On 08 Jun 2017, at 02:05, Bruce Kellett wrote:
On 7/06/2017 10:38 pm, Bruno Marchal wrote:
On 07 Jun 2017, at 11:42, Bruce Kellett wrote:
On 7/06/2017 7:09 pm, Bruno Marchal wrote:
On 06 Jun 2017, at 01:23, Bruce Kellett wrote:
I have been through this before. I looked at Price again this
morning and was frankly appalled at the stupidity of what I saw.
Let me summarize briefly what he did. He has a very cumbersome
notation, but I will attempt to simplify as far as is possible.
I will use '+' and '-' as spin states, rather than his 'left',
'right'.
He write the initial wave function as for the case when you and
I agree in advance to have aligned polarizers:
|psi_1> = }me, electrons,you> = |me>(|+-> - |-+>)|you>
= |me, +,-,you> - |me,-,+,you>
He says that at this point no measurements have been made, and
neither observer is split. But his fundamental mistake is
already present.
A little test for you: what is wrong with the above set of
equations from a no-collapse pov?
skipping some tedium, he then gets
|psi_3> = |me[+],+,-,you[-]> - |me[-],-,+,you[+]>
where the notation me[+] etc means I have measured '+', you[-]
means you have measured '-'.
He then claims that the QM results of perfect anticorrelation in
the case of parallel polarizers has been recovered without any
non-local interaction!
Spoiler -- in order to write the final line for |psi_1> he has
already assumed collapse, when I measure '+', you are presented
*only* with '-', so of course you get the right result -- he has
built that non-locality in from the start.
?
From the start shows that it is local.
Your failure to see the problem here is symptomatic of your
complete failure to understand EPR in the MWI.
I could say the same, but emphatic statements are not helping. My
feeling is that you interpret the singlet state above like if it
prepares Alice and Bob particles in the respective + and - states,
but that is not the case. The singlet state describe a multiverse
where Alice and Bob have all possible states, yet correlated.
The singlet state is rotationally invariant, yes, and can be
expanded in any basis of the 2-d complex Hilbert space. That has
never been in doubt.
OK.
Then in absence of collapse, all interactions, and results are
obtained locally, and does not need to be correlated until they
spread at low speed up their partners.
That does not follow. Although there are an infinity of possible
bases for the singlet state, these are potential only,
I don't understand this. Potential? That is no more the MW.
and do not exist in any operative sense until the state interacts
with something that sets a direction.
That looks more like Bohr than Everett.
You appear to claim that A and B exist in separate worlds
corresponding to each of this infinity of bases.
Yes. It is the rotaional invariance of the singlet states "taken
seriously" when we drop the idea of collapse, or of special dualism
between observer and the observed.
But that is a misunderstanding. They are in superpositions in every
base, sure, but that does not mean that there are 'worlds'
corresponding to each possible base until some external interaction
occurs.
This is even more fuzzy than the collapse. It looks like consciousness
not only reduce the wave, but create the physical reality. That is
correct in Mechanism, but that is another story.
As you yourself have said, a world is something that is closed to
interaction. But superpositions are not closed to interaction, they
can interfere -- as in the two slit experiment, and essentially
every other application of QM.
Right.
So there are no separate worlds corresponding to every possible
orientation of the polarizers. Worlds can arise only after
interaction and decoherence has progressed so that the overlap
between the branches of the superposition is zero (FAPP if you
like). It is only then that the branches can no longer interfere
(interact) and are closed to interaction, and thus constitute
different worlds.
We will have to disagree with this. I use the Y=II rules, like
Deutsch. In this case the reading of the singlet state gives
2^aleph_zero constantly spreading histories figuring Bob and Alice.
With mechanism, those worlds/histories are more like dreams. They will
be epistemological personal (and plural in the spreading interaction
based spheres).
The standard procedure in quantum mechanics when one is faced with a
superposition that interacts with something external, is to expand
the superposition in a base that corresponds to the external context.
OK. In this case, Alice choose to measure her spin. This will only
self-localized here in one (actually still aleph_0) histories, where
she will know her states, and the states of any Bob she could soon or
later interact with, but not of the inaccessible Bobs, who might found
non correlated result. yet,n him too will be able to met only the
Alice(s) having the correlated spin.
That is what happens when an unpolarized spin meets a polarizer
aligned in a particular direction -- one expands the rotationally
symmetric unpolarized state in the basis matching the external
context. That is all that is happening with the singlet state above;
when Alice comes to measure the symmetric state, it is convenient to
expand the singlet state in a basis that corresponds to the
orientation of Alice's polarizer.
OK. But that does not make his branch more real. In the MW picture,
all outcomes are found by Alice in the "parallel universe/dream".
Then the result of the interaction is easily calculated. If one use
some other basis, in some other direction, one would end up with a
superposition of states after measurement, and that superposition
would be exactly the same as the eigenstate obtained when one
expanded in the aligned basis. So using a different basis merely
complicates the calculation, it doesn't actually change anything. It
is like trying to drive from Melbourne to Sydney using a map based
on an orthographic projection based on Brisbane. You might manage
it, but it would be needlessly difficult.
I am sorry that I have had to spend so much time on this diversion
into Quantum Mechanics 101, but you seem determined to fail to
understand the application of the most fundamental of quantum
principles.
So, in the measurement of the singlet state
|psi> = (|+>|-> - |->|+>),
the basis is arbitrary until someone wants to measure this state. If
Alice measures the state, we expand in Alice's basis and get the
above; Alice has a 50/50 chance of getting '+' or '-'. What is the
state after Alice makes her measurement? According to quantum
mechanics, the measurement reduces the state to the eigenvalue
corresponding to the measurement result.
That is not the MW. There is no measurement reducing anything. The
singlet superposition is just lifted to Alice memory. You really seem
to work in pre-Everett quantum mechanics.
This is entirely local, and is necessary because of the experimental
fact that repeated measurements of the same state give the same
result.
Yes, that is true for all Alices.
So if Alice got '+', the state reduces to |+>|->, and if she got
'-', the state reduces to |->|+>.
?
From her perspective, it looks like that, but what actulaly happenes
is that |psi> has become first (|Alice>|+>|-> - |Alice>|->|+>), which
keeps the rotational symmtery.
This is fine for Alice locally, she is actually measuring only the
first part of the superposition |psi>, the part corresponding to her
particle. But the second part of the state, the '|->' part in |+>|-
>, corresponds to the particle that Bob has at his remote location.
If everything is local, then Alice's measurement cannot affect Bob's
particle,
Indeed.
so Bob must also be presented with the original state |psi>.
Which Bob?
His situation is then exactly like Alice's, we expand the symmetric
singlet state in the basis corresponding to Bob's polarizer, and
find that he, too, has a 50/50 chance of getting '+', or '-'. It
follows immediately that if the two measurements are indeed
independent, and they are both measuring the same state unaffected
by the other's measurement, both get a 50/50 mix of the two possible
results. And, crucially, their results will be totally independent,
there will be no correlation. Independent measurements must lead to
uncorrelated results, that is what 'independent' means.
But we know that, experimentally, Alice's and Bob 's results are
correlated,
In their respective parallel realities.
anything between -1 and +1, depending on the relative orientation of
their polarizers. So the measurements that Alice and Bob make cannot
be independent: Bob's measurement is affected, in some way or
another, by the measurement that Alice makes (or vice versa). That
is the origin of the claim of non-locality.
Once Alice make a measurement, she only localized herself in he worlds
where Bob *has* the non independent corresponding state. But all
results have been obtained (here + and -, times 2^aleph_0).
Before Bell, one could imagine that there was some hidden variable
that carried an interaction from Alice to Bob. That might have been
reasonable if Alice and Bob had a timelike separation, so that Bob's
measurement was in Alice's forward light cone. But experiment shows
that the correlations are the same even if Alice and Bob make their
measurements at space-like separations, so no sub-luminal hidden
variable interaction could connect the two measurements. That is non-
locality.
That non-locality is not questioned. Only that it shows some action at
a distance.
The question then, is whether many worlds can provide a fully local
account of this situation. I claim, with most present day
physicists, that MWI does not provide any such local account.
After all this, we can go back to Price as above. He writes:
|psi_1> = |me, electrons,you> = |me>(|+-> - |-+>)|you> = |me,
+,-,you> - |me,-,+,you>.
His expansion of 'electrons' into the singlet state is correct, but
he then takes this to give:
|me>|+->|you> - |me>|-+>|you>.
So that if I measure '+', you are presented with the collapsed state
|+>|-> (in my basis). Similarly if I measure '-', you receive the
corresponding collapsed state. But the |+>|-> in my basis state
corresponds to a |+> polarization for my electron and a |->
polarization for your electron -- and you and I are widely separate,
possibly by indefinitely large space-like distances! In other words,
Price has built the standard quantum mechanical non-local collapse
into his account.
I don't see this. There are no collapse having occur at all.
Not unnaturally, he gets the correct correlation results, but then
he has done nothing different from the standard non-local quantum
account, so it is no surprise that he gets the same answers.
Tipler does exactly the same thing with his account of measurements
at arbitrary polarizer angles, differing by theta. And I hope it
will not be necessary for me to go through this tedious analysis for
that case too -- it is exactly the same mistake, doing the standard
QM calculation and claiming that it is totally local.
I see the QM non-locality, but the apparent action at a distance would
exist only if we suppress the parallel realities in which Bob get the
non correlated results, despite both of them will be able to interact
only with their correlated partner.
Another argument is that the linear wave description is described
by a differential equation which imposes locality, and make the non-
locality only apparent in *all* branches (assuming the singlet
state to be 100% pure).
The argument from linearity fails because Schrödinger's equation is
linear only in configurations space, and the two-particles singlet
state is also defined only in configuration space -- each particle
exists in its own 3-subspace of the total configuration space. So
while the particles may be widely separated in ordinary physical 3-
space, they are in different subspaces of configuration space, and
that might be completely local! So it might be the case that
linearity implies locality in configuration space, but that does not
carry over into ordinary 3-space.
There is no ordinary 3-space, but 2^aleph_0 3-spaces. Quantum
mechanics without collapse consists in taking the configuration space
seriously.
As an aside, on an historical note, apparently Schrödinger
originally envisaged his 'wave' as a physical wave in space-time,
just like an electromagnetic wave or some such, and that his
equation governed the local deterministic evolution of this wave in
3-space. When Schrödinger's formalism was applied to two-body
systems, such as the hydrogen atom, it was realized that each of the
two particles had to exist in separate subspaces of configurations
space. Schrödinger was devastated by this finding, and apparently
even went so far as to say that he wished he had never invented that
'stupid equation' (or something similar).
No doubt that quantum mechanics is conceptually shocking. The wave is
physical, but quite unlike sound wave living in a 3-d space.
I agree it is weird that the "phase space is the real thing", but
that is where the quantum weirdness comes from. Yet, the MWI just
abandon the CFD, I don't see, in the Bell inequality violation any
reason to believe that a influence at a distance should be called
for.
As I have said, this simply means that you have not understood it
properly. Incidentally, CFD is just a red herring -- nothing in
either Bell, CI, or MWI ever depends on the violation of CFD.
It is always supposed by thinking that Alice and Bob have the same
identity from the beginning to the end of the experience.
I can go through that in the sort of tedious detail that I have used
above if you really must, but I would prefer that you just accept
normal physical practice:
The problem is not in the practice, but in looking at the complete MW
picture. We do not put the violation of Bell's inequality into doubt.
Only the claim that it shows spooky action at a distance. That is a
mono-branch account. (Sorry for having use "local" with that meaning
in some post, which is of course confusing here).
which is that when faced with a superposition, a detailed
calculation on a typical member of the superposition is all that is
required. We then sum over the result for that typical component,
with weights appropriate for the weights of each component in the
superposition, in order to get the final result. So if there are
several terms in the superposition, there is no violation of
counterfactual definiteness, and one can calculate on just one
typical member. Once again, that is all that happens here, and it is
just standard quantum mechanics.
That practice is very good ... for applying the theory, and Shor
results shows that we can exploit the Bell base, and so it is fine,
and non-locality, or better non separability, is quite real. But to
infer from this the existence of some action action at a distance is,
I think, quite incorrect. You need to take into account the fact that
when Alice and Bob are space-separated, what they will measure does
not need to be correlated, and they will belong to separate branches
of the "universal wave", and will never been able to talk with each
other and compare their result. They can compare their results only in
their own branches obtained from some local decoherence spreading of
they respective result measurement, and conclude that they are
correlated. No need for a physical "real" action at a distance *in*
any of the multiple branches of the wave. The uncorrelated results
which can be obtained makes their corresponding eigenstate orthogonal
or quasi-orthogonal.
Bruno
Bruce
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