From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 3 Aug 2018, at 13:43, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 2 Aug 2018, at 12:54, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 1 Aug 2018, at 21:12, Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
Indeed. But the common-cause explanation doesn't work for all
choices of measurement angle.
It does. Well, it does not if you assume only one Bob and Alice,
but the whole point is that it does if you take into account all
Alices and Bobs in the multiverse. QM explains why in all
branches, Alice and Bob will see the violation of Bell’s
inequality, and this without any physical instantaneous causality
on a distance. The MW theory is NOT an hidden variable theory in
the sense of EPR or Bohm. The MW theory is based on the first
person indeterminacy, and illustrate the first person plural
aspect (contagion of duplication). Hidden variable theory in the
sense of de Broglie, Böhm, or Einstein incompleteness are pure 3p
theories, not involving the role of the person in the picture.
In that case you have a different theory, which is not quantum
mechanics. You can believe anything you like about your own private
theories, but you cannot expect others to join in. If we are
talking about quantum mechanics, then it would be polite to stick
to that theory.
I am talking about Quantum Mechanics without collapse. You are the
one seeming to interpret ud + du as a superposition of worlds with
Alice having a particle in state u (and Bob having the corresponding
particle in state d) with worlds with Alice having a particle in
state d (and Bob having the corresponding particle in state u). That
would contradict the rotational symmetry of the singlet state.
The rotationally symmetric singlet is ud - du. The state you mention,
ud+ du, is the spin zero component of the triplet, which is not
rotationally symmetric.
I meant ud-du, which is the same state as u’d’-d’u’ up to some phase
e^i*theta.
You ask how I interpret the singlet in MWI. That is quite simple --
it is the same as in a collapse theory.
?
In MWI you just retain all the branches, branches that are discarded
in the single world theory. In both cases, the ud - du state is
rotationally symmetric when prepared, but that rotational symmetry is
destroyed as soon as the spin component of one particle is measured
in a particular direction.
In the MWI it is never destroyed. It is just entangled with the memory
of the observer (or the local environment containing the observer.
That is a remarkably silly thing to say. The only thing in this context
that is rotationally symmetric is the singlet state itself. The
laboratory in which it was prepared is not rotationally symmetric; the
apparatus that prepared it is not rotationally symmetric; the technician
who operated the preparation apparatus is not rotationally symmetric;
the experimenter who measures it is not rotationally symmetric. So as
soon as the singlet interacts with any of these things -- becomes
entangled with a non-symmetric object -- then the rotational; symmetry
of the state is lost. This is just elementary physics of symmetry
principles.
Alice (ud -du) = Alice ud - Alice du = Alice see up ud - Alice see
down ud
There, can't you see what you have just done? You have explicitly
invoked a collapse! (And there is a sill typo in the last part of the
equation -- it should read 'Alice see down du'. Alice can't see down
from the ud component!)
But if we write this out a bit more explicitly so that the tensor
product is evident (using Dirac notation) we have:
|Alice> (|u>|d> - |d>|u>) --> |Alice sees up>|u>|d> - |Alice sees
down>|d>|u>.
I have used the arrow (-->) to indicate that this step involves an
interaction between the singlet and Alice and her apparatus -- which
necessarily breaks the symmetry. (It is not actually an equality.) But
you have collapsed the wave function in this step, because 'Alice sees
up' only on the first half of the original wave function, so that Bob
necessarily sees only the |u>|d> portion of the original symmetric state
when Alice sees up -- he then necessarily gets the correlated (Bob sees
down) result when Alice sees up (for aligned measurement axes).
Similarly, in the second part of the equation, 'Alice sees down'
collapses the wave function to the |d>|u> component, meaning that Bob
necessarily sees only |u>.
This is the mistake that Price makes in his Q32 that you attached. I
have pointed this out many times, but it seems to have passed you by.
This builds in the non-local collapse of the original singlet wave
function right at the start of your argument. You split the wave
function following Alice's measurement so that Bob sees only the
correlated part -- he doesn't see a non-collapse singlet state! The
argument here is made for aligned measurements, but the same argument
applies to the general case of non-aligned measurements. Tipler spells
out the general case, but he makes exactly the same mistake -- he builds
in the non-local collapse without ever being aware of what he has done
-- just as you are clearly unaware of what you have done.
Bob(ud -du) = Bob ud - Bob du = Bob see down ud - Bob see up ud
Alice and Bob get their opposite spin, without transmission of action
faster than light, still less instantaneous.
You have built in an instantaneous collapse. Get used to it!!!!
If they measure in arbitrary direction, or the one to verify Bell’s
inequality violation, the reasoning is more long, but see Price
(below) for a good approximation.
As stressed. Price makes the same mistake of building in a non-local
collapse in the general case as well.
If in some branches there has been a FTL action, you might need to
explain to me how that is possible, and why to postulate this. It does
not follow from EPR which assumes definite results for a measurement,
where we get only definite result in the memory of the observer(s).
Trying to bring in counterfactual definiteness and the fact that this
happens only in the memory of the observers is just blowing smoke to
confuse the issue. You have got it wrong, Bruno. Why not man up to the fact!
The external magnet is not rotationally symmetric, so as soon as it
interacts with the singlet, the overall rotational symmetry is lost.
That is surely obvious.
The overall rotational symmetry is lost for the individual particles,
but not for the state Alice + two particles (even if far apart). I
mean the state
(Alice see up ud - Alice see down ud)
is still rotationally in variant.
Rubbish. You appear not to have the remotest understanding of what
rotational symmetry involves.
That is why I don't understand why you go on about infinities of
Alice's and Bob's who can measure in any direction continuing after
the first measurement interaction.
It only needs to the entanglement of the observers with the particles.
No rotational symmetry is lost, except for the first person pop of the
observer, but that is only because of their ignorance or abstraction
from the real quantum state. You persist talking like if some collapse
did occur after the measurement, but that never happens. So when we
get (Alice see up ud - Alice see down ud), that is still equal to
(Alice see up u’d' - Alice see down u’d’), as no collapse have
occurred. We keep an infinity of worlds where Alice found always up,
but with different spin direction. If the choice of direction was
decided or not change nothing to this: because (Alice see up ud -
Alice see down ud) = e^i.theta (Alice see up u’d' - Alice see down
u’d’), and the phase factor would not change the measurement that
anyone could do in principle on the overall state (which would be
technically difficult to here, but that is not relevant for our
attempt to agree (or not) on the interpretation of the MW theory.
You have used the rotational symmetry of the (|u>|d> - |d>|u>) state,
but as soon as this state interacts with the non-symmetric Alice, the
overall symmetry is lost. Sure, Alice could have measured at any angle
transverse to the direction of motion. But the point is that she
actually made a measurement at only one (randomly chosen) angle. So the
interpretation of the combined state after entanglement with Alice and
the rest is different. This is known as the contextuality of measurement.
The symmetry is lost, so there can only ever be four worlds: the uu,
ud, du, dd, worlds that I have been mentioning all along. These are
the worlds that survive from one measured singlet pair in MWI. Each
branch of this can be considered a single world, and since the
branches are disjoint, the relevant statistics must be separately
satisfied in each such branch.
That survive in the mind of Alice and Bob, when they have decided the
direction in advance, I can agree with this, but no worlds has ever
disappeared, and indeed, Alice could have measure u’/d’ instead of
u/d, and that plays a role to explain the violation of Bell’s
inequality in the local MW way, like the one by Price (which we have
discussed, and eventually you did agree that there is no FTL, just
inseparability).
Sure, Alice and Bob measure along randomly chosen axes. This is
necessary to observe the violation of the inequalities experimentally.
And the inequalities are a consequence of the non-separability of the
state -- there is no FTL information transfer. But the measurements do
collapse the state instantaneously so that the measurement at one end
influences the probabilities of the results that can be obtained at the
other end. As I say, there is no FTL transfer of physical information.
How you interpret this instantaneous influence at spacelike separations
is a personal matter. But there can be no instantaneous signalling, so
the situation respects special relativity. So you can have no basis for
complaint on that score -- it does not violate relativistic covariance.
It is not actually very difficult to understand once you have broken
the initial symmetry. A series of trials on such singlets will just
lead to a branching tree of 2^N copies of matched Alices and Bobs. It
is the fact that they always interact with the components of the same
singlet state in each trial that keeps the worlds in order. But the
measurements that each make are made non-locally.
Well indeed, and that leads to Price “psi-3”. The measurement are
local, but the splitting of the “universe” propagate locally in all
circumstances.
Price is an idiot. He uses collapse without being aware of the fact.
And the relative probabilities of their separate results
(probabilities of the 'worlds' or 'branches') depend on the
non-locally set relative orientation of their measurements. Bell's
theorem is then just the observation that the observed correlations
cannot be reproduced by a local hidden variables, such as would
represent a 'common cause' that is carried along from the point of
creation of the singlet
In one world. But in The MW the common cause is made in all words, and
propagate locally to the correlated state in each branches. See the
Q32 in Price's FAQ. We can discuss it again step by step. Bell’s
theorem discard local hidden variable which would determine the state
in each branch, or in the unique reality. That does not happen, as
Alice and Bob have a trans-world identity: as long as they have not
measured their spin, or got the spin result communicated, they exists
on different world/branches simultaneously. May be this is what you
are missing.
Maybe I am not missing anything, and you are just talking rubbish.
. Bell's theorem applies to each branch in the many-worlds
superposition and cannot be deflected by appeals to counterfactuals
or any such irrelevance.
I guess you mean that in each branch the violation of Bell’s
inequality occur.
No, I mean what I say. Bell's theorem applies in every branch, so local
accounts are impossible in every branch. Which means that locality is
violated in any and all branches, and so in the MWI wave function as a
whole. You appear to fail to understand the way in which superpositions
are handled in ordinary quantum theory -- what happens for a typical
branch happens for the whole.
Bruce
I agree. But the reason why that occurs without any FTL is typically
due to the trans world identity of Alice and Bob.
Bruno
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