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PLAN OF 0.FIRST AND SECOND ENLIGHTENMENT
0a outline
FIRST ENLIGHTENMENT
0b galilean relativity and newton
0c descartes
0d aether and dogmatic thinking
SECOND ENLIGHTENMENT
0e einstein and extended relativity
0f kant and einstein
Og EPR Paradox
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0B.GALILEAN RELATIVITY AND NEWTON'S MODEL
Pre-Galilean, Aristotelian Physics considered immobility as
steady state of a body on which no force was acting. Under
action of force the body moved at speed proportional to the
force. When force ceased to act, the body returned to
immobility. It may look strange to us, but 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 on which no
forces act 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: all IR's 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" when it undergoes modifications entirely
determined by the transformation. This notion of "covariance"
under transformation should not be confused with "vector
covariance"
defined in DAB.VECTORS
============================================================
Invariant physical constructs are considered as absolute within a concerned Model.
Relative constructs are Covariant upon the Transformation of a concerned Model.
Galilean Relativity and Newton's Model are partially based upon an absolute
construct, the Galilean #Space. (#Space designates an abstract topological concept
such as Riemann #Space, sharply distinct from its unfortunate homonym "space" of
direct perception.)
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 (DAD AFFINE AND METRIC SPACES), while
Einstein's 4D continuum, as we shall see in 0D EINSTEIN AND EXTENDED RELATIVITY,
is Metric LighttimeSpace where the Galilean component "Time" is replaced by
"Lighttime" Ct having the measure of distance commensurable with the components
of Space.
Incommensurability of Galilean Time and Space excludes the notion of Time-Space
Interval and, consequently, of Transformation involving the entire Galilean
TimeSpace. On the other hand, constancy of speed 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 0D EINSTEIN AND EXTENDED RELATIVITY.
Given two IR's: R(O,X,Y,Z,T) and r(o,x,y,z,t) moving with respect to one another
along the common axe X-x at speed V the Time and Space Translations from R to r
are respectively:
t = T; x = X + a + VT; [1]
where a is the distance of o, origine of r 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 VDx with respect ot r moves at VDX = VDx + V with
respect to R:
Speed is additively Covariant under Galilean Transformation, which, after a few
simple mathematical operations results in the rule:
MECHANICS AND DYNAMICS ARE COVARIANT UNDER GALILEAN TRANSFORMATION
Relativity was doubtless Galileo's principal contribution to Foundations of
science, rigorous, complete and capable to support 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 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. In order to investigate
it from the point of view of Relativistic Dialectic we shall start by trying to
assign it to one of the basic classes: Continuous or Discrete. This classification
is essential, as -In order to truly map the Subject/Object Dialectic of Universe,
it (the Model) has to be based in "Subjective" Continuity and symbolize
"Objective" Discreteness as its Singularities.- (1D MAPPING AND MODELING).
At the first glance the answer seems obvious: Discrete. At Newton's time and for
centuries afterwards the fabric of Universe was dogmatically considered to be
corpuscular. Newtonian #Space was compactly filled with corpuscles acting on one
another like billiard balls and thus pretending to support Mechanics, Causality
(whatever it may 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 Universe, 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 Universe, ushered in the
Aether concept which dominated Physics till the beginning of the 20th century.
The corpuscular theory fell into oblivion until it apparently resurrected in the
Quantum Theory, at an incomparably higher level of complexity and in a form having
nothing to do with rudimentary mechanistic thinking.
Leaving for the moment Optics we shall move to Newton's Dynamics.
It's based upon 3 Laws of Motion:
1.In absence of force any object moves at constant speed.
2.Accelaration of an object 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
Dynamics, 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 start with 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 Universe 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 Universe.
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.
Now, Field is a factual construct and #Space an abstraction, so by virtue of the
Principle of Preponderance of Facts, it's Newtonian #Space that is primarily
called into question by the Second Paradox and should be reexamined in the first
place. We shall see below that the Paradox has been indeed considered and solved
in that way by the General Relativity.
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 the
calculus, which Newton had done so much to invent but largely left out of the
Principia.
And who says calculus, talks about Continuity. This argument seals our conviction
that Newton's Model was, at least implicitly, the first pioneering Continuous
Field Model which founded and determined the subsequent progress of Physics till
our own days.
