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SECOND SCIENTIFIC REVOLUTION
Aether and dogmatic thinking
In Newton's Model Physics found a rigorous representation
of Gravity, which ruled unchallenged for centuries and even
currently continues to be the most pertinent approximation
for low speeds and weak Field areas.
Optics, on the contrary, lacked a consistent theory and
accumulated without cease new problems and difficulties.
As we said above ("FIRST SCIENTIFIC REVOLUTION"), physicists
abandoned the corpuscular theory of light replacing it with
wave theory, without, unfortunately, renouncing the dogma
of mechanistic cosmos. Following this dogma, they founded
Optics in a supreme noumenal crutch, in a hypothetical
corpuscular "substance" called Aether. It has been conceived
by analogy with well known wave phenomena such as sound whose
propagation is supported by discrete media, by oscillating
particles of corpuscular fluids - gases or liquids.
Light manifesting however, essentially different behavior than
sound, like propagating through vacuum, the theory started with
severe problems whose apparent solutions created other, still
more complex ones, reaching the apogee after the discovery of
electro-magnetic field by Maxwell. The complexity of mathematics
trying obstinately to save the purely a priori noumenal crutch,
surpassed that of most known theories. Aether was probably the
largest waste of effort and ingenuity in the history of science
which shows how dangerous it is to found scientific theories
in a priori metaphysical beliefs such as the mechanistic dogma.
This seems to be a crucial lesson for us living in an epoch
ruled increasingly by irrational beliefs, torn by religious,
chauvinistic wars and genocides, where dogmatism is gaining
all social domains including established science and education,
where exorcists graduating from the Pontifical Regina Apostolorum
University of Vatican, together with other Creationists and
Intelligent Designists infiltrate "scientific education" and
start talking about resurrecting geocentric cosmology founded
in sacrosanct verbatim interpretation of Genesis. Amidst this
deluge of aggressive Dogmatism, the souvenir of Aether mishaps
may help to save at least the Rationality of Science.
As the Aether theory has been irremediably scrapped, we shall
just mention some of its principal problems without entering
into details of involved complex mathematics.
Light propagates through vacuum and "matter" such as glass or
water, thus the whole cosmic space must be filled by Aether,
whether the apparent vacuum or "material substances".
Mechanistic view suggests that Aether should present resistance
to movements of stellar bodies. but no such effect has been
observed and they keep on moving undisturbed through interstellar
space.
So, Aether had to be retackled to make it interact with light but
not with "matter". Mathematic difficulties apart, how could such
a "substance" be reconciled with mechanistic view, is a mystery.
Apparently, the Olympus of a priori allows to stretch any point
to make it fit any dogmatic construct.
Anyway, all these efforts were in vain: going through glass or
water light changes speed, so Aether has to interact with "matter".
New mathematical crutches reached hardly ever equaled complexity
having to take care of an additional difficulty, namely polarization
requiring transverse light waves. Those require in turn the
propagating medium to behave as a solid.
So one had to deal with a "substance" which behaves like a solid
with respect to light, like no-interaction vacuum with respect to
"matter" of stellar bodies, while interacting with "matter" which
it permeates like glass or water in a way to modify the speed of
light waves in function of their length. Mathematical problems apart,
the pile of contradictions involved by such "substance" should
have indicated its aberration, but one would shirk nothing to save
a dogmatic belief: mathematical acrobatics described a "substance"
vacuum-like at macroscopic sizes, solid-like at ultramicroscopic
sizes, sometimes interacting with "matter" and sometimes not.
It could be expected that Maxwell's definition of light being
a particular case of electro-magnetic Field propagating at the
speed C, would sound the knell of Aether phantasm. Especially,
considering that Galilean Relativity banning absolute speed and
privileged referentials, required this C to be the same in all
IR's (Inertial Referentials). But the mechanistic dogma was
too strong and rather than call it in question, physicists
sacrificed on its altar the very base of their contemporary physics,
the Galilean Relativity. Aether became a universal, ABSOLUTE,
absolutely immobile referential, in which light moves at C.
Strangely enough nobody noticed, or at least nobody mentioned
that mechanics being at the time defined and covariant exclusively
in IR's, it was illegal to apply mechanistic principles to the
absolute Aether, nor that all other IR's became absolute by virtue
of their relations to Aether, thus making Physics universally
unfounded and undefined.
Be it as it may, light was supposed to move in other referentials,
for instance at Earth, at speed Ce = C + Ve, where:
Ce is speed of light with respect to Earth,
Ve is speed of Earth with respect to Aether.
This assumption called for empiric verification: Ce measured as
different from C would confirm the existence of Aether and
determine the ABSOLUTE spead of Earth with respect to ABSOLUTELY
immobile Aether.
However, the Michelson-Morley experiment proved that light moved
with respect to Earth at Maxwell's speed C, thus refuting the
hypothesis of universal, absolute and absolutely immobile Aether.
With unbelievable obstination some physicists made last superhuman
efforts to save the mechanistic dogma by restructuring Aether so
that it would be "dragged" by stellar bodies thus moving in their
vicinity at their speed. However, this hypothesis would involve C
depending of the speed of light source which was experimentally
refuted and Aether finally died taking with it into the grave
the metaphysical mechanistic dogmatism.
This critique of the Aether Model may look rather severe, but it
may by no means be interpreted as looking down on Planck, Maxwell,
Lorentz and other great physicists who argued for it with ingenuity
surpassing most other scientific endeavors.
It is meant to emphasize the dangers of founding theories dogmatically
in a priori metaphysical beliefs, actually more serious for socio-
political than for physical theories. For physics such dangers are,
after all, restricted to science. For socio-political domain dealing
with demography, ecology, religious and ethnic fundamentalism,
globalized economy, politics and warfare, they cast doubt upon the
very survival of the mankind.
EINSTEIN AND EXTENDED RELATIVITY
The Extended Relativity (ER) may be seen as a super-model
realized in two steps - the Special and the General Relativity.
Derivation and internals of ER are shown in Tome 2. Here we
shall look at it from outside, from the epistemological point
of view concerning its context, foundations and impact.
The impact of ER exceeds even that of Heliocentrism and Evolution.
Besides similarly revolutionizing the Weltanschauung, ER brought
about a wholly new reason, by radically dissociating rationality,
and science from the "common sense" and by founding it in the basic
structure of the human Universe - in the Continuum/Discreteness
(CD) polarity.
If by its impact ER is the most important contemporary model,
it stands alone by the simplicity of its epistemological
foundations. We shall review them in two sections refering to
Special and General Relativity, preceded by a brief overview
of their context.
CONTEXT
The Michelson-Morley experiment sounded the knell of Mechanistic
Dogmatism and of the Aether's phantasm. Physics, deprived of
foundations lost momentarily its essential meaning. However, the
void was not complete. Aether left in its ruins some most
ingenious recipes hanging for the moment in emptiness, but ready
for constructive use, once some firm ground reestablished.
To mention two of them:
1.Maxwell described the structure of electromagnetic Field,
has shown that light is electromagnetic wave and determined
analytically its speed C getting exact agreement with empiric
data. But speed with respect to what? Apparently, to Aether,
the unique absolute, omnipresent Referential, even if such
absolute Referential wrecks Galilean Relativity. But it was
Aether that got wrecked by the Michelson-Morley experiment.
2.Lorentz conceived an ingenious recipe, the Lorentz
Transformation (L-Tr) which replaced Galilean Transformation
and supported the invariance of C in Aether's context. It was
the last attempt to save the Aether and failing it the L-Tr
lost its physical foundation and sense.
In the meantime Mathematics made great progress. Rieman and
Lobatschevski conceived parabolic and hyperbolic SPACES,
Levi-Civita developed Tensor Calculus, which allowed to
define metrics of non-Euclidean SPACES, to deal with their
curved coordinates and to formulate physical laws in
covariant form.
SPECIAL RELATIVITY (SR)
In this context, unlike other physicists, who tried to mend
their collapsed dogmatic crutches, Einstein dared to throw
them away and to set out walking by himself. We shall try to
retrace some of his most eventful walks.
After the collapse of Aether and of the mechanistic Dogma,
Physic found itself devoid of foundations and lacking a Model
capable to represent Electromagnetism and Light. The
astounding effectivity of Newton's Model and Galilean
Relativity in representing mechanics from local to cosmic
scale pleaded for extending them over Electromagnetism and
creating an "Extended Relativity" (ER) rather than starting
all from the scratch.
This extension posed two essential problems:
1.With Aether Physics has lost the support of Field and was
left with two apparently disparate and unrelated Continua,
Field and SPACE. One had therefore to look for some way of
reconciling them. Field being a factual construct and SPACE
an abstraction, first to reexamine was Newtonian SPACE, by
virtue of the Principle of Preponderance of Facts.
The first step consisted therefore in researching some new
SPACE capable of founding a Model supporting in IRs the
covariance of Electromagnetism alongside with that of
Mechanics.
2.Incompatibility of the Galilean Transformation with
invariance of C in IRs. We have seen above that, trying
vainly to save Aether, Lorentz conceived his famous L-Tr
which supports the invariance of C. However, deprived of
foundation after Aether's collapse L-Tr stayed an ingenious
mathematical construct void of physical sense.
Consequently the new SPACE of the SR, besides reconciling
itself with Field has to support a Transformation similar
to the L-Tr, or if possible identical with it.
Derivation of SR and of its underlying SPACE is described
with mathematical details requiring basic knowledge of
Tensor Calculus in the Tome 2, Here, we shall concentrate
on the intuitive creativity in Einstein's train of thought,
limiting mathematical tools to the Theorem of Pitagoras and
recalling that L-Tr postulates that for an IR moving with
respect to an observer, time appears to the observer to slow
down and length of physical bodies to shrink in the direction
of the movement.
Quadratic Form of Euclidean SPACE
Let's recall the concept of Elementary Displacement in the
Euclidean SPACE of the Galilean Relativity.
Let RR: O,X1,X2,X3 be an IR with center in O and orthogonal
coordinates X1,X2,X3.
For a point distant from O by Elementary Displacement dS we
have by virtue of the Theorem of Pitagoras:
dS^2 = dX1^2 + dX2^2 + dX3^2
Now, let rr: o,x1,x2,x3 be another IR with axes x1,x2,x3
respectively parallel to X1,X2,X3, moving with respect to RR
in direction X1/x1 at speed V.
As distance is Invariant under Galilean Transformation dX1
transforms from RR to rr invariantly: dx1 = dX1.
Axes x2,x3 are not affected by the movement: dx2=dX2, dx3=dX3
and finally:
ds^2 = dx1^2 + dx2^2 + dx3^2 = dX1^2 + dX2^2 + dX3^2 = dS^2
ds^2 = dS^2: dS is invariant under Galilean Transformation
We shall call dS^2 = dX1^2 + dX2^2 + dX3^2
the "Characteristic Quadratic Form" of Euclidean SPACE
and note that
QUADRATIC FORM OF EUCLIDEAN SPACE IS INVARIANT
UNDER THE GALILEAN TRANSFORMATION.
Derivation of the Quadratic Form of SR SPACE
Derivation of SR Model boils down to research of an invariant
Quadratic Form characterizing a SPACE which would replace
Galilean Transformation with one supporting invariance of C,
if possible, with the already existing Lorentz Transformation.
Let RR: O,X1,X2,X3,T and rr: o,x1,x2,x3,t be two IRs, moving
relatively at subluminal Vl. at t=T=0 both referentials coincide
spacially and O of RR emits a light signal propagating as a
sphere. After elementary time increment dT O will find itself
in the center of light sphere of radius dR = CdT. By virtue of
the Pitagoras Theorem for each point of the sphere we have:
dR^2=dX1^2+dX2^2+dX3^2 or (CdT)^2=dX1^2+dX2^2+dX3^2 [1]
Now, due to the invariance of C, o of rr will find itself
also in the center of light sphere:
(Cdt)^2 = dx1^2 + dx2^2 + dx3^2 [2]
Transferring CdT and Cdt to the right hand side of [1],[2]
dX1^2+dX2^2+dX3^2-(CdT)^2 = dx1^2+dx2^2+dx3^2-(Cdt)^2 = 0
In order to maintain notation similar to that of the Euclidean
Quadratic Form we shall write "-(CdT)^2" as "X4^2" and
"-(Cdt)^2" as "x4^2" and say that the Quadratic Form of the
SR SPACE is invariantly equal zero:
dS^2=dX1^2+dX2^2+dX3^2+dX4^2=ds^2=dx1^2+dx2^2+dx3^2+dx4^2=0 [3]
[3] defines the 4 dimensional SR SPACE having 3 real coordinates
x1,2,3 and one imaginary x4=sqrt(-(Cdt)^2) = iCdt or LightTime (LT)
(where i=sqrt(-1)).
Expressing these coordinates in units we get the "signature" of
this SPACE: 1,1,1,i
SPACE of this signature is known as Minkowski SPACE (M-SPACE).
Let's note that M-SPACE is Metric as its all 4 dimensions
including LT have the measure of distance. Thus it transforms
covariantly in all 4 dimensions. In other terms SR SPACE,
unlike the absolute Newtonian, is relative, being covariant
under L-Tr (anticipation of Tome 2. In particular, covariance
of x4=-iCt, with invariant C implies covariance and relativity
of time.
Now, a transformation may consist of translation, rotation or
a combination of both. We have seen that translation would make
C depending on the relative speed of source and observer, so it's
excluded by the Axiom of C invariance and we are left with
rotation: for rr moving along x1, the transformation amounts to
rotation in the plane x1/x4 (or x1/iCdt). x4 being imaginary,
the plane is complex and the rotation is called "pseudo-rotation".
As shown in Tome 2, this pseudo-rotation is equivalent with Lorentz
Transformation.
SR is therefore sometimes called "Rotational Relativity" as
contrasted with the Galilean "Translational Relativity".
SR marked the demise of dogmatic, noumenalistic science and
philosophy laying down the outset of axiomatic, rational science
and rational ontology. We shall return to its philosophical
impact in conclusions of this chapter, after having reviewed
the General Relativity. Now we shall briefly recollect some
essential findings and restrictions of SR. ("V" will mean the
speed of observed referential relatively to the observer.)
Findings:
1.Phenomenal nature of Field observable as Force it exerts on
detectors.
2.Phenomenal Equivalence of Field and SPACE resulting from
dropping all physical supports of Field else than SPACE
itself.
3.Phenomenal nature of SPACE; corollary of 2 and subject of
covariant transformations
4.Distance contraction and Time dilation increasing with V.
5.Phenomenal Equivalence of Mass and Energy (E=MC2)
6.Increse of Mass (and Energy, corollary of 5.) with V.
7.Phenomenal Equivalence of Field, Energy (and Mass,
corollary of 5).
Comment of 5. In the postface of Tome 2 "derivation of e=mc2"
we say:
***
E=MC**2 illustrates the P-Equivalence of Mass and Energy.
This simple statement has surprisingly deep implications.
Indeed, Mass and Energy have no phenomenal sense and are
just coefficients in formulas representing phenomenal,
observable construct "Field". Under the disguise of pure
abstractions, E=MC**2 implies P-Equivalence of Electro-
Magnetism and the fields constructing subatomic particles.
A decaying particle converts involved quantity of a strong
field to enormous amount of radiation weaker by factor C**2.
Seen from Special Relativity, E=MC**2 appears as anticipation
not only of the General Relativity, but also of the Quantum
Field Theory.
***
Restrictions:
The French call SR "La Relativite Restreinte" (Restricted
Relativity), which describes it quite well: SR, while
extended over electromagnetism, maintains the Galilean
restriction to inertial referentials (IRs). Yet, no strictly
inertial referential has ever been observed and the
observable cosmos seems to consist exclusively of NIRs
(Non Inertial Referentials). True, many can be approximated
as IRs and SR is an acceptable approximate model of a vast
range of phenomena. Nevertheless, as one could not a priori
except the possibility of some other phenomena, incompatible
with IRs, it appeared vital to extend the SR over NIRs, i.e.
over the total observable cosmos.
We shall now review this extension known as the General
Relativity.
GENERAL RELATIVITY (GR)
It may be said that the more complex a Model is in detail,
the simpler are its foundations. GR is founded on three
astoundingly simple principles: The Covering Principle,
Reducibility to SR and Axiom of Equivalence.
-Covering Principle: For the first time in history an
ontological principle is used directly as an axiom of a
physical model. We defined it in "NATURAL MODEL" as the
general principle of discrete events measuring the SPACE
continuum. For physics it boils down to the requirement
of measuring distance with physical rods complying with
physical rules, such as the Lorentz Contraction.
-Reducibility to SR: Just as SR is an extension of Newton's
Model and reduces to it for slow speeds, GR was postulated
as an extension of SR reducible to it locally for weak
Field areas of NIRs.
-Axiom of Equivalence: Since Galileo's Experiment, inertial
and gravitational mass were known to be equal, but it has
been attributed to coincidence. Einstein elevated this
equality to identity, improperly called "Equivalence".
Using "masses" shortcuts it means that gravitational and
inertial fields are indistinguishable from inside of
a system. It extends over gravity the GR initially derived
for inertial field (see "ROTATING DISK" below).
Never a deeper scientific, intellectual and philosophical
revolution has been founded on simpler Postulates.
ROTATING DISK
The actual derivation was just as simple as the Postulate:
it boils down to a simple mental experiment known as
"Rotating Disk" which we describe here very superficially.
(Details in Tome 2).
Given on a stationary and rotating disk circles of radius R
and circumference S, Euclidean Geometry tells us that on the
stationary disk S=2 pi R. On the Rotating Disk we'll measure
R and S with elementary physical rods ("Einstein's Covering
Principle"). Along R the rods perpendicular to the rotation
are not affected by it and R conserves its Euclidean length.
However, upon S they move in rotation sense and experience
the Lorentz Contraction by virtue of Reducibility to SR.
Thus rotating S will need more contracted rods to be covered
than in Euclidean SPACE and its length will be measured as
longer. On the Rotating Disk we have S > 2 pi R. This
defines Lobachevsky or hyperbolic curved SPACE and indicates
that rotation determines geometry and SPACE.
And that's it, GR is derived. There follows the extension to
gravity via the Equivalence Postulate and a lot of most
complex mathematical expressions, but it all rests on the
simple "Rotating Disk". The most complex theory rests on
the simplest mental experiment.
FIELD AND SPACE
The NIR "Rotating Disk" suggests that rotation determines
SPACE. However, Relativity tells us that if NIR rotates with
respect to IR, then reciprocally, IR rotates with respect to
NIR. And yet, IR's geometry is Euclidean. In other terms the
old Galilean definition of IR based upon relative movement is
no more sufficient and we have to look for some other criterion
to distinguish IRs and NIRs.
Now, a detector placed on the circumference S of the Rotating
Disk experiences centrifugal force directed towards disk's
exterior: our NIR is a seat of inertial field. On the contrary,
a detector placed in IR will detect no centrifugal force and
no inertial field.
REDEFINITION OF IR AND NIR
Thus Inertial Field is the essential difference between IRs
and NIRs and SPACE is determined by inertial field engendered
by rotation rather than by rotation itself. As, by virtue of
the Equivalence Principle, inertial and gravitational fields
are equivalent we may consider field (indiscriminately inertial
or gravitational), as the criterion allowing to distinguish
between IRs and NIRs.
Finally, we may formulate the relation between field and SPACE
as follows:
-Field determines SPACE, whose curvature increases with field's
strength.
-SPACE determines field's strength, which increases with SPACE
curvature.
This mutual, reciprocal determination of SPACE and field solves
Newton's SPACE-Field Paradox: Newtonian field was determined
by distance (SPACE), but had no impact on SPACE, which contradicts
the Action-Reaction Principle.
Einstein considered solving this Paradox as the most gratifying
of his achievements because he admired and venerated Newton as
his Master.
A FEW WORDS ON NON-EUCLIDEAN SPACES
We are all familiar with "S = 2 pi R" in the "flat" Euclidean
SPACE.
The "S < 2 pi R" of Riemann or parabolic SPACE may be
easily visualized and verified with pieces of string and
circles drawn on any sphere.
Euclidean SPACE may be considered as a limit case of
Riemannian sphere getting "infinitely large", its radius
tending to infinity and the curvature of the increasing
sphere tending towards zero, or "flatness", giving
"S = 2 pi R".
Hyperbolic SPACE may be imagined as going past this limit,
where our surface gets "superflat", or its curvature gets
negative, giving "S > 2 pi R".
PHILOSOPHICAL IMPLICATIONS OF EXTENDED RELATIVITY
SR marked the demise of dogmatic and the outset of axiomatic,
rational and falsifiable Science. One may object that its
predecessor, the Aether Theory was already an Axiomatic
Theory founded on the Axiom of Aether.
It's true enough, but let's keep in mind that, besides its
own "intrinsic" Axioms, a Theory has usually other,
"external" foundations. When founded on an external Theory,
it accepts the external assertions as its own Axioms.
Intrinsic Axioms of the founded Theory must be compatible
with the external assertions and often, as in the case of
the Aether Theory, instantiate them.
Now, the Aether Theory, as the whole pre-Einsteinian Physics,
was founded on dogmatic belief that Physics deals directly
with transcendental, noumenalistic "Reality", having the
mechanistic structure of "billiard balls". Light has been
considered as wave and in mechanistic world waves must have
some corpuscular fluid support, like air or water. Light
propagating through vacuum as well as through transparent
"matter", its mechanistic fluid support had to be universally
present. Hence the Axiom of Aether, a universal mechanistic
support of light, which was not only compatible with the
metaphysical mechanistic Dogma, but actually instantiated it.
Consequently, Aether was a very particular concept, Axiom
and Dogma at the same time. It was an Axiom within the
Aether Theory, an ultimate premise of a perfectly legitimate
inferential structure exposed to inductive verification /
falsification. Yet, it was also an instance of the
mechanistic Dogma. As Axiom it has been falsified by the
MM Experiment, but as Dogma it opposed unusual resistance to
refutation. Greatest scientists endeavored to save it at the
cost of superhuman efforts. Lorentz for instance derived his
famous L-Tr, a mathematical construct compatible with the
invariance of C. However, it was void of physical sense in
the mechanistic Newtonian SPACE, affine in space/time
planes, thus ignoring in them the notion of distance and,
consequently, of any transformation. Facts contradicted
Aether, but Lorentz believed in it and endeavored to save it
at any price.
One recalls Hegel who, informed that observations contradict
his astronomical a priori drivel, that facts disagree with
his speculations, answered: "So much the worse for the facts".
However, Lorentz was not a conceited metaphysical preacher,
but a great sincere scientist trapped in the universal
belief in the apparently necessary Foundation of Physics,
the transcendental mechanistic view.
It shows how deeply rooted and how difficult to eradicate is
a Dogma, once it takes over a domain of human cognition.
It stresses also the courage it took to get rid of the Dogma
with all involved crutches and to set out walking by oneself
over the swampy land lacking any founding bedrock. Physics
deprived of mechanistic foundation seemed to hang in the air;
light waves propagating without support defied the reason.
In that situation Einstein conceived new foundation of
Physics providing the so far purely mathematical constructs
Field and SPACE with astounding physical, Phenomenal sense
and Equivalence. Physics and Science, got new, purely
Phenomenological Foundations.
All Concepts fell from the inaccessible heights of the
Transcendental Olympus of Apriori into the controllable
domain of empiric, phenomenal adequacy.
Just as the Scientific Revolution of the First Enlightenment,
Einstein's Extended Relativity revolutionized the Foundations
of Science which laid the cornerstone of the Second
Enlightenment and its Phenomenological Weltanschauung.
However, facing tenacious resistance of the still dominating
Noumenalism it could not rise far beyond this cornerstone.
While Popper's Epistemology and Heidegger/Sartre's Ontology
display some of its sprouts, they neglect several fundamental
concepts such as Polarity, the base of Relativistic Dialectic
which in our opinion embodies the Reason of the Second
Enlightenment. Established Logic, untouched by it, is still
entirely noumenalistic and so are its explicit or implicit
applications to human and socio-political domains. The world
is governed by inhuman devastating Dogmatism calling in question
the very survival of the mankind. Einstein's assertion "A new
manner of thinking is essential if humankind is to survive"
gets every day more pressing.
