,
you will get the quantum result right. But if they are taken apart,
they might get results that violated the correlations, but they will
not been able to verify this, as they will decohere in orthogonal
realities.
You can multiply them as many times as you like, as Jesse seems to
want to do, but it is a basic fact of statistics that if you take an
ensemble of a very large number of a limited set of states, any
random selection from that ensemble will result in one of the states
that you originally put in -- nothing new is generated. The four
possible worlds arising from our scenario are |+>|+'>, |+>|-'>, |->|
+'>, and |->|-'>, no different combinations can ever arise.
You continue to talk like if there were a collapse leading to such
result. But that never occurs. Price explains how to proceed without
introducing such collapse. When Alice (A) do a measurement on the
singlet state, she just entangles herself with (|+>|-> - |->|+>) we
get the superposition (A|+>|-> - A|->|+>) and Bob makes it worst (see
Price for the details, or Rubin's paper).
This crucial thing here, though, is that these four possibilities
are not equally probable. The distinct probabilities for each
possible world are given by the fundamental quantum calculation,
which is independent of the interpretation you overlay on the
theory: the probabilities depend only on the relative orientations
of the magnets of Alice and Bob -- they depend on nothing else. To
get the relative orientation of the magnets you have to compare the
separate orientations for Alice and Bob -- at remote, potentially
spacelike, separate locations. That is why QM is said to be non-
local.
Once you know that you talk about the Alice and Bob sharing the same
universe, but this Alice and Bob cannot know by any local measurement,
and they will have to interact again for knowing that, but then the
correlation they get is quantum one, and that without any physical
action at a distance.
Nothing that you have said obviates anything in the above argument.
The conclusion is sound; you merely obfuscate by your talk of and
indefinite number of possible worlds.
I just never collapse the wave.
On further reflection, I think you are really confused by the basis
issue. I suggest that you think more carefully about the role of
contextuality in the selection of an appropriate basis. You need
only one basis for each experimenter -- all other bases are
irrelevant.
It is "shocking" because it is really the self-multiplication which
explains the apparent non-locality, but then that was also the case
for the apparent indeterminacy.
Put in a different way: when Alice and Bob make their measurement,
they might get result violating the correlation, but that would
make their belonging to different cross-product term of the final
superposition, so they would not been able to compare those
forbidden results.
There are no such cross terms in the expansion. They get only |+> or
|->,
They get both of them. They get only |+> or |-> from their own first
person of view, but all such views are realized.
and any possible combination is allowed in general (unless the
theory gives an exactly zero probability for one or more of the four
possible worlds). Forbidden results are forbidden by the laws of
physics, and the indication that a particular combination is
forbidden is that the corresponding probability is calculated to be
zero. So there are no "forbidden cross-product terms". You are
talking nonsense.
They are no forbidden cross-product, due to the singlet state
structure, but that is what make locality preserved in each branch of
the evolving wave.
Bruno
Bruce
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