Locality and nonlocality

Date: Wed, 18 Oct 1995 16:21:11 -0700
From: Rhett Savage 
Reply to: quantum-d@teleport.com
To: Subscribers of quantum-d 
Cc: Henry Stapp , rhett@nonlocal.com
Subject: QUANTUM-D: RE: locality and nonlocality

Mitchell Porter posted a beautiful comment by Gerard 't Hooft which 
mentioned the possibility of explaining the violations of the Bell 
inequalities and related results using purely local causes. I don't 
think that the proposed solution works, for the kind of conspiracy 
that 't Hooft invokes is bizarre! Let me briefly review the problem 
which 't Hooft is trying to solve...

I. Entangled states

In 1935 Einstein and two of his students Podolsky and Rosen brought 
attention to multi-particle quantum systems. We can gain information 
about one of a pair of particles without going anywhere near it, by 
measuring the other particle; in a real sense we are indirectly yet
definitively measuring the particle at a distance. E, P and R viewed 
this as a clear indication that what measurement does is to uncover 
pre-existing facts - the alternative is that measurements may effect 
changes at a distance, instantaneously!

Of course, 29 years later in 1964 John Bell showed that some sort of
nonlocal effect must be occurring - according to a rigorous analysis, 
local facts could not through any possible cleverness be arranged so
as to be prepared, at one and the same time, to answer every possible 
consistency question which we might pose to the whole system. 
 
In other words, pre-existing localized facts are formally incapable of 
generating run-of-the-mill quantum correlations.

II. Bell's theorem

Bell considered the various possible measurements on one particle of 
a multi-particle state: we might measure 'this' (eg. polarizer angle) 
or 'that,' depending on our whim.

Meanwhile, our  choice of measurement results in our obtaining various 
kinds of information about other, distant parts of the system. To the
extent that we believe in the locality of influence it seems that we 
imagine that throughout the system are pre-existing "facts," ready to 
swim to the surface, corresponding to each possible question we might
pose... 

On a given run of the experiment an outcome happens and we might say
that some set of pre-existing facts underlay that; then it turns out 
that this particular set of "facts" would have given a different (in 
fact less correlated) outcome than quantum theory if we had measured
something else. No matter how we seek we cannot find any local set of
facts which would give consistent answers to all possible choices of 
measurement.

Modern versions of Bell's theorem, such as those due to Greenburger,
Horne, and Zeilinger (GHZ) show bluntly that no set could behave in 
the right way for every possible measurement. 

Thus, correlation in quantum systems does not seem to be a matter of  
pre-existing facts after all; the world must really be making it up 
as it goes along. Local properties of quantum systems emerge "all at 
once," and often at a distance. Quantum wavefunctions collapse at a
distance as surely as they do so locally. 

III. Nonlocality

An even sharper formulation of nonlocality is possible...

Quantum nonlocality is *this* tangible: what is measured in one place 
leads to different outcomes in other, nonlocally distant places than 
would otherwise have happened. 

Henry Stapp formulated the result in 1977 as follows: 

  "What happens macroscopically in one space-time region must 
   in some cases depend on variables that are controlled in 
   far-away, space-like separated regions... [ie.], there is 
   no way within the set of all conceivable combinations of 
   conceivable results for the results in each region to be 
   independent of the choice made in the other region."

IV. Locality regained?

Of course, there are many excellent reasons that physicists mistrust 
and even actively dislike nonlocal connections - what room remains to 
wriggle here? 

Into the fray leaps 't Hooft...

On Thu, 28 Sep 1995 Mitch Porter wrote:

> A remark from Gerard 't Hooft, which can be found in _Physics and our
> view of the world_, ed. Jan Hilgevoord (Cambridge U.P., 1994), p28:
> 
> In my opinion (but I stress that this is a minority view), there
> may nevertheless be a compromise [between locality and Bell's
> theorem]. This is that there is no direct action at a distance,
> but there is some sort of "conspiracy". With this I mean that the 
> "state" of Nature that we now call "vacuum" is actually a very
> complicated dynamical solution of the equations of motion, 
> showing correlations over space-like distances. Einstein, Rosen,
> Podolsky and Bell never took such correlations completely
> into account. With correlations we can have apparently impossible
> "coincidences" spreading faster than the speed of light, but which
> are not in conflict with the requirement of special relativity
> that information cannot spread faster than the speed of light.
> 

Let us mark clearly the nature of this "conspiracy" - 't Hooft must 
be suggesting a complete abandonment of free-will even in its most 
general form.

Isn't he imagining an orderly, local universe where apparent nonlocal 
patterns are the result of one pre-determined pattern being laid atop 
of another? 

And one of these patterns is the sequence of polarizer angles chosen 
at either end of an EPR apparatus...!

The formal aspect of Bell's argument which 't Hooft questions is the 
contemplation of different possible measurements, with the discovery 
that no set of localized facts could be ready for them all - if there 
are not many possible measurements, if the world knows ahead of time 
just what polarization angles will be compared, then the cosmic deck 
could easily be stacked with local variables so as to act apparently 
consistently, even at a distance.

What is distinctive about 't Hooft's comments is the ease with which 
he locates the conspiratorial mechanism:

> the "state" of Nature that we now call "vacuum" is actually a very
> complicated dynamical solution of the equations of motion, 
> showing correlations over space-like distances... 

A very lovely thought, and no doubt true; but can this be considered 
to be a suitable exorcism of nonlocality as t'Hooft offered it? He
said that 

>                                            Einstein, Rosen,
> Podolsky and Bell never took such correlations completely
> into account. With correlations we can have apparently 
> impossible "coincidences" spreading faster than the speed 
> of light...

Yet the correlations that he is referring to include my choice of what
to measure - Is my choice really fixed by the underlying equations of 
motion, in just the right way as to ensure consistency in the particle 
experiment? 

How could it be!?

What if my choice *is* fixed (and this is how the world plays quantum 
theory, with a stacked local deck) and then i begin to base my choice 
on the swishing of a cat's tail? (When she swishes one way i rotate a 
polarizer thusly, and vice versa.) Would such swishes of the tail now 
be locally fixed by the underlying pattern of the vacuum precisely so 
as to correspond to my orientation of polarizers at angles which make 
the particle experiment come out right?
 
And if i turn all control over to some kind of random event such as a 
radioactive decay which could determine the polarizer angle then this 
also would not be truly random, but again would be part of a solution 
of the underlying equations of motion of the universe and by virtue of 
that be magically bound to other pseudo-random events in the particle 
experiment in such a way that the two local sets of events conspire to 
produce a coordinated global consistency...?

Nostalgia for free will aside, this is unreasonable. My brain, a cat's 
tail, and radioactive decay do not stand in the same physical relation 
to the nearby particle experiment. The imagined bond is too magical as 
it freely crosses from one level to another. After all, the connection 
between the photon pairs, the cat's tail, and even the "random" events 
was made in my subjectivity - where *else* is the link mediated?

What I am saying (and it has been said many times) is that this kind of
conspiracy involves abandoning the type of connection on which science 
is  based to a more profound degree than does acceptance of limitations 
on the principle of locality.

rhett



references
----------

A. Einstein, N. Rosen and B. Podolsky, "Can Quantum Mechanical 
            Description of Nature Be Considered Complete?" Phys. Rev. 
            47, 777 (1935)

J.S. Bell, "On the Einstein-Podolsky-Rosen paradox" Physics 1 (1964)

           "Free variables and local causality" Epistemological 
            Letters, February 1977 

           "Bertlmann's socks and the nature of reality" Journal de    
            Physique, Colloque C2, 3, 42 (1981)

          ...all three reprinted in J.S.Bell, "Speakable and unspeakable 
            in quantum mechanics" Cambridge University Press (1987)

Greenburger, Horne, Shimony, and Zeilinger, "Bell's theorem without 
            inequalities" Am. J. Phys., 58, 1131-43 (1990)

                    ...in this regard see also sections 5.3 and 5.18 of    
            R. Penrose, "Shadows of the Mind" Oxford (1994) 

H.P. Stapp, "Are superluminal connections necessary?" Nuovo Cimento,
            40B, 1, 191-204 (1977)