From C^3 to C^4 Advanced Conscious Intelligence

Think of this as a combination of Jazz and Chamber Music. Paola Zizzi
playing the cello with me on the Jazz saxophone improvising in Caffe Beat.


Excerpts, with my Commentaries, from:

“HOLOGRAPHY, QUANTUM GEOMETRY, AND QUANTUM
INFORMATION THEORY
P. A. Zizzi
Dipartimento di Astronomia dell’ Università di Padova, Vicolo dell’
Osservatorio, 5
35122 Padova, Italy
e-mail:
ABSTRACT
We interpret the Holographic Conjecture in terms of quantum bits
(qubits). N-qubit states are
associated with surfaces that are punctured in N points by spin
networks’ edges labelled by the spin-
1/2 representations of SU(2) , which are in a superposed quantum state
of spin "up" and spin
"down". The formalism is applied in particular to de Sitter horizons,
and leads to a picture of the
early inflationary universe in terms of quantum computation. A discrete
micro-causality emerges,
where the time parameter is being defined by the discrete increase of
entropy.

Then, the model is analysed in the framework of the theory of presheaves
(varying sets on a causal
set) and we get a quantum history. A (bosonic) Fock space of the whole
history is considered.
The Fock space wavefunction, which resembles a Bose-Einstein condensate,
undergoes decoherence
at the end of inflation. This fact seems to be responsible for the
rather low entropy of our universe.
Contribution to the 8th UK Foundations of Physics Meeting, 13-17
September 1999, Imperial
College, London, U K..

1 INTRODUCTION
Today, the main challenge of theoretical physics is to settle a theory
of quantum gravity that will
reconcile General Relativity with Quantum Mechanics.

There are three main approaches to quantum gravity: the canonical
approach, the histories approach,
and string theory. In what follows, we will focus mainly on the
canonical approach; however, we
will consider also quantum histories in the context of topos theory [1-2].

A novel interest in the canonical approach emerged, about ten years ago,
when Ashtekar introduced
his formalism [3] which lead to the theory of loop quantum gravity [4].

In loop quantum gravity, non-perturbative techniques have led to a
picture of quantum geometry. In
the non-perturbative approach, there is no background metric, but only a
bare manifold. It follows
that at the Planck scale geometry is rather of a polymer type, and
geometrical observables like area
and volume have discrete spectra.

Spin networks are relevant for quantum geometry. They were invented by
Penrose [5] in order to
approach a drastic change in the concept of space-time, going from that
of a smooth manifold to that
of a discrete, purely combinatorial structure. Then, spin networks were
re-discovered by Rovelli and
Smolin [6] in the context of loop quantum gravity. Basically, spin
networks are graphs embedded in
3-space, with edges labelled by spins j = 0, 1/2, 1, 3/2...and vertices
labeled by intertwining
operators. In loop quantum gravity, spin networks are eigenstates of the
area and volume-operators

However, this theory of quantum geometry, does not reproduce classical
General Relativity in the
continuum limit.”

JS: Note that.

PZ: “For this reason, Reisenberg and Rovelli [8] proposed that the
dynamics of spin
networks could be described in terms of spacetime histories, to overcome
the difficulties of the
canonical approach. In this context, the spacetime histories are
represented by discrete
combinatorial structures that can be visualised as triangulations. The
merging of dynamical
triangulations with topological quantum field theory (TQFT) has given
rise to models of quantum
gravity called "spin foam models" [9] which seem to have continuum limits.”

JS: What is the relation of Hagen Kleinert’s “world crystal lattice” to
spin foam dynamical triangulations?

PZ: Anyway, as spin foam models are Euclidean, they are not suitable to
recover causality at the Planck scale.
For this purpose, the theory should be intrinsically Lorentzian.
However, the very concept of causality
becomes uncertain at the Planck scale, when the metric undergoes quantum
fluctuations as Penrose [10] argued.
So, one should consider a discrete alternative to the Lorentzian metric,
which is the causal set
(a partially ordered set-or poset- whose elements are events of a
discrete spacetime).
Such theories of quantum gravity based on the casual set were formulated
by Sorkin et al. [11].

Rather recently, a further effort in trying to recover causality at the
Planck scale, has been undertaken by Markopoulou and Smolin [12]. They
considered the evolution of spin networks in discrete time steps, and
they claimed that the evolution is causal because the history of
evolving spin networks is a causal set. However, it is not clear yet
whether causality can really be achieved at the Planck scale, at least
in the context of causal sets.

In this paper, we also consider the issue of causality at the Planck
scale in the framework of causal sets, although our results do not
promote this aspect as decisively as in [12]. In our opinion, the very
concept of causality makes sense in the quasi-classical limit, in
relation with the fact that an observer is needed, and this observer
cannot "stand" on the event at the Planck scale. Moreover, our picture
is related to some other issues, mainly the holographic conjecture
[13-14] and quantum information theory.

The issue of quantum information started with Neumann [15], who gave a
mathematical expression of quantum entropy in photons and other
particles subjected to the laws of quantum mechanics.
However, Neumann’ s entropy lacked a clear interpretation in terms of
information theory. It was
Schumacher [16], who showed that Neumann’s entropy has indeed a related
meaning. Moreover,
Holevo [17], and Levitin [18], found that the value of quantum entropy
is the upper limit of the
amount of quantum information that can be recovered from a quantum
particle (or from a group of
particles). Quantum information differs from classical information
[19], in several aspects.

The elementary unit of classical information is the bit, which is in one
of the two states "true" = 1 and
"false" = 0, and obeys Boolean logic. A classical bit is
contextual-free. i.e. it does not depend on what
other information is present. Finally, a classical bit can be perfectly
copied.

In quantum information, the elementary unit is the quantum bit (or
qubit), a coherent superposition
of the two basis states 0 and 1. The underlying logic is non-Boolean.
Different from classical bits, a
qubit is contextual [20], and cannot be copied, or "cloned" [21].”

JS: Clearly our inner thoughts are contextual more like quantum bits
than classical bits. But that is not enough. Cloning or copying the
thought is needed for intelligent non-random creative evolution. The
inability to clone or copy a qubit comes from the linearity of
superposition in micro-quantum theory and is associated with “signal
locality”, i.e. the inability in micro-quantum theory to use controlled
entanglement as a stand-alone conscious-command-control-communication
channel C^4 that is both its own lock and key. Antony Valentini showed
that signal locality is an artifact of “sub-quantal heat death” or
“sub-quantal thermodynamic equilibrium” manifested in the Born
probability density interpretation dP/dx^3N ~ |psi(x)|^2 in N-particle
configuration space. Bohm and Hiley showed that signal locality comes
from the “fragility” of the “quantum potential”, i.e. from lack of
“generalized phase rigidity” (P.W. Anderson). The rules of the game
change in the “More is different” ground state phase transition from
micro-quantum to MACRO-QUANTUM theory where there is a tradeoff:

Nonlocality - locality

Quantum entropy as log of phase space volume of ground state decreases.

Linearity of nonlocal Schrodinger eq. - nonlinearity of local
Landau-Ginsburg eq.

Breakdown of Born probability game.

Fragile micro-quantum potential - robust MACRO-QUANTUM POTENTIAL
with generalized phase rigidity and the possibility of signal nonlocality.

PZ: “The emerging fields of quantum computation [22], quantum
communication and quantum
cryptography [23], quantum dense coding [24], and quantum teleportation
[25], are all based on
quantum information theory. Moreover, quantum information theory is
expected to illuminate some
conceptual aspects of the foundations of Quantum Mechanics.

In this paper, we shall illustrate, in particular, the interconnections
between quantum information
theory and quantum gravity.

As spin networks are purely mathematical entities, they do not carry any
information of their own
because information is physical [26]. However, they do carry information
when they puncture a
surface transversely. Each puncture contributes to a pixel of area (a
pixel is one unit of Planck area)
and, because of the holographic principle, this pixel will encode one
unit of classical information (a
bit).”

JS: The idea of “puncture” is really 3D duality. A string theory line
is dual to a loop quantum gravity area, and a point is dual to a 3D
volume. One can generalize this to N-Dim bosonic hyperspace. The SU(2)
qubit transformations are 2x2 Pauli “spintronic” matrices that introduce
the hypercomplex fermion dimensions of supersymmetry (fermions - bosons).

The idea then is that each component of 4-vector Xu is really a
quaternion rather than a real number xu. This gives a non-commutative
space-time geometry. This is not the same as representing an ordinary
first rank tensor as a quaternion. That is we do not have a 4D real
vector space, but rather a 16 D real vector space or an 8D complex
vector space or a 4D quaternion vector space.

PZ: “The starting idea of our paper is that a surface can be punctured
by a spin network’s edge (labeled by the j = 1/2 representation of SU
(2)), which is in a superposed quantum state of spin "up" and spin
"down". This induces the pixel to be in the superposed quantum state of
"on" and "off", which encodes one unit of quantum information, or qubit.
By the use of the Bekenstein bound [27], we show that the entropy of an
N-punctured surface is in fact the entropy of an N-qubit.

Moreover, because of the Holevo-Levitin theorem [17-18], our picture
provides a time parameter in
terms of a discrete increase of entropy. Thus the time parameter is
discrete, and quantized in
Planck’s units. “

JS: The problem here is how to make this Diff(4) symmetric independent
on how the space-time in classical limit is sliced. On the other hand
R. Kiehn says that Diff(4) is “reversible”. You need something else to
get arrow of time. Pfaff dimension 4?

PZ: “This is in agreement with Penrose’ s argument [28], that a theory
of quantum gravity
should be time-asymmetric. However, our result is not strong enough to
claim that causality is
actually being recovered at the Planck scale. In fact, the thermodynamic
arrow of time is related to
the psychological arrow of time, and at the Planck scale, the latter is
missing because there are no
observers. This is not just a matter of philosophy, but it is a real
handicap.

The "events" of our causal set are not just points of a discrete
spacetime, but they are the elements
of a poset whose basic set is the set of qubits and whose order relation
follows directly from the
quantum entropy of the qubits.

Events that are not "causally" related (qubits with the same entropy)
form space-like surfaces (or
antichains).

The use of topos theory (in particular the theory of presheaves [29])
makes it possible to attach a
Hilbert space to each event, and to build up discrete evolution
operators [30], between different
Hilbert spaces. In this way, we get a quantum history, which turns out
to be a quantum information
interpretation of the theory of inflation.

However, as we already pointed out, we find an internal contradiction,
in considering causality in
the framework of causal sets: an observer seems to be required for
consistency.

In fact presheaves (or varying sets on a causal set) obey the Heyting
algebra which implies the
intuitionistic logic [31-32], which in turn is related to the concept of
time flow. One can then
imagine a Boolean-minded observer who has to move in time [33], in order
to grasp the underlying
quantum logic of the universe.”

JS: Why a Boolean-minded observer? This is an error. While my motor
activity my body is Boolean, my inner consciousness is non-Boolean even
without psycho-active drugs.

PZ: “Obviously, this picture has no meaning at the Planck time, when
there was no observer at all. The above picture strictly depends on the
fact that in the theory of presheaves we consider Boolean sub-lattices
of the quantum lattice. To drop the Boolean observer, one should discard
Boolean sub-lattices and consider the entire quantum lattice as a whole,
endowed with a non-Boolean logic. However, we cannot get the Hilbert
space of the entire history, because of the existence of unitary
evolution operators among different Hilbert spaces. Thus, in order to
escape the "problem of the observer" we perform the tensor sum of all
the Hilbert spaces attached to the events of the causal set, and we get
a (bosonic) Fock space. Although we find that the logic associated with
the Fock space is Boolean, we are able to eliminate the observer at the
Planck scale by depriving him of time evolution. In fact, the Fock space
wave function Y , which is the coherent quantum superposition of all the
events (qubits), leads to an atemporal picture of the early universe.

The wavefunction Y is the coherent quantum state of multiple bosonic
qubits, and resembles a
Bose-Einstein condensate [34].”

JS: Only “resembles”? How about “is”? Like Feynman reading Dirac on the
Lagrangian in quantum theory.

PZ: “It can maintain coherence as far as thermal noise is absent, that
is, as far as inflation is running: a cosmological era when the universe
is cool and vacuum-dominated. We find that the coherent quantum state
decoheres at the end of inflation, giving rise to the (rather) low
entropy of our universe. In fact, the present entropy seems to be
related to the quantum information stored in Y , which was lost to the
emerging environment when thermal decoherence took place [35]. Only
after Y has decohered, one can in principle retrodict the quantum past
[36], "as" it was recorded by some ancient observer. It seems to us that
only in this sense causality can be "restored" at the Planck scale.”

JS: John Wheeler in his “Delayed Choice” “Law without law” “Universe as
a self-excited circuit” seems to invoke the “Once and Future”
“Observer-Participator”. So did Sir Fred Hoyle in “The Intelligent
Universe”.

PZ: This paper is organised as follows.
In Sect.2, we review the holographic conjecture by ’ t Hooft and
Susskind, and we interpret the
information stored on a boundary surface in terms of quantum bits rather
than classical bits.

In Sect.3, we illustrate the relation between spin networks that
puncture a boundary surface, and the
qubits stored on the surface.

In Sect.4, we put forward the mathematical formalism. We select the
subspace of un-entangled
symmetric qubits of the full 2 ^N-dimensional Hilbert space of N
qubits. We find that the symmetric
1-qubit acts as a creation operator in this subspace. Then the formalism
is applied to de Sitter
horizons, which are interpreted as qubits. This leads to an
interpretation of inflation in terms of
quantum information.

In Sect.5, we show how the vacuum (the classical bit) at the unphysical
time t=0, evolved to the 1-
qubit at the Planck time by passing through a quantum logic gate.

In Sect.6, we show that in this model a discrete micro-causality
emerges, where the time parameter
is given in terms of the discrete increase of entropy.

In Sect.7, we formalise our model within the framework of the theory of
presheaves. Qubits are
interpreted as events of a causal set, where the order relation is given
in terms of the entropy. We
get thus a quantum history which is the ensemble of all the
finite-dimensional Hilbert spaces of N qubits.

We find that the wavefunction of the entire history resembles a
Bose-Einstein condensate.

In Sect.8, we consider decoherence of the Bose-Einstein condensate. We
find that the rather low
value of the entropy of our present universe can be achieved only if the
wavefunction collapsed at
the end of inflation.

In Sect.9, we interpret the N-qubits as N quantum harmonic oscillators.
This allows us to find the
discrete energy spectrum, and in particular, the energy at the time when
inflation ended. This energy
is interpreted as the reheating temperature.”

JS: In my theory, a local macro-coherent vacuum order parameter survives.
The reheating is still tiny because matter is only 4% of all the stuff
in our at least
Tegmark “Level 1” Hubble bubble universe confined to our past light cone.
Gravity is from the phase ripples in this coherent order and dark
energy/matter
that is 96% of The Right Stuff of The World is from the amplitude
ripples in
this coherent order. The oil calming the waters.
This is Sarfatti’s decoding of “The Cipher of Genesis.”

This is Sarfatti’s decoding of “The Cipher of Genesis.”



Pure crap actually. Try stringing together a single sentence that makes
sense.