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**These are excerpts and elaborations from my book "The Nature of Consciousness"**

Loop Quantum Gravity The ultimate
goal of Loop Quantum Gravity (LQG) is still the "quantization" of
general relativity, but the way it approaches the problem is very different: it
is purely geometric. Roger Penrose
(“Applications of negative dimensional tensors “, 1971) toyed with the notion of a "spin network" (derived from
Louis Kauffman's "knot
theory") in an attempt to explain the structure of three-dimensional
space. A spin network is a graph whose edges are labeled by integers,
corresponding to the possible values of the angular momentum. Penrose sensed that these could be the simplest geometric structures to describe space. The revolutionary
assumption was that space and time are not primitive entities but are
themselves constructed out of something more primitive. In quantum terms, space
and time can fluctuate, as long as casual sequences are preserved. The Canadian
physicist Bill Unruh (“Notes on black-hole evaporation”, 1976)
discovered that an accelerating observer must measure a temperature (a
black-body radiation) where an inertial observer observes none, the temperature
being proportional to the acceleration.
You see vacuum in a field that is at rest with you where an accelerating observer sees a thermal bath.
This means that the very concept of
"vacuum" depends on the state of motion of the observer: an
accelerating observer will never observe any vacuum. (This also proved that
Einstein's principle of
equivalence was slightly incorrect: a constantly-accelerating observer and an
observer at rest in a gravitational field are not equivalent, as the former
would observe a temperature and the latter would not). Every accelerating
observer has a hidden region (all the photons that cannot reach her because she
keeps accelerating, getting closer and closer to the speed of light) and a
horizon (the boundary of her hidden region). Jakob Bekenstein’s theorem implies that every
horizon separating an observer from her hidden region has an entropy. That
entropy turns out to be proportional to the information that is hidden or
trapped in the hidden region (the missing information). According to Bekenstein's theorem, the entropy of the
radiation that the accelerated observer experiences is proportional to the area
of her horizon. Lee Smolin and the Italian physicist
Carlo Rovelli ("Knot theory and quantum gravity", 1988) put
Unruh and Bekenstein together and realized something that is built into any theory of
"quantum gravity" (into any quantization of relativity): the volumes
of regions in space must come in discrete units, just like energy comes in
discrete units. If energy comes in discrete units, then space must come in
discrete units. Just like matter is made of discrete particles, space itself
must be made of discrete units. A volume cannot be divided forever: there is an
elementary unit of volume. Smolin used
Bekenstein’s and Unruh’s theorems to prove that
spacetime must be discrete. If spacetime were continuous, then a volume of
spacetime (no matter how small) would contain an infinite amount of
information. But for any volume of spacetime an accelerating observer would
observe a finite entropy (finite because it is proportional to the surface of
the volume) and therefore a finite amount of missing information. The amount of
information is finite because the surface of the horizon is finite and
therefore entropy is finite. The amount of information within a volume of
spacetime must be finite, therefore spacetime cannot be continuous. Spacetime
must have an “atomic” structure just like matter has an atomic structure. (This
conclusion had been reached independently by Jacob Bekenstein in his studies on the thermodynamics of black holes). Kenneth Wilson had first hypothesized that
space was a discrete lattice (“Confinement of Quarks”, 1974). What Smolin did
was to make Wilson's discrete lattice also change dynamically, able to evolve
in time, as General Relativity requires. In his formulations the
inter-relationships among Wilson's structures (the "loops") define
space itself. Smolin used the work of two Indian scientists. Abhay Ashtekar (“New Variables for Classical
and Quantum Gravity “, 1986) came up with the "loop-space model",
based on a theory by Amitaba Sen (“Gravity as a Spin System”,
1982) that splits time and space into two distinct entities subject to quantum
uncertainty (analogous to momentum and position). The solutions of Einstein's equations would then be quantum states that resemble loops. Smolin's
theory was simply a theory of loops and how they interact and combine. (The
Uruguayan physicist Rodolfo Gambini had independently reached
similar conclusions). In this way
Einstein’s theory of
gravitation (General Relativity) is reformulated to resemble Maxwell's theory of electromagnetism,
with loops playing the role of field lines. Loop-quantum gravity has dramatic implications on cosmology. For example, the Big Bang turns out to be a “Big Bounce” from an imploding universe to an expanding universe. The world as we know it with all its galaxies, stars and moons was created by tiny ripples in spacetime (otherwise the universe would be a boring homogeneous lattice). The Big Bounce contains quantum fluctuations that would explain those tiny ripples and therefore our galaxy, sun, planet and, ultimately, myself typing these words. Ashtekar ("Quantum Nature of the Big Bang", 2006) showed that the Big Bang would not come from a singularity but from a previous universe: you canÎéÎ÷t retrace the universe all the way back because the contraction eventually causes a repulsive force that starts a new expansion. The Uruguayan physicists Rodolfo Gambini and Jorge Pullin reached a similar conclusion for a black hole: there is no singularity in the center of the black hole, but instead a tunnel to another space-time ("Loop Quantization of the Schwarzschild Black Hole", 2013). Loop-states
turned out to be best represented by Penrose's spin networks. The lines of a
spin network carry units of area. The structure of spin networks generates
space. The space that
we experience is continuous. Spin networks, instead, are discrete. They are graphs with edges labeled by spins
(that come in multiples of 0.5) and with three edges meeting at each
vertex. As these spin networks become
larger and more complex, they "yield" our ordinary, continuous,
smooth 3-dimensional space. A spin
network, therefore, "creates" geometry. It is not that a spin network
yields a metric (the metrics being what define the geometry of a region of
space) but that each vertex of a spin network creates the volume of a region of
space. An evolving spin
network (a "spin foam") is basically a discrete version of Einstein's spacetime. Spin-foams are
four-dimensional graphs that describe the quantum states of spacetime, just
like spin networks describe the quantum states of space. Spin foams describe
the quantum geometry of spacetime (not just space). A spin foam may be viewed
as a quantum history. Spacetime emerges as a quantum superposition of spin
foams (topologically speaking, it is a two-dimensional “complex”). The way spin
networks combine to form space is not clear, as there seems to be no
"natural law" (no equivalent of gravitation or of electromagnetism)
at work. Spin networks
"spontaneously" combine to form space. The formation of space
resembles the Darwinian process that creates order via natural selection of
self-organizing systems. Space appears
to be the result of spontaneous processes of self-organization à la Stuart
Kauffman. The hypothesis
that space is discrete also helps remove some undesired "infinites"
from Quantum Theory. For example, charged particles interact with one another
via electromagnetic fields. The electromagnetic field gets stronger as one gets
closer to the particle. But a particle has no size, so one can get infinitely
closer to it, which means that the field will get infinitely strong. If space
is discrete instead of continuous, the paradox is solved: there is a finite
limit to how close to a particle one can get. Spin networks
thus solve "quantum gravity" in three dimensions. Spin networks
describe the quantum geometry of space. In order to introduce the (fourth)
temporal dimension, a concept of “history” has been added by some researchers. Basically,
Einstein’s great
intuition is that spacetime is not just a stage but an actor in the story of
the universe, a story that evolves from its interaction with matter, and Loop
Quantum Gravity shows that it is made of its own atoms just like matter is made
of its own atoms. The US physicist
Martin Bojowald (“Loop Quantum Cosmology”, 2008) deduced that a true singularity
cannot exist, as each space atom can only contain a finite amount of
energy-matter. Therefore he revised Big Bang cosmology: the Big Bang was a
moment of maximum density that must have come from a previous Big Crunch. In
other words, the story of the universe should be roughly symmetric (or, better,
a mirror image) before and after the Big Bang: there was a collapsing universe
before the Big Bang created an expanding universe. The Greek
physicist Fotini Markopoulou showed that spin networks evolve in time in discrete steps: at
every step, the change of each vertex of the spin network only depends on its
immediate neighbors. This is reminiscent
of Von Neumann's cellular
automata and of algorithm-based thinking, as opposed to the traditional
formula-oriented thinking of Physics. Markopoulou ("The Internal Description of a Causal Set", 1999)
introduced causality in Loop Quantum Gravity.
In her view, time is not an illusion, just an approximation. She
compares it to the river that seems to flow in a smooth way even though the
motion of its water molecules is chaotic. Causality does exist at a very fundamental
level, although it may not be the one that we perceive in our daily life. The idea of Loop
Quantum Gravity was further expanded by Causal Dynamical Triangulation, a
theory introduced in the 1990s by Renate Loll (Dutch), Jan Ambjorn (Danish) and Jerzy Jurkiewicz (Polish) that constructs spacetime from elementary structures
called “four-simplexes”. A four-simplex is the four-dimensional equivalent of a
tetrahedron. Yet another
approach to quantum gravity is purely mathematical. For example, Markopoulou noticed similarities between the “categories” used by General
Relativity and those used by Quantum Theory. These have little in common with
the traditional category of Physics whose objects are sets and whose morphisms
are functions. In her view Quantum Theory is better understood as a theory of
spacetime. Back to the beginning of the chapter "The New Physics" | Back to the index of all chapters |