On 11 Jun 2017, at 12:24, David Nyman wrote:
On 11 June 2017 at 10:14, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 09 Jun 2017, at 20:21, David Nyman wrote:
On 9 June 2017 at 12:34, Bruno Marchal <marc...@ulb.ac.be> wrote:
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.
Why?
That is due to the singlet state. [Alice Bob ( up down - down
up) ]= [Alice Bob up down - Alice Bob down up] keeps its rotational
symmetry, even after the interaction took place. The correlation are
built in by the preparation of that state, and is valid whatever the
spin direction are, so you can add prime to up and down, for the
other direction, and the correlation does not depends on the base,
and evolve locally. When space separated, they are independent, but
by virtue of the singlet state, if they do measurement, they will
put themselves in "independent" and possible different
superposition, which will 'contagiate' their respective environment
up to *different* partners who will get the right correlation by the
math of the singlet state which will not allow any Alice and Bob to
not confirm the singlet , highly correlated state. The singlet state
describe an infinity of Alice and Bob, having all their spin being
correlated, and they localize themselves in which one when doing
measurement. This can be used to show that they will conclude that
Bell's inequality is violated, despite no influence at a distance
exist. There is only spreading superposition, and all Alice and Bob
can only meet their corresponding partners.
If this is so easy to describe, why isn't it the 'obviously
correct' answer in MWI terms?
It is mysterious indeed. I think that Tolstoy might have got the
explanation:
“The most difficult subjects can be explained to the most slow-witted
man if he has not formed any idea of them already; but the simplest
thing cannot be made clear to the most intelligent man if he is firmly
persuaded that he knows already, without a shadow of doubt, what is
laid before him.” (Tolstoy)
In Wallace's book, whilst he says that the correlated measurements
are 'inseparable', he doesn't go so far as to give an explanation in
the clear-cut terms you outline above. I think we need to explore
your idea of 'contagiate' a little more.
I have not read Wallace book, but I did read some of its paper, which
seems to be close to what I say. I don't think Wallace interprets non-
locality as making possible some action/influence at a distance (above
the non-signaling at a distance). The term "Contagion" is useful to
remind that when we do a measurement we don't split the entire
universe in some simultaneous way, but the "splitting of universe" or
"consciousness differentiation" spread locally, very quickly, but much
more slowly than light speed. Decoherence is a physical and local
phenomenon.
Why did Einstein miss the Many-World? Is not MW a consequence of 1)
Non-Spooky-Action-@-a-distance + 2) Schroedinger or Dirac equation?
Of course the most natural idea was to conceive hidden variables, in
an implicite mono-universe theory, but even EPR shows that their
influence should be non local (Bell shows just precisely how).
Why did Gödel missed Church's thesis?
Why does almost everyone miss that Church's thesis rehabilitates
Pythagorus, and that Gödel's theorem rehabilitates Theatetus'
definition of knowledge? Which is basically a theory of consciousness.
It is normal, I think. When you see that cannabis is still in schedule
one despite 70 years of debunking of the alledged evidences of danger,
you realize it will take time to get serious on the fundamental
questions where the lies are 1500 years old.
Some denies evidences because it threats their most deep metaphysical
beliefs. That is something I can respect.
But 98% can deny evidences because their fear for their notoriety and
the gossip of the colleagues. They fear their carrier threatened, and
their money. Materialism will die, I guess, like Vitalism, but I am
afraid it will take some time. People prefer fake comfortable news
than uneasy questions. In theology the humans still shut down their
corpus callosum. The left brain, assuming it plays the role of the box
(Bp) just cannot hear what the right brain, assuming it plays the role
of either the outer god (p) or the inner god (Bp & p) says without
words.
Bruno
PS I have a run of full day oral exams. I will continue the comment
without change if you abstract from the possibly long delays :)
David
Bruno
David
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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