From: "Intervalic Theory" <intervalictheory@movistar.es>Subject: Intervalic Theory
Dear colleague:Please find attached the book INTERVALIC THEORY IN PHYSICS, that describes the intervalic structure of subatomic particles, deduced from the very last foundations of Physics, which involves an extraordinary change of paradigm in Physics.An "Abstract" is also attached (likewise in pdf format) which is the same chapter titled "Introduction" of the book.I hope it may be of interest to you.With best wishes.
Sincerely,Sydney d'Agvilo
President
INTERVALIC INSTITUTE
IntervalicTheory@movistar.es
Filadelfia 7
28028 Madrid
Spain
Fax: +34 91 741 11 01
The Intervalic Theory is the major paradigm shift that has occurred in
the history of mankind, affecting all disciplines. It was originally postulated
by Sydney d'Agvilo in 1987 in the field of Music, in 2005 in Physics, and in
2016 in the Economy, disciplines that respectively represent the bastions of
the three major branches of knowledge: the arts, the hard sciences and social
sciences.
From a historical standpoint the Intervalic Theory closes, in the most
unexpected way, the long gap existing between relativity and quantum
mechanics, two theories of Nature that are mutually incompatible: the first
one, of geometric nature; the second one, probabilistic. Most physicists have
been working for decades on trying to discover a theory of everything which
includes relativity in the quantum paradigm. On the contrary, the Intervalic
Theory has surprisingly formulated a theory of everything absorbing the
correct parts of quantum mechanics within the relativistic paradigm, which
from now on is also encompassed in a theory of everything more general: the
Intervalic Theory, which converts all Physics in geometry. This means the
failure of the probabilistic conception of knowledge and of the world, and
the triumph of the geometric vision; or in other words, the failure of pseudo
scientific empirical-inductive method, and the triumph of true scientific
method par excellence, the logical-deductive one.
Intervalic Theory, in any medium, is based on a single axiom: the
intervalic axiom, which simply states: "an interval exists". In physics, branch
that enjoys precedence over all others for obvious reasons, because it is what
explains the generation of the Universe, the intervalic axiom means that a
one-dimensional space line —an interval—, is the only thing whose
existence is postulated before the creation of the Universe, when there was
absolutely nothing, that is, neither matter nor energy, time or three-
dimensional space, much less the so-called "quantum vacuum". The
existence of a linear space interval necessarily implies the existence of
mathematics. Well, from the mathematical logic and a space interval of any
length there will necessarily generate time, energy, matter and all the
Universe we know. That interval is the intervalic length, ħ, very similar to
the Planck’s length value, although it could have taken any other value and
the Universe thus created would be identical and indistinguishable to the
current one because all physics constants —including the elementary
charge— are not fundamental indeed, but they are logically derived from the
only two fundamental constants of Nature, which compose the intervalic
dimensional basis of the intervalic system of physical quantities (and
because you can not measure anything from "outside" the Universe).
The interval axiom determines an intervalic dimensional basis, which is
different and not equivalent to the traditional ones (comprising length, mass,
time, etc.), being composed exclusively of length, L, and the imaginary
number i = √-1, both derived from the intervalic axiom. Alternatively, the
intervalic dimensional basis can also be deduced logically and necessarily
from the definition of time as imaginary space (T = iL), which is the
definition of time that was originally postulated in the Intervalic Theory in
Music.
The intervalic dimensional basis shows the astonishing fact that the
equation of dimensions of the two fundamental constants of Nature, namely
Planck's constant, and the speed of light, c, respectively coincide with the
two elements comprising the intervalic dimensional basis (L, i), being L the
dimension of ħ, and i the dimension of c (or i =-1, which produces an identical
dimensional system). The systematic combination of L and i generates
logically the intervalic group of all existing physical quantities, which are
exactly 40. As each and every one of the physical quantities thus generated is
a certain combination of ħ —the quantum of length— and c —the limit of
speed and of energy at subatomic scale—, we have got the remarkable result
that all physical quantities are simple combinations of the two fundamental
constants of Nature, ħ and c, and therefore all of them are geometrically
delimited by a lower mark —quantum— or a higher mark —limit—. This
means that there can not be infinite values for any physical quantity, and not
only for speed or action, as believed by quantum mechanics. This means, for
example, that there are no infinite masses or energies, which implies that
singularities can not exist (black holes) as they are described by some
science fantasy tales that make an improper use of relativity. In fact, the
intervalic cosmology, closely linked to the particle physics theory, shows
what is the intervalic structure of very massive stars, which are described
using some equations common to subatomic particles, being this study a
fascinating branch of the Intervalic Theory which explains a lot of
astronomical phenomena in a completely unattainable way for quantum
mechanics.
Traditional systems of physical quantities and units do lack of
epistemological range, meaning that two distinct physical quantities can have
the same equation of dimensions, that is to say, the equation of dimensions of
a physical quantity is not significant except formally. By contrast, the
intervalic system of physical quantities has got an epistemological range,
which means that if two physical quantities have the same equation of
dimensions equation, that means that they are the same magnitude, although
we have misinterpreted them as different in the past. This happens, for
example, with speed and energy, which are actually a single physical
quantity, or equally with acceleration and gravitational field, whose
discovery was, in words of Albert Einstein, “the happiest thought in my life”,
which led him to postulate the general relativity theory.
Algebraic operations between different physical quantities can’t be
performed on a single axis as in traditional systems, but as a result of the
introduction of the imaginary number i in the intervalic dimensional basis,
two axes are needed: a real one (representing the real component, L) and an
imaginary one (representing the imaginary component, i) —in mathematical
terms, an Argand space—. Because of the peculiar properties of the i
number, each successive integer powers of the speed of light, c, whose
intervalic dimension is i= -1, represents a turn of ±90° on the dimensional axes
of coordinates:
The geometric representation of any physical quantity on these
dimensional coordinates gives automatically an invariant geometric
measurement, which is to say that the transformations of Lorentz-Einstein of
special relativity are already included in the properties of the intervalic
dimensional space, being inherent to the intervalic metric itself, so it affects
to all physical quantities, standing out for its simplicity the intervalic
transformations of space, time, energy, mass or time regarding temperature,
as can be seen in the graph.
Some of the most important equations of physics, such as all of special
relativity, are derived in an independent way by the Intervalic Theory as
mere geometric statements of its intervalic equation of dimensions, since in
the Intervalic Theory all equations are relativistic, so there is no a non-
relativistic mechanics as in quantum mechanics. Among these geometric
statements it must be stand out what is possibly the most important formula
of Physics, the equation of intervalic energy, I, which establishes the
equivalence between electric charge, Q, and energy:
I = c±2 ħ Q-2
This equation, painfully unknown by quantum mechanics, plays a role
analogous to: E = c±2 m, which establishes the equivalence between mass and
energy, Einstein's famous equation now also deduced in an independent way
to relativity, as a simple geometric statement by the Intervalic Theory (please
note that the geometric constant c is always written ahead of the variables,
and their power is ±2 instead of +2, as the -2 power produces an identical
rotation (in single intervalic units where the value of c and ħ is set to the
unit).
Similarly is deduced geometrically the equation of the photon
momentum, which until now was only an empirical result: E = c p. It should
be noted that these important physical equations are always invariant
because they are mere geometric statements which describe the dimensional
equivalence between two physical quantities, which does not depend on the
frame of reference chosen.
Furthermore, when comparing the equivalent energy of mass and
electric charge is further exposed the initial gross mistake on which the
standard model is based, whose complex Lagrangian formalism can not hide
its serious inconsistency of misapplying the formula of the electromagnetic
potential energy to a particle which, according to the standard model itself, is
a mysterious "energy density" lacking of structure. But if this particle is not
composed by other sub particles, then, it can not possess electromagnetic
energy, since, by definition, this energy only makes sense applied to a
particle or to a body with structure, as it is well known by any high school
student. Clumsy inconsistencies like that, among several others as the
unwarranted use of about 20 arbitrary constants set ad hoc, were what led
Albert Einstein to never accept the validity of the standard model, who
always regarded it as merely provisional and baseless. It has been now
confirmed with overwhelming logic by the Intervalic Theory.
The systems of physical quantities and units have no physical meaning
(beyond the formal one), nor have any logical link with the equations of
physics. On the contrary, the entire corpus of physics and all the results
derived by the Intervalic Theory —which has not a single arbitrary
constant—, are geometric and logical statements necessarily deduced from
the intervalic quanta and limits of the intervalic system of physical quantities
and units, without the mediation of any complex mathematical formalism.
This is an outstanding feature of the strong logic economy with what has
been deduced the theory. This implies that the intervalic structure of
subatomic particles and the fundamental symmetries of Nature will never be
able to be discovered by quantum mechanics or any other theory that does
not use the intervalic —or natural— system of physical quantities, which
differs essentially from the rest ones because it includes the imaginary
number i = √-1 in its dimensional basis, which makes sense when you
consider that the i number i appears in most physics equations. Therefore,
any dimensional basis that does not contain the i number will not be able to
have any logical bond with physical equations (except symbolically), nor to
Mass Electric charge
Equivalent energy E = c±2 m I = c±2 ħ Q-2
Field energy U = G m2
/ r U = (1/4πε) Q2
/ r
11
deduct any of them. Hence, quantum mechanics is by his reason in an
impasse which impedes it to make further progress, as its last foundations are
incomplete and inconsistent.
The theoretical definition and the exact geometry value of the
elementary charge, e, and of the fine structure constant, α, are
straightforwardly deduced starting from the intervalic system of physical
quantities. Indeed, the definition and the geometric value of the intervalic
quantum of electric charge, qI, which is automatically deduced by simple
dimensional analysis, is:
qI = √-(c-1ħ) = 1 (i
-1/2L1/2) = 5.93398995 · 10-22 (C)
As it is usually explained in textbooks, the fine structure constant, α, is
a measure of the squared value of the elementary charge in natural units.
This value implies that the value of e is 270 in natural units, which coincides
exactly with the value of the elementary charge in intervalic units, so we can
say that the intervalic units are the genuine natural units, hitherto unknown:
e = 270 qI = 270 √-(c-1ħ) = 1.60217733 · 10-19 (C)
α = 2702
· 10-7 = 1/137.1742112 (1) —valor exacto—
This result, as final as obvious, had not been accepted by quantum
mechanics as a result of its absurd prejudice that subatomic particles lack of
structure, a quasi religious dogma, completely wrong, on which the standard
model is based, that has prevented significant progress in theoretical physics
for decades.
From here we can get the exact geometric values of fundamental
constants, rather than the traditional empirical values, of which c was set by
hand, e was empirically set, and ħ was derived indirectly from the previous
one. Now we know that there is a deviation of about 5/10,000 somewhere in
all these traditional empirical values gathered. Since the value of c is taken
by definition and e is quite reliable, we conclude that this small deviation is
on ħ, which can now be corrected and thus to define the exact geometric
values of the two fundamental constants of Nature (expressed in arbitrary
traditional units) from the exact theoretical value of the fine structure
constant:
c = 2702 ħ e
-2 = 2.9979246 · 108
(m/s)
ħ = 270-2
c e
2
= 1.0556363 · 10-34 (m)
The fact that the value of the elementary charge is 270 in intervalic or
natural units necessarily implies that the elementary charge is not the
quantum of electric charge, as previously thought, but that subatomic
particles have got structure, i.e., they are composed by other sub particles
even more fundamental. This result bankrupts the root paradigm of quantum
mechanics, which conceives subatomic particles as "energy densities without
structure", while according to the Intervalic Theory they are composite
particles, which have an intervalic structure —of extraordinary logical
economy and mathematical beauty—, of which all their physical properties
and also all fundamental interactions of physics are deduced, whose origins
were unknown to quantum mechanics.
In this way, subatomic particles are states of minimum energy that have
become very deep wells of electromagnetic potential energy, which is the
reason why they are all identical, and not because they obey certain
quantum, mysterious and inexplicable numbers, as postulated by the standard
model, or because there is an essential difference between the physical nature
of the subatomic world and the other one of the macroscopic or cosmological
world.
In fact, the results of the Intervalic Theory show that there is not such
difference, even between the organic and the inorganic world, as it is shown,
for example, by means of the ratio of the constituent energies —intervalic
and electromagnetic— of nucleon, which are ruled by the golden mean or the
Φ number, which also determines the pattern of so-called harmonious growth
of living beings. Well, it has been found that the Φ number also rules the
primordial intervalic synthesis of subatomic particles:
Structural energy ratios of nucleon
‹I(N)/U(N)› = 1.618829402 ~ Φ
‹I(N)/E(N)mass› = 0.618143766 ~ Φ-1
‹U(N)/E(N)mass› = 0.381855365 ~ 1 - Φ-1
Deviation from the golden mean, Φ
Δ[‹I(N)/U(N)›] = +0.0491593%
Δ[‹I(N)/E(N)mass›] = +0.0177623%
Δ[‹U(N)/E(N)mass›] = -0.0289759%
Among the thousand first natural numbers, 270 is what most classes or
symmetries possesses, each one of them indicates the existence of a well of
electromagnetic potential energy under the principle of minimum energy and
also under the intervalic principle of minimum information, being the former
one a simple corollary. From the point of view of chaos theory, the number
270 would be the principal attractor at subatomic scale, and its divisors the
13
secondary attractors. These 16 classes are natural dividers of 270, which
determine the values of the electrical charges of subatomic particles allowed
by the intervalic symmetries of the elementary charge, and are as follows
(expressed in natural units: e = 270):
1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Of these, half are unstable below its threshold temperature of synthesis,
being stable: 2, 3, 5, 6, 18, 30, 45 and 270. Although these intervalic
symmetries has been uncovered by the logical-deductive way, which is the
scientific method par excellence, the truth is that it could have also been
discovered via empirical-inductive, as far as it is an empirical evidence that
massive subatomic particles detected till today have got masses whose
values are proportional to the inverse square of 270, 45, 30, 18, 6 and 5, as
anyone can easily check. If this incontrovertible empirical data has not led to
the discovery of the Intervalic Theory previously, this is due to the absurd
prejudice of quantum mechanics to believe that subatomic particles are
punctual entities without structure, childish dogma, comparable to medieval
believing about the Earth as the centre of the Universe, which have
prevented the advance of Physics for decades. Certainly, in the annals of
Physics, after the missed belief in a flat Earth, the standard model of particles
without structure will be history as the most ridiculous mistake in Physics.
The synthesis of subatomic particles is always made obeying one of the
most fundamental principles of Nature: the spin-statistics theorem, of
mathematical origin, which states that any identical particles have a degree
of freedom, what means that the constituent particles of a subatomic particle
can only be in a symmetric or antisymmetric state under interchange, being
also generated both states in accordance with the general principle of
intervalicity, which allows only logical and necessary relationships between
the elements of the theory (or under the so-called universality assumption of
quantum mechanics, which would be a corollary of the above).
The fundamental law that rules the intervalic structure and the physical
properties of all subatomic particles is the intervalic principle of energy
balance, which states that the total energy or structural energy, A, of all
subatomic particles is composed by three factors: intervalic energy, I,
electromagnetic energy, U ≈ I-1 —whose magnitude is in inverse proportion
to the above—, and the spin energy, EJ —being the latter the only one not
manifested as mass but as kinetic energy—, according to the following basic
equation, also written in developed form below:
14
I - I-1 - EJ = 0
c±2 ħ Q-2 - [ 1⁄2(1/4πε0)Q2
/ r ] - m r2
ωJ
2 = 0
The intervalic energy, I, represents half of the structural energy, A, of
the subatomic particle, which coincides precisely with the Schwarzschild’s
mass for the particle:
A = 2 I
A = I + I-1 + EJ = c
±2 mSchw
If all the structural energy was manifested as mass, all particles would
have got exactly the minimum mass to be black holes. This never happens
because the spin energy does not contribute to the mass but it is manifested
as kinetic energy, being able to define the spin energy according to these
values:
EJ = c±2 (mSchw - m)
This further gives us a new definition of the Schwarzschild’s mass for
subatomic particles, since its magnitude is simply twice the intervalic
energy:
I = 1⁄2 c±2 mSchw
This is the energy balance that determines the fundamental underlying
architecture that forms the intervalic structure of all subatomic particles with
extraordinary beauty and logical simplicity.
Well, from here, it follows logically and inevitably the synthesis of all
subatomic particles that make the energy and matter in the universe, both
visible and dark, totalizing 108 visible particles (without including baryons
and mesons, which are monteverdinos) and 39 dark particles, whose
intervalic structures and physical properties have been described with full
geometric precision by the Intervalic Theory. The way that Nature has made
this, starting exclusively from the existence of an interval, is a way plenty of
logical elegance and disarming economy. Although the description of the
primordial intervalic synthesis of subatomic particles can not be condensed
into a short essay, we will try to offer some tables that show graphically the
intervalic structure of the most important subatomic particles.
The primordial intervalic synthesis of intervalic structures, which
originated from nothing all subatomic particles and fundamental interactions
of physics, has seven consecutive phases. In each phase it is synthesized an
intervalic structure in both symmetric and antisymmetric state under
interchange, being one of them visible matter or energy —particles which in
turn are the constituent sub particles of the next phase, which is still
synthesizing a new type of intervalic structure in symmetric and
antisymmetric state under interchange—, and other one dark matter or
energy —which does not continue with the process of synthesis, causing a
symmetry breaking, so that at each stage only one of the two states continues
the process of synthesis that leads to the next phase—.
Along with singularities (black holes), antimatter universes and parallel
universes, another one of the misleading myths that the Intervalic Theory
invalidates is that one of the Big Bang considered as a haphazard and
random explanation of the origin of the Universe. On the contrary, the
Intervalic Theory shows what the origin of the Big Bang, which was a huge
release of energy that came in the 4th phase of the primordial intervalic
synthesis: the dalino-synthesis —where dalinos were synthetized, which are
the first particles with electromagnetic energy—, a phase that began between
1.521843955 · 10-10 and 1.979589614 · and 10-9 seconds after the beginning
Main differences between the
INTERVALIC SYSTEM of PHYSICAL QUANTITIES
and all other systems of units and dimensions
• It is the unique dimensional system whose dimensional basis —(L,
i)— is just composed by the single intervalic dimensions of the last
fundamental constants of Nature, ħ and c: dim ħ = (L), dim c (i
-1).
Of course, the system has two formulations: dim c = (i
-1) or dim c =
(i), which are absolutely equivalent.
• Existing physical quantities are generated by all algebraic combina-
tions between the two dimensional basis —L and i— which makes a
finite and ordered set of 40 physical quantities. The number of physi-
cal quantities is given by the formula: 4 + 12n, being n the number of
actual dimensions of space.
• There are no physical quantities whose equation of dimensions have
more than the actual dimensions of space (3) and time (1), as in other
systems, which is absolutely a nonsense or, at least, an inconsistency.
• There are neither different physical quantities with the same equation
of dimensions (as in traditional units), nor different dimensions with
the same physical quantity (as in the misleading called “geometrized”
units, which is the poorest system of units ever made, not even being
consistent).
• The intervalic dimensions of all physical quantities can operate alge-
braically with the signs of its corresponding magnitudes in any equa-
tion.
• The own definition of all existing physical quantities as an algebraic
combination of c (i
-1) and ħ (L) yields unavoidably a geometric height
for every physical quantity, making the full set of INTERVALIC
QUANTA and INTERVALIC LIMITS, which form not only the
Intervalic Units, but above all, the foundations of the underlying
fundamental geometry of Nature, from which are derived the
genuine intervalic symmetries of Nature, long time searched by
Physics.
• Therefore, every physical quantity can not acquire any value, as each
of them is geometrically closed by its corresponding height: an inter-
valic quanta or limit, which is another great difference between the in-
tervalic system of units and the remaining systems, which like to play
with infinites and singularities.
• Being the intervalic dimensions the truthful units of Nature, the inter-
valic physical quantities have got an epistemological rank by means
6
of their equations of dimensions have got an heuristic value, which is
lacked in other systems. The most important example is the merging
of two traditional physical quantities into a new one because their in-
tervalic dimensions are identical. That is the case of: velenergy
(velocity-energy), frequorce (frequency-force) and poweration
(power-acceleration)-gravitational field strength. The merged physical
quantities means that they are really the same underlying physical
quantity, although in phenomenology there may appear as different in
incomplete or false dimensional systems. All this allow to unify inter-
valic dimensions, physical quantities and units in a unique concept, if
desired.
• When applying basic geometry to the intervalic dimensions inside the
Argand-like Intervalic Dimensional Space, a full set of invariant In-
tervalic Transformations of physical quantities is geometrically de-
rived. The Intervalic Transformations comprise the former Lorentz-
Einstein transformations of Special Relativity, which stays as a spe-
cific case inside a much wider geometry.
• Contrarily to supposed, the Intervalic System of Dimensions is the
unique system which is not equivalent to all the remaining dimen-
sional systems of units (which are, from now on, irrelevant in Physics
research).
• All results yielded in the Intervalic Theory of Particle Physics are geo-
metric statements logical and unavoidably deduced from the intervalic
quanta and limits of the Intervalic System of Units without using any
mathematical formalism.
• The Intervalic Theory is the unique Physics theory ever postulated
which has no one arbitrary constant.
• Inasmuch as c and ħ are universal constants, the intervalic quanta and
limits are reliable physical quantities of universal validity. The Inter-
valic System of Units is not an arbitrary one but the genuine system of
units of Nature. It must be noted that the intervalic symmetries of Na-
ture can not be deduced by means of any other dimensional system,
but only from the intervalic one. Thus its knowledge might be viewed
as a clue of the scientific degree of development of a civilization, and
so it is also apparent that the Intervalic Units are the unique which
could be shared with hypothetical advanced extraterrestrial intelligen-
ces.
• Any value expressed in intervalic units can be interpreted as a dimen-
sionless interval or ratio and Physics really becomes truthful Geome-
try. Hence the name of the Intervalic Theory.