Henry Stapp answer questions about the role of
nonlocality in the relative state (MWI) interpretation.
He always quotes my email in full with a > in front i.e.:

Stapp
> Plaga
>> Stapp

On Thu, 8 Mar 2001, Rainer Plaga wrote:

> Dear Dr Stapp,
> 
> I read with great interest the material on the many-worlds interpretation
> on your server. I was deeply impressed by your discussion of locality in MWI
> in FP 10,767(1980) with which I fully agree.
> I also see locality as THE strength of MWI, because I feel renouncing
> locality requires a completely new philosophical foundation for science.
> As Max von Laue said, new physics results can never FORCE us to change
> our philosophical perspective, so MWI must "remain on the agenda" - 
> until proven wrong, or at least until proven fruitless.
> 
> I was amazed and puzzled
> to find in personal discussions that two prominent MWI adherents -
> Hans-Dieter Zeh from Heidelberg and
> Max Tegmark from Pennsylvania - VERY strongly disagreed (to put it mildly)
> with the standpoint that QM within MWI is local.
> For them nonlocality remains a necessity to "explain" entanglement
> (or rather they say: entanglement automatically entails nonlocality), even
> within MWI!

Zeh in Found.  of Physics  Letters 13  June 2000 p.22
defines quantum nonlocality to be "quantum correlations or
`entanglement'". So with that definition everyone would
agreed that MWI is highly nonlocal: entangled states exist.
But no action or influence at a distance, or faster than light,
is needed in a MWI version of (relativistic) quantum field theory.

I believe that we have here just  a matter of terminology, with
no real different at the  level of the physics.




> 
> MWI adherents are willing to give up
> their biggest asset!
> 
> I see three possibilities:
> 1. both of us are wrong in thinking MWI is local
> 2. Max and Hans-Dieter Zeh are wrong in thinking entanglement cannot be understood
>    locally within MWI 
> 3. or we are are all right: this would probably mean MWI is untenable
> 
> So my simple question to you is: can I understand entanglement
> without nonlocality within MWI?
> 
> To make my question more concrete:
> 
> Let us have the following initial wavefunction of an excited atom A*
> (I leave out normalisations) in two spatial modes 1,2
> (setup is Scully et al.,Nature 351,p.111,1991).
> 
> |initial> = (A1* + A2*)
> 
> pictorial (arrows are direction of motion):
> A1*-->
> 
> A2*-->
> 
> Each mode goes through a cavity, where the atom fully deexcites
> without significant exchange of momentum
> leading to the entangled state of deexcited atom A and photon p:
> 
> 
> |final> = (A1 p1 + A2 p2)
> 
> pictorial:
> 
>          p1                A1-->
>  
>          p2                A2-->
> 
> A moves away so A and p are spatially seperated.
> p is a "which way" marker.
> 
> The atom components A1 p1 and A2 p2 do not interfere 
> when they spatially overlap (experimental fact).
> Why?
> 
> IFF physics is local, there must be some LOCAL parameter which is different 
> in A1 and A2.
> Correct?
> 

The local state of the EMF in the cavity is different, of course.

> If we do not want to introduce new physics there is only ONE possibility 
> (there
> are no other degrees of freedom!):
> quantum phase (the parameter canonically conjugate to particle number in 
> 2nd quant. theory).
> So what happens WITHIN MWI:
> when the atom goes through the cavity and deexcites, the quantum phase gets 
> locally kicked
> so that interference gets washed out.
> Luis,Sanchez-Soto PRL,81,4031(1998) discuss this kicking in detail without 
> embarkig
> on the fundamental questions.
> The "locally inaccessible information" of David Deutsch
> is encoded in the relative QUANTUM (not spatial!!) phase between A1 and A2.
> 
> Can this naive picture be correct (assuming MWI is correct)??

In MWI one understands  this "kicking of the phase" in more detail:
the phase is  not  a  property of an individual subsystem of an
interacting pair of systems: it is  a shared property of the  product
state of the pair of systems. So when one considers  an interaction
within MWI one must consider the whole  quantum system, and then the non
overlap of the "pointer" states of second (observing) system after
a good measurement is equivalent to an averaging over an unknown
phase of the relative phase  between  the  two states of  the observed
system. The  justifies  and explains  simpler treatment  in terms
of the  phase of  the observed system alone. 

> (If yes, option 2. above would hold).
> (see also Bhandari PRL,69,3720 (1992) who advocates it, though the
> locality issue is not explicitly mentioned)
> Itīs exactly what our QM prof warned us NOT to believe in grad school, right?
> (MY prof did not discuss MWI though).
> 
> thanks for your interest 
> rainer plaga
> 



On Tue, 13 Mar 2001, Rainer Plaga wrote:

> Dear Dr Stapp,
> thanks a lot for your explanation.
> 
> stapp@thsrv.lbl.gov wrote:
> 
> > Zeh in Found.  of Physics  Letters 13  June 2000 p.22
> > defines quantum nonlocality to be "quantum correlations or
> > `entanglement'". So with that definition everyone would
> > agreed that MWI is highly nonlocal: entangled states exist.
> 
> If seen as a definition, of course.
> But I think primarily 
> everybody connects with the term "quantum nonlocality" a
> fundamental nonlocality, i.e. MORE than a mere classical correlation,
> a la "Bertelmanīs socks" of Bell.

Everyone agrees that quantum  entangement exists, and that QT without
collapse generates quantum entanglement, but is "dynamically"
local. But Zeh "calls" entanglement "nonlocality": this is merely
a somewhat devient use of the word "nonlocality"; he would I am sure
agree that MWI (He prefers, quite properly, the term many minds MMI)
is "dynamically" local: there is no actual causal influence
the extends over spacelike intervals withinin MMI or MWI.

> 
> And where people seem to disagree (or at least I am confused) is
> whether WITHIN MWI one can understand entanglement as a mere classical
> correlation, 

quantum correlations are not mere classical correlations!


so that no "quantum nonlocality" exists.

One must distinguish quantum entanglement from action or influence
that acts over a spacelike interval.



> 
> David Deutsch writes(http://www.edge.org/3rd_culture/deutsch/deutsch_index.html):
> 
> "What about the famous experiments that demonstrate quantum non-locality
> in the lab? They don't. They demonstrate quantum entanglement: one of the
> fundamental quantum phenomena, but a local one."
> 

True!


> he squarely contradicts Zeh (FP-L 13,22 (2000)) in this.
> 

False! Zeh means by nonlocality merely quantum  entanglement,
whereas DD emphasizes the quantum entanglement does entail
any dynamical action over spacelike intervals within MWI.
 
> It seems this disagreement is beyond terminology.

NO!
> 
> Entanglement is an innate feature of the Schroedinger eq., to this all agree.
> Assuming MWI,
> can entanglement be understood as the classical correlation of
> purely local quantitities of QM in the standard formalism?
> 


Quantum entangement is not classical-type correlation!

> Here Zeh (FP-L 13,22 (2000) and pers.comm.)
> and Tegmark (pers.comm.) answer "no", 

They are right!

>Frank Tipler definitely "yes" (quant-ph/0003146
> and pers.comm.)
> and Deutsch apparently "yes" (quant-ph/9906007) (but this I infer only from his writings).
> 
> What is your answer?
>

We all agree!

 If this is not possible, what is the proof for this impossibility?
>
> Zeh in the paper mentioned by you (FP-L 13,22(2000)) quotes the exp. 
> violation of Bellīs
> inequalities as generally valid proof. 

Of quantum entalgement.

> This is definitely wrong as pointed out by
> Deutsch and Tipler. 

They agree that quantum entangement exists.


> MWI is not definite counterfactual and Bellīs inequalities
> are then irrelevant. Sowithin MWI Bellīs inequalities are irrelevant.

They are relevant to quantum entanglement.


> Do you agree to that?

To what?

> 
> Is there another proof, valid also under the assumption of MWI?
> 
Proof of what?


> > But no action or influence at a distance, or faster than light,
> > is needed in a MWI version of (relativistic) quantum field theory.
> 
> yes this is generally agreed within MWI.
> 
> 
> > > IFF physics is local, there must be some LOCAL parameter which is different
> > > in A1 and A2.
> > > Correct?
> > >
> > 
> > The local state of the EMF in the cavity is different, of course.
> 
> yes of course. But is this the ONLY difference of A1 and A2 when they spatially overlap?
> This is the same question as I asked above. Or do A1 and A2 have finite
> relative quantum phase locally,and this makes them different, and prevents
> interference?
> 

I explained why the "phase" explanation is  just a  short-hand
for the more detailed explanation. 


> > the phase is  not  a  property of an individual subsystem of an
> > interacting pair of systems: it is  a shared property of the  product
> > state of the pair of systems. So when one considers  an interaction
> > within MWI one must consider the whole  quantum system, and then the non
> > overlap of the "pointer" states of second (observing) system after
> > a good measurement is equivalent to an averaging over an unknown
> > phase of the relative phase  between  the  two states of  the observed
> > system. The  justifies  and explains  simpler treatment  in terms
> > of the  phase of  the observed system alone.
> 
> In the treatment of Luis/Sanchez-Soto (PRL,81,4031(1998))
> the quantum-phase kick affects both observing and observed system("A" and "p").
> After the kick BOTH systems have a relative phase that allows
> to understand the non-interference between overlapping
> components.
> So why is a completely local description of the observing system
> impossible? Why is the relative phase not a property of the individual
> observing system?
> 

The basic laws of quantum theory involve systems that are composites of
several systems: when  in doubt, or when wantsto do a "correct" treatment
one should  go back to the basics, which really cannot be avoided,
even though simple-minded explanations are sometimes useful.



On Thu, 15 Mar 2001, Rainer Plaga wrote:

> Dear Dr Stapp,
> 
> thanks a lot for your very helpful explanations.
> Please excuse me for not understanding more rapidly.
> 
> The difference in terminology is quite confusing to a
> nonspecialist. E.g. it is not yet clear to me:
> Is MWI a local-realistic theory in the usual sense of this term?
> 
> Zeh explicitely states that it is not. However you and other researches stress
> the locality of MWI (which is surely realistic I guess).
> 
> Deutsch: The results  blow
>  the 'quantum non-locality' misconception clean out of the water.
> 
> Zeh: The problems arise as a consequence ...of quantum nolocality (entanglement)....
> This fundamental quantum property...
> 
> (refs. of last email).
> 
> These emphatically different uses of terminology leave open the question
> of which is preferable. If two deep thinkers with a very similar standpoint (
> preferall of MWI) use a most central term so differently, this remains interesting.
> 
> Because I discussed the issue personally with Hans Dieter Zeh I hope I
> understand his standpoint:
> 
> "The non-interference of spatially overlapping entangled components of a wavefunction is due to
> 
> their quantum entanglement with space-like quantitities.
> This is a fundamental quantum property,  a necessary consequence of the Schroed. eq. and goes
> beyond mere classical correlations."
> 
> If this is accepted, it seems logical to think of the non-interference as some "influence"
> that acts over a space-like interval. Then it sounds logical to call this "quantum nonlocal".
> I guess that is the reason for Zeh's choice of terminology (I did not ask him explicitely).
> 
> >One must distinguish quantum entanglement from action or influence
> >that acts over a spacelike interval.
> 
> How exactly is entanglement distinguished from an "influence" over
> a space-like interval? 


"Action" or "influence" over a spacelike interval is when a person's
free choice made in one region affects the truth of a statement whose
truth
is specified by possible events located in a spacelike separated region.

That is not the same as correlation between spacelike  separated  events.
  
> After all, non-interference
> of components has a dynamical influence on temporal evolution of the total wavefunction.
> (Of course without the possibilty to send signals etc., but similar
> to the "action" leading to a definite result in non-MWI interpretations, something that
> IS called generally "non-local").
> 
> thanks again a lot for your time
> rainer plaga

On Mon, 19 Mar 2001, Rainer Plaga wrote:

> Dear Dr Stapp,
> 
> Please allow me one last question, which I
> could not deduce from your previous very helpful answers.
> 
> Assuming MWI, is QM a local-realistic
> theory in the usual Einsteinian sense?
> 
> In other words: Assuming MWI, can a complete description of a composite
> system be always deduced from complete descriptions of
> the subsystems?
> 
> best regards and thank you
> rainer plaga
> 

MWI QT is not local-realistic!

The "correct" QT is Relativistic Quantum Field Theory.
It is intrinsically a many-particle theory. Just as a
probability function for N particles is a function
P(x_1, x_2, ....,x_N) of 3N variables, so is a wave 
function a function of 3N variable, or more precisely
a collection of many such functions with different N's.
The interaction is local because the evolution is
"free-particle" evolution except when two of the arguments
coincide. Or in terms of fields instead of particles,
the evolution is free-field evolution except when the two
fields are at (essentially) the same point.
So the theory is local in the sense that all interactions
are contact interactions. But all sorts of correlations
can be generated and the wave function of each individual
particle depends upon the arguments x_1, x_2,   x_N
of all the other particles.

One hardly ever, except just after a product state is created,
has a wave function that is simply a product of wave functions
of the individual particles. What is local is the interaction:
but the STATE is generally highly entangled, and hence not
"local-realistic" in the EPR sense. In the first place the results are
not UNIQUE, as is required for a theory that is local-realistic in the EPR
sense. That is the BIG reason why EPR local-realism fails in WWI QT.
Because the results are not unique one cannot even formulate the
locality requirement that "what happens" in one region cannot depend
upon which experiment is performed in another region: everything
happens.

Henry


> Dear Dr Stapp,
> 
> Thanks indeed for your detailed and very clear answer!!
> I think I understand your point.
> Just to be absolutely sure, the answer to my "last question", second version:
> 
> > > In other words: Assuming MWI, can a complete description of a composite
> > > system be always deduced from complete descriptions of
> > > the subsystems?
> 
> must be:
> NO! This is utterly impossible except for special cases, also within MWI.
> OK? (a simple "yes" from you is enough; just to be sure...).
> 
> thanks and all the best rainer 

The point is that the "wave function" is a function
of 3N variables, and therefore the wave function
of a single particle is not well defined (except
in very special cases): the wave function as a function
of x_1 is a function of x_2, x_3, ...

Of course, a probability function is normally a function
of all the {e.g., 3N} variable, but ordinary reality
is not. In this sense "entanglement" (the non-product form
of the wave function) is a kind of "nonlocality", even
though it is generated in MWI by a local dynamics.

I hope this clears everything up.

Henry

On Thu, 22 Mar 2001, Rainer Plaga wrote:

> Dear Dr Stapp,
> 
> yes, your standpoint is now quite clear and seems eminently 
> reasonable.
> Indeed it is very similar to the one of Hans Dieter Zeh 
> (perhaps except the
> exact importance of Bellīs inequalities for the MWI), who 
> was kind enough
> to explain it to me personally.

I doubt that Zeh and I disagree about the significance of 
Bell's theorem in the context of MWI. I think I have always 
found myself in agreement with everything of his that I 
have read.


> 
> In view of your description of entanglement:
> 
> >the wave function of each individual
> >particle depends upon the arguments x_1, x_2,   x_N
> >of all the other particles.
> 
> I would further plead that Hans Dieter Zehīs terminology to 
> call entanglement
> "quantum nonlocal" is justified and useful.

Its  OK if one understands that it means only quantum
entanglement, which no one denies exists. But
I think the key *question* is FTL causal influence 
(transfer of information over a spacelike interval). 
There is no nonlocality of THAT kind in MWI.

> 
> However - and this seems trivial - then a complete description of a composite
> system CANNOT always be deduced from complete descriptions of
> the subsystems EVEN WITHIN MWI.
> 
> Disturbingly, David Deutsch emphatically and expicitely 
> claims exactly this on p2 of quant-ph/9906007
> (Proc.Roy.Soc.A456,1759(2000))

> Because I find it unthinkable that David Deutsch commits 
> trivial errors, I ask MYSELF (I promised to ask no more 
> questions :-))
> if it could be that he found something that goes BEYOND 
> (not against!!!)
> yours and Hans Dieter Zehīs understanding of MWI.

DD's main results are consequences of the result
that MWI is local, in the sense that there is no FTL 
transfer of information: the theory of local in that sense.
Thus information flow can be traced locally.

DD's other claim, about being able to describe the state
in terms of the values associated with the individual
systems, with these values not depending on what distant
observers do, is OK, in his context, which is his way of
constructing conplex states out of operations on a basic
factorized state |0,0,0, ... ,0; 0>. Of course, the 
description of a complex state depends on the complex
set of operations that, together with the values of the
quantities that specify the individual systems, specify
the state. So a lot of information besides the values
of those quantities is needed. It is interesting, and
I think nontrivial, that one can do this. But the basic
reason that he can do this is that MWI is (dynamically)
local. The step-by-step equations for the evolution
of the quantities that characterize the individual systems
bring in, of course, all of the nonlocal correlations, but
the dynamics is local and what one does in one place
indeed does not affect the simultaneously defined
quantities that characterize the distant systems.

> To stress this: I hope I understand the depth of your considerations:
> neither can they be trivially wrong!
> The clue to resolve this is perhaps the "locally inaccessible
information"
> in Deutschīs paper, which physical nature is not quite clear to me.
> 
> thanks again for you willingness and time to answer my questions,
> rainer
> 
>