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Flash
from Deep Space: Supernews on Supernovas
At
a January, 1998 meeting of the American Astronomical Society, it was
announced that a survey of distant supernovae by an international
team of astronomers indicates that cosmic expansion is being
accelerated by an unknown repulsive force…a force that appears
strong enough to prevent gravity from collapsing the universe.
The
supernovae are of an extensively studied variety known as type
Ia. Type Ia
supernovae, which result from the explosion of certain white dwarf
stars, are so similar and steady in luminosity that they can be used
as standard candles,
or reliable measures of astral brightness. Because they
always shine with the same intrinsic intensity, it is possible to
infer their distances by the dimness of their light.
Distance can then be plotted against speed of recession as
calculated from frequency reductions due to cosmic redshift.
Such a plot turns out to be increasingly nonlinear as
distance increases, suggesting an unexpected acceleration.
Most
of those analyzing the data agree on the implications.
Because the observed supernovae are dimmer than would be
expected had the rate of cosmic expansion remained constant since
their parent stars exploded, expansion must have accelerated since
the supernovae were born, and some kind of accelerative force must
pervade the universe. As
early as February, 1998, an independent group calling itself the High-z
Supernova Search Team (z
means redshift) confirmed
this finding with a statistical confidence of 98.7-99.99%.
Since then, further observations have provided yet more
confirmation.
Among
the candidates for a repulsive force are Einstein’s cosmological
constant, representing a form of antigravity associated with
General Relativity, and quantum mechanical vacuum
energy, which produces outward pressure through the spontaneous
creation and annihilation of virtual particle-antiparticle pairs.
Also receiving welcome air time are more bizarre ideas like X-matter
and quintessence, strange
forms of background energy that might be produced by mysterious
physical processes as yet unidentified.
In
the minds of most theorists, the best bet is a combination of
cosmological constant and vacuum energy.
That would deliver the steady effect that has been observed,
as opposed to the fluctuations that might accompany X-matter and
quintessence. Unfortunately,
none of the experts can give a constructive reason for why any of
these influences should themselves exist.
No conventional theory incorporating the Standard Big Bang
Model of cosmology can explain why an expansive force should be
evident or how it might have originated.
However,
an alternative theory does exist.
It is virtually unknown to most physicists, whose stock
repertoire is limited to theories that have been published by other
physicists in exclusive scholastic journals unreceptive to strange
new ideas emanating from unknown, academically uncredentialed
sources. It has,
however, been published for a highly intelligent readership in a
journal called Noesis.
This theory is called the CTMU.
Although Noesis is
not, strictly speaking, a peer-reviewed journal, the CTMU has been
extensively criticized and defended within it over the last decade
on the basis of published descriptions.
The
CTMU is not an ordinary physical theory.
Instead of being just another system of ad
hoc equations purporting to describe some limited aspect of the
physical universe, it has a unique logical structure designed to
embed the very foundations of mathematics and philosophy.
Yet, unlike many predominantly rationalistic theories, it is
designed to resolve paradox on both rational and observational
levels, and thus makes verifiable statements regarding the nature of
observable reality. Some
of these statements, which range in application from quantum physics
to cosmology, relate to cosmic expansion.
To
query the universe regarding its true nature is to ask a very deep
question. There was
always a strange and touching mixture of humility and hubris in the
idea that physicists could obtain an answer to this question simply
by looking through their instruments and carefully describing what
they saw. After all,
reality contains features like mind,
cognition and
consciousness that do not lend themselves to empirical
techniques or scientific reductionism.
Yet, they are basic, unavoidable ingredients of every
scientific measurement ever performed and every theoretical
explanation ever devised. Without
conscious minds subjecting reality to cognition, science could not
exist.
The
CTMU provides physics and cosmology with a logical framework that
incorporates these missing ingredients in a way reflecting the
nature of their involvement in measurement and theorization.
And as a bonus, it does what no other theory can: while
painlessly absorbing the bulk of modern physical science and
resolving many of its most stubborn and destructive paradoxes, it
coherently explains the cosmological implications of the evidence
for accelerative recession of type Ia supernovae in the context of a
self-contained, self-creating universe.
Physics
and Metaphysics
(© 1998 - 2002 by C.M. Langan)
Today
: Metaphysics :: Tomorrow : Physics
Today’s
dominant theory of small-scale physics, quantum
mechanics, did not begin its long and successful run as a
physical theory. The
reason is logical; its major premise, the Heisenberg
Uncertainty Principle, sets absolute limits on the accuracy to
which quanta can be measured, and cursory logical analysis reveals
that this defines a relation between measurer and measured object
that cannot be expressed in a language describing measured objects
alone. Since classical
physics was the latter kind of language, neither the uncertainty
principle nor quantum mechanics could be immediately classified as
“physics”. Rather,
they belonged to a logical metalanguage of physics called metaphysics.
Indeed, even at a time when physics routinely explains what
the ancients would have seen as “magic”, some physicists view
quantum mechanics with a touch of uneasy skepticism.
The reason: it raises too many metaphysical-looking issues
without satisfactorily resolving them.
Relativity
too was initially a metaphysical theory based on the formation of
higher-order predicates, spacetime
and spacetime curvature,
that had not existed in physics, drawing in the interests of
self-containment a higher-order causal relationship between the
fundamental physical parameters space,
time and matter on a
combination of empirical and mathematical grounds (a higher-order
relation is a relation of relations…of relations of primitive
objects, defined at the appropriate level of predicate logic).
Since this describes a semantic operation that cannot be
effected within the bare language of physics as it existed at the
time, relativity was metaphysical rather than physical in nature.
Nevertheless, it achieved quick recognition as a physical
theory…not only because Einstein was already recognized as a
professional physicist, but because it made physical predictions
that classical physics alone did not make.
It
was recognized long before Einstein that observations of physical
objects vary subjectively in certain parameters.
For example, although objects are identical when viewed under
identical conditions, they vary in size when viewed from different
distances, display different shapes from different angles, and seem
to be differently colored and shaded under different lighting
conditions. Einstein
expanded the range of subjective variation of physical phenomena by
showing that objects also look different when viewed at different relative
velocities. But in
keeping with classical objectivism, he showed in the process that
such perceptual variations were a matter of objective circumstance,
in effect treating perception itself as an objective phenomenon.
Because this kind of empirical objectivization is exactly
what is expected of the objective empirical science of physics,
attention was diverted from nagging metaphysical questions involving
the interplay of rational and empirical factors in perception.
Although
he never got around to enunciating it, Einstein may well have sensed
that perception cannot be understood without understanding the logic
of this interplay, and that this logic is instrumental to the
inherently metaphysical operation of theoretical unification.
Nevertheless, perhaps encouraged by his own apparent success
in sidestepping this particular metaphysical issue, he spent the
second half of his career on a doomed attempt to unify physics in a
purely physical context - that is, in the context of a spacetime
model which went only as far as Relativity Theory.
Since then, many bright and well-educated people have
repeated roughly the same error, never realizing that physical
theory truly advances only by absorbing profoundly creative
metaphysical extensions on which no ordinary physicist would
wittingly sign off.
Like
quantum mechanics and the Theory of Relativity, the CTMU is a
metaphysical theory that makes distinctive predictions and
retrodictions not made by previous theories.
However, the CTMU makes no attempt in the process to sidestep
difficult metaphysical issues.
For example, Einstein introduced the cosmological constant to
stabilize the size of the universe, but then dropped it on the
empirical grounds of apparent universal expansion.
In contrast, the CTMU goes beyond empiricism to the rational
machinery of perception itself, providing cosmic expansion with a
logical basis while predicting and explaining some of its features.
Relativity pursues the goal of explanatory self-containment
up to a point; spacetime contains matter and energy that cause
spacetime fluctuations that cause changes in matter and energy.
The CTMU, on the other hand, pursues the goal of
self-containment all the way up to cosmogenesis.
And while neither GR nor QM does anything to resolve the
fatal paradoxes of ex nihilo
creation and quantum nonlocality, the CTMU dissolves such paradoxes
with a degree of logical rectitude to which science seldom aspires.
To
understand how the CTMU is a natural extension of modern physics,
let us review the history of the physicist’s and cosmologist’s
art in the context of Cartesian coordinate systems.
The
Cartesian Architecture of Split-Level Reality
Modern
physics is based on, and can be described as the evolution of,
rectilinear coordinate systems.
Called Cartesian
coordinate systems
after their leading exponent, René
Descartes, they are particularly well-suited to the objective
modeling of physical phenomena, that is, to the algebraic
representation of static and dynamic relationships without respect
to their locations or the special vantages from which they are
observed or considered. This
property of Cartesian spaces relates directly to another invention
of Monsieur Descartes called mind-body
dualism, which merely states in plain language what Cartesian
coordinate systems seem to graphically depict: namely, that
cognition and physical reality can be factored apart at our
philosophical and scientific convenience.
Since
the time of Descartes, there have been numerous attempts to clarify
the exact relationship between mind and reality and thereby solve
the "mind-body problem".
Hume, for example, held that reality consists exclusively of sense
impressions from which concepts like “mind” and “matter”
are artificially abstracted. Kant
countered with the view that the mind knows deep reality only
through cryptic impressions molded to its own cognitive
categories. More
recently, Lewes’ dual-aspect
monism maintained that reality consists of a neutral substance
of which mind and body are just complementary aspects,
while the mind-stuff theory
of Clifford and Prince was a form of psychical monism positing that
mind is the ultimate reality, that ordinary material reality is
simply mind apprehended by mind, and that the higher functions of
mind emerge from smaller pieces of mind that do not of themselves
possess higher mental attributes (an idea previously attributable to
Leibniz, Spencer and others).
But
while each of these theories contains a part of the truth, none
contains the whole truth.
Only recently have the parts been assembled in light of
modern logic and science to create a dynamic, comprehensive theory
of reality that solves the mind-body problem for good.
Classical
Mechanics: The Infinitesimal Worm in Newton’s Apple
The
next big representational advance in physics, Newtonian mechanics,
relied on a new kind of analytic geometry based on vector
modeling and vector
analysis of physical motion in Cartesian coordinate systems in
which space and time are represented as independent (orthogonal)
axes. Its Langrangian
and Hamiltonian formulations
occupy the same mathematical setting.
From the beginning, the featureless neutrality of Cartesian
space accorded well with the evident nonpreference of physical laws
for special coordinate systems…i.e., for the homogeneity and
isotropy of space and time. However,
this property of Cartesian spaces also rendered position and motion
completely relative in
the Galilean sense. Finding
that this made it hard to explain certain physical phenomena - e.g.,
inertia, and later on, electromagnetic wave propagation - Newton and
his followers embraced the concept of a stationary
aether against whose background all dimensions, durations and
velocities were considered to be fixed.
The aether was an unusual kind of “field” over which the
center of mass of the universe was perfectly distributed, explaining
not only inertia but the evident fact that all of the matter in the
universe was not gravitating toward a central point in space.
In
order to work with his vector model of physical reality, Newton had
to invent a new kind of mathematical analysis known as infinitesimal
calculus. Specifically,
he was forced in calculating the velocity of an object at each point
of its trajectory to define its “instantaneous rate of change”
as a ratio of "infinitesimal" vectors whose lengths were
“smaller than any finite quantity, but greater than zero”.
Since this is a paradoxical description that does not
meaningfully translate into an actual value – the only number
usually considered to be smaller than any finite quantity is 0 - it
is hard to regard infinitesimal vectors as meaningful objects.
But even though they could not give a satisfactory account of
infinitesimal vectors, post-Newtonian physicists at least knew where
such vectors were located: in the same Cartesian space containing
ordinary finite vectors.
Better yet, the celebrated mathematician Gauss discovered
that they could be confined within the curves to which they were
tangential, an insight developed by Riemann into a comprehensive
theory of differential
geometry valid for curved surfaces in any number of dimensions.
However, although differential geometry would later prove
useful in formulating a generalization of Cartesian space, its
“intrinsic” nature did not resolve the paradox of
infinitesimals.
For
many years after Newton, mathematicians struggled to find a way
around the infinitesimals paradox, first lighting on the Weierstrass
epsilon-delta formalism purporting to characterize infinitesimals
within standard Cartesian space.
But later – in fact, years after Newtonian mechanics was
superseded by a more general theory of physics – they finally
satisfied their yearning to understand infinitesimals as timeless
mathematical objects.
They accomplished this by reposing them in a hypothetical nonstandard
universe where each point of the standard universe is surrounded
by a nonstandard neighborhood containing infinitesimal objects (in
logic, a theory is justified by demonstrating the existence of a model
for which it is true; as a model of infinitesimals and their
relationships with finite numbers, the nonstandard universe
justifies the infinitesimal calculus).
Ignoring the obvious fact that this could have a metaphysical
bearing on physical reality, mathematicians took the nonstandard
universe and carried it off in the purely abstract direction of nonstandard
analysis.
Quantum
Mechanics: Space and Time Get Smeared (and Worse)
After
standing for over two centuries as the last word in physics, the
differential equations comprising the deterministic laws of
Newtonian mechanics began to run into problems.
One of these problems was called the Heisenberg
Uncertainty Principle or HUP.
The HUP has the effect of “blurring” space and time on
very small scales by making it impossible to simultaneously measure
with accuracy certain pairs of attributes of a particle of matter or
packet of energy. Because
of this blurring, Newton’s differential equations are insufficient
to describe small-scale interactions of matter and energy.
Therefore, in order to adapt the equations of classical
mechanics to the nondeterministic, dualistic (wave-versus-particle)
nature of matter and energy, the more or less ad
hoc theory of quantum mechanics (QM)
was hastily developed. QM
identifies matter quanta with “probability waves” existing in ¥-dimensional
complex Hilbert space, a
Cartesian space defined over the field of complex numbers a+bi
(where a and b are real numbers and i = Ö-1)
instead of the pure real numbers, and replaces Hamilton’s
classical equations of motion with Schrodinger’s wave
equation. QM
spelled the beginning of the end for Laplacian determinism, a
philosophical outgrowth of Newtonianism which held that any temporal
state of the universe could be fully predicted from a complete
Cartesian description of any other.
Not only uncertainty but freedom
had reentered the physical arena
Unfortunately,
the HUP was not the only quantum-mechanical problem for classical
physics and its offshoots. Even
worse was a phenomenon called EPR
(Einstein-Podolsky-Rosen) nonlocality, according to which the
conservation of certain physical quantities for pairs of correlated
particles seems to require that information be instantaneously
transmitted between them regardless of their distance from each
other. The EPR paradox
juxtaposes nonlocality to the conventional dynamical scenario in
which anything transmitted between locations must move through a
finite sequence of intervening positions in space and time.
So basic is this scenario to the classical worldview that EPR
nonlocality seems to hang over it like a Damoclean sword, poised to
sunder it like a melon. Not
only does no standard physical theory incorporating common notions
of realism, induction and locality contain a resolution of this
paradox - this much we know from a mathematical result called Bell's
theorem - but it seems that the very foundations of physical
science must give way before a resolution can even be attempted!
The
Special Theory of Relativity: Space and Time Beget Spacetime
Another
problem for Newton’s worldview was the invariance of c,
the speed of light in vacuo.
Emerging from Maxwell’s equations and direct
experimentation (e.g., Michelson-Morley), c-invariance defies
representation in an ordinary Cartesian vectorspace.
Einstein’s Special
Theory of Relativity (SR),
arising at about the same time as quantum mechanics, was designed to
fill the breach. To
accomplish this, Einstein had to generalize Cartesian space in such
a way that distances and durations vary with respect to distinct
coordinate systems associated with various states of relative
motion. The particular
generalization of Cartesian space in which these motion-dependent
coordinate systems are related, and in which the velocity of light
can be invariantly depicted, is called Minkowski
spacetime. In
spacetime, space and time axes remain perpendicular but no longer
represent independent dimensions.
Instead, spacelike and timelike domains are separated by null
or lightlike geodesics
(minimal trajectories) representing the "paths" traced by
light, and the constant velocity of light is represented by the
constant (usually 45°)
orientation of the corresponding spacetime vectors.
The space and time axes of moving coordinate systems are
skewed by the Lorentz
transformation functions according to their relative angles of
propagation (velocities) through timelike domains, resulting in
relative distortions of space and time vectors between systems.
General
Relativity: Spacetime Develops Curvature
Flat
or Euclidean
spacetime suffices for the representation of all kinds of
physical motion up to constant linear acceleration.
However, gravity – which Newton had regarded as a force and
represented as an ordinary Cartesian vector – causes other kinds
of motion as well, e.g. orbital motion.
So in order to generalize Minkowski spacetime to explain
gravity, Einstein had to undertake a further generalization of
Cartesian space accommodating non-flat or curved
spacetime. In this
generalization of Cartesian space, spacetime curvature is
represented by algebraically well-behaved generalizations of vectors
called tensors, which are
just mathematical functions that take ordinary spacetime vectors as
input and yield other vectors (or numbers) as output.
Calculating these entities can be as exacting and tedious as
counting sand grains, but they are mathematically straightforward.
By modeling physical reality as a curved tensor manifold,
Einstein was able to explain how gravity affects motion and thus to
create the gravitational extension of Special Relativity known as General
Relativity or GR.
While the gravitational calculations of GR match those of
classical mechanics under most conditions, experiment favors GR
decisively in certain situations.
Although
GR is based on differential geometry intrinsic to curved surfaces
– geometry in which one need never leave a surface in order to
determine its properties – distances and curvatures are ultimately
expressed in terms of minute spatiotemporal vectors or "line
elements" which must be made infinitesimal to ensure that they
never leave the "surface" of spacetime.
Thus, GR avoids the mensural necessity of an external
hyperspace only by inheriting Newton’s infinitesimals paradox.
Since GR, like classical mechanics, treats these line
elements as objects to be
used in forming ratios and tensors, it requires an
"object-oriented" (as
opposed to a Weierstrass-style procedural) definition of
infinitesimals. But
such a definition requires a nonstandard universe on model-theoretic
grounds. So GR depends
on a nonstandard universe as much as its predecessors, and is not as
self-contained as the concept of intrinsic curvature might lead one
to expect.
Strictly
speaking, Newtonian mechanics and all subsequent theories of physics
require a nonstandard universe, i.e. a model that supports the
existence of infinitesimals, for their formulation.
The effect of this requirement is to blur the distinction
between physics, which
purports to limit itself to the standard universe of measurable
distances, and metaphysics,
which can describe the standard universe as embedded in a
higher-dimensional space or a nonstandard universe containing
infinitesimals. The
fast acceptance of GR as a "physical" theory thus owed at
least in part to the fact that physicists had already learned to
swallow the infinitesimals paradox every time they used the
infinitesimal calculus to do classical mechanics!
Only much later, with the advent of an infocognitive
spacetime internally accommodating necessary metaphysical
self-extensions, could the infinitesimal line elements of GR be
properly embedded in a neoCartesian model of reality as abstract
ingredients of certain distributed computations (see Appendix
A).
The
moral of the story up to this point is abundantly clear: both before
and after Newton, the greatest advances in physics have come through
the creation and absorption of metaphysical extensions.
Unfortunately, most physicists are sufficiently unclear on
this fact that the word “metaphysics” remains all but
unmentionable in their deliberations.
But
change finds a way.
The
Search for a Unified Field: Spacetime Gains New Dimensions
Having
found so satisfying a mathematical setting for gravitation, Einstein
next tried to create a Unified
Field Theory (UFT)
by using the same model to explain all of the fundamental forces of
nature, two of which, electricity and magnetism, had already been
unified by Maxwell as electromagnetism
or EM for short
As a natural first step, Einstein tried to formulate the EM
force as a tensor. Unfortunately,
EM force is governed by quantum mechanics, and 4-dimensional GR
tensors lack intrinsic quantum properties.
This alone limits General Relativity to a calculational
rather than explanatory bearing on electromagnetism.
Because the branch of quantum mechanics called quantum
electrodynamics (QED), which treats the EM force as a particle
interchange, better explained the properties and dynamics of
electrons and electromagnetic fields, Einstein’s geometrodynamic
approach to the UFT was widely abandoned.
After
a time, however, the trek was resumed.
Kaluza-Klein
theory had already added an extra dimension to spacetime and
curled it up into a tight little loop of radius equal to the Planck
length (10-33 cm, far smaller than any known particle).
This curling maneuver explained more than the extra
dimension’s invisibility; because only a discrete number of waves
can fit around a loop, it also seemed to explain why particle
energies are quantized,
and thus to provide a connection between relativity theory and QM
(in 1921, Kaluza observed that light could be viewed as the product
of fifth-dimensional vibrations).
Though temporarily forgotten, this idea was ultimately
revived in connection with supersymmetry,
an attempt to unify the fundamental forces of nature in a single
theory by defining GR-style tensors accommodating 7 additional
spacetime dimensions. Shortened
and rolled up in bizarre topological configurations, these
dimensions would exhibit fundamental frequencies and quantized
harmonics resembling the quantum properties of tiny particles of
matter.
Although
supersymmetry was eventually dropped because its 11-dimensional
structure failed to explain subatomic chirality (whereby nature
distinguishes between right- and left-handedness), its basic
premises lived on in the form of 10-dimensional superstring
theory. Again, the
basic idea was to add additional dimensions to GR, slice and splice
these extra dimensions in such a way that they manifest the basic
features of quantum mechanics, and develop the implications in the
context of a series of Big Bang phase transitions (“broken
symmetries”) in which matter changes form as the hot early
universe cools down (mathematically, these phase transitions are
represented by the arrows in the series GàHà…àSU(3)
x SU(2) x U(1)àSU(3)
x U(1), where alphanumerics represent algebraic symmetry
groups describing the behavioral regularities of different kinds
of matter under the influence of different forces, and gravity is
mysteriously missing)
Unfortunately,
just as General Relativity did nothing to explain the origin of 4-D
spacetime or its evident propensity to “expand” when there would
seem to be nothing for it to expand into,
string theory did nothing to explain the origin or meaning of the
n-dimensional strings into which spacetime had evolved.
Nor did it even uniquely or manageably characterize
higher-dimensional spacetime structure; it required the same kind of
nonstandard universe that was missing from GR in order to properly
formulate quantum-scale dimensional curling, and eventually broke
down into five (5) incompatible versions all relying on difficult
and ill-connected kinds of mathematics that made even the simplest
calculations, and extracting even the most basic physical
predictions, virtually impossible.
Worse yet, it was an unstratified low-order theory too weak
to accommodate an explanation for quantum nonlocality or measurable
cosmic expansion.
Recently,
string theory has been absorbed by a jury-rigged patchwork called
“membrane theory” or M-theory
whose basic entity is a p-dimensional object called, one might
almost suspect eponymically, a “p-brane” (no, this is not a
joke). P-branes display
mathematical properties called S-
and T-duality which
combine in a yet-higher-level duality called the
Duality of Dualities (again, this is not a joke) that suggests a
reciprocity between particle size and energy that could eventually
link the largest and smallest scales of the universe, and thus
realize the dream of uniting large-scale physics (GR) with
small-scale physics (QM).
In some respects, this is a promising insight; it applies
broad logical properties of theories (e.g., duality) to what the
theories “objectively” describe, thus linking reality in a
deeper way to the mental process of theorization.
At the same time, the “membranes” or “bubbles” that
replace strings in this theory more readily lend themselves to
certain constructive interpretations.
But
in other ways, M-theory is just the same old lemon with a new coat
of paint. Whether the
basic objects of such theories are called strings, p-branes or
bubble-branes, they lack sufficient structure and context to explain
their own origins or cosmological implications, and are utterly
helpless to resolve physical and cosmological paradoxes like quantum
nonlocality and ex nihilo
(something-from-nothing) cosmogony… paradoxes next to which the
paradoxes of broken symmetry “resolved” by such theories
resemble the unsightly warts on the nose of a charging rhinoceros.
In short, such entities sometimes tend to look to those
unschooled in their virtues like mathematical physics run wildly and
expensively amok.
Alas,
the truth is somewhat worse. Although
physics has reached the point at which it can no longer credibly
deny the importance of metaphysical criteria, it resists further
metaphysical extension. Instead of acknowledging and dealing
straightforwardly with its metaphysical dimension, it mislabels
metaphysical issues as “scientific” issues and festoons them
with increasingly arcane kinds of mathematics that hide its
confusion regarding the underlying logic.
Like a social climber determined to conceal her bohemian
roots, it pretends that it is still dealing directly with observable
reality instead of brachiating up vertiginous rationalistic
tightropes towards abstractions that, while sometimes indirectly
confirmed, are no more directly observable than fairies and
unicorns. And as
science willfully distracts itself from the urgent metaphysical
questions it most needs to answer, philosophy ignores its parental
responsibility.
Reality
as a Cellular Automaton: Spacetime Trades Curves for Computation
At
the dawn of the computer era, the scientific mainstream sprouted a
timely alternative viewpoint in the form of the Cellular
Automaton Model of the Universe, which we hereby abbreviate as
the CAMU.
First suggested by mathematician John von Neumann and later
resurrected by salesman and computer scientist Ed Fredkin, the CAMU
represents a conceptual regression of spacetime in which space and
time are re-separated and described in the context of a cellular
automaton. Concisely,
space is represented by (e.g.) a rectilinear array of computational
cells, and time by a perfectly distributed state transformation rule
uniformly governing cellular behavior.
Because automata and computational procedures are inherently
quantized, this leads to a natural quantization of space and time.
Yet another apparent benefit of the CAMU is that if it can be
made equivalent to a universal computer, then by definition it can
realistically simulate anything that a consistent and continually
evolving physical theory might call for, at least on the scale of
its own universality.
But
the CAMU, which many complexity theorists and their sympathizers in
the physics community have taken quite seriously, places problematic
constraints on universality. E.g.,
it is not universal on all computational scales, does not allow for
subjective cognition except as an emergent property of its
(assumedly objective) dynamic, and turns out to be an unmitigated
failure when it comes to accounting for relativistic phenomena.
Moreover, it cannot account for the origin of its own
cellular array and is therefore severely handicapped from the
standpoint of cosmology, which seeks to explain not only the
composition but the origin of the universe.
Although the CAMU array can internally accommodate the
simulations of many physical observables, thus allowing the CAMU’s
proponents to intriguingly describe the universe as a
“self-simulation”, its inability to simulate the
array itself precludes the adequate representation of
higher-order physical predicates with a self-referential dimension.
Reality
as Reality Theory:
Spacetime Turns Introspective
Now
let us backtrack to the first part of this history, the part in
which René Descartes
physically objectivized Cartesian spaces in keeping with his thesis
of mind-body dualism. Notice
that all of the above models sustain the mind-body distinction to
the extent that cognition is regarded as an incidental side effect
or irrelevant epiphenomenon of objective laws; cognition is
secondary even where space and time are considered non-independent.
Yet not only is any theory meaningless in the absence of
cognition, but the all-important theories of relativity and quantum
mechanics, without benefit of explicit logical justification, both
invoke higher-level constraints which determine the form or content
of dynamical entities according to properties not of their own, but
of entities that measure or interact with them.
Because these higher-level constraints are cognitive
in a generalized sense, GR and QM require a joint theoretical
framework in which generalized cognition is a distributed feature of
reality.
Let’s
try to see this another way. In
the standard objectivist view, the universe
gives rise to a theorist
who gives rise to a theory
of the universe. Thus,
while the universe creates the theory by way of a theorist, it is
not beholden to the possibly mistaken theory that results.
But while this is true as far as it goes, it cannot account
for how the universe itself is created.
To fill this gap, the CTMU Metaphysical
Autology Principle or MAP
states that because reality
is an all-inclusive relation bound by a universal quantifier whose
scope is unlimited up to relevance, there is nothing external to
reality with sufficient relevance to have formed it; hence, the real
universe must be self-configuring.
And the Mind-Equals-Reality
(M=R) Principle says
that because the universe alone can provide the plan or syntax
of its own self-creation, it is an "infocognitive" entity
loosely analogous to a theorist in the process of introspective
analysis. Unfortunately,
since objectivist theories contain no room for these basic aspects
of reality, they lack the expressive power to fully satisfy
relativistic, cosmological or quantum-mechanical criteria. The
ubiquity of this shortcoming reflects the absence of a necessary and
fundamental logical feature of physical analysis, a higher order of
theorization in which theory
cognitively distributes over theory, for which no conventional
theory satisfactorily accounts.
In
view of the vicious paradoxes to which this failing has led, it is
only natural to ask whether there exists a generalization of
spacetime that contains the missing self-referential dimension of
physics. The answer, of
course, is that one must exist, and any generalization that
is comprehensive in an explanatory sense must explain why.
In Noesis/ECE 139,
the SCSPL paradigm of the CTMU was described to just this level of
detail. Space and time
were respectively identified as generalizations of information and
cognition, and spacetime was described as a homogeneous
self-referential medium called infocognition
that evolves in a process called conspansion.
Conspansive spacetime is defined to incorporate the
fundamental concepts of GR and QM in a simple and direct way that
effectively preempts the paradoxes left unresolved by either theory
alone. Conspansive
spacetime not only incorporates non-independent space and time axes,
but logically absorbs the cognitive processes of the theorist
regarding it. Since this includes any kind of theorist
cognitively addressing any aspect of reality, scientific or
otherwise, the CTMU offers an additional benefit of great promise to
scientists and nonscientists alike: it naturally conduces to a
unification of scientific and nonscientific (e.g. humanistic,
artistic and religious) thought.
CTMU
>> CAMU in Camo
Before
we explore the conspansive SCSPL model in more detail, it is
worthwhile to note that the CTMU can be regarded as a generalization
of the major computation-theoretic current in physics, the CAMU.
Originally called the Computation-Theoretic
Model of the Universe, the CTMU was initially defined on a
hierarchical nesting of universal computers, the Nested
Simulation Tableau or NeST,
which tentatively described spacetime as stratified
virtual reality in order to resolve a decision-theoretic paradox
put forth by Los Alamos physicist William Newcomb (see Noesis
44, etc.). Newcomb’s
paradox is essentially a paradox of reverse causality with strong
implications for the existence of free will, and thus has deep
ramifications regarding the nature of time in self-configuring or
self-creating systems of the kind that MAP shows it must be.
Concisely, it permits reality to freely create itself from
within by using its own structure, without benefit of any outside
agency residing in any external domain.
Although
the CTMU subjects NeST to metalogical constraints not discussed in
connection with Newcomb’s Paradox, NeST-style computational
stratification is essential to the structure of conspansive
spacetime. The CTMU
thus absorbs the greatest strengths of the CAMU – those attending
quantized distributed computation – without absorbing its a
priori constraints on scale or sacrificing the invaluable legacy
of Relativity. That is,
because the extended CTMU definition of spacetime incorporates a
self-referential, self-distributed, self-scaling universal
automaton, the tensors of GR and its many-dimensional offshoots can
exist within its computational matrix.
An
important detail must be noted regarding the distinction between the
CAMU and CTMU. By its nature, the CTMU replaces ordinary
mechanical computation with what might better be called protocomputation.
Whereas computation is a process defined with respect to a specific
machine model, e.g. a Turing machine, protocomputation is logically
"pre-mechanical". That is, before computation can
occur, there must (in principle) be a physically realizable machine
to host it. But in discussing the origins of the physical
universe, the prior existence of a physical machine cannot be
assumed. Instead, we must consider a process capable of giving
rise to physical reality itself...a process capable of not only
implementing a computational syntax, but of serving as its own
computational syntax by self-filtration from a realm of syntactic
potential. When the word "computation"
appears in the CTMU, it is usually to protocomputation that
reference is being made.
It
is at this point that the theory of languages becomes indispensable.
In the theory of computation, a "language" is anything fed
to and processed by a computer; thus, if we imagine that reality is
in certain respects like a computer simulation, it is a language.
But where no computer exists (because there is not yet a universe in
which it can exist), there is no "hardware" to
process the language, or for that matter the metalanguage simulating
the creation of hardware and language themselves. So with
respect to the origin of the universe, language and hardware must
somehow emerge as one; instead of engaging in a chicken-or-egg
regress involving their recursive relationship, we must consider a
self-contained, dual-aspect entity functioning simultaneously as
both. By definition, this entity is a Self-Configuring
Self-Processing Language or SCSPL. Whereas ordinary
computation involves a language, protocomputation involves SCSPL.
Protocomputation
has a projective character consistent with the SCSPL paradigm.
Just as all possible formations in a language - the set of all
possible strings - can be generated from a single distributed
syntax, and all grammatical transformations of a given string can be
generated from a single copy thereof, all predicates involving a
common syntactic component are generated from the integral component
itself. Rather than saying that the common component is
distributed over many values of some differential predicate - e.g.,
that some distributed feature of programming is distributed over
many processors - we can say (to some extent equivalently) that many
values of the differential predicate - e.g. spatial location - are
internally or endomorphically projected within the common
component, with respect to which they are "in
superposition". After all, difference or multiplicity is
a logical relation, and logical relations possess logical coherence
or unity; where the relation has logical priority over the reland,
unity has priority over multiplicity. So instead of putting
multiplicity before unity and pluralism ahead of monism, CTMU
protocomputation, under the mandate of a third CTMU principle called
Multiplex Unity or MU, puts the horse sensibly ahead
of the cart.
To
return to one of the central themes of this article, SCSPL and
protocomputation are metaphysical concepts. Physics is
unnecessary to explain them, but they are necessary to explain
physics. So again, what we are describing here is a
metaphysical extension of the language of physics. Without
such an extension linking the physical universe to the ontological
substrate from which it springs - explaining what physical reality
is, where it came from, and how and why it exists - the explanatory
regress of physical science would ultimately lead to the
inexplicable and thus to the meaningless.
Spacetime
Requantization and the Cosmological Constant
The
CTMU, and to a lesser extent GR itself, posits certain limitations
on exterior measurement. GR
utilizes (so-called) intrinsic spacetime curvature in order to avoid
the necessity of explaining an external metaphysical domain from
which spacetime can be measured, while MAP
simply states, in a more sophisticated way consistent with
infocognitive spacetime structure as prescribed by M=R
and MU, that this is a
matter of logical necessity (see Noesis/ECE
139, pp. 3-10). Concisely,
if there were such an exterior domain, then it would be an
autologous extrapolation of the Human
Cognitive Syntax (HCS)
that should properly be included in the spacetime to be measured.
[As previously explained, the HCS, a synopsis of the most
general theoretical language available to the human mind
(cognition), is a supertautological formulation of reality as
recognized by the HCS.
Where CTMU spacetime consists of HCS infocognition
distributed over itself in a way isomorphic to NeST – i.e., of a
stratified NeST computer whose levels have infocognitive HCS
structure – the HCS spans the laws of mind and nature.
If something cannot be mapped to HCS categories by acts of
cognition, perception or reference, then it is HCS-unrecognizable
and excluded from HCS reality due to nonhomomorphism; conversely, if
it can be mapped to the
HCS in a physically-relevant way, then it is real
and must be explained by reality theory.]
Accordingly,
the universe as a whole must be treated as a static domain whose
self and contents cannot “expand”, but only seem
to expand because they are undergoing internal rescaling as a
function of SCSPL grammar. The
universe is not actually expanding in any absolute,
externally-measurable sense; rather, its contents are shrinking
relative to it, and to maintain local geometric and dynamical
consistency, it appears to expand relative to them.
Already introduced as conspansion
(contraction qua
expansion), this process reduces physical change to a form of
"grammatical substitution" in which the geometrodynamic
state of a spatial relation is differentially expressed within an
ambient cognitive image of its previous state. By running this
scenario backwards and regressing through time, we eventually arrive
at the source of geometrodynamic and quantum-theoretic reality: a
primeval conspansive domain consisting of pure physical potential
embodied in the self-distributed "infocognitive syntax" of
the physical universe…i.e., the laws of physics, which in turn
reside in the more general HCS.
Conspansion
consists of two complementary processes, requantization
and inner expansion.
Requantization downsizes the content of Planck’s constant by applying a quantized
scaling factor to successive layers of space corresponding to levels
of distributed parallel computation.
This inverse scaling
factor 1/R is just the reciprocal of the cosmological
scaling factor R, the ratio of the current apparent size dn(U)
of the expanding universe to its original (Higgs condensation) size
d0(U)=1. Meanwhile,
inner expansion outwardly distributes the images of past events at
the speed of light within progressively-requantized layers.
As layers are rescaled, the rate of inner expansion, and the
speed and wavelength of light, change with respect to d0(U)
so that relationships among basic physical processes do not
change…i.e., so as to effect nomological covariance.
The thrust is to relativize
space and time measurements so that spatial relations have different
diameters and rates of diametric change from different spacetime
vantages. This merely continues a long tradition in physics; just as
Galileo relativized motion and Einstein relativized distances and
durations to explain gravity, this is a relativization for
conspansive “antigravity” (see Appendix
B).
Conspansion
is not just a physical operation, but a logical one as well.
Because physical objects unambiguously maintain their
identities and physical properties as spacetime evolves, spacetime
must directly obey the rules of 2VL (2-valued
logic distinguishing what is true from what is false).
Spacetime evolution can thus be straightforwardly depicted by
Venn diagrams in which the truth attribute, a high-order
metapredicate of any physical predicate, corresponds to topological
inclusion in a spatial domain corresponding to specific physical
attributes. I.e., to be
true, an effect must be not only logically but topologically
contained by the cause; to inherit properties determined by an
antecedent event, objects involved in consequent events must appear
within its logical and
spatiotemporal image. In short, logic equals spacetime
topology.
This
2VL rule, which governs the relationship between the Space-Time-Object
and Logico-Mathematical
subsyntaxes of the HCS, follows from the dual relationship
between set theory and semantics, whereby predicating membership
in a set corresponds to attributing a property
defined on or defining the set.
The property is a “qualitative space” topologically
containing that to which it is logically attributed.
Since the laws of nature could not apply if the sets that
contain their arguments and the properties that serve as their
parameters were not mutually present at the place and time of
application, and since QM blurs the point of application into a
region of distributive spacetime potential, events governed by
natural laws must occur within a region of spacetime over which
their parameters are distributed.
Conspansive
domains interpenetrate against the background of past events at the
inner expansion rate c, defined as the maximum ratio of distance to
duration by the current scaling, and recollapse through quantum
interaction. Conspansion
thus defines a kind of “absolute time” metering and safeguarding
causality. Interpenetration
of conspansive domains, which involves a special logical operation
called unisection
(distributed intersection) combining aspects of the set-theoretic
operations union and intersection,
creates an infocognitive relation of sufficiently high order to
effect quantum collapse. Output
is selectively determined by ESP interference and reinforcement
within and among metrical layers.
Because
self-configurative spacetime grammar is conspansive by necessity,
the universe is necessarily subject to a requantizative
“accelerative force” that causes its apparent expansion.
The force in question, which Einstein symbolized by the cosmological
constant lambda, is all but inexplicable in any nonconspansive
model; that no such model can cogently
explain it is why he later relented and described lambda as “the
greatest blunder of his career”.
By contrast, the CTMU requires it as a necessary mechanism of
SCSPL grammar. Thus,
recent experimental evidence – in particular, recently-acquired
data on high-redshift Type Ia supernovae that seem to imply the
existence of such a force – may be regarded as powerful (if still
tentative) empirical confirmation of the CTMU.
Metrical
Layering
In
a conspansive universe, the spacetime metric undergoes constant
rescaling. Whereas Einstein required a generalization of
Cartesian space embodying higher-order geometric properties like
spacetime curvature, conspansion requires a yet higher order of
generalization in which even relativistic properties, e.g. spacetime
curvature inhering in the gravitational field, can be progressively
rescaled. Where
physical fields of force control or program
dynamical geometry, and programming is logically stratified as in
NeST, fields become layered stacks of parallel distributive
programming that decompose into field
strata (conspansive layers) related by an intrinsic
requantization function inhering in, and logically inherited from,
the most primitive and connective layer of the stack.
This "storage process" by which infocognitive
spacetime records its logical history is called metrical
layering (note that since storage is effected by inner-expansive
domains which are internally atemporal, this is to some extent a
misnomer reflecting weaknesses in standard models of computation).
The
metrical layering concept does not involve complicated reasoning.
It suffices to note that distributed
(as in “event images are outwardly distributed in layers of
parallel computation by inner expansion”) effectively means “of
0 intrinsic diameter” with respect to the distributed attribute.
If an attribute corresponding to a logical relation of any
order is distributed over a mathematical or physical domain, then
interior points of the domain are undifferentiated with respect to
it, and it need not be transmitted among them.
Where space and time exist only with respect to logical
distinctions among attributes, metrical differentiation can occur
within inner-expansive domains (IEDs) only upon the introduction of consequent
attributes relative to which position is redefined in an overlying
metrical layer, and what we usually call “the metric” is a
function of the total relationship among all layers.
The
spacetime metric thus amounts to a Venn-diagrammatic conspansive
history in which every conspansive domain (lightcone cross section,
Venn sphere) has virtual 0
diameter with respect to distributed attributes, despite
apparent nonzero diameter with respect to metrical relations among
subsequent events. What
appears to be nonlocal transmission of information can thus seem to
occur. Nevertheless,
the CTMU is a localistic theory in every sense of the word;
information is never exchanged “faster than conspansion”, i.e.
faster than light (the CTMU’s unique explanation of quantum
nonlocality within a localistic model is what entitles it to call
itself a consistent “extension” of relativity theory, to which
the locality principle is
fundamental).
Metrical
layering lets neo-Cartesian spacetime interface with predicate logic
in such a way that in addition to the set of “localistic”
spacetime intervals riding atop the stack (and subject to
relativistic variation in space and time measurements), there exists
an underlying predicate logic of spatiotemporal contents obeying a
different kind of metric. Spacetime
thus becomes a logical construct
reflecting the logical evolution of that which it models,
thereby extending the Lorentz-Minkowski-Einstein generalization of
Cartesian space. Graphically, the CTMU places a logical,
stratified computational construction on spacetime, implants a
conspansive requantization function in its deepest, most
distributive layer of logic (or highest, most parallel level of
computation), and rotates the spacetime diagram depicting the
dynamical history of the universe by 90°
along the space axes. Thus, one perceives the model’s
evolution as a conspansive overlay of physically-parametrized Venn
diagrams directly through the time (SCSPL grammar) axis rather than
through an extraneous z axis artificially separating theorist from
diagram. The cognition
of the modeler – his or her perceptual internalization of the
model – is thereby identified with cosmic time, and infocognitive
closure occurs as the model absorbs the modeler in the act of
absorbing the model.
To
make things even simpler: the CTMU equates reality
to logic, logic
to mind, and (by
transitivity of equality) reality
to mind.
Then it makes a big Venn diagram out of all three, assigns
appropriate logical and mathematical functions to the diagram, and
deduces implications in light of empirical data.
A little reflection reveals that it would be hard to imagine
a simpler or more logical theory of reality.
The
CTMU and Quantum Theory
The
microscopic implications of conspansion are in remarkable accord
with basic physical criteria. In
a self-distributed (perfectly self-similar) universe, every event
should mirror the event that creates the universe itself.
In terms of an implosive inversion of the standard (Big Bang)
model, this means that every event should to some extent mirror the
primal event consisting of a condensation of Higgs energy
distributing elementary particles and their quantum attributes,
including mass and relative velocity, throughout the universe.
To borrow from evolutionary biology, spacetime ontogeny
recapitulates cosmic phylogeny; every part of the universe should
repeat the formative process of the universe itself.
Thus,
just as the initial collapse of the quantum wavefunction (QWF) of
the causally self-contained universe is internal to the universe,
the requantizative occurrence of each subsequent event is
topologically internal to that event, and the cause spatially
contains the effect. The
implications regarding quantum nonlocality are clear.
No longer must information propagate at superluminal velocity
between spin-correlated particles; instead, the information required
for (e.g.) spin conservation is distributed over their joint
ancestral IED…the virtual 0-diameter spatiotemporal image of the
event that spawned both particles as a correlated ensemble.
The internal parallelism of this domain – the fact that
neither distance nor duration can bind within it – short-circuits
spatiotemporal transmission on a logical level.
A kind of “logical superconductor”, the domain offers no
resistance across the gap between correlated particles; in fact, the
“gap” does not exist! Computations
on the domain’s distributive logical relations are as perfectly
self-distributed as the relations themselves.
Equivalently,
any valid logical description of spacetime has a property called hology,
whereby the logical structure of the NeST universal automaton –
that is, logic in its entirety - distributes over spacetime at all
scales along with the automaton itself.
Notice the etymological resemblance of hology to holography,
a term used by physicist David Bohm to describe his own primitive
nonlocal interpretation of QM.
The difference: while Bohm’s Pilot
Wave Theory was unclear on the exact nature of the
"implicate order" forced by quantum nonlocality on the
universe - an implicate order inevitably associated with conspansion
- the CTMU answers this question in a way that satisfies Bell's
theorem with no messy dichotomy between classical and quantum
reality. Indeed, the
CTMU is a true localistic theory in which nothing outruns the
conspansive mechanism of light propagation.
The
implications of conspansion for quantum physics as a whole,
including wavefunction collapse and entanglement, are similarly
obvious. No less
gratifying is the fact that the nondeterministic computations
posited in abstract computer science are largely indistinguishable
from what occurs in QWF collapse, where just one possibility out of
many is inexplicably realized (while the CTMU offers an explanation
called the Extended Superposition Principle or ESP, standard
physics contains no comparable principle).
In conspansive spacetime, time itself becomes a process of
wave-particle dualization mirroring the expansive and collapsative
stages of SCSPL grammar, embodying the recursive syntactic
relationship of space, time and object.
There
is no alternative to conspansion as an explanation of quantum
nonlocality. Any
nonconspansive, classically-oriented explanation would require that
one of the following three principles be broken: the principle of realism,
which holds that patterns among phenomena exist independently of
particular observations; the principle of induction,
whereby such patterns are imputed to orderly causes; and the
principle of locality,
which says that nothing travels faster than light.
The CTMU, on the other hand, preserves these principles by
distributing generalized observation over reality in the form of
generalized cognition; making classical causation a stable function
of distributed SCSPL grammar; and ensuring by its structure that no
law of physics requires faster-than-light communication. So
if basic tenets of science are to be upheld, Bell’s theorem must
be taken to imply the CTMU.
As
previously described, if the conspanding universe were projected in
an internal plane, its evolution would look like ripples (infocognitive
events) spreading outward on the surface of a pond, with new ripples
starting in the intersects of their immediate ancestors.
Just as in the pond, old ripples continue to spread outward
in ever-deeper layers, carrying their virtual 0 diameters along with
them. This is why we
can collapse the past history of a cosmic particle by observing it
in the present, and why, as surely as Newcomb’s demon, we can
determine the past through regressive metric layers corresponding to
a rising sequence of NeST strata leading to the stratum
corresponding to the particle’s last determinant event.
The deeper and farther back in time we regress, the higher
and more comprehensive the level of NeST that we reach, until
finally, like John Wheeler himself, we achieve “observer
participation” in the highest, most parallelized level of NeST...the
level corresponding to the very birth of reality.
Appendix
A
Analysis
is based on the concept of the derivative, an "instantaneous
(rate of) change". Because an "instant" is
durationless (of 0 extent) while a "change" is not, this
is an oxymoron. Cauchy and Weierstrass tried to resolve this paradox
with the concept of "limits"; they failed. This led to the
discovery of nonstandard analysis by Abraham Robinson. The CTMU
incorporates a conspansive extension of nonstandard analysis in
which infinitesimal elements of the hyperreal numbers of NSA are
interpreted as having internal structure, i.e. as having nonzero
internal extent. Because they are defined as being indistinguishable
from 0 in the real numbers Rn, i.e. the real subset of
the hyperreals Hn, this permits us to speak of an
"instantaneous rate of change"; while the
"instant" in question is of 0 external extent in Rn,
it is of nonzero internal extent in Hn. Thus, in taking
the derivative of (e.g.) x2, both sides of the equation
Dy/Dx
= 2x + Dx
(where D
= "delta" = a generic increment) are nonzero, simultaneous
and in balance. That is, we can take Dx
to 0 in Rn and drop it on the right with no loss of
precision while avoiding a division by 0 on the left. More
generally, the generic equation
limDxÎH®0ÎRDy/Dx
= limDxÎH®0ÎR[f(x
+Dx)
- f(x)]/Dx
no longer involves a forbidden "division by 0"; the
division takes place in H, while the zeroing-out of Dx
takes place in R. H and R, respectively "inside" and
"outside" the limit and thus associated with the limit and
the approach thereto, are model-theoretically identified with the
two phases of the conspansion process L-sim and L-out, as
conventionally related by wave-particle duality. This leads to the
CTMU "Sum Over Futures" (SOF) interpretation of quantum
mechanics, incorporating an Extended Superposition Principle (ESP)
under the guidance of the CTMU Telic Principle, which asserts that
the universe is intrinsically self-configuring.
In this new CTMU extension of nonstandard analysis, the universe can
have an undefined ("virtually 0") external extent while
internally being a "conspansively differentiable
manifold". This, of course, describes a true intrinsic geometry
incorporating intrinsic time as well as intrinsic space; so much for
relativity theory. In providing a unified foundation for
mathematics, the CTMU incorporates complementary extensions of
logic, set theory and algebra. Because physics is a blend of
perception (observation and experiment) and mathematics, providing
mathematics with a unified foundation (by interpreting it in a
unified physical reality) also provides physics with a unified
foundation (by interpreting it in a unified mathematical reality).
Thus, by conspansive duality, math and physics are recursively
united in a dual-aspect reality wherein they fill mutually
foundational roles.
[If you want to know more about how the CTMU is derived using logic
and set theory, check out these on-line papers:
- On Absolute Truth
- Introduction to the CTMU
- CTMU: A New Kind of Reality Theory (pdf)
I'm currently working on additional papers.]
Appendix
B
Because
the value of R can only be theoretically approximated, using R or
even R-1 to describe requantization makes it appear that
we are simply using one theory to justify another.
But the R-to-R-1 inversion comes with an addition
of logical structure, and
it is this additional structure that enables us to define a
high-level physical process, conspansion,
that opposes gravity and explains accelerating redshift. Conspansive
requantization is uniform at all scales and can be seen as a
function of the entire universe or of individual quanta; every part
of the universe is grammatically substituted, or injectively mapped,
into an image of its former self…an image endowed with
computational functionability.
To understand this, we must take a look at standard
cosmology.
Standard
cosmology views cosmic expansion in terms of a model called ERSU,
the Expanding Rubber Sheet
Universe. For
present purposes, it is sufficient to consider a simplified
2-spheric ERSU whose objects and observers are confined to its
expanding 2-dimensional surface.
In ERSU, the sizes of material objects remain constant while
space expands like an inflating balloon (if objects grew at the rate
of space itself, expansion could not be detected).
At the same time, spatial distances among comoving objects
free of peculiar motions remain fixed with respect any global
comoving coordinate system; in this sense, the mutual rescaling of
matter and space is symmetric.
But either way, the space occupied by an object is considered
to “stretch” without the object itself
being stretched.
Aside
from being paradoxical on its face, this violates the basic premise
of the pure geometrodynamic view of physical reality, which
ultimately implies that matter is “space in motion relative to
itself”. If we
nevertheless adhere to ERSU and the Standard Model, the expansion
rate (prior to gravitational opposition) is constant when expressed
in terms of material dimensions, i.e., with respect to the original
scale of the universe relative to which objects remain constant in
size. For example, if
ERSU expansion were to be viewed as an outward layering process in
which the top layer is “now”, the factor of linear expansion
relating successive layers would be the quotient of their
circumferences. Because
object size is static, so is the cosmic time scale when expressed in
terms of basic physical processes; at any stage of cosmic evolution,
time is scaled exactly as it was in the beginning.
The
idea behind the CTMU is to use advanced logic, algebra and
computation theory to give spacetime a stratified computational or
cognitive structure that lets ERSU be “inverted” and ERSU
paradoxes resolved. To
glimpse how this is done, just look at the ERSU balloon from the
inside instead of the outside.
Now imagine that its size remains constant as thin,
transparent layers of parallel distributed computation grow inward,
and that as objects are carried towards the center by each
newly-created layer, they are proportionately resized.
Instead of the universe expanding relative to objects whose
sizes remain constant, the size of the universe remains constant and
objects do the
shrinking…along with any time scale expressed in terms of basic
physical processes defined on those objects.
Now imagine that as objects and time scales remain in their
shrunken state, layers become infinitesimally thin and recede
outward, with newer levels of space becoming “denser” relative
to older ones and older levels becoming “stretched” relative to
newer ones. In the
older layers, light – which propagates in the form of a
distributed parallel computation – “retroactively” slows down
as it is forced to travel through more densely-quantized overlying
layers.
To
let ourselves keep easy track of the distinction, we will give the
ERSU and inverted-ERSU models opposite spellings.
I.e., inverted-ERSU will become USRE.
This turns out to be meaningful as well as convenient, for
there happens to be an apt descriptive phrase for which USRE is
acronymic: the Universe as a
Self-Representational Entity.
This phrase is consistent with the idea that the universe is
a self-creative, internally-iterated computational endomorphism.
It
is important to be clear on the relationship between space and time
in USRE. The laws of
physics are generally expressed as differential equations describing
physical processes in terms of other physical processes
incorporating material dimensions.
When time appears in such an equation, its units are
understood to correspond to basic physical processes defined on the
sizes of physical objects. Thus,
any rescaling of objects must be accompanied by an appropriate
rescaling of time if the laws of physics are to be preserved.
Where the material contents of spacetime behave in perfect
accord with the medium they occupy, they contract as spacetime is
requantized, and in order for the laws of physics to remain
constant, time must contract apace.
E.g.,
if at any point it takes n time units for light to cross the
diameter of a proton, it must take the same number of units at any
later juncture. If the proton contracts in the interval, the time
scale must contract accordingly, and the speed and wavelength of
newly-emitted light must diminish relative to former values to
maintain the proper distribution of frequencies.
But meanwhile, light already in transit slows down due to the
distributed “stretching” of its deeper layer of space, i.e., the
superimposition of more densely-quantized layers.
Since its wavelength is fixed with respect to its own
comoving scale (and that of the universe as a whole), wavelength
rises and frequency falls relative to newer, denser scales.
Complementary
recalibration of space and time scales accounts for cosmic redshift
in the USRE model. But
on a deeper level, the explanation lies in the nature of space and
time themselves. In ERSU, time acts externally on space, stretching
and deforming it against an unspecified background and transferring
its content from point to point by virtual osmosis.
But in USRE, time and motion are implemented wholly within
the spatial locales to which they apply.
Thus, if cosmic redshift data indicate that “expansion
accelerates” in ERSU, the inverse USRE formulation says that spacetime
requantization accelerates with respect to the iteration of a
constant fractional multiplier…and that meanwhile, inner expansion
undergoes a complementary "deceleration" relative to the invariant
size of the universe. In
this way, the two phases of conspansion work together to preserve
the laws of nature.
The
crux: as ERSU expands and the cosmological scaling factor R rises,
the USRE inverse scaling factor 1/R falls (this factor is expressed
elsewhere in a time-independent form r).
As ERSU swells and light waves get longer and lower in
frequency, USRE quanta shrink with like results.
In either model, the speed of light falls with respect to any
global comoving coordinate system; cn/c0 = R0/Rn
= Rn-1/R0-1 (the idea
that c is an “absolute
constant” in ERSU is oversimplistic; like material dimensions, the
speed of light can be seen to change with respect to comoving space
in cosmological time). But
only in USRE does the whole process become a distributed logico-mathematical
endomorphism effected in situ
by the universe itself…a true local implementation of physical law
rather than a merely localistic transfer of content based on a
disjunction of space and logic.
The point is to preserve valid ERSU relationships while
changing their interpretations
so as to resolve paradoxes of ERSU cosmology and physics.
In
Noesis/ECE 139, it was
remarked that if the universe were projected on an internal plane,
spacetime evolution would resemble spreading ripples on the surface
of a pond, with new ripples starting in the intersects of old ones.
Ripples represent events, or nomological (SCSPL-syntactic)
combinations of material objects implicit as ensembles of
distributed properties (quantum numbers).
Now we see that outer (subsurface) ripples become internally
dilated as distances shorten and time accelerates within new ripples
generated on the surface.
CTMU
monism says that the universe consists of one “dual-aspect”
substance, infocognition,
created by internal feedback within an even more basic (one-aspect)
substance called telesis.
That everything in the universe can manifest itself as either
information or cognition (and on combined scales, as both) can
easily be confirmed by the human experience of personal
consciousness, in which the self exists as information
to its own cognition…i.e.,
as an object or relation subject to its own temporal processing.
If certain irrelevant constraints distinguishing a human
brain from other kinds of object are dropped, information and
cognition become identical to spatial
relations and time.
In
a composite object (like a brain) consisting of multiple parts, the
dual aspects of infocognition become crowded together in spacetime.
But in the quantum realm, this “monic duality” takes the
form of an alternation basic to the evolution of spacetime itself.
This alternation usually goes by the name of wave-particle
duality, and refers to the inner-expansive and collapsative
phases of the quantum wave function.
Where ripples represent the expansive (or cognitive) phase,
and their collapsation into new events determines the informational
phase, the above reasoning can be expressed as follows: as the
infocognitive universe evolves, the absolute rate of spatiotemporal
cognition cn at time n, as measured in absolute
(conserved) units of spacetime, is inversely proportional to the
absolute information density Rn/R0 of typical
physical systems...i.e., to the concentration of locally-processed
physical information. As light slows down, more SCSPL-grammatical
(generalized cognitive) steps are performed per unit of absolute
distance traversed. So with respect to meaningful content, the
universe remains steady in the process of self-creation.
©
1998-2002 by Christopher Michael Langan
Partial
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