Do Entangled Systems Share Information
Non-Locally?: A Key Question for Understanding the NonExtended Nature of Qualia
Logan Trujillo, M.A.
Department of Psychology/Department of Physics
University of Arizona, Tucson, Arizona, USA
Email: logant@u.arizona.edu
URL:www.u.arizona.edu/~logant
Quantum Mind 2003: Consciousness, Physics, The Brain. March
15-19, 2003. Tucson, AZ, USA
Where Lieth Consciousness?
The hard problem - accounting for the existence of experience
in a physical world
Qualia as information
- Chalmers (1996) “double aspect” principle: Information has
material and phenomenal aspects
Spatiotemporal limitations of consciousness
Spatiotemporal parameters governing qualitative/informational
dynamics may not be restricted to the ranges allowed for by
material (energetic) causation (Trujillo, 1999; 2000a).
=> information has a degree of independence from energy
=> qualitative-informational and energetic-brain changes may
not be isomorphic with respect to one another
Physical: Immaterial (information) vs. Material (matter/energy)
distinction
Consciousness is instantiated by immaterial, physical processes.
Bell’s Theorem: Reality is Non-Local
z1
z
1
+1
-1
2
k1
s
k2
+1
y
-1
x1
x
Correlated photon pair production (Aspect , 2002) : J = 0 → J = 1 → J = 0
1
 
[cos( ) z1z2  sin(  ) z1x2  sin(  ) x1z2  cos( ) x1x2
2
Williams and Clearwater, 1998
-2 ≤ S(x1,x2,z1,z2) = 3cos(2θ) – cos(6θ) ≤ -2
where S(x1,x2,z1,z2) is the combination of the four polarization
correlation coefficients associated with the two measurement
axes.
This inequality is violated for angles
0 < θ < π/5.3, 0 > θ > -π/5.3, π/3.2 < θ < π, -π/3.2 > θ > -π
Maximum violations S = 2(2)1/2 and S = - 2(2)1/2 at θ = ±π/8 and
θ± 3π/8 respectively (Aspect, 2002).
Bell’s theorem implies that either quantum mechanics is
incomplete, or that any hidden variables within the theory are
non-local. What does this mean?
Maudlin (1994) - Violations of Bell’s inequality necessitate
superluminal information transmission (or sharing)
between particles, but not superluminal matter/energy
transport
Another view: information is not localized in that it manifests
across the entire spatio(temporal) state distribution of a system
(Aspect,2002; Williams and Clearwater,1998)
It is claimed that information sharing between entangled systems
is impossible because no information transmission is possible
between experimenters at the different ends of the experiment
(“There ain’t no such thing a a Bell telephone!” [Maudlin, 1994])
What is the basis of this claim?
1) Collapse outcomes are probabilistic and difficult (or impossible)
to control (Eberhard’s Theorem).
2) Non-local correlations are only apparent by comparing results
of measurements across experimental wings; hence necessitates
correspondence via a classical signal
My Hypothesis: These constraints rule out information
transmission/sharing between observers outside the system at the
time of measurement, not observers inside the system itself (i.e.
the system components)
Need to determine the information content of the entangled
system and see if it is non-zero
 I ( X )  I (Y )  I ( X , Y )
Mutual Information
A measure used in neurobiology to assess the total differentiation
or informativeness among neural subsystems, without reference
to external observers (Edelman, 2000).
P( X , Y )
I mutual    P( X , Y ) log 2 [
] dXdY
P( X ) P(Y )
 I ( X )  I (Y )  I ( X , Y )
Rieke et al., 1997; Dayan and Abbott, 2001
I ( X )   pi log 2 pi
where I(X) is the iShannon entropy,
I ( X )    P( X ) log 2 P( X )
Two Key Interpretations of Mutual Information
(1) Since mutual information is independent of observers “outside”
the system => Information has an “objective physical reality”.
(2) Mutual information is a joint property of the ENTIRE system;
analogous to the concept of potential energy
V
Im
V
Im
Mutual information is distributed across the system
What is Im for a pair of entangled photons?
z1
1
 
[cos( ) z1z2  sin(  ) z1x2
2
x1
 sin(  ) x1z2  cos( ) x1x2
QM Single particle probabilities
QM Joint Probabilities
1
PEntangled  Pz1z2  Px1x2  cos 2 
2
1
PEntangled  Pz1x2  Px1z2  sin 2 
2
1
PSingle  Pz1  Px1  Pz2  Px2 
2
2
4
i 1
j 1
I m  2 I Single  I Entangled  2 PS log 2 PS   PE log 2 PE
 1  cos 2  log 2 cos 2   sin 2  log 2 sin 2 
What is Im for a pair of entangled spin-1/2 particles?
z1
sin(  )
2 cos   sin 
 
 z1 , z2 
 z1 , z2
2
2
2 cos   sin 
sin(  )

 z1 , z2 
 z1 , z2
2
2
QM Single particle probabilities (PSingle)
P z1  P z1  P z2  P z2
1

2
QM Joint Probabilities (PEntangled)
 2 cos  sin  

2
P z1 ,  z2
 2 cos  sin  

2
P z1 ,  z2
4
4
1
P z1 ,  z2  P z1 ,  z2  sin 2 
4
2
4
i 1
j 1
I m  2I Single  I Entangled   2 PS log 2 PS   PE log 2 PE


2




2


2
2
sin 
2 cos   sin 
2 cos   sin 
2

log 2 sin  
log 2 [ 2 cos   sin  ] 
log 2 [ 2 cos   sin  ]
2
2
2
2
Since Im is non-zero in these cases, we may ascribe true physical
presence of information within these systems of which both
particles share or have access.
However, this access/sharing does not involve superluminal
information transfer because there is no actual “transmission”
occurring between the particles.
Since Im is a joint property of the system, Im is not localized in that
it manifests across the entire spatio(temporal) state distribution of
a system.
Other evidence: recent physics experiments (Mugnai et al., 2000)
showing that information in a light wave is not localized to central
wavefront (leads to apparent violations of speed of light
External observers cannot gain access to this information at the
time of measurement; however the particles always “know” the
state of the other, and this knowledge may causally influence their
behavior (Maudlin, 1994). => privacy of subjectivity?
Implications of Non-Local Information for Theories of
Consciousness and Qualia
EX1: phenomenal binding and the apparent spatial non-extension
of the mind
Biological evidence of brain modularity and cognitive-perceptual
compartmentalization  “The Binding Problem”
- Binding => Neural Synchrony => Global NCC (Trujillo, 2000b)
Global nature of neural interactions (as evidenced by large-scale
synchrony) suggests that information is non-localized within the
brain (and maybe even the body).
This property of nonlocalization may be what is meant when one
speaks of the "nonextended" nature of the mind.
The description of mental events as nonspatial is a
mischaracterization.
Provides solution to problem of “phenomenal binding”:
- The information/qualia associated with the various brain areas
could be said to span across all these areas.
The question of how spatially distinct qualitative properties are
merged into the spatially unified character of conscious
experience disappears because such qualitative properties are not
spatially distinct in the first place.
EX 2: PSI - psychokinesis, remote viewing, presentiment,
OOBEs, etc.
Certain psi phenomena (like so-called “telepathy”) have
been characterized as “shared feeling states”.
These possibilities may allow actual “Bell Telephone” in
that entangled partners may be able to behavioral report
on subjective expression of shared states/knowledge.
Ex: Non-local correlations between human brains and
physiology (Grunbaum-Zylberg(1994); Richards et al.
(2003); Bohm (1985)
References
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