in other words, the failure of pseudo scientific empirical-inductive method

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.