On 8 Jun 2017 1:05 a.m., "Bruce Kellett" <bhkell...@optusnet.com.au> 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.
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, and do not exist in any
operative sense until the state interacts with something that sets a
direction. You appear to claim that A and B exist in separate worlds
corresponding to each of this infinity of bases. 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. 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.
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.
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. 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. 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. This
is entirely local, and is necessary because of the experimental fact that
repeated measurements of the same state give the same result. So if Alice
got '+', the state reduces to |+>|->, and if she got '-', the state reduces
to |->|+>. 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,
so Bob must also be presented with the original state |psi>. 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, 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. 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.
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.
I suspect I'm being obtuse in some way here but, rereading the quote
attributed to Bell himself by Wikipedia about superdeterminism, it strikes
me that MWI seems to describe a species of this sort of thing. IOW when
Alice and Bob make their measurements, the consequence in terms of branches
is a spectrum of all the possible outcomes. Indeed one could say that this
is what has been propagating from one to the other, rather than a
'particle'. Let's say then that the various versions of Alice and Bob that
consequently coexist in MWI terms, however far apart they may have been,
eventually meet to compare notes. Again, the spectrum of possible outcomes
implicit in the global MWI perspective travels with them, as it were.
However, of all the possible pairings of the two, it appears to be
'superdetermined' that each observed encounter must be consistent with the
predictions of QM. And so it would appear that the paired results of their
joint measurements are somehow inseparable, in Wallace's language, without
there having been any action at a distance. If this depiction were to make
any sense, one might then enquire what common cause, or other explanatory
device, could account for this apparent superdetermination of observed
outcomes?
David
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. 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.
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.
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).
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.
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: 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.
Bruce
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an
email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
