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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.
KANT'S FOUNDATIONAL VIEW
Kant's view may only be understood as foundation of the First
Enlightenment, as ontological support of the First Scientific
Revolution culminating in Newton's Model. We have seen that the
latter led to paradoxes which Newton dodged with his "hypotheses
non fingo" implying that physics does not deal with philosophical
foundations. Kant could of course not follow him there, as his
job consisted precisely in dealing with philosophical foundations.
Consequently, he conceived paradoxical foundations of paradoxical
science. With the advent of our Second Scientific Revolution,
Kant's view lost all avail and keeps for us only historical and
methodological interest. Especially the latter, showing how one
can sincerely derive an ontology rigorously supporting concurrent
science art and know-how. We follow this example endeavoring
to conceive an ontology rigorously underlying Einstein's Second
Scientific Revolution.
Kant's obsoleteness is the best guarantee of his greatness.
Philosophical views, unlike the scientific, don't follow a progress,
but come and go like waves on a pond, apparently contradicting one
another without these contradictions affecting them in any way,
nor thwarting them from springing in again.
There is little, if any sincere research of truth in established
philosophy. A view ressurrects just because a clever guy picks it up
for his thesis, knowing that it will flatter his supervisor and such
"peers" as he knows will review it. Neo-platonisms, neo-phenomenalisms,
neo-pata-physicalisms follow one another like waves on the ducks
pond ot the Reeking Valley without leaving any traces.
But Kant, leaving for obsoleteness left behind as deep traces as Newton
whom he underlaid.
KANT's AXIOMATIC
Discussing Kant may follow one of two ways:
1.Learn to use his terminology inside of the Universe of
discourse of his time. Only after having accomplished that
would we be able to talk reasonably about "synthetic
judgements a priori" and their role in "transcendental logic,
or aesthetic".
2.Express his Weltanschaung in contemporary terms.
We shall follow the second approach.
Any theory is for us, today, axiomatic. What would we see as
axioms and theorems of Kant's Weltanschauung?
Axiom A1: necessary and universal science exists.
Axiom A2: Science is created by inductive inference.
Axiom A3: Only a priori inference is necessary and
universal.
Axiom A4: Induction a priori requires subjective
representations a priori (categories) encompassing space and
time.
Axiom A5: Space and time are subjective representations a
priori. (According to Kant we can imagine "empty space"
without any "objects"[3] but we can only represent objects
in space. The same holds for time.)
Theorem T1, concluded from Axioms: Induction a priori is
possible, necessary and universal.
COMMENTS
A1: At Kant's epoch the First Scientific Revolution had
culminated in Newton's Model, whose rules and concepts were
considered as exact, necessary and universal. Even the 19th
century mechanistic Physics claimed those qualities. Only
the Einstanian Second Scientific Revolution turned to consider
science as fuzzy, relative and restricted, making A1
unacceptable for us.
A2: We nearly agree with it: for us the inductive inference
"verifies" rather than "creates" science.
A3,A4,T1: We accept now only induction a posteriori.
A5: Kant's main objective was to create the
"Transcendental Logic" with induction a priori in its
center. For this purpose A5 was a necessary addition
to A1. Yet, "Empty space" and "objects in space" are
clearly illusions of the "Naive View" (aka "Naive
Realism"). We had to wait for the Extended Relativity
to see the "empty space" abolished and replaced with
P_Equivalence of SPACE and Field. [4]
Transcendental Logic: Kant tried to create what
appears to us as a "prototype" of Propositional
Calculus. He failed due to missing mathematical and
logical tools, mainly the Boole Algebra.
He considered only statements, or, as we would say
"operands", but neglected the operators. His 'Logic"
was in fact just a classification of statements:
-Statements analytical a priori which we would call
deductive,
-Statements synthetical a posteriori which we would
call inductive,
-Statements synthetical a priori supposed to support
the induction a priori, unacceptable for us.
[3] The term "object" does not exist in Physics. In the
metalanguage it is multivalued and charged with noxious
metaphysical connotations. We use it here in order not to
diverge too far from Kant's terminology, as synonym
of "event".
[4] Phenomenal Equivalence (P-Equivalence):
Association of Aspects of a Phenomenon (Field Density
and SPACE curvature are P-Equivalent Aspects of the
Phenomenon "Cosmos"). P-Equivalence is often confused
with Causality. Its customary to say that "Field
curves SPACE", which is false, as they are both
"equally ranked" Aspects of a Phenomenon, coexisting
but not causing one another.
Similarly, continuous Field wave and discrete photons
are P-Equivalent Aspects of the Phenomenon "Light".
Einstein's lapsus
Einstein:
Concepts and Conceptual Systems get justified exclusively
by their capacity to coordinate events. They cannot be
justified in any other way. Therefore, it is, in my opinion,
one of the most pernicious acts of Philosophers to have
transferred some conceptual bases of Natural Science from
the controllable domain of empiric adequacy into inaccessible
height of the Necessary Apriori. This applies particularly
to our concepts of time and space, which the Physicists
- forced by the facts - had to descend from the Olympus
of Apriori in order to repair them and make them usable.
Einstein blamed Kant for having transferred some conceptual
bases of Natural Science (mainly time and space) from the
controllable domain of empiric adequacy into the inaccessible
heights of the Necessary Apriori.
Tatarkiewicz stood up for Kant who sincerely and rigorously
derived his view from his concurrent physics.
It's the Galilean Relativity which was based on absolute time
and space, and Einstein should have more justly blamed Galileo
and Newton. But, on the one hand, one does not see Einstein
blaming his masters on whose shoulders he always declared to
stand, and, on the other hand, they could hardly be blamed,
as nothing in their time could possibly call in question the
absolute time and space.
Newton's and Kant's Paradoxes
Newton's Paradoxes
-First Paradox: Gravity attraction intervenes between such
remote bodies as sun and earth which appears as Action at
Distance violating the basic Mechanistic dogma of "billiard
balls" acting locally on one another.
-Second Paradox: Gravity attraction is determined by space
(distance), but does not affect it in any way, which
violates the Reciprocity Principle (Action / Reaction).
Newton was perfectly aware of the Paradoxes which clearly
called into question the Noumenalistic dogma of absolute
space and its Mechanistic fabric of "billiard balls".
Questioned about them he refused to be dragged into
metaphysical speculations and answered with his famous
"Hypotheses non fingo", implying that Science coordinates
empiric data into consistent, predictable and verifiable
Models, but refrains from explaining them in terms of
Transcendency.
(Closer to us, Dirac repeated it in similar situation with
coarser terms: "Shut up and compute".)
The Paradoxes were solved by Einstein's Relativity replacing
Mechanistic dogma with the Phenomenal concept of Field and
its P-Equivalence with SPACE, both expanding at invariant
speed C as a continuous propagation of Local impulses.
Einstein rated the solution of Newton's Paradoxes as his
topmost achievement, because he admired Newton and considered
him as his Master.
We find it rather diverting that Newton's First Paradox may
be seen in inverted order. His Gravity apparently acting at
distance, in fact anticipated (extended) Locality by the
implication of continuous Field. On the other hand, the
pretended local action of hypothetical "billiard balls"
meant actually Action at Distance, small or rather undefined
distance of "balls" diameter, but distance anyhow.
Kant's Paradoxes
Kant has the historical merit of deriving Ontology of the
First Enlightenment from empirically verifiable Science,
rather than founding it, as it was the habit, in arbitrary,
aprioristic speculations. He derived his system from the
summit of his contemporary Science represented by Newton's
Model with additional postulate of Science being exact,
necessary and universal, thus absolute. Now, Newton's Model,
as all Physics of his time was based upon metaphysical dogma
of absolute time/space affine between time and space (lacking
a common measure) and having the fabric of "billiard balls".
These dogmatic foundations were in contradiction with Model's
physical laws. Facing it, Newton dodged the issue with his
famous "Hypotheses non fingo" implying that he restricted
himself to Physics and dismissed Philosophy.
Kant could of course not follow Newton in dismissing
Philosophy, as it was his essential dedication. Consequently,
and unlike Newton, he did endeavor to "make hypothesis", to
conceive Foundations of Science consistent with Newton's
Model. In doing so he chose the sincere, bona fide attitude
of deriving Ontology from the bedrock premise of empirically
verifiable physical Model. However, no matter how rigorous
the inference, the conclusion is only as good as the
premise: from a paradoxical Model Kant rigorously derived
a paradoxical Ontology.
1.Having rightly banned noumena (Dinge an Sich) from human
cognition, he created a Noumenalistic Ontology based on such
noumena as absolute time and space, and other absolute
categories of "Pure Reason", governing the Transcendency
from the heights of the Olympus of A Priori.
2.His Synthetic (in fact inductive) Propositions A Priori
reposed upon these aprioristic, dogmatic noumena in order
to satisfy the postulate of exact, necessary, absolute
Science.
Now, as Kant was first to admit, scientific induction stems
a posteriori from fuzzy Observations. He attempted
unsuccessfully to replace it with the Synthetic Propositions
A Priori destined but failing to prop up fuzzy observations
with necessary and absolute categories of "Pure Reason".
