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FIRST SCIENTIFIC REVOLUTION
GALILEAN RELATIVITY AND NEWTON'S MODEL
Pre-Galilean, Aristotelian Physics considered immobility as
steady state of a body experiencing no forces. Under action
of force the body was assumed to move at a speed proportional
to the force and to return to immobility upon disappearance
of the force.
This theory was universally accepted during 2000 years until
Galileo discovered that the steady state of a body is not
immobility, but uniform movement at constant speed. A body
experiencing no forces moves at constant speed in an unchanged
Euclidean direction. Galileo called such a body associated with
concrete or virtual Observer an "Inertial Referential" (IR).
This definition excludes absolute movement of an IR. They all
move relatively to one another at constant speeds and none is
in any way privileged.
Question arose if concepts and laws describing mechanical
phenomena in some IR keep their validity transformed to other
IR's and, if they do, then by being invariant or covariant.
(A construct is "invariant upon a transformation" when after
being transformed it stays unchanged; it is "covariant under
transformation" when it undergoes modifications entirely
determined by the transformation. This notion of "covariance"
should not be confused with "vector covariance" defined in
Tome 2.
Within a given model invariant physical constructs are considered
as absolute and covariant - as relative.
Galilean Relativity and Newton's Model are partially based upon
an absolute construct, the Galilean SPACE.
Galilean SPACE, in contradiction to the widely spread belief, is
4 dimensional: an event is determined by 1 Time and 3 Space values.
It's indeed a TimeSpace, a 4D SPACE encompassing two sub-spaces of
our direct perception:
-1 dimensional Time
-3 dimensional Euclidean Space.
The confusion attributing "TimeSpace" to Einstein is due to Galilean
time and space being incommensurable or affine, while Einstein's 4D
continuum is metric "LighttimeSpace" where the Galilean component
"time" is replaced by "Lighttime" Ct having the measure of distance
commensurable with the components of Space. (Details in Tome 2).
Incommensurability of Galilean Time and Space excludes the notion
of Time-Space interval and, consequently, of a transformation
involving the entire Galilean TimeSpace. On the other hand, constancy
of speed value and direction among IR's excludes rotation and we are
left with two independent translations, one in time and one in space,
which accounts for Galilean Relativity being sometimes called
"Translational" as opposed to the "Rotational Relativity" of Einstein,
which latter term we justify in the chapter "SECOND SCIENTIFIC
REVOLUTION".
Let's take two IRs R(O,X,Y,Z,T) and r(o,x,y,z,t), of coordinate origins
O and o, moving with respect to one another along the common axe X-x
at speed V.
Time and space translations from R to r are respectively:
t = T; x = X + a + VT; [1]
where a is the distance of o from O at T = 0.
[1] is called the Galilean Transformation. It supports invariant or
absolute time and distance, i.e. space.
Indeed, distance DX in R DX = X2 - X1, transforms into Dx in r:
Dx = x2 -x1 = (X2 + a + VT) - (X1 + a + VT) = X2 - X1 = DX
Intervals of time and space are invariant under the Galilean
Transformation, or in epistemological terms,
GALILEAN TIME AND SPACE ARE ABSOLUTE.
A Detector moving along X/x at uDx with respect ot r
moves at uDX = uDx + V with respect to R:
Speed is additively covariant under Galilean Transformation, which,
after a few simple mathematical operations results in the rule:
MECHANICS ARE COVARIANT UNDER GALILEAN TRANSFORMATION
Relativity was doubtless Galileo's principal contribution to science.
It's rigorous, complete and capable to support most of physics till
our days, where it continues to be a valid approximation of low speed
Mechanics. Yet, it was not the only one.
Besides Relativity Galileo fostered the deductive/inductive method
implying axiomatic falsifiable models in our sense, emerging upon
the background of traditional purely deductive, so called "axiomatic"
methods, whose "axioms" verified exclusively by their "self-evidence"
were indeed camouflaged Dogmas.
He restricted inquiry to observable aspects of phenomena, banning
speculations about the incognizable transcendental "true nature" which
clearly postulates Phenomenology and bans Noumenalism.
Galilean Relativity reached its apogee in Newton's Model. We shall
examine it in the light of our fundamental CD polarity (Continuum/
Discreteness) and our postulated fundational preponderance of its
continuous aspect (chapter "TIME, AWARENESS AND EVENTS").
At the first glance it seems that Newton's model contradicts our
continuum preponderance postulate and is founded in discreteness.
At Newton's time and for centuries afterwards the fabric of cosmos
was dogmatically considered to be corpuscular. Newtonian SPACE was
assumed to be compactly filled with corpuscles acting on one
another like billiard balls and thus pretending to support mechanics,
causality (whatever it could mean) and local action. It's rather
amusing to note that with respect to the latter the protagonists
of mechanistic dogma overlooked a contradiction: only continuum may
admit local action. Granular mechanistic fabric implies action at
distance equal to the size of the elementary granule. Now, we don't
know anything about the elementary "balls", neither their size, nor
their internal structure and behavior. Nobody ever observed them and
there are no hints about their basic attributes such as size or mass.
They represent an ad hoc "crutch", a hypothetical corpuscular "matter
substance", introduced in order to formulate a microscopic model
based intuitively upon macroscopic billiard. Still, hypothetical
or not, this corpuscular "matter" appeared to support reasonably the
laws of mechanics.
However, serious difficulties arose with optics. In agreement with
the postulate of discrete cosmos, light was mapped as a flow of
corpuscles thus introducing an additional ad hoc crutch, a
"luminiferous" corpuscular substance. It supported rectilinear
progression and reflection of light, as well as refraction (with help
of hypothetical interactions between "material" and "luminiferous"
substances). In order to account for dispersion, or separation of
white light into spectral components, it was necessary to split the
"luminiferous" substance into several substances, one per colour,
propagating for some reason each at different speed through various
"material" substances. One accumulated uncountable ad hoc crutches,
all hypothetical and not supported empirically. One grew a habit to
add for each new problem some new "substance" which looked more like
tautologies than solutions.
Finally, realizing that no conceivable new "substances" could possibly
account for such phenomena as diffraction and interference patterns,
physicists abandoned the corpuscular theory of light to the advantage
of wave theory which, in conjunction with the discrete, billiard-like
view of cosmos, ushered in the Aether dogma which dominated Physics
till the beginning of the 20th century (see chapter "SECOND SCIENTIFIC
REVOLUTION").
The corpuscular theory fell into oblivion until it apparently
resurrected in the Quantum Theory, however at an incomparably higher
level of complexity and in a form having nothing to do with
rudimentary mechanistic thinking.
Shelving for the moment Optics we shall move to Newton's mechanics.
It's based upon 3 laws of motion:
1.In absence of force a body moves at constant speed.
2.Accelaration of a body is directly proportional to force acting
on it and inversely to its mass.
3.For every action, there is an equal and opposite reaction.
Let's note that only 2. and 3. are original. 1. is a redefinition
of Galilean inertial referentials.
On the other hand, a fundamental concept is missing, that of
kinetic energy.
It has been conceived and formulated at age of 16 by Pierrette
Paulze - Lavoisier who, astounding as it may seem, fell into almost
complete oblivion. Maybe not so astonishing after all: she was a
woman; she did not belong to any Academy, none would accept a woman
in 17th Century; and married to Lavoisier she was overshadowed by him.
Not by his fault. She married him at age of 13 and from the first day
became his full-fledged collaborator, which he emphasized at every
occasion so that the rare cognoscenti who heard about her call them
"Father and Mother of modern Chemistry". But there it is, hardly
anybody heard about her.
Thus, if we consider Newton as founder of modern Physics and perhaps
the greatest scientist of history, it's not because of his unconvincing
optics, nor of his mechanics, certainly great, but incomplete and
amended by a nearly unknown 16 years old girl. His outstanding
significance is due to "Gravitation", which we shall further call
"Newton's Model".
It boils down to the following Law of Gravitation:
Attracting gravity force between two masses F(r)=G(m1*m2)/r**2
where G: gravity constant, m1,m2: respective masses, r: distance.
Let's return to our basic question: Is Newton's Model continuous
or discrete? On the face of it it seems discrete, according to the
contemporary mechanistic view of cosmos and to his own explicit
statements. However, this assumption leads immediately to paradoxes:
First Paradox: Gravity acts at very large, astronomic distances which
contradicts the local action principle of the mechanistic view.
Second Paradox: SPACE (distance) determines the gravity force, while
this Force does not act in any way on the SPACE, which contradicts
the action/reaction principle.
Both Paradoxes represent facts contradicting dogmas of SPACE being
absolute and mechanistic. Questioned about it Newton answered with
the famous "hypotheses non fingo" clearly implying that science
carries out experiments and orders their results, but does not deal
with transcendencies. He stopped short of converting mechanistic
dogmas to axioms and, once falsified, to drop and replace them. He
did not dare to do it under the pressure of his contemporary
dogmatism, but clearly distanced himself from them. Closer to us,
questioned about founding problems of Quantum Theory, Dirac
reiterated Newton's answer in cruder terms: "Shut up and calculate!".
With "hypotheses non fingo" Newton rather clearly formulated what
we shall call the Principle of Preponderance of Facts, stating that
in case of conflict between facts and abstractions, the latter should
be adjusted if possible to fit the former or, else, disregarded.
The First Paradox, Action at Distance in a Discrete Model, is not
just a contradictory detail, but an essential inconsistency which
casts doubt upon the very base of the Model. Consequently, question
arises if Newton's Model was not de facto continuous, perhaps
implicitly, against author's own explicit belief in the universally
accepted discrete fabric of cosmos.
Indeed, taking the formula of gravitational Force: F(r)=G(m1*m2)/r**2,
we may combine G*m1/r**2 into g(r)=G*m1/r**2 and define "g(r)"
as "Gravity Field in any point r of SPACE.
Then, F(r)=g(r)*m2 and replacing m2 with detector of mass m2=1, we get
F(r)=g(r) - gravity force exerced by field g(r) on a unit mass in every
point r of SPACE.
Once we replace corpuscles acting paradoxically at distance, with
continuous field acting locally in all points of SPACE, Newton's Model
becomes continuous as well as consistent with local action and
causality; a pertinent foundation of modern Physics, precursor of
Einstein's Relativity and of the Quantum Field Theory.
In this perspective, the Second Paradox involves Field rather than
Force. Indeed, SPACE being a continuum and force a point event,
the original version of the second Paradox is not paradoxical but
simply meaningless. On the contrary, both field and SPACE being
continua, SPACE determining Field without reciprocal reaction
becomes a meaningful albeit yet unsolved inconsistency. It has been
finally solved by the General Relativity (see chapter "SECOND
SCIENTIFIC REVOLUTION").
Finally, let's recall that a major part in the acceptance of
Newton's ideas was due to Euler's re-writing of his entire family
of ideas in the language of calculus, which Newton had done so
much to invent but largely left out of the Principia.
And who says calculus, means continuity. This argument seals our
conviction that Newton's Model was, at least implicitly, the first
pioneering continuity based field model which founded and determined
the subsequent progress of physics till our own days.
DESCARTES
Addressing the logical positivists of the Vienna Circle Popper said:
"The empirical basis of objective science is *nothing absolute.* [1]
Science does not rest on a rockbed. Its towering edifice, an amazingly
bold structure of theories, rises over a swamp. The foundations are
piers going down into the swamp from above. [2]
They do not reach a natural base, but go only as deep as is necessary
to carry the structure. One does not stop driving them down because
one has reached firm ground. Rather, one resolves to be satisfied
with their firmness, hoping they will carry the structure. [3]
(If the structure proves too heavy and begins tottering, it sometimes
does not help to drive the piers further down. It may be necessary
to have a new building, which must be constructed on the ruins
of the collapsed structure's piers.) [4]
*The objectivity of science can be bought only at the cost of relativity.*
(He who seeks the absolute must seek it in the subjective.)" [5]
This vade mecum of current rational Epistemology could have been
written by Descartes:
[1] and [5] are compatible with Galilean Relativity armed by Descartes
with exact mathematical tools: Cartesian Referentials and Analytic
Geometry which founded calculus and most of modern science.
[5] is entirely contained in "Cogito ergo Sum", which turned upside
down all traditional beliefs in transcendental "objective reality"
and established the preponderance of subjectivity in cognition
and science. (see "COGITO" below).
[2],[3] and [4] illustrate rational deductive/inductive axiomatization
such as it has been conceived by Galileo and completed with Cartesian
Doubt or Uncertainty.
Ergo, standing on the shoulders of Galileo, Descartes simply created
the concept and the methodology of modern science founding all
subsequent rational Epistemology holding till our own days.
Unfortunately, rationality is far from dominating our thinking.
First Enlightenment did not entirely eradicate its contemporary
dogmatism and soon collapsed under its reactionary assaults
The reaction of Dogmatism went on uninterrupted till our epoch
which is dominated by aggressive dogmatic obscurantism out of
which try timidly to emerge the cornerstones of Second
Enlightenment. (see the chapter "SECOND SCIENTIFIC REVOLUTION").
COGITO
Descartes' main epistemological concept was that of permanent
doubt as source of inquiry, which completed Galileo's
axiomatization with uncertainty. When I think about something
I sense, perceive, hear, read or infer, I find that it is
uncertain. I doubt it and in this doubt find the motivation
to clarify it, to inquire. Yet, however uncertain this inquiry,
it reposes upon a certain bedrock, I am certain at least that
I doubt.
The adage "Cogito ergo Sum", is a simple corollary of Permanent
Doubt, expressed in a concise form meant to serve as motto of
the subjective, doubt based epistemology and not to be taken
at face value.
He who insists to build an ontological discourse upon the motto
"I think ergo I am", should remember that empty copula does not
predicate anything, unless tacitly assumed. "John is" does not
mean anything, but if you ask "who is tall?", the answer "John is"
means "John is (tall)". Tacitly assuming Descartes' epistemology,
the apparently meaningless "I think ergo I am" takes on the
meaning "I think ergo I am (certain of it)". In other terms,
thinking being thematic, I doubt its theme, but am certain of
thinking itself.
Insistence to construct and to argue pseudo-cartesian ontologies
upon the empty copula of Cogito produced the biggest heap of
nonsense equaled only by taking at face value Plato's Allegory
of the Cave.
Shelving the metaphysical nonsense and returning to epistemology
we see Cogito as motto of rational inference, based on primacy
of subjective aspect of observation over the objective, eradicating
traditional beliefs in transcendental "objective reality" and
remolding Science by founding it in subjectivity.
