It
is the purpose and scope of this work to
establish a rational foundation for
understanding Nature from one single principle,
law, cause, or "logic" of operation. The method
employed here, never used before in the form
presented herein, is modeled from Mathematics
where we start with certain primary
propositions, called axioms, and then using
rational thinking --and only rational thinking--
an entire theory is build up.
Unlike
for Mathematics (where those axioms can be
any proposition that cannot be derived
from anything else and cannot lead to rational
contradictory results), in TRUTON
--The Rational Unified Theory Of
Nature, those primary propositions, in
addition, must have physical roots and
connotations that cannot "offend" our given
common sense.
Our
modeled mathematical method of discovering
things in Nature, should not be confused with
the long standing method of using Mathematics as
a tool in deriving results. We will not use
Mathematics per se, but instead we
will use the method or the model of Mathematics
of how it obtains its results and nothing
else.
TRUTON
in a way is, par excellence, a direct outgrow
from Classical Physics of Sir Isaac Newton and
its followers.
On
July 5, 1686, Sir Isaac Newton published his
seminal and revolutionary work entitled
Philosophiæ Naturalis Principia
Mathematica (Mathematical Principles of
Natural Philosophy) or in short
Principia. The object of Principia was to
establish in a rational fashion a "mechanical"
Universe where all motions studied to be able to
be derived from coherent mathematical-mechanical
principles. It was Newton who first coined the
term Rational Mechanics to distinguish it from
the study of Empiric Mechanics. Newton,
following into the steps of Copernicus, Kepler,
Galileo Galilei, and many others preceding them,
saw clearly the close and profound
interrelationship that existed between
Mathematics (in his case, the Euclidean
geometry) and Mechanics and how one draws from
another their own existence. In his Preface to
the First Edition of Principia, Newton noted:
(Principia, vol. I, Univ. of California Press,
1966, pp. xvii-xviii)
"The
ancients considered mechanics in a twofold
respect; as rational, which proceeds
accurately by demonstration, and practical.
To practical mechanics all the manual arts
belong, from which mechanics took its name.
... To describe right lines and circles are
problems, but not geometrical problems. The
solutions to these problems is required from
mechanics, and by geometry the use of them,
when so solved, is shown; and it is the glory
of geometry that from those few principles,
brought from without, it is able to produce
so many things. Therefore geometry
is founded in mechanical practice, and is
nothing but that part of universal mechanics
which accurately proposes and demonstrates
the art of measuring. But since
the manual arts are chiefly employed in the
moving bodies, it happens that geometry is
commonly referred to their magnitude, and
mechanics to their motion. In this sense
rational mechanics will be the science of
motions resulting from any force whatsoever,
and of the forces required to produce any
motions, accurately proposed and
demonstrated.
....
I consider philosophy rather than arts and
write not concerning manual but natural
powers, and consider chiefly those things
which relate to gravity, levity, elastic
force, the resistance of fluids, and the like
forces, whether attractive or impulsive; and
therefore I offer this work as the mechanical
principles of philosophy, for the whole
burden of philosophy seems to consist in this
--from the phenomena of motions to
investigate the forces of nature,
and then from these forces to demonstrate the
other phenomena; and to this end the general
propositions in the first and second Books
are directed. In the third Book I give an
example of this in the explanation of the
System of the World; for by the propositions
mathematically demonstrated in the former
Books, in the third I derive from celestial
phenomena the forces of gravity which bodies
tend to the sun and the several planets. Then
from these forces, by other propositions
which are also mathematical, I deduce the
motions of planets, the comets, the moon, and
the sea." [Underline and underscore
supplied.]
Then,
recognizing the limitation of his work, Newton
noted his disappointment in his Preface to
Principia (ibidem) with a glimpse at what
future theoretical work may be needed to unlock
the ultimate secrets of Nature (underscore
supplied):
"I
wish we could derive the rest of the
phenomena of Nature by the same kind of
reasoning from mechanical principles,
for I am induced by many reasons to
suspect that they may all depend upon certain
forces by which the particles of bodies, by
some cause hitherto unknown, are either
mutually impelled towards one another, and
cohere in regular figures, or are repelled
and recede from one another. These
forces being unknown, philosophers have
hitherto attempted the search of Nature in
vain; but I hope the principles here laid
down will afford some light either to this or
some truer method of philosophy."
And
at the end of his work Newton clearly was
disappointed of not being able to discover the
deepest interconnections that govern Nature
--from the origin of gravity to the origin of
other forces, (ibidem, vol. II,
pp. 546-547), as he noted:
"Hitherto
we have explained the phenomena of the
heavens and of our sea by the power of
gravity, but we have not assigned
the cause of that power. This is
certain, that it must proceed from a cause
that penetrates to the very centers of the
sun and planets, without suffering the least
diminution of its force; that operates not
according to the quantity of the surfaces of
the particles upon which acts (as mechanical
causes used to do), but according to the
quantity of solid matter which they contain
and propagates its virtue on all sides to
immense distances, decreasing always as the
inverse square of the distance.
...
But
hitherto I have not been able to
discover the cause of those
properties, of gravity from
phenomena, and I frame no
hypotheses;" [Emphasis
supplied.]
Because
of this impasse that continuously was present
and which was never been able to be overpassed
by all generations that followed Newton, it was
in the end a path that was abandoned altogether
and replaced for the first time with a novel
path containing elements of the irrational with
countless of speculations over speculations.
Indeed, the foundation of Newton's Mechanics
(dubbed today as Classical Mechanics) and which
reigned supreme until the beginning of the 20th
century was challenged first by Albert
Einstein
twice --through a so-called Relativistic
mechanics in a novel fashion incorporating
irrational thinking and elements of the
absurd:
1)
first time, in 1905 with the introduction of
his so-called Special Theory of Relativity
(where Newton's fundamental concepts of
space, time and simultaneity were being
challenged and mashed together into an absurd
and meaningless 4-dimensional continuum
called space-time where to the Euclidean
geometrical 3-dimensional space, time was
being added as the 4th dimension of the newly
created space. If t is the time
variable, and x, y, z are the
geometrical coordinates of a point, the space
[x(t), y(t), z(t)] was
transformed into the meaningless
4-dimensional space
[x, y, z, t] and that
absurdity is being considered today as a
revolution in viewing and understanding
Nature.
2)
the second time, 10-11 years later, with the
introduction of Einstein's so-called General
Theory of Relativity purporting to be the
theory of gravity where the space itself was
postulated to have a "curvature" and other
properties that where outside of the realm of
Euclidean geometry. Gravity was now being
"explained" through that willy-nilly
postulate of a so-called curvature of the
space where the Euclidean geometry was
replaced willy-nilly with the Riemannian
geometry as the true geometry of the physical
space of the Universe.
Once
the gates towards irrational were opened and
various Mathematical models were introduced that
had nothing to do with the reality and the
physical word they purported to represent, the
landscape of Physics has changed in a most
dramatic way. New irrational implants were able
now to find a fertile ground for development. A
non-Newtonian mechanics, called Quantum
mechanics, founded on massive speculations,
aberrations of logic and lack of common sense
were wrapped up into beautiful and elegant
Mathematics that has had no rational
justification for being associated with the
description and the representation of
Nature.
Since
the rational thinking was no longer a
prerequisite in explaining Nature in the new
"modern" Physics and, since the irrational
arguments were gaining tacit acceptance more and
more trough Einstein's Relativistic mechanics, a
new scientific climate was able to emerge with
Physics at its forefront followed by Astronomy
and Chemistry.
In
Physics more than in any other Natural Science,
willy-nilly Mathematics began to cover a vast
amount of physical speculations creating in the
end elaborate advanced mathematical theories of
speculative results. These speculative results
in a way became seductive because of the beauty
of the language of Mathematics that was able to
describe them.
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The
Physics and Astronomy part of TRUTON,
of course, can considerably be enhanced
and beautified with expressing those
results in the beautiful language
provided by Mathematics as outlined in
here below.
If
TRUTON is designed to be the
exclusive theory of Nature, then
that representation must be
independent of our sense
perceptions. In TRUTON all forces
and concepts of Nature are real and
not fictional and its results should
never ever be derived from our
perceptions of how we see or
perceive certain physical phenomena
from different systems of references
or systems of coordinate or other
particular conditions. The Theory
of Perception (TOP) as
interesting as it may be, lies
outside of the realm of TRUTON as
its results need not depend of how
the humans or other livings perceive
their surroundings in various
conditions or circumstances.
Based
on this fundamental principle that
in TRUTON all of its results must be
independent from any particular
coordinate system, the question that
arise is what model would be
acceptable in here and what
Mathematics can be used. Well,
Continuum Mechanics (known
also as The Rational
Mechanics) is the model suited
for TRUTON where the Tensor Calculus
(and Tensor Analysis, in general)
represents its mathematical backbone
since a tensor in Mathematics has an
existence independent of any
particular coordinate system.
Physical laws when expressed, as in
Continuum Mechanics, by tensor
equations are universal in the sense
that if they are valid in one
coordinate system, they are valid in
any other coordinate system. That
beauty of invariance of tensor
equations regardless of the
coordinate system employed makes
that tensor approach universal in a
theory of Nature.
So
yes, the mathematical blueprint and
formalization of TRUTON for its
Physics and Astronomy components
must be the one currently employed
in the advanced Continuum
Mechanics.
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As the irrational method of "explaining" things
has gradually entered into the mainstream
science, it was not long before cosmologists
began entertaining out-of-the-blue speculative
concepts as dark matter, dark energy, black
holes, and so on, as being "ingredients" of our
Universe.
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In
TRUTON, for instance, the concept of
dark matter (that is called
xenodust) is not a speculative
willy-nilly concept, but is being
introduced --through the process of its
formation-- as a logical consequence of
the primeval dynamics of
Nature.
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The Universe itself is being speculated as being
originated somehow from a point of infinite
density and temperature that somehow began
expanding and continue to expand. Such a
postulated origin of the Universe defy all
logic, all common sense, and most importantly
all Physics --as Physics (as oppose to
Mathematics) does not allow infinite parameters
into its arsenal. All physical parameters of
Nature are finite indeed.
Troubling
questions, that could have triggered an alarm,
such as how a point of infinite density and
temperature could have been formed in the first
place, that is in a blatant defiance to all
Physics and its concepts of describing Nature,
did not stop the Big-Bang Cosmology to became
the dominant cosmology of nowadays. God, if
there is one, surely is having a field day in
seeing how far off the current science is in the
understanding of the Universe's origin and its
formation.
The
novelty of the new "modern" science is its
ability to place, side by side, the irrational
with the rational and mush them
indistinguishable into a mathematical format. As
long as that "modern" setting is allowed to
exist, Natural Sciences are indeed at a very
great peril. A beautiful Mathematics should
never ever replace or be a camouflage for the
missing Physics in deciphering the secrets of
Nature.
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TRUTON
most certainly deals with the
cosmological issue of the Universe
creation and replaces the Big-Bang
speculation with the Big-Expand
Theory Of Nature (BETON) where the
creation of our Universe is seen not as
a singular willy-nilly event in Nature,
but as a logical part of creation and
self-destruction of many
universes.
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The flood of speculations that continued
unabated in Physics has proliferated into all
Natural Sciences. From the many examples that
could be given, we could mention the ludicrous
speculation for the mass extinction of the
dinosaur some 65 million years ago as a result
of some catastrophic cosmic event generated by
the collision of our planet with some real or
imaginary meteor. (As we shall see, the mass
extinction of the dinosaur with ease can be
explained through rational
arguments
--not as an accident, but as a necessity--
derived from Evolutionary Biology.)
The
new "modern" field of speculations over
speculations has created indeed an extremely
fertile terrain for writing "scientific" papers.
Everybody appeared to be happy of the new found
bottomless reservoir: the universities and other
research institutions were delighted of the new
found wealth of papers that their members were
able to produce as that wealth of papers was
able to justify to the society (which has been
footing the bill) of the necessity of continuing
with the ever increasing funding.
From
Particle Physics, the bottom-end frontier of
Physics --the mother of all Natural Sciences,
there is absolutely no evidence that our
understanding of Nature has been enhanced at all
with the advent of both Relativity and Quantum
mechanics and, it is the aim of TRUTON not only
to eliminate them both, but also to restore and
continue the rational path cemented by Isaac
Newton, a path that may be called the
Trutonian path.
What
was wrong, one may ask, with Newton's method of
discovering "things" in Nature and why
with his approach which was so adequate in many
respects, we could not "descend" and "see" the
cause of existence of various phenomena that
govern Nature such as gravity or "see" the cause
of all other interactions that govern our
particle world?
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!
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Well,
it is perhaps important to note right
here that the primary propositions or
axioms which Newton has chosen in
building up his Theory Of Nature (TON)
were much too "high up" in the
evolutionary ladder of the Universe and
thus, from there no one could "descend"
below the base platform of his axioms
and primary propositions. Indeed,
Newton's Axioms for his TON, from where
his entire theory was build, were his
famous three (3) Laws of Motions
that were indeed far too high from the
"bottom"-level of Nature. And since
from a given set of Axioms one can go
only upwards in a meaningful way, the
"level" of those axioms were clearly
far above the atomic and subatomic
world and hence from that starting
point it was impossible to tackle the
world "below". This was the fundamental
limitation of Newton's TON and this is
why Newton's TON could not be made
applicable to the world
"below".
That
recognition is monumental for TRUTON.
Indeed, we in TRUTON shall begin our
journey from the absolute "bottom"-line
level of Nature from where there will
be no "below" or "underneath". Then,
from that absolute "bottom" line of
Nature we shall, exactly as in
Mathematics, build up the entire theory
of Nature, our TRUTON. Clearly, by
building TRUTON from the "bottom" up,
we shall expect that all Newton's
axioms or laws of motion to be derived
as straightforward consequences from
the foundation of TRUTON.
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It
is also important to note that while Newton
clearly had indicated in Principia's
Preface (see the underlined text above) the
reason why he chose the Euclidean geometry
as the mathematics capable of
describing the forces and phenomena of Nature,
Einstein and their followers and those embracing
the Quantum mechanics, never ever were able to
provide a justification for their mathematics
employed except to say that with such departure
"it works!" [sic!] meaning that we can
write a lot of papers containing a lot of
beautiful mathematics.
Finally,
let us note one more time that throughout the
entire history of Physics and for that matter of
the rest of Natural Sciences, the direction of
theoretical work was done, if you will,
"inwards":
we
started with the result (provided by
observations or experiments) and
went "inwards" attempting to find an
explanation for the result
obtained.
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In
Mathematics, as we have noted, the
method of obtaining theoretical results
has been exactly opposite being, if you
will, in the "outwards"
direction:
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you
start with certain primary
propositions called axioms beyond
which there are no more meaningful
inquiries to be made and then, you
work your way "up" deriving results
which are build up from the previous
results and so on.
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It
is this "outwards" direction from the
ground up that we shall attempt to
initiate as the new direction of
studying Nature.
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To travel with us in our contemplated journey,
you need not have any special mathematical
training because the principles of TRUTON can be
understood from physical considerations alone
and nothing else. In other words, the entire
"skeleton" of TRUTON is "pure" Physics. The
Mathematics that can be applied to TRUTON's
skeleton can give rise to a beautiful
theoretical "body" whose elegance only
Mathematics can provide. But before one can
dress TRUTON with elegant garments provided by
Mathematics, we need first to know what we are
dressing and making sure that this is the body
that we want to dress.
.
