TABLE OF CONTENT

1. INSUFFICIENCIES OF THE 20-TH CENTURY THEORIES

1.1. THE LEGACY OF LAGRANGE AND HAMILTON.

1.2. INSUFFICIENCIES OF SPECIAL RELATIVITY

1.3. INSUFFICIENCIES OF GENERAL RELATIVITY

1.4. INSUFFICIENCIES OF EINSTEIN'S THEORIES FOR ANTIMATTER

1.5. INSUFFICIENCIES OF QUANTUM MECHANICS

1.6. INSUFFICIENCIES OF NUCLEAR PHYSICS

1.7. INSUFFICIENCIES OF PARTICLE PHYSICS

1.8. INSUFFICIENCIES OF QUARKS AND NEUTRINOS CONJECTURES

1.9. INSUFFICIENCIES OF QUANTUM CHEMISTRY

1.10. INSUFFICIENCIES OF BIOLOGY

1.11. INSUFFICIENCIES OF ASTROPHYSICS AND COSMOLOGY

1.12. INTRODUCTORY READINGS

2. SANTILLI'S DISCOVERIES IN MATHEMATICS

2.1. FOREWORD

2.2. DISCOVERY OF NEW NUMBERS
2.2A. Discovery of isonumbers (1983)
2.2B. Discovery of genonumbers (1993)
2.2C. Discovery of hypernumbers (1994)
2.2D. Discovery of isodual numbers (1993)

2.3. ISO-, DISCOVERY OF GENO-, HYPER-DIFFERENTIAL CALCULI AND THEIR ISODUALS (1996)

2.4. DISCOVERY OF ISO-, GENO-, HYPER-, SPACES AND THEIR ISODUALS (1983).

2.5. DISCOVERY OF ISO-, GENO-, HYPER-SYMPLECTIC GEOMETRIES AND THEIR ISODUALS (1996)

2.6. UNIFICATION OF MINKOWSKIAN AND RIEMANNIAN GEOMETRIES (1998)

2.7. ISOTOPIC COVERING OF LIE'S THEORY AND ITS ISODUAL (1978)

2.8. LIE-ADMISSIBLE COVERING OF THE LIE-ISOTOPIC THEORY AND ITS ISODUAL (1967)

2.9. INTEGRABILITY CONDITIONS FOR THE EXISTENCE OF A LAGRANGIAN
2.9A. Integrability conditions in Newtonian mechanics (1978).
2.9B. Integrability conditions in field theory (1975)

3. SANTILLI'S DISCOVERIES IN PHYSICS

3.1. FOREWORD

3.2. ETHER AS A UNIVERSAL SUBSTRATUM (1952-1955)

3.3. ORIGIN OF THE ELECTRIC AND MAGNETIC FIELDS (1955-1957)
Ethical notes

3.4. ORIGIN OF THE GRAVITATIONAL FIELD (1974)
Ethical notes

3.5. SYMMETRY OF THE ETHER (1970)
Ethical notes

3.6. QFT (AND QCD) LIMITS FROM DISCRETE SYMMETRY VIOLATIONS (1974)
Ethical notes

3.7. RESOLUTION OF THE HISTORICAL IMBALANCE ON ANTIMATTER (1994)
3.7A. Newton-Santilli isodual equation for antimatter
3.7B. Isodual representation of the Coulomb force
3.7C. Hamilton-Santilli isodual mechanics
3.7D. Isodual special and general relativities
3.7E. Antigravity
3.7F. Experiment on antigravity
3.7G. Isodual quantum mechanics
3.7H. Experimental detection of antimatter galaxies
3.7I. The new isoselfdual invariance of Dirac's equation
3.7J. Isoselfdual spacetime machine
3.7K. Original literature
Ethical notes

3.8. INITIATION OF q-DEFORMATIONS OF LIE THEORY
Ethical notes

3.9. THEOREMS OF CATASTROPHIC INCONSISTENCIES OF
NONCANONICAL AND NONUNITARY THEORIES

The majestic consistency of Hamiltonian theories.
3.9B. Theorems of catastrophic inconsistencies of noncanonical and nonunitary theories.
3.9C Examples of catastrophically inconsistent theories.
Ethical notes

3.10. SANTILLI ISO-, GENO-, AND HYPER-RELATIVITIES AND THEIR ISODUALS (1978)
3.10A. Historical notes
3.10B. Santilli's opening statement
3.10C. Coneceptual foundations
3.10D. Mathematical foundations
3.10E. Invariance and universality of Santilli's isotopies.
3.10F. Poincare'-Santilli isosymmetry and its isodual
3.10G. Isorelativity and its isodual
3.10H. Experimental verifications
3.10I. Isogravitation and its isodual
3.10J. Absence of expansion of the universe
3.10K. Absence of dark matter in the universe
3.10L. Proposed astrophysical experiments
3.10M. Isotopic reconstruction of exact spacetime symmetries when conventionally broken
3.10N. Geno- and hyper-relativities and their isoduals
3.10O. Primary literature

Ethical noltes

3.9. HADRONIC MECHANICS
UNDER CONSTRUCTION
<3,9A. Foreword
Newton-Santilli isoequations
Hamilton-0Santilli isomechanics
Animalu-Santilli isoquantization
Heoisenberg-Santilli isoequations
Experimemntal verifications
Primary literature
Ethical notes
NEUTRON SYNTHESIS
MESONS SYNTHESIS
KALNAY-SANTILLI QUARK CONFINEMENT

3. SANTILLI DISCOVERIES IN CHEMISTRY

3. EPILOGUE

*********************************************

PREFACE

Santilli's discoveries have been the subject of a large number of contributions by scientists around the world we regret not to be able to review here to prevent a prohibitive length. For contributions by other authors, interested scholars may consult the 90 pages long General Bibliography on Santilli Discoveries

Interested researchers or historians are suggested to exercise caution in using preprints of various works that are still circulating in the scientific community, because Santilli had the habit of quickly writing papers, sending them to colleagues for comments and criticisms, and finalizing them only at the time of publication. In same cases, due to the vast nature of the scientific production and Santilli's multiple duties, unedited versions ended up being published, thus requiring errata-corrige. Serious scholars should be aware of this occurrence, and verify the final character of the papers prior to expressing their views. In the event verifications of final character of a given work is needed, scholars are suggested to contact "board(at)santilli-foundation(dot)org".

1. INSUFFICIENCIES OF THE 20-TH CENTURY THEORIES

Santilli conducted his graduate studies in theoretical physics in the late 1960s at the University of Torino, Italy, where J. L. Lagrange lived and conducted his research. In this way, Santilli had the opportunity of studying the original papers by Lagrange (some of which had been written in Italian), thus learning Lagrange's originator conception of his celebrated analytic representation of nature (dating to 1788) as requiring two quantities:

1) A function L(r, v) = K(v) - V(r), today known as the Lagrangian, where r = (r^k), k = 1, 2, 3, are the coordinates, v = dr/dt represents the velocity, K(v) = v² m/2 is the kinetic energy, and V(r) represents all action-at-a-distance forces derivable from a potential, plus

2) The external terms, F(t, r, v), that is, terms external to his analytic equations representing all forces not derivable from a potential or a Lagrangian.

Santilli then studied in British libraries the original works by W. R. Hamilton and discovered that in 1834 he had essentially the same conception as that by Lagrange for the analytic representation of nature as characterized by a function, today known as the hamiltonian representing the total energy in a space (today called cotangent bundle) with local coordinates r and p = m v,

The advent in the early 1900 of special relativity and quantum mechanics caused a major alteration of the original analytic conception of nature by Lagrange and Hamilton. In essence, both special relativity and quantum mechanics are strictly Hamiltonian theories, that is, they only admit one quantity, a Lagrangian or, equivalently, a Hamiltonian, and show no possibility of accommodating the external terms short of a major structural revisions.

Consequently, the widespread posture of the 20-th century physics was to eliminate Lagrange and Hamilton external terms and solely work with equations today called the truncated Lagrange and Hamilton equations. A general argument was that the forces represented by the external terms are "fictitious" (sic) because, the argument says, when a system in our environment is reduced to its elementary constituents, all non-Lagrangian or non-Hamiltonian forces "disappear" (sic) and nature assumes the analytic structure of the truncated equations.

The first historical scientific contribution by Santilli was to formulate and prove the following theorem shopwing that the above posture is a mere manifestation of academic politics without scientific credibility.

\ THEOREM 1.1: A macroscopic system with forces that are nonconservative and/or irreversible over time cannot be consistently decomposed into a finite number of elementary particles all with solely conservative forces derivable from a potential and, vice versa, a finite number of elementary particles all in conservative conditions cannot consistently yield, under the correspondence principle or other means, a macroscopic system with nonconservative and/or irreversible forces.

The historical character of this theorem is set by the fact that the non-Lagrangian or non-Hamiltonian forces of our macroscopic environment, rather than "disappearing" at the particle level to please academia, originate at the most elementary level of nature, thus confirming the depth of the analytic conception of nature by Lagrange and Hamilton.

As an illustration, Theorem 1.1 establishes that the resistance experienced by a spaceship during re-enmtry in our atmosphere is due to the superposition of a large n umber of contact, nonlinear, nonlocal and nonpotential interactions between the peripheral atomicv electrons of the spaceship and corresponding atomic electrons in the atmosphere.

Another significance of Santilli's Theorem 1.1 is to establish ab initio that special relativity and quantum mechanics are not universal theories valid for all possible conditions in nature and for the rest of time, as essentially implied by a widespread posture of the 20-th century science, but have instead clear limitations.

Numerous additional historical implications of Theorem 1.1 will be indicated throughout this presentation. At this moment, we merely mention the huge technical difficulties caused by the inclusion of external terms in the analytic equations. In essence, the physics of the 20-th century was based on Lie algebras with antisymmetric brackets [A, B] = - [B, A] that appear in the time evolution of a physical quantity Q(r, p) of the truncated Hamilton's equations, dQ/dt = [Q, H], where the brackets are the celebrated Poisson brackets. The appearance of Lie algebras at the foundation of dynamics, the time evolution, then allowed a rigorous construction of the various aspects of special relativity and quantum mechanics.

Santilli identified since his graduate studies that, when the external terms are added, the time evolution of a quantity Q(r, p) is given by

The loss of all algebras in the time evolution then causes the irreconcilable inapplicability of all Hamiltonian methods and theories developed in the 20-th century, including special relativity and quantum mechanics.

Rather than being discouraged by this occurrence, in the 1960s Santilli set as his main research goal the developement covering mathematical and physical theories suitable for the implementation of Lagrange and Hamilton analytic conception of nature while restoring an algebnra in the b rackets of the time evolution.

This presentation is essentially a review of Santilli's studies conducted since that time. As he puts it in his works: Quantitative sciences will never admit final theories. No matter how beautiful any given theory may appear, its structural generalization is only a question of time.

1.2. INSUFFICIENCIES OF SPECIAL RELATIVITY

Santilli has repeatedly stated in his writings that special relativity has a majectic axiomatic structure, for which reason he assumed said axioms for his covering relativities.

However, a widespread belief in the physics of the 20-th century has been that special relativity is valid under whatever conditions exist in the universe, to such an extent that the universe has been often adapted to verify special relativity, rather than adapting the theory to physical reality, with consequences that can only be qualified as characterizing a serious scientific obscurantism.

An important contributions made by Santilli in physics has been the identification of:

1) The conditions of clear validity of special relativity, given by the conditions originally conceived by the founding fathers, namely, for point-particles and electromagnetic waves propagating in vaccuum (empty space) or, equivalently, by all conditions in which particles can be well abstracted as being point-like, such as the electron in the hydrogen structure, particles in accelerators, and many other systems;

2) The condition of mere approximate character of special relativity, given by all conditions of particles at mutual distances equal or smaller than their wavepacket or charge distributions or, equivalently, for the motion of particles and electromagnetic waves within physical media, such as liquids, atmospoheres, chromospheres or the hyperdense media inside hadrons, nuclei and stars. These conditions cause mutual penetrations of wavepackets and charge distributions under which particles cannot be effectively approximated as being dimensionless points due to contact, nonlinear, nonlocal and non-Hamiltonian effects expected from Theorem 1.1 and other reasons reviewed in Section 3. In particular, special relativity can only be approximately valid for the structure of hadrons, nuclei and stars;

3) The conditions of inapplicability of special relativity (and not violation because the theory was not conbceived for that), such as the classical representation of antimatter (see Section 1.4), irreversible systems such as energy releasing processes, due to the strictly reversible character of special relativity compared to the strict irreversibility over time of the processes considered, and other conditions recalled in Section 3.

It shoudl be indicated that Albert Einstein identified quite clearluy in his writings the above indicated Conditions 1) for the applicability of his studies. The extension of special relativity to conditions dramatically beyond those identified by Einstein without a serious scrutiny has been perpetrated by Einstein's followewrs, who are indeed responsible for the scientific obscurantism indicated earlier and documented in more details in the rest of this presentation.

1.3. INSUFFICIENCIES OF GENERAL RELATIVITY

Unlike his view on special relativity, Santilli believes that Einstein's conception of gravitation via a curved space, despite its unquestionable mathematical beautiy, is one of the most controversial theories in history, with fundamental, yet unrestlved physical inconsistencies.

This severe view is motivated by various quantitative studies indicated in more details in Section 3. At this introductory stage, we recall Santilli's confirmation that the Riemannian geometry provides a good mathematical description of gravitys, but Santilli is unable to accept space as being truly curved by gravitation in the actual physical sense because of:

1) The impossibility of representing with curvature the weight of bodies when in stationary conditipons;

2) The impossibility of representing with curvature the free fall of bodies along a straight radial line;

3) The absence of curvature in the bending of light when passing near a celestial body, since that curvature is due to Newtonian attraction, rather than curvature of space as we shall see in Section 3, and other reasons.

At a deeper level, it should be recalled that special relativity is physically consistent because it verify the crucial condition of invariance over time, namely, the prediction of the same numerical values under the same conditoions but at different times, which invariance is ultimately due to the canonical-Hamiltonian structure of the theory and to its invariance under the Poincare' symmetry.

By contrast, Santilli has proved that the Riemannian geometry does not yield numerical values invariant over time because of the well known fact that the conception of gravitation on a curved space requires a "covariance", rather than a strict invariance, with consequential alteration of numerical values under the same conditions at different times.

Additionally, the predictions of special relativity under given conditions are unique. By contrast, Santilli has shown that the numerical prediction of general relativity for given conditions are not unique in view of the well known fact that general relativity is a nonlinear theory whose solution requires one or another approximation. It then follws that the numerical predictions depend on the selected expansion as well as the selected parameter for a given expansion.

Santilli has also shown that: general relativity violates the fifth identity of the Riemannian geometry, the Freud identity, for the case of neutral bodies (due to the lack of a source tensor in the exterior problem in vacuum); general relativity is incompatible with quantum electrodynamics (also because of the lack of a source tensor in vacuum); general relativity verifies the Theorems of Catastrophic Mathematicxal and Physical Inconsistencies for Noncanonical or Nonunitary Theories (Section 3.9); and the theory has other basic unrestolved problems generally ignored by researchers in the field, thus fueling the indicated scientific obscurantism.

1.4. INSUFFICIENCIES OF EINSTEIN'S THEORIES FOR ANTIMATTER

Another reason for the scientific obscurantism of the 20-th century is that special and general relativities were widely believed to apply for all possible conditions existing in the universe, while in reality they are unable to provide a valid classical representation of antimatter,

In fact, said theories can solely represent antimatter via the change of the sign of the charge. Consequently, said theories provide no distinction whatsoever between neutral bodies made up of matter and antimatter. Even when considering charged particles, quantization leads to inconsistencies, due to a resulting "particle" with the wrong sign of the charge, rather than the charge conjugated antiparticle.

In Santilli's words: One of the biggest scientific imbalances of the 20-th century has been the treatment of matter at all possible levels of study, from Newton to second quantization, while antimatter was solely treated at the level of second quantization. Hence, he decided to resolve this historical imbalance by discovering a new theory of antimatter that, as it is the case for matter, is applicable at all levels of study from Newtonian mechanics to second quantization, and he did indeed achieve such a goal, as we shall see in Section 3.7.

1.5. INSUFFICIENCIES OF QUANTUM MECHANICS

Santilli has repeatedly stated that quantum mechanics has made historical contributions to manking, by possessing a majectic axiomatic structure he assumed for the construction of hadronic mechanics, besides having an impressive body of expermental verifications under the conditions of its original conception and construction.

Despite these achievements, physics is a discipline that will never admit a final theory valid to the end of time. In fact, Santilli became a physicist because of authoritative doubts on the final character of quantum mechanics expressed during his high school years even in the Italian press for the general public. In fact, with the passing of time, we had the following authoritative voices of doubt:

A) The view by Albert Einstein on the "lack of completion" of quantum mechanics (in fact, Santilli constructed hadronic mechanics precisely as a "completion" of quantum mechanics in honor of Albert Einstein);

B) The doubts expressed by Enrico Fermi as to whether quantum mechanics holds in the interior of mesons (Santilli quoted repeatedly Fermi's doubt as being at the foundation for his studies on the structure of hadrons);

C) The limitations of quantum mechanics voiced by Werner Heisenberg, one of the very founders of the mechanics, from the linear character of the theory compared to the evident nonlinearity of the physical world (Santilli corresponded with Heisenberg on this topic prior to heisenberg's death in 1976);

D) The authoritative doubt voiced by Paul M. Dirac, another major founder of quantum mechanics, on the need for a revision of the theory permitting convergent perturbative expansions (Santilli met Dirac in Florida in 1982 to discuss the capability of hadronic mechanics to turn divergent quantum series into convergent forms, as reported by Santilli in his books);

E) The arguments by various philosophers of science on the need to surpass quantum mechanics with broader theories, such as Karl Popper, who was a strong supporter of Santilli's proposal to build the hjadronic covering of quantum mechanics, as stated in the Preface of his last book of 1978; and other doubts.

With the passing of time, these authoritative doubts were first ignored; then the authors were discredited via the abuse of academic authority, including the discreditation of Heisenberg, Dirac, Popper and other famous scientists for the lack of aliognment of their research with the predominant politicxal lines of the academic time; and any additional qualified doubt was prohibited to appear in print in the journals of leading physical societies, while its appearance in the press was opposed or discredited.

This evident organized manipulation of scientific knowledge and suppression of scientific democracy of qualified inquiries for personal interests lead to the widespread assumption in the last part of the 20-th century that quantum mechanics (and its Galilean and special relativity backgrounds) are the final theories for all possible conditions existing in the universe to the end of time, resulting in a manifest scientific obscurantism of historical proportions.

It is a duty duty of future historians to identify the reasons for the suppression of these authoritative doubts, as well as the responsibilities by leading academic institutions and governmental agencies funding the research, by identifying the origination of the rather universal trend of adapting all possible conditions in the universe to verify quantum mechanics and its underlying relativities.

A notorious exception is that by Santilli who honored the indicated authoritative doubts, conducted comprehensive mathematical, theoretical and experimental research on the limitations as well as the surpassing of quantum mechanics in a way completely oblivious to organized ascientific interests, and did indeed change the history of physics, as we shall see.

To begin our review in the field, another major scientific contribution by Santilli has been the restoration of a serious scientific process on quantum mechanics and its underlying relativities as follows:

1) A theory is said to be exactly valid for given conditions when it represents the totality of the physical data from primitive axioms without adulterations (such as throwing into the equations unknown parameters, arbitrary functions, and the like). This is the case for the structure of the hydrogen atoms, particles in accelerators, crystals, and numerous other systems. By analyzing the local-differential topology and mathematics underlying the theory, Santilli has confirmed that the conditions for the exact validity of quantum mechanics are the same as those for special relativity (as expected from the deep synergy of these theories), namely, quantum mechanics can be safely assumed to be exactly valid for particles and electromagnetic waves propagating in empty space or, more generally, for particles at mutual distances sufficient bigger than their size and/or charge distribution to allow their effective point-like abstraction.

2) A theory is said to be approximately valid when it does not represent all experimental data (this is the case for nuclear physics indicated below), or the representation of experimental data requires parameters and/or arbitrary functions that are then fitted from the data themselves (this is the case for numerous particle events). In particular, Santilli has proved that said arbitrary parameters and/or functions are, in reality, a direct measure of the deviations of the basic axioms of the theory from the system at hand. Numerous illustrative examples in both quantum mechanics and quantum chemistry were then worked out (see the Sections 3 and 4).

3) A theory is said to be inapplicable (rather than "violated") when the parameters thrown into the equations are incompatible with the basic axioms, or the does not admit any quantitative representation at all of experimental data.

Illustrations suitable for these introductory lines are the following:

3A) The use of four parameters necessary for the representation by quantum mechanics of the experimental data via the Bose-Einstein correlation (called "chaoticity parameters") is prohibited by quantum axioms, because the two point correlation function for a two-dimensional Hermitean (thus diagonal) operator could at best admit two parameters (the additional two parameters would be off-diagonal, thus against the Hermiticity of the Hamiltonian);

3B) Quantum mechanics is inapplicable for the synthesis of the neutron from a proton and an electron as occurring in stars because, in this case kept quite secrt by academia, the Schroedinger equation becomes inconsistent, an occurrence that is the historical motivation for the very birth of the covering hadronic mechanics, as we shall see;

3C) Santilli also proved that quantum mechanics is inapplicable for all processes that are irreversible over time, such as nuclear fusions, becausequantum mechansics is reversible over time, thus admitting the time reversal event (such as the synthesized nucleus spontaneously decomposing itself into the original two nuclei) with embarrassing violations of energy conservation, causality and other basic laws.

By looking in retrospect at a lifetime of research, we can quote Santilli's statement that: The selection of the appropriate generalization of quantum mechanics for physical conditions more complex than those of its conception and experimental verification, should indeed be the subject of scientific debates, but the aprioristic assumption of quantum mechanics as being exact for all conditions existing in the universe is ascientific, amoral and asocial particularly when ventured by physicists at leading academic institutions.

1.6. INSUFFICIENCIES OF NUCLEAR PHYSICS

The contributions of quantum mechanics to nuclear physics are well known, the most notorious being the atomic bomb and nuclear power plants. Santilli points out that these events deal with fission processes whose debris admit a good approximation as being point-like, thus allowing quantum mechanics to be effective.

As a result of said historical achievements, quantum mechanics was assumed throughout the 20-th century as being exactly valid for all possible nuclear structures and processes. Yet, Santilli pointed that quantum mechanics cannot possibly be exactly valid for fusion processes, since the theory is reversible over time. Thus, jointly with the probability of nuclear syntheses of two nuclei into a third, N₁ + N₂ → N₃ plus energy, quantum mechanics admits a finite probability for the spontaneous time reverrsal reaction

With the understanding that the approximate validity of quantum mechanics in nuclear physics is out of question, Santilli believes that one of the most pernicious manifestations of the scientific obscurantism of the 20-th century existed in nuclear physics, due to the religious assumption of the exact validity of quantum mechanics in the field when quantum mechanics has failed to achieve an exact representation of all experimental data of the simplest possible nucleus, the deuterium, because:

1) Quantum mechanics has been unable to represent the spin 1 of the deuterium since quantum axioms require that the sole stable bound state of two particles with spin 1/2, the proton and the neutron, must be the singlet state with spin zero;

2) Quantum mechanics has been unable to represent the magnetic moment of the deuterium despite 100 years of research and the use of all possible relativistic corrections;

3) Quantum mechanics has been unable to explain the stability of the neutron when coupled to the proton in the deuterium, since the neutron is a naturally unstable particle (when isolated) with about 14 minutes lifetime; and other insufficiencies.

The assumption of quantum mechanics as being exactly valid in nuclear physics reaches historical proportions when proffered by experts in the field from authoritative academic institutions, or by editors of leading physics societies, when one consider that the huge deviations of quantum mechanics from the experimental data of large nuclei, such as the zirconium.

Santilli qualifies as distressing the inability by quantum mechanics to reach a serious understanding of the nuclear force, because quantum mechanics is strictly Hamiltonian, as indicated above. Hence, all research over the past century has been studiously restricted to represent the nuclear force with a potential. The impossibility of representing experimental data then forced the addition of more and more potentials to the extreme that nuclear forces have recently reached up to 35 different potentials without achieving the needed exact representation,

Above all, Santilli has never accepted quantum mechanics to be exactly valid for nuclear physics because its basic symmetries, the Galilei and the Poincare' symmetries, solely apply for Keplerian systems, thus requiring a nucleus, and states: Quantum mechanics cannot possibly be exactly valid for nuclear structures because nuclei do not have nuclei, as a consequence of which the basic Galilean and Poincare' symmetries must be broken, thus causing incontrovertible deviations from quantum axioms.

As we shall see in Section 3, the "completion" of quantum mechanics into a covering mechanics achieving an exact representation of nuclear data permits the prediction and quantitative treatment of new clean energies so much needed by our society. Hence, the resolution of the approximate character of quantum mechanics in nuclear physics has major societal, let alone physical relevance.

By following Santilli, we can then again state that the selection of a mechanics more adequate than quantum mechanics for nuclear structures should indeed be the subject of scientific debates, but the aprioristic assumption of quantum mechanics as being exactly valid in nuclear physics creates serious problems of scientific ethics and accountability (with inevitable legal overtones).

1.7. INSUFFICIENCIES OF PARTICLE PHYSICS

Santilli believes that the biggest scientific obscurantism exists in particle physics with particular reference to claimed "experimental results" for high and very high energy particle collisions, and/or deep inelastic scattering, that he calls experimental beliefs.

The argument is that all these data are based on the use of the conventional potential scattering theory, namely, a theory based on the religious assumption that particles remain point-like also at very high energy collisions (a condition necessary to apply quantum mechanics) and, as such, the particles solely experience action-a-a-distance interactions derivable from a potential.

However, hadrons have in reality an extended and hyperdense charge distribution and even the electron has an extended wavepacket irrespective of its point-like charge. It then follows that the conventional, potential scattering theory can only be approximately valid for high energy scattering experiments, since it is notoriously unable to incorporate nonpotential effects due to mutual wave overlappings and/or deep mutual penetrations of hyperdense charge distributions. Under these premises, the approximate character of the "experimental results" cannot be dismissed without raising serious problems of scientific ethics and accountability.

We hope the reader begins to see in this way additional historical implications of Santilli's Theorem 1.1, since it requires the emergence of nonpotential forces precisely at the level of deep inelastic scatterig or collisions, as it is the case of the spaceship during re-entry in our atmosphere. But these forces are non-Hamiltonian, thus requiring a necessary nonunitary covering of the scattering theory, which is one of the primary objective of hadronic mechanics in view of its nonunitary structure.

Whatever nonunitary scattering theory emerges to be correct for high energy particle scattering experiments, it is clear that it will mandate a re-inspection of all "experimental beliefs" in particle physics to ascertain whether the results claimed under sole potential forces are exact or merely approximate, thus in need of basic revisions of the numerical results.

1.8. INSUFFICIENCIES OF QUARKS AND NEUTRINOS CONJECTURES

Santilli has always accepted SU(3)-color theories as providing the final Mendeleev-type classification of hadrons into families; has accepted quarks as being necessary for the elaboration of said Mendeleev classification; but he has never accepted quarks as being physical particles actually existing in our spacetime for numerous reasons, such as:

a) Quark can only be technically defined as purely mathematical representations of a purely mathematical internal symmetry, defined on a purely mathematical internal, complex-valued unitary space, without any possibility of being consistently definable in our spacetime (because prohibited by the Poincare' symmetry and other reasons);

b) Quarks cannot have any gravity because, as stated by Albert Einstein, gravity can be solely defined for masses in our spacetime, while quarks cannot be seriously defined in our spacetime.

c) Nuclei, atoms and molecules have required one model for their classification into family and a different, yet compatible model for the structure of each individual element of a given family, and the same occurrence is expected for the classification and streucture of hadrons.

To illustrate the basic dichotomy classification versus structure, Santilli has stated that: If one of my graduate students would ask me to supervise a thesis whereby the Mendeleev table for atoms is also used for the structure of each individual atoms of a given family, I would immediately request his/her expulsion from the department, because classification and structure are dramatically different problems, requiring dramatically different methods and theories.

In fact, the Mendeleev table was formulated via classical chemnical and other methods, while the structure of the atoms required the advent of quantum mechanics. As we shall see, we have a very similar situation for hadrons because the linear, local and Hamiltonian character of quantum mechanics is effective for the classification of hadrons under their point-like approximation, but the use of the same mechanics for structure problems has been shown to be inadequate due to inevitable nonlinear, nonlocal and non-Hamiltonian effects occurring within hyperdense media inside hadrons.

Similarly, Santilli never believed that the neutrinos are physical particles in our spacetime for numerous reasons, the first being the fact that the neutrino is assumed to be emitted during the synthesis of neutrons from protons and electrons inside stars,

This is due to the fact that the neutron is 0.782 MeV heavier than the sum of the rest energies of the proton and the electron,

A) All bound states characterized by quantum mechanics (such as nuclei, atoms and molecules) must have a "mass defect," namely, the rest energy of the resulting state must be smaller than the sum of the rest energies of the constituents, resulting in the familiar "negative binding energy." By contrast, reaction (1.6) requires a kind of "mass excess," thus requiring a "positive binding energy," under which the Schroedinger and other equations of quantum mechanics become inconsistent.

B) The assumption of the "missing energy" of 0.782 MeV as being provided by the relative kinetic energy of the proton and the electron is inconsistent and untenable, because at that energy the cross section of protons and electrons is virtually null., thus prohibiting any bound state;

C) The belief that the conjugate expression

The advent of the standard model has caused additional, rather serious, unresolved problems because Fermi's original conception of one massless and chargeless neutrino and its antiparticle had to be first extended to three different neutrinos and their antiparticles without any serious identification of their differences; then this enlargement had to be further enlarged to admit that neutrinos have masses; then the latter enlargement had to be further broadened with the additional belief that neutrinos have different masses; then the latter assumption had to be further modified with the conjecture that neutrinos "oscillates" (that is, change from one into the other); with the expectation of additional unverifiable conjectures introduced to bypass the problems unsolved by the preceding conjectures, yet under very large public funds dispersed at major international laboratories on these pure theoretical theologies without any serious scrutiny by society, thus confirming the ongoing scientific obscurantism.

Any denials of the need for a basic re-inspection of physical laws for the most fundamental syntheses in nature, that of the neutron, can only raise serious problems of scientific ethic s and accountability (also with inevitable legal overtones).

Santilli states: Until I live, I will refuse to accept that massive particles, as neutrinos are believed nowadays to be, can traverse entire planets and stars, thus passing through an enormous number of nuclei, without any collision. Instead of accepting such a theology, I will look for alternative theories more plausible than that of the neutrinos, and so, in fact, he did, by introducing his theory of "longitudinal" impulses propagating through the ether as a univbersal substratum, thus explaining the lack of collision (see Section 3).

Unreassuringly, Santilli has also stated that: Quarks and neutrinos have been claimed to exist as physical particles in our spacetime by organized high ranking academic interests because their assumption is essential to preserve the validity of special relativity and quantum mechanics.

In any case, the various claims of leading particle laboratories to have "discovered" or "detected" this or that quark is extremely anti-scientific for me because the correct scientific statement should have been that of having detected physical particles in our spacetime "predicted" by quark conjectures, with the understanding that the same particles could be predicted by other conjectures.

In the final analysis, the conjecture that quarks are physical particles in our spacetime prohibits the study of possible new clean energies because quarks must be assumed as being permanently confined in the interior of hadrons, while all energies obtained from nuclear, atomic and molecular structures are based on the capability of extracting the constituents free.

1.9. INSUFFICIENCIES OF QUANTUM CHEMISTRY

With the acknowledgment that quantum chemistry has also made historical contributions to society, beginning with the time of his graduate studies in the 1960s, Santilli never accepted quantum chemistry as a final discipline for numerous reasons he has identified in his works. For instance, he states that:

The fundamental quantum chemical notion of valence bond, as presented in the 20-th century literature, is a pure nomenclature without quantitative content because, to be quantitative, the notion should:

1) Identify clearly the force between two identical valence electrons;

2) Prove that such a firce is attractive, as an evident necessary pre-requisite to claim the bond needed for a molecule; and

3) Prove that such a clearly identified clearly attractive force verifies indeed experimental data on molecular structures.

These conditions are impossible for quantum chemistry, because two identical electrons must "repel" each other according to quantum mechanics, and they cannot possibly "attract" each other.

Therefore, Santilli set his goal to achieve the missing quantitative notion of valence, and he did achieve it, as we shall see in Section 4, giving birth to the new discipline of hadronic chemistry

Santilli has also identified additional structural problems of quantum chemistry, among which most visible is the prediction (verified by one of his graduate students) that all substances are paramagnetic, in great disagreement with evidence establishing that only certain substances are paramagnetic.

This insufficiency can be verified with the hydrogen molecule that is indeed diamagnetic. The origin of the problem rests in the absence of a clearly identified, sufficiently "strong" valence bond among the pair of valence electrons of the H₂ molecule, as a result of which the orbitals of individual hydrogen atoms remain essentially independent, thus available for a joint polarization via an external magnetic field, contrary to evidence.

Santilli had another graduate student prove that, under the current notion of valence, there is no reason to have the sole molecule H₂, since it is possible to bond together three, four or more hydrogen atoms, contrary to evidence. The origin of this additional insufficiency is, again, the lack of a "strongly" attractive valence bond restricting the correlation to valence electron "pairs" only, thus allowing the bonding of additional electrons, contrary to evidence (as we shall see in Section 4, the species H₃, H₄ at times detected in gas chromatography have been proved by Santilli to have a bond other than that of valence).

Santilli proved additionally that quantum chemistry cannot be exactly valid for the study of chemical reactions, by showing that, jointly with the prediction of the synthesis of the water molecule H₂ + O → H₂O, quantum chemistry admits a finite probability for the time reversal event, the spontaneous disintegration of the water molecule into its original constituents,

It is then evident to all serious scholars outside academic politics that quantum chemistry cannot possibly be the final theory for chemistry, the most serious limitations occurring for chemical reactions. Of course, the applicable new chemistry is open to scientific debates, but the denial of its need can only raise issues of scientific ethics and accountability (again, with inevitable legal overtones).

1.10. INSUFFICIENCIES OF BIOLOGY

Among all sciences of the 20-th century, that considered most distressful by Santilli is biology treated via quantum mechanics. In fact, he writes: Had quantum mechanics be applicable to biological processes, my body should be perfectly rigid and perfectly eternal.

This insufficiency is due to the well known incompatibility of quantum mechanics with the deformation theory (since deformations would cause the breaking of the central pillar, the rotational symmetry), as a result of which quantum mechanics is ideally suited to represent rigid structures such as crystals. Additionally, the insufficiency poriginates from the reversibility of quantum mechanics over time, compared to the finite life of all biological processes.

Particularly distressing for Santilli is the study of the DNA structure via the elementary mathematics of the 20-th century, such as conventional numbers dating back to pre-biblical times, while the complexity of biological processes is simply beyond our imagination at this time.

1.11. INSUFFICIENCIES OF ASTROPHYSICS AND COSMOLOGY

According to Santilli, the climax of the scientific obscurantism of the 20-th century can be seen in astrophysics and cosmology, because these disciplines have seen true extremes in the adaptation of the universe to verify Einsteinian doctrines without a serious scrutiny.

To begin, the study of the antimatter component of the universe, the consequential expected existence of antigravity between matter and antimatter and related topics, have been systematically ignored because notoriously not compatible with Einsteinian doctrines (Sections 2.4 and 3.7).

Additionally, Santilli believes that the ongoing views on the expansion of the universe, the acceleration of the expansion with the distance, and the so-called "big bang" theory, are a consequence of the intent of preserving the constancy of the speed of light throughout the universe. On serious scientific grounds, we can say that the speed of light is indeed a constant, but solely under the conditions established by experiments until now, when propagating in vacuum conceived as a totally empty space.

The widespread claim of "the universal constancy of the speed of light" is a political, rather than a scientific statement when ventiured without the crucial words "in vacuum", because disproved by evidence when dealing with propagation of light within physical media. It is today well established that the speed of electromagnetic waves C = c/n has the constant value c only in vacuum, while having otherwise a locally varying character depending on the characteristics of the medium in which it propagates represented by the index of refraction n. Santilliu argues that at intergalactic distances, space cannot be considered empty, thus voiding the foundations of current cosmological theologies.

Above all, one of Santilli's major contribution in astrophysics and cosmology has been the focusing of the attention on ether as a fundamental universal medium (substratum) with very high energy density. A star at its initiation synthesizes from hydrogen a very large number of neutrons estimated to be of the order of 10⁵⁰ neutrons per seconds or more. But the synthesis of a neutron requires 0.782 MeV, as noted above. According to orthodox views the missing energy is provided by the star environment. However, in this case a star could never initiate to produce light, since at its initiation the star would lose (rather than produce) energy at the rate of 10⁵⁰ MeV per seconds or more.

The sole possibility for a scientific solution of this fundamental problem is the ether, whose study is seen by Santilli as the ultimate frontier of knowledge, with possible advances simply beyond our most vivid imagination at this time, such as possible longitudinal communications through space at speeds millions of times bigger than that of the transversal electromagnetic waves, or travel to the stars at unrestricted speeds without fuel tanks because the needed propulsion and energy may be available everywhere in the ether, provided, of course, we have basically new theories suitable for the study of these advances.

As we shall see, one of the ultimate motivations for the construction of hadronic mechanics has been to provide means for quantitative studies of possible interchanges between the ether as a universal substratum and the visible universe, a study definitely not possible with quantum mechanics.

1.12. INTRODUCTORY READINGS

Scholars with a serious interest in acquiring an in depth knowledge of Santilli's discoveries, are suggested to initiate their study with introductory readings, rather than with technical treatments, since the latter may appear to be disconnected from the larger scientific edifice. A first recommended reading is that on the insufficiencies of the 20-th century theories available in the

Forum on Old Theories

A comprehensive technical presentation of said insufficiencies can be found in the monograph available for free download in pdf format

Hadronic Mathematics, Mechanics and Chemistry, Volume I: Limitations of Einstein's Special and General Relativities, Quantum Mechanics and Quantum Chemistry
R. M. Santilli, International Academic Press (2008)

Santilli has been one of the firsts to present in 1981 various arguments according to which quarks cannot be physical particles in our spacetime. See the paper

An intriguing legacy of Einstein, Fermi, Jordan and others: The possible invalidation of quark conjectures
R. M. Santilli, Found. Phys. Vol. 11, 384-472 (1981).Br>

A detailed technical treatment of the insufficiencies of 20-th century theories and a denunciation of their lack of addressing dated 1984 was presented by Santilli in the book also available in free pdf download

Ethical Probe of Einstein's Followers in the USA: An Insider's View
R. M. Santilli, Alpha Publishing (1984)

The related 1,315 pages long documentation dated 1985 is also available in free pdf download from
Documentation of the Ethical Probe
R. M. Santilli, Alpha Publishing (1985)

The Foundation is attempting to secure copies of Santilli's personal documentation following 1985 that has been donated to a European Institution.

2. SANTILLI'S DISCOVERIES IN MATHEMATICS