2016 NOBEL PRIZE IN PHYSICS

Professor Ruggero Maria Santilli

Chief Scientist, Thunder Energies Corporation

Office Tel. +1-727-940-3944, mobile +1-727-688-3992,

Email "research(at)thunder-energies(dot)com"

*for the representation of the synthesis of the neutron from the hydrogen in the core of stars*

submitted to:

**The 2016 Nobel Committee for Physics: Prof. Olle InganŠs (Chairman), Prof. Olga Botner, Prof. Mats Larsson, Prof. Thors Hans Hansson, Prof. Nils MŒrtensson, Prof. Gunnar Ingelman (Secretary)**

via registered mail at

Sturegatan 14, Stockholm 1436, Sweden

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via fax at +46 (0)8 660 38 47

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http://www.nobelprize.org/prog/php/tellfriend/tell-info.php?head=1&top=1

**THE NOMINEE. **

I hereby nominate for the 2016 Nobel Prize in Chemistry, the Italian-American scientist, **Prof. Ruggero Maria Santilli,** formerly from MIT, Harvard University, and other leading institutions, who is the author of about 250 post Ph. D. papers and 18 monographs published by refereed journals and leading publishers around the world (see the curriculum) http://www.world-lecture-series.org/santilli-cv and the scientific archive http://www.santilli-foundation.org/news.html and the historical archive http://www.i-b-r.org/ir00022.htm); the founder and editor in chief of the 37 year old Hadronic Journal, Algebras, Groups and Geometries, and other post Ph. D. scientific journals (http://www.hadronicpress.com); the founder and President of the 35 year old Institute for Basic Research (http://www.i-b-r.org); a speaker of keynote lectures at numerous international scientific meetings with over fifty years of research (http://www.world-lecture-series.org/); the recipient of numerous scientific prizes (http://www.santilli-foundation.org/santilli-nobel-nominations.html); the founder and Chief Scientist of the U. S. publicly traded company Magnegas Corporation (http://www.magnegas.com); the founder and Chief Scientist of the additional U. S. publicly traded company Thunder Energies Corporation (http://www.thunder-energies.com); and the originator of additional scientific and industrial activities.

NEW SCIENCES FOR A NEW ERA [46].

**1. INAPPLICABILITY OF QUANTUM MECHANICS AND SPECIAL RELATIVITY FOR THE NEUTRON SYNTHESIS**

It is generally believed in academia, that quantum mechanics and special relativity apply for whatever conditions exist in the universe, expectedly, until the end of time, resulting in a political, rather than scientific position, since it has been established in history that all theories admit limitations in favor of covering theories.

In line with this historical teaching, when he was a member of the faculty of Harvard University in the early 1980s under support from the Department of Energy (DOE contracts ER-78-S-02-47420.A000, AS02-78ER04742, DE-AC02-80ER1065, DE-AC02-80ER-1065.A001, and DE-AC02-80ER.1065), Prof. R. M. Santilli showed that:

**I. Conditions of exact validity:** Quantum mechanics and special relativity are *exactly valid* under the conditions clearly stated by their originators, namely, for mutual distances of particles sufficiently large enough to allow their point-like approximation requested by the local-differential character of the underlying mathematics.

**II. Conditions of approximate validity:** Under mutual distances of particles in the order of their charge distributions or of their wavepackets (about 10-13 cm), there is the emergence of non-linear, non-local and non-Hamiltonian interactions caused by the mutual penetration of particles under which quantum mechanics and special relativity can at best be *approximately valid.*

**III. Conditions of inapplicability:** There exist particle conditions under which quantum mechanics and special relativity are *inapplicable* in the sense that, when applied, they produce no quantitative treatment at all.

A first illustration of Condition III has been provided to the Nobel Foundation via the preceding nomination of Prof. R. M. Santilli for the 2016 Nobel Prize in Chemistry "for the discovery of an attractive force between covalence electron pairs in molecular structures," which discovery was solely possible via the use of a covering of quantum chemistry known as *hadronic chemistry.*

*Figure 1. A star initiates its life as an aggregate of hydrogen. The first synthesis in the core of stars is that of the neutron from the hydrogen atom as originally conceived by H. Rutherford in 1920 [2] and experimentally verified by J. Chadwick in 1932 [3]. The production of light requires nuclear fusions that can only occur following the neutron synthesis and of the subsequent synthesis of the deuteron, tritium, helium, and other nuclides. *

This nomination deals with additional Conditions III, this time in physics, given by the synthesis of the neutron from the hydrogen atom in the core of stars, as originally conceived by Rutherford [2] and experimentally verified by Chadwick [3]. Fermi [4] achieved the first quantum mechanical formulation of the neutron synthesis via the conjecture of the emission of the neutrino emitted in the neutron synthesis.

(1) p^{+} + e^{-} => n + v,

In memoirs [5,6] and monographs [7] of 1978, Santilli proved that Fermi's conjecture of the neutrino did indeed verify the conservation of the angular momentum (because the proton, the electron and the neutron have spin 1/2), but did not salvage quantum mechanics and special relativity are inapplicable for the neutron synthesis because the rest energy of the neutron is 0.782 MeV *bigger* than the sum of the rest energies of the proton and the electron.

(2a) E_{p} = 938.272 MeV, E_{e} = 0.511 MeV, E_{n} = 939.565 MeV, E_{v} = ?.

(2b) E_{n} - (E_{p} + E_{e}) = 0.782 MeV.

Recall that the Schroedinger equation for the bound state of two particles with reduced mass m is given by (for h-bar = 1)

(3) [− (1/m) Δ − V(r) ] ψ = E ψ

Achieved simply historical results with the non-relativistic representation of the structure of then hydrogen atom to a simply astonishing accuracy.

Note that the negative value of the l.h.s. of Eq. (3) requires that the binding energy E to be *negative,* E <.; 0, resulting in the well known *mass defect* which is the source of energy released by the Sun (Figure 1).

Santilli noted that neutron synthesis (1) requires a *positive* binding energy resulting in a *mass excess,* both occurrences being anathema for quantum mechanics. In particular, Santilli proved, that under the above conditions, the indicial equation of the Schroedinger equation no longer admits physically meaningful solutions * for bound states* (free particles certainly admit positive kinetic energy in which case the l.h.s. of Eq. (3) is positive).

Recall that the Dirac equation on a conventional Minkowski space M(x,η,I) with spacetime coordinates x = (x^{1}, x^{2}, x^{3}, x^{4} - ct), metric η = Diag. (1, 1, 1, -1) and unit I = Diag. (1, 1, 1, 1),

(4a) [γ^{μ}(p_{μ} - ieA_{μ}) - (imc)] ψ(x) = 0,

(4b) {γ^{μ},γ^{ν}} = γ^{μ} γ^{ν} + γ^{ν} γ^{μ} = η^{μν}

achieved an equally historical relativistic representation of the structure of the hydrogen atom in astonishing agreement with experimental data. Recall also, that the Dirac equation is the ultimate embodiment of special relativity in particle physics since said equation is derived via the linearization of the second order Casimir invariant of the fundamental symmetry of special relativity, the Lorentz-Poincare' symmetry.

Santilli has shown in Refs. [3-5] that, despite these achievements, the Dirac equation, and consequently special relativity, are totally inapplicable for neutron synthesis (1) on numerous counts, such as (Figure 2):

A. The application of Dirac's equation (4) to neutron synthesis (1) provides no consistent quantitative treatment at all;

B. During "Rutherford's compression" [2] of the electron inside the proton, there is the total penetration of the electron's wavepacket within the hyperdense medium inside the proton, with the ensuing emergency of non-linear, non-local and non-Hamiltonian interactions dramatically beyond the representational capabilities of special relativity;

C. The Lorentz-Poincare' symmetry, is solely valid for Keplerian systems, namely, for a system of particles orbiting around Keplerian nucleus (Figure 3). Santilli insists that *"The neutron has no nucleus",* thus implying the inapplicability for the neutron synthesis of the Lorentz-Poincare';- symmetry with consequential inapplicability of special relativity.

*Figure 2. A picture used by Prof. R. M. Santilli in his studies to illustrate Rutherford's compression" of the hydrogen atom into the neutron, with ensuing total penetration of the wavepacket of the electron in the hyperdense medium inside the proton. *

**2. INAPPLICABILITY OF QUARK CONJECTURES**

In Refs. [5-7], and particularly in Ref. [8], Santilli has proved that there is no possibility of achieving a quantitative representation of neutron synthesis (1) via quark conjectures for a number of technical reasons, such as:

a) The impossibility to achieve a credible conversion of physical electrons into conjectural quarks;

b) Compatibility of protons and electron with the Lorentz-Poincare' symmetry compared to the incompatibility of quarks with the same symmetry; c) Impossibility for quarks to be truly point like due to their need to have wavepackets of the same size of hadrons, and for other reasons.

Santilli fully accepts the "standard model" of particle physics, but solely for the Mendeleev-type *classification* of particles into families, while adopting the view by Gell-Mann and others that quarks are purely mathematical representations of purely mathematical internal symmetries defined over a purely mathematical, complex-valued space.

*Figure 3. An illustration of another historical discovery by Santilli, the proof that conventional spacetime symmetries, including the Galileo and the Lorentz-Poincare' symmetry, solely apply for "Keplerian systems," that is, systems of particles orbiting around a heavier particle called the "Keplerian center." This feature implies the evident validity of the Galileo and the Lorentz-Poincare symmetries for the structure of the hydrogen atoms, but the same feature implies the evident inapplicability of said symmetries for the neutron synthesis because, as stated various times by Santilli, "the portion has no Keplerian nucleus". This historical feature forced Santilli constrictor the isotopic generalization of the Galileo and the Lorentz-Poincare' symmetries with consequential emergence of covering relativity for the dynamics of extended particles moving within physical media. *

Santilli admits that quarks are necessary for the *mathematical elaboration* of SU(3) and other internal symmetries, but quarks are not physical particles in our spacetime. In any case, Santilli has shown that:

1. Quarks cannot be consistently defined in our spacetime (because they cannot be irreducible representations of the Lorentz-Poincare' symmetry) and, therefore, they are purely conjectural.

2. The exact "quark confinement," which is so necessary for the consistency of quark conjectures, can only be achieved via an incoherence between the internal and external Hilbert spaces, thus requiring the relaxation of the uncertainty principle and other basic quantum laws in the interior of hadrons.

3. The inability to produce quarks as free detectable particles, even at the extremely high energies available at CAERN and other laboratories, has confirmed that quarks cannot be the physical constituents of hadrons at large, and of the neutron in particular.

Recall that atoms required *two models,* the Mendeleev classification of atoms into families, and complementary models for the structure of individual atoms of a given family, the latter models requiring a covering of the theories needed by the former, namely, quantum mechanics.

Along this historical teaching, Santilli has shown in Refs. [5-7] the need for two models in particle physics too, the standard model for the classification of particles into families, and compatible new models for the structure of individual hadrons of a given family, the latter models also requiring a covering of the theories used for the former due to the inapplicability of quantum mechanics and special relativity for the synthesis of hadrons.

By remembering that "point-like quarks" were introduced for the specific, although unspoken intent of maintaining special relativity for the hadronic structure, during his stay at Harvard University in the early 1980s, Santilli had "irreconcilable disagreements" on quark conjectures as physical particles with his colleagues at Harvard, S. Weinberg, S. Glashow and S. Coleman (see, later on, books [76]).

In fact, Santilli is on record by stating to his Harvard colleagues: *"I cannot possibly accept that, at the time of the neutron synthesis, the permanently stable proton and electron 'disappear' to be replaced by hypothetical quarks. Additionally, I cannot possibly accept that, at the subsequent tie of the neutron decay, the hypothetical quarks 'disappear' and the proton and electron 'reappear' for the intent of maintaining special relativity within the hyperdense medium inside hadrons. Rather than adapting nature to special relativity, I prefer to adapt the theory to nature. *

**3. THE NEED FOR NEW INTERACTIONS**

Santilli argued in Refs. [5-7] that the use of all interactions admitted by quantum mechanics and special relativist, essentially the electroweak interactions (since the electron cannot experience strong interactions) cannot possibly allow a quantitative representation of a bound state with a positive binding energy producing a mass excess according to Eqs. (1) and (2).

Therefore, Santilli argued that the sole possibility for a quantitative representation of neutron synthesis (1) is to admit *new interactions* beyond the representational capabilities of quantum mechanics and special relativity, thus requiring the construction of appropriate covering theories.

Santilli has always admitted the existence of *point-like charges,* as it is the case for the electron, but he has repeatedly stated that *"There exist no point-like wavepackets in nature."* This simple observation implies that the new interactions emerging in the total penetration of the electron wavepacket within the hyperdense medium inside the proton are of non-linear, non-local and non-potential type, thus not being representable with a Hamiltonian, and proved that these interactions are *variationally non-selfadjoint* [7a].

*Figure 4. An illustration of the historical meaning of isomathematics since it signals the transition from the notion of point-like particles under potential interactions by Newton, Galileo and Einstein to Santilli's notion of extended, non spherical and deformable particle under the most general known Hamiltonian and non-Hamiltonian forces. This historical advance was mandatory for the neutron synthesis because its representation is solely possible by admitting contact interactions during "Rutherford's compression" of the electric inside the hyperdense proton. As illustrated in this original figure used in santilli's work, points cannot experience contact interactions, since they are dimensionless. This occurrence motivated Santilli to generalize the Newton-Leibnitz differential calculus into a covering form admitting extended, non-spherical and deformable particles under the most general known interactions. *

**4. THE BIRTH OF ISOMATHEMATICS**

Santilli was fully aware that point-like particles cannot experience contact interactions when moving within a physical medium because they are dimensionless, for which reason point-like particles solely admit *variationally self-adjoint interactions* [7a], that generally are of linear, local and potential, action-at-a-distance type.

Consequently, the representation of particles as *extended* while moving within a physical medium was necessary to achieve a representation of the broader *variationally non-selfadjoint interactions* [7a] that are generally of non-linear, non-local and non-Hamiltonian type.

An inspection of mathematics available in the middle of the 20th century revealed the absence of a mathematics capable of representing the proton as an extended particle. An additional insufficiency of available mathematics was the inability to provide a physically consistent representation of composite system with non-linear internal interactions. Therefore, the needed mathematics had to be built.

Santilli introduced in Refs. [5-7] the foundations of the new mathematics based on the generalization of the conventional associative product AB among generic quantities (functions, matrices, operators, etc, into the form)

(5) AB = A×B → A×*B = AT*B,

where T* is a fixed function, matrix or operator solely subject to the condition of being positive-definite, T* > 0, but T* otherwise possesses an unrestricted functional dependence on any needed local quantity such as time t, coordinates r, speed v, frequency ω, energy E, density &xi.;, temperature τ, wavefunction ψ their derivatives ∂ψ, etc. T* = T*(t, r, v, ω, E, ξ, τ, ψ, ∂ψ, ...) > 0.

The positive-definite character implies that T* can always be diagonalized into the form in (3+1)-dimensions

(6a) T* = Π_{ξ = 1,..., N}Diag. (1/n_{ξ1}^{2}, 1/n_{ξ2}^{2}, 1/n_{ξ3}^{2}, 1/n_{ξ4}^{2}) exp{Γ(ψ,...)∫ψ ψ^{†} dv} > 0,

(6b) n_{μ} = n_{μ}(t, r, v, ω, E, ξ, τ, ψ, ∂ψ, ...) > 0, μ = 1, 2, 3, 4,

where:

1) n_{k}^{2}, k - 1, 2, 3, represents the semiaxes of the charge distribution of the particle considered (assumed for simplicity to be a spheroid ellipsoid) normalized to the sphere n_{k}^{2} = 1 in vacuum;

2) n_{4}^{2} represents the density of the particle considered also normalized to the value n_{4}^{2} = 1 for the vacuum; and

3) the exponential represents non-linear, non-local and non-Hamiltonian interactions among extended constituents as it is most typically the case for the nuclear structure (see Picture 5).

*Figure 5. Nuclei constitute some of the best applications of Santilli's isosymmetries because they are composed of extended particles in conditions of partial mutual penetration of the charge distributions (as established by comparing experimental data on nuclear volumes and those on the volume of protons and neutrons). these conditions imply the existence of internal non-linear, non-local and non-Hamiltonian interactions that are ideally represented by isomathematics, see Eqs. (6), while verifying the conventional ten total conservation laws of total quantities when stable and isolated. *

In this way, physical theories are characterized by *two* quantities, then conventional Hamiltonian H(r, p) for the representation of linear, local and potential interactions, and quantity T* for the representation of the broader non-linear, non-local and non-Hamiltonian interactions.

The new product A×*B preserves the associativity of the original product AB. Therefore, Carla Santilli suggested in 1978 for the new product the name of *isoproduct,* and the quantity T* was called the *isotopic element.* where the prefix "iso" is intended in the Greek meaning of preserving the original axioms. Since the time of that proposal, the prefix "iso" or the terms "isotopic liftings" are referred to axiom-preserving mathematical, physical or chemical theories preserving the original axions.

Following the fundamental proposal to generalize the associative product, Eq. [5], Santilli presented in In Ref. [5] (see in particular monographs [7]) the first known isotopic lifting of 20th century applied mathematics via the use of isoproduct (5) applied to functions, matrices, operators, etc.

Given a N-dimensional Lie algebra with (Hermitean) generators J_{k}, k = 1, 2, ..., N, Santilli achieved in Ref. [5] (see also the detailed presentation in Ref. [7b]) the first known structural generalization of the various branches of Lie's theory, including:

A) The isotopies of universal enveloping associative algebra with infinite dimensional isobasis

(7) I, J_{i}×*J_{j} i ≤ j , J_{i}×*J_{j}×*J_{k} j ≤ j ≤ k, .....

B) The isotopies of Lie algebras with generalized commutation rules

(8) [J_{i},J_{j}]* = J_{i}×*J_{j} - J_{j}×*J_{i} = C_{ij}^{k} ×* J_{k},

today known as *Lie-Santilli isocommutators,* and Lie transformation groups, such as the isotopies in one dimension

(9) U(t) = e*^{Jti} ×* U(0) ×* e*^{-itJ} = e^{JT*ti} × U(0) × e^{-itT*J}

today known as the *Lie-Santilli isogroups, where e* is the isoexponential function characterized by the infinite basis (7).*

Subsequently, Santilli recognized that the above non-unitary theory remained afflicted by major mathematical and physical insufficiencies because it's still formulated on a conventional Hilbert space over a conventional numeric field. In particular, the above isotopic theories were unable to predict the same numerical values under the same conditions at different times.

In 1981, Santilli and the late mathematicians H. C. Myung [8] recognized that the conventional Hilbert space is inapplicable to isotopically lifted theories and introduced the first known iso-Hilbert space today known as the *Hilbert-Myung-Santilli isospace* (see, e.g., Ref. [9]).

Despite the latter advance, isotopic theories remained insufficient for consistent physical or chemical applications for various technical reasons. In order to resolve the impasse, while visiting in the summer of 1993 the *Joint Institute for Nuclear Research* in Dubna, Russia, Santilli recognized that a reason for the insufficiencies is that the generalized iso-Hilbert space was still defined on conventional numbers using a conventional product.

In this way, Santilli was [10] forced to reinspect the historical classification of numbers into real, complex and quaternionic numbers by Gauss, Cayley, Hamilton and so many other distinguished mathematicians and discovered that such a classification was incomplete because the abstract axioms of a numeric field do not require the associative unit to be the trivial unit "1" used since Biblical times, since it can be an arbitrary, positive-definite quantity, provided that the multiplication is lifted in a complementary way.

These studies lead to the discovery of basically new numeric fields, today known as *Santilli isofields* [10], which are given by the infinite family of isotopies F*{n*,×*,I*) conventional numeric field F(n,×,1) characterized by the generalized multiplicative unit

(10) I* = 1/T* >. 0,

today known as *Santilli isounit*, generalized product (5)

(11) n* ×* m* - (nm)I*,

under which which I* is indeed the correct left and right unit

(12) I*×*n* = n* ×* I* = n* (10) n* ∈ F*,

and new numbers

(13) n* = nI*,

known as *isoreal, isocomplex and isoquaternionic numbers,*where n is an ordinary real, complex or quaternionic number.

Recall that physical quantities (such as coordinates r, linear momenta p, energy E, etc.) must have their values on a conventional field. For consistency, all physical quantities of isotopic theories must be *isoscalars,* that is, must have values on an isofield, thus leading to *isocoordinates* r* = rI*, *isomomenta* p* = pI*, * isoenergy* E* = EI*, etc.

Despite the reformulation on isospaces over isofields, isotopic theories remained afflicted by inconsistencies. In particular, they were unable to predict the same numeric values under the same conditions at different times.

Following extensive efforts, during the heat of the sessions of the 1995 *Second International Conference on the Lie-admissible treatment of non-potential interactions* held at the Castle Prince Pignatelli in Italy, Santilli was left with no additional option than that of reinspecting the most fundamental calculus of 20th century theories, the Newton-Leibnitz differential calculus.

In this way, Santilli [12] discovered that, contrary to a general belief in mathematics for about four centuries, the ordinary differential calculus does indeed depend on the unit of the base field. The conventional differential calculus holds for the particular case when said unit is a constant or it does not dependent on the variable of differentiation. However, when said unit does depend on the variable of differentiation, Santilli discovered the following generalized differential and derivative

(14a) d*r* = T*d r* = T* d [rI*(t, r,p, ...)] = dr + T*dI*,

(14b ) ∂* f*(r*)/∂* r* = I* ∂ f*(r*)/∂ r*.

In the same memoir [21], Santilli reformulated the isotopies of the main aspects of 20th century applied mathematics, including the isotopies of numeric fields, functional analysis, differential calculus, metric spaces, geometries, algebras, symmetries, etc., and showed the achievement of the needed mathematical and physical consistency.

Nowadays, *isomathematics* is referred to a mathematics, characterized at all levels by an arbitrary, positive-definite, multiplicative unit I* = 1/T* >. 0 and isoproduct (5), thus including the isotopies of all aspects of 20th century mathematics without exceptions.

Isomathematics has been the subject of vast studies, including yearly international workshops. To avoid a prohibitive length, we are regrettably forced to quote independent mathematical works [12-19] that are of direct relevance for this nomination. We mention in particular the *six volumes* of Refs. [18] on the isodifferential calculus by the mathematician S. Georgiev, in recognition for this unprecedented contribution, the new calculus underlying isomathematics is nowadays called the *Santilli-Georgiev isodifferential calculus.*

It should be noted that Santilli proposed isomathematics as a particular case of the broader *genomathematics* characterized by the covering of Lie algebras and Lie-Santilli isoalgebras known as *Santilli Lie-admissible algebras* that are necessary for the representation of processes irreversible over time, as presented in detail in a forthcoming nomination.

This nomination is restricted to isomathematcs because the neutron synthesis is reversible over time, thus being fully treated by isomathematics in view of the anti-commutativity of the Lie-Santilli isocommutators.

**5. THE BIRTH OF ISOSYMMETRIES**

*NON-RELATIVISTIC ISOSYMMETRIES*

Santilli was fully aware that the most rigorous non-relativistic characterization of the Schroedinger and Hamilton equations of quantum mechanics is that done via the primitive *Galileo symmetry.*

In view of the local-differential character of the underlying mathematics, the Galileo symmetry can only characterize particles as being point-like under action-at-a-distance, potential interactions. Such a characterization has been proved to be valid for large mutual distances of particles as existing in the hydrogen atom, but the same symmetry is grossly insufficient for the neutron synthesis, or for the nuclear structure at large, because, in the latter case, the proton and the neutron must be represented as an extended particle.

Additionally, the Galileo symmetry is known to be valid for Keplerian systems (Figure 3). As such, said symmetry cannot be valid for the neutron synthesis since, as recalled by Santilli various times, *"The proton and the neutron have no nuclei".* Therefore, non-relativistic studies of the synthesis of the neutron from the hydrogen atom required a structural generalization of the Galileo symmetry.

Santilli constructed a generalization of the Galileo symmetry under the conditions of preserving the conventional ten conservation laws (for the total energy, the linear and angular momentum and the uniform motion of the center of mass for an isolated composite system at short mutual distances), while admitting conventional as well as non-linear, non-local and non-Hamiltonian internal forces due to mutual penetration of the wavepackets of the constituents [21-25].

The preceding efforts on the isotopies of Lie's theory [5-7] turned out to be crucial for the achievement of the needed new isosymmetry. These studies lead to the isotopies of the Galileo symmetry, today known as the *Galileo-Santilli isosymmetry* that were published in papers [21-23] and then presented in monographs [24[ all published in 1991.

It should be indicated that Santilli was the very last scientist to be invited in 1991 by the Nobel laureate, Abdus Salam (just prior to his death) to deliver a series of lecture on the isotopies of the Galileo symmetry and relativity at the International Center for Theoretical Physics (ICTP) in Trieste, Italy. These lectures were attended by Salam despite his terminal illness, as well as by other scientists who published the lecture notes in monograph [226] which is an excellent review of Santilli's non-relativistic studies prior to the discovery of the isonumbers and of the isodifferential calculus.

It should be also indicated that, during his stay at the ICTP in 1991, Santilli wrote twelve papers released as ICTP publican numbers IC/ 45, 46, 47, 48, 258, 259, 260, 261, 263, 264,265, 266/91, which have been collected and are now in press jointly with other papers [25].

*RELATIVISTIC ISOSYMMETRIES*

As it is equally well known, a most rigorous characterization of the Dirac equation is that via the spinorial covering of the Lorentz-Poincare' symmetry, since the former is provided by the linearization of the second order Casimir invariant of the latter.

However, the Lorentz-Poincare' symmetry is inapplicable to the neutron synthesis because it can only characterize point-like particles and their Keplerian distribution, thus needing a Keplerian center for its validity (Figure 3). Consequently, no representation of the neutron synthesis was expected without a structural generalization of the fundamental spacetime symmetry of 20th century physics.

,p> In view of the above occurrences, Santilli dedicated decades of studies to the systematic isotopic generalization of each and every aspect of the Lorentz-Poincare' symmetry, that include the isotopies of: the rotational symmetry [27,28]; the SU(2) symmetry [29,30]; the Lorentz symmetry at the classical [31] and operator [32] levels; the Poincare' symmetry [33,34]; the spinorial covering of the Poincare' symmetry [35] (see also later on Ref. [zzzzzz]); and the Minkowskian geometry [36].

Refs. [37] presented the proof of the universality of the isotopies of the Lorentz-Poincare' symmetry for the invariance of all infinitely possible, symmetric, non-singular, line elements in (3+1)-dimensional spaces, thus including the invariance of all possible Minkowskian, Riemannian Fynslerian and other line elements (see the independent confirmations [43.44]).

Ref. [38] achieved the important proof of the compatibility of locally varying speeds of light within physical media with the abstract axioms of special relativity, with intriguing and far reaching implications.

Ref. [39] presented the first known application of the Lorentz-Poincare;-Santilli isosymmetry to a new, invariant theory of gravitation formulated on the Minkowski-Santilli isogeometry [36], rather than the Riemannian geometry, although by maintaining and reformulating Einstein-Hilbert field equations via isomathematics..

The above comprehensive studies were systematically presented in monographs [40] of 1995 that remains to this day the best reference in the field. The subsequent monographs [41,42] presented applications and experimental verifications of the new isosymmetries. Among a large number of contributions in the field, we note the above quoted quote: Refs. [43,44] and monographs [45,46] with comprehensive literature.

In view of the above systematic studies, the isotopies of the Lorentz-Poincare' symmetry are today known as the *Lorentz-Poincare'-Santilli isosymmetry* )see. e.g., Refs. [43-46]_.

We cannot possibly review such comprehensive studies. Nevertheless, in order to render this nomination minimally self-sufficient, it is necessary to review at least Santilli's central discovery, the generalization of the Lorentz symmetry for extended and deformable particles moving within physical media that was i first achieved in Refs. [31,32] of 1983 and then studies in numerous works.

Recall that the Lorentz symmetry provides the invariance for relativistic point particles in vacuum (conditions also known as *exterior dynamical problem*) formulated on the conventional Minkowski space M(x,×I) with spacetime coordinates

(15) x = (x^{1}, x^{2}, x^{3}, x^{4} = ct),

metric

(16) η = Diag. (1, 1, 1, -1),

unit

(17) I =- Diag. (1, 1,1, 1),

and invariant

(18) x^{2} = x^{μ} ×η_{μν} × x^{ν} = (x_{1}^{2} + x_{2}^{2} + x_{3}^{2} - c^{2} t^{2}) I

The Lorentz symmetry in the (3,4)-plane can then be written

(19a) x^{1}' = x^{1}, x^{2}' = x^{2},

(19b) x^{3}' = γ (x^{3} - β x^{4}),

19c) x^{4}' = γ (x^{4} - β x^{3}),

where

(20a) β = v_{3}/c,

(20b) γ* 1/ √(1 - β^{2}).

The covering Lorentz--Santilli isosymmetry provides the invariance for relativistic extended particles moving within a physical medium (conditions also known as *interior dynamical problems*) formulated on the Minkowski-Santilli isospace M*(x*,η*,I*_ with spacetime isocoordinates

(21) x* = (x^{1}, x^{2}, x^{3}, x^{4} = ct) I*,

isometric

(22) η*(t, r, v, ω, E, ξ, τ, ψ, ∂ψ, ...) = T*(t, r, v, ω, E, ξ, τ, ψ, ∂ψ, ...) η,

isotopic element

(23) T* = Diag. (1/n_{1}^{2}, 1/n_{2}^{2}, 1/n_{3}^{2}, 1/n_{4}^{2}),,

characteristic quantities of the medium considered, Eq. (6b), i.e.,

(24) n_{μ} = n_{μ}(t, r, v, ω, E, ξ, τ, ψ, ∂ψ, ...) > 0.

isounit

(25) I* = 1/T* > 0

and isoinvariant

(26) x*^{2*} = x*^{μ} ×* η*_{μν} ×* x*^{ν} = [ x_{1}^{2}/n_{1}^{2} + x_{2}^{2}/n_{2}^{2} + x_{3}^{2}/n_{3}^{2} - t^{2} (c^{2}/n_{4}^{2}) ] I*

The universal symmetry of isoinvariant (23) in the (3,4)-isoplane [31,342] (see Refs. [40] for the general case) can be written in its projection in the conventional Minkowski space

(27a) x^{1}' = x^{1}, x^{2}' = x^{2},

(27b) x^{3}' = γ* [x^{3} - β* x^{4} (n_{3}/n_{4})],

27c) x^{4}' = γ* [x^{4} - β* x^{3} (n_{4}/n_{3})],

where

(28a) β* = (v_{3}/n_{3}) / (c/n_{4}),

(28b) γ* - 1/ √(1 - β*^{2}).

The first historical advance achieved by the above studies has been the * solution of the historical Lorentz problem,* namely, *the invariance of the locally varying speed of light within physical media* (when transparent) [31]

(29) c* = c/n_{4}. As,

As well known to historians, Lorentz attempted the achievement of such an invariance, but failed to do so because of insurmountable technical difficulties, and had to content himself with the invariance of the *constant* speed c.

Santilli understood that Lorentz's difficulties originated from the inapplicability of Lie's theory within physical media. Therefore, he dedicated years of research to generalize Lie's theory into the Lie-isotopic covering theory [7] after which the solution of the historical Lorentz problem in was achieved in only two pages of letter [31].

*Figure 6. It is generally believed that the speed of light is c under whatever conditions exist in the universe. Santilli has identified physical inconsistencies of this belief due to incompatibility with experimental evidence, such as the impossibility for a credible reduction to photons of infrared and radio waves propagating within a medium, and has shown that the abstract axioms of special relativity admit in reality 'arbitrary' speeds, whether smaller or bigger than c. The local value of the speed of light within physical media is represented via the mutation of the light cone depicted in this figure, with the understanding that, when isorelativity is formulated via isomathematics, the light cone remains the conventional light cone in vacuum [32]. *

The second historical advance achieved by the above studies has been the establishing, with experimental verifications outlined below, that *the maximal local speed within physical media can be arbitrarily bigger or smaller than the speed of light in vacuum.* Tis result can be see from the *light isocone* in the k-direction (figure 7)

((30) x*^{2*} = x_{k}^{2}/n_{k}^{2} - t^{2} c^{2}/n_{4}^{2} = 0.

as a result of which we have the maximal causal speed in the k-direction

(31) V_{max} = c (n_{k} / n_{4}) < = > c ,

As a first illustration, udder the assumption of isotropy and homogeneity, the maximal causal speed in water is given by the known local speed of light

(32) V_{max} = 2c/3 < c, n_{k} - 1, k = 1, 2, 3, n_{4} = 3/2.

For the case of a spinning hadron such as the proton, thus being an oblate spheroid, we have the space characteristics quantities originating from their normalization to 1, Eqs., (6),

(33) n_{1} = n_{2} > 1, ,

the forth characteristic quantity is predicted to be smaller than 1 from the fit of particle data experiments (Section zzz),

(34) n_{4} < 1,

resulting in a tangential maximal causal speed in the equatorial plane which is bigger than c

(35) n_{k}/n_{4} > 1 V_{max} = c (n_{k}/n_{4}) > c ,

It should be stressed that, contrary to popular beliefs, the above superluminal character *is not* in conflict with special relativity because such a theory solely applies for point particles in vacuum, thus solely admitting action-at-a-distance interactions derivable from a potential. Under these assumptions, there is the well known need of infinite energy to reach the speed of light c.

In paper [47] of 1982, Santilli pointed out that for the case of dynamics within the hyperdense media existing in the interior of hadrons, we have additional *contact zero-range interactions* for which any energy consideration has no physical value, thus allowing arbitrary speeds as confirmed by experimental fits outlined below.

*Figure 7. The rendering of the tangential speed at the equatorial plane of an electron totally immersed within the hyperdense medium in the interior of proton according to Rutherford's "compression": of the hydrogen atom [1]. According to the Lorentz-Santilli isosymmetry, the proton is represented as an extended and deformable charge distribution whose spin caused the shape of an oblate spheroid. The Lorentz symmetry (19) predicts that c is the maximal causal speed of the electron moving in vacuum around the proton. By contrast, the Lorentz-Santilli isosymmetry (26) predicts that the maximal causal speed of the same electron when totally immersed within the proton is arbitrary, Eqs.. (30). The fit of experimental data in particle physics reviewed in Section ZZZZ establishes that, the maximal causal speed of the latter case is bigger than c.*

The third historical advance achieved by the above studies is the compatibility of arbitrary speeds with the abstract axions of special relativity [38]. This result was achieved thanks to the local isomorphism of the Lorentz symmetry and the Lorentz-Santilli isosymmetry, thanks to the preservation of the structure constants in the Lie-Santilli isotopies (8) of the related algebras.

Additionally, the advance was achieved by by showing that the replacement of c with the maximal causal speed (31) turns the conventional Lorentz transforms (19)) into the Lorentz-Santilli isotransforms (7). In fact, under the replacements

(36) c → V_{max} = c (n_{k} / n_{4})

or, equivalently, the replacements

(37) X^{3} → x*^{3} = x^{3}/n_{3}, , x^{4} → x*^{4} = x^{4}/n_{4},

we have

(38) β → β*, γ → &gamma'*,

and transforms (19) are indeed turned into isotransforms (27) [38]. Additional advances permitted by the Lorentz-Santilli isosymmetry will be indicated later on.

In the final analysis, the Lorenz symmetry characterizes a *generic* quantity c as the maximal causal speed. Its identification with c = 300,000 Km/s is a purely *physical* assumption. Consequently, lifting (36) is fully compatible with the abstract axions of special relativity [38[].

Recall that the Lorentz-Poincare' symmetry is the ultimate foundation of 20th century relativistic studies. It is hen a truism to state that, among all Santilli;s discoveries in various branches, the structural generalization of the Lorentz-Poincare' symmetry for extended particles moving within physical media is is the most important discovery by Santilli because it has caused a corresponding compatible generalization of the virtual entirety of 20th century knowledge.

Remarkably, Santilli conceived all the above isosymmetries as the particular case for time-reversal invariant systems of the broader Lie-admissible genosymmetries for irreversible systems that will be presented in a future nomination.

**6. THE BIRTH OF ISORELATIVITIES**

*ISOTOPIES OF THE GALILEO RELATIVITY*

As it is well known, Galilei relativity is provides the physical laws for non-relativistic point-particles moving in vacuum (conditions also known as *non-relativistic exterior dynamical problems*). The isotopies of the Galileo symmetry led Santilli to the isotopies of Galilei relativity for the characterization of the physical laws of non-relativistic extended particles moving within a physical medium (conditions also known as *non-relativistic interior dynamical problems*) [21-25] . The emerging new relativity is today known as the *Galileo-Santilli isorelativity* (see, e.g., also the excellent independent review [26]).

One of the most important implications of the new relativity is the introduction of a basically new notion of particles, called by Santilli *isoparticles,* for the characterization of extended particles in interior conditions which are technically characterized by isounitary isoirreducible isorepresentations of the Galileo-Santilli isosymmetry.

The main characteristics of isoparticles is the alteration, called *mutation,* of the *internal* characteristics of exterior conditions, thus implying a mutation of rest energy, magnetic moments, spin, etc.[23]. A technical knowledge of these mutations is crucial for an understanding of the non-relativistic synthesis of the neutrons from the hydrogen atom

*Figure 8. Galileo Galilei studied the free fall of masses on Earth's gravitational field by assuming the masses to be pint-like, thus ignoring the resistance due to our atmosphere. Santilli studied the same free fall, this time by representing the object with its actual extended size, thus including the representation of resistive forces caused by our atmosphere via his isomathematics and realizations of the isounit of type (6). *

*ISOTOPIES OF SPECIAL RELATIVITY*

A main objective of Santilli's fifty years of research has been the isotopic, thus axiom-preserving, generalization of special relativity for the representation of stable and isolated (thus time reversal invariant) bound systems of extended particles under conditions of mutual penetration, as it is the case for the neutron (Figure 2) or nuclei at large (Figure 5). Under these conditions, the systems verify the ten conventional conservations of total quantities, while admitting conventional, as well as non-linear, non-local and non-Hamiltonian internal forces.

The foundations of the new relativity were achieved in memoir [5] of 1978 written by Santilli at Harvard University under DOE support. The new relativity was then presented in the 1983 papers [31,32] for the classical and operator profiles, respectively. Thereafter, the new relativity was subjected to comprehensive studies [27-42]. The main presentation of the new relativity remains to this day that of monographs [50] of 1995, with applications and experimental verifications provided in Refs. [41-42].. The resulting new relativity is today known as *Lorentz-Poincare'-Einstein-Santilli (LPES)isorelativity,* or *isorelativity* for short (see monographs [45,46] for independent reviews with vast literatures).

It should be indicated that Santilli presented in memoir [5] 9see also memoir [48]) the new relativity at the covering Lie-admissible level for irreversible systems, which will be the subject of a future nomination. In this nomination, we restrict the review to the Lie-isotopic, thus time reversible particular case because the synthesis of the neutron is indeed reversible over time. Also, this nomination is restricted to the case solely dealing with *matter,*since the study of *antimatter*in general, and that of the synthesis of the antineutron, requires a different mathematics [49] and it will be the subject of a future nomination.

The isoaxioms characterizing the physical laws for the dynamics of an extended particle moving within a physical medium in the k-directions are uniquely and unambiguously characterized by the Lorentz-Santilli isosymmetry, and are given by [loc. cit.]:

*ISOAXIOM I: The maximal causal speed within a physical medium in the k-direction is given by*

(39) V_{max} = c (n_{k} / n_{4}),

* ISOAXIOM II: The local isospeed of light within a physical medium is given by*

(40) c* = c / n_{4},

*ISOAXIOM III: The addition of isospeeds in the k-direction follows the isotopic law *

(41) V_{tot} = (v_{1k}/n_{k} + v_{2k}/n_{k}) / [1 + (v_{1k}v_{2k}/c^{2})(n_{4}^{2} / n_{k}^{2}) ],

* ISOAXIOM IV: The isodilatation of time, the isocontraction of lengths, the variation of mass with isospeed, and the mass-energy isoequivalence principle follow the isotopic laws *

(421) t' = t γ*_{k},

(43) L' = L' / γ*_{k},

(44) m' = m γ*_{k},

(45) E' = m V_{max}^{2} = m c^{2} ( n_{3}^{2} / n_{4}^{2} )..

*ISOAXIOM V: The frequency isoshift of light propagating within a physical medium in the k-direction follows the Doppler-Santilli isotopic law*

(46) ω_{e} = ω_{o} ( 1 ± β* ) cos α.

*where ω _{e} is the frequency experimentally measured in the outside, ω_{o} is the frequency at the origin within the physical medium, and we have ignored for simplicity the isotopies of trigonometry (see Refs. [zzzzzz] for brevity).*

The understanding of this nomination requires a knowledge of the following implications of the new isorelativity (and their verifications outlined below) due to their departures from 20th century knowledge.

As it is well known, physical media are generally inhomogeneous and anisotropic. Consequently, the numerical value of the isoaxioms generally changes with the change of the space-direction. Said numerical value also changes with the change of the density of the medium considered.

As indicated in the preceding section, the Lorentz-Santilli isosymmetry is isomorphic to the conventional symmetry. This implies that that special relativity and isorelativity coincide at the abstract, realization-free level when each relativity is formulated with its appropriate mathematics. Therefore, technically unsubstantiated criticisms of the new isorelativity are criticisms of Einstein;s axioms.

A most salient implication of the LPES isorelativity is the characterization of *relativistic isoparticles* which are technically achieved as isounitary isoirreducible isorepresentations of the isotopies of the spinorial covering of the Lorentz-Poincare' group.

In particular, all Isoaxioms I to V provide a characterization of the mutations of the conventional intrinsic characteristics of particles. Particularly important is the *mutation (also known as isorenormalization) of the rest energy,* Eq. (24) which will soon emerge as being crucial to resolve the inconsistencies caused by the excess rest energy of the neutron compared to the sum of he rest energies of the proton and the electron (Section 1).

All isoaxioms (39) to (45) are given by their *projection* in the conventional Minkowski space over a conventional field. When the same expressions are written on Minkowski-Santilli isospaces over Santilli isofields, they *coincide* with the conventional axioms to such an extend that the maximal causal speed is c and not V_{max} [40].

*ISOTOPIES OF GENERAL RELATIVITY*

As it is known to serious scholars, recent studies have confirmed the historical objection according to which the celebrated "bending of light" when passing near the Sun is due to the refraction of light passing through the Sun chromosphere, plus the conventional Newtonian attraction, without any actual curvature of space. General relativity remains valid, although only as a mathematical representation of gravity [39].

Consequently, Santilli has conducted comprehensive studies on the isotopies of general relativity that initiated with the achievement of the invariant e of all possible Riemannian line elements in papers [33,34], continued with the isotopic reformulation of the Riemannian geometry via the isoflat Minkowski-Santilli isogeometry done in memoir [36], and culminated with the unified exterior and interior formulation of gravitation in memoir [39] under the name of *isogravitation.*

The above studies are important for this nomination because the isometric η*(t, r, v, ω, E, ξ, τ, ψ, ∂ψ, ...) of the generalized Dirac equation (57) providing a relativistic representation of the neutron synthesis appears to have an interior gravitational content that can be solely identified via Santilli isogravitation.

*Figure 9. According to a historical, but forgotten, criticism of Einstein's general relativity, Sunset is a visual evidence of the lack of actual, physical, curvature of space because we still see the Sun at the horizon, while in reality it is already below the horizon due to the refraction of light passing through our atmosphere. Consequently Santilli [39] points out that, according to incontrovertible physical evidence, the 1.74 arc-seconds 'bending' of star light when passing near the Sun is due to the refraction of light when passing through the dense Sun chromosphere, plus a contribution from conventional Newtonian gravitation, without any contribution whatsoever from the curvature of space. Santilli additionally provides technical arguments according to which the conjecture of the curvature of space has rendered general relativity incompatible with all remaining branches of 20th century physics, including the prohibition to reach as grand unification of all known interactions,. For these and other reasons, Santilli has presented in the historical memoir [39] a new theory of gravitation under the name of 'isogravitation' because based on the locally isoflat Minkowski-Santilli isogeometry [36] which" A) Achieves full compatibility of gravitation with 20th century theories, including compatibility with quantum axioms; B) Permits the first known geometrically consistent grand unification and; and C) Achieves the first known unified formulation of exterior and interior gravitational problems. *

**7. THE BIRTH OF ISOMECHANICS**

*NON-RELATIVISTIC ISOMECHANICS*

Jointly with the proposal of isoproduct (5) and of the isotopies of Lie's theory, Santilli proposed the construction of *hadronic mechanics* (see Ref. [5], page 260) as a non-unitary covering of quantum mechanics with the broader Lie-admissible structure (also called *genomechanics*) for the representation of irreversible processes, which is the subject of a future nomination.

As a particular case for the representation of processes reversible over time, which include the neutron synthesis, Santilli proposed in Refs. [3-5] a particular case of genomechanics called *isomechanics* which is based on the Lie-Santilli isotheory.

*Figure 10. A classification of the various branches of hadronic mechanics for matter and its isoduals for antimatter according to Santilli's 'opera magna' [42]. *

Isomechanics is based on the following isotopic generalization of Heisenberg equation for the time evolution of an observable A in the finite form (see Ref. [5] page 152)

(47) idA/dt = [A. H]* = A×*H - H×*A = ATH - HTA,

and in its exponentiated/finite form

(48) U(t) = e*^{Hti} ×* U(0) ×* e*^{-itH} = e^{HT*ti} × U(0) × e^{-itT*H}

whose Lie-Santilli isotopic structure is evident from Eqs. (8) and (9).

Refs. [5-7] also proposed the isotopic generalization of Schroedinger equation

(49) H ×* ψ* = E* ×* ψ* = E ψ*,

Nowadays, Eqs. (47), (48) are known as the *Heisenberg-Santilli isoequations,* and Eqs. (49) are known as the*Schroedinger-Santilli isoequations,* respectively.

Despite numerous contributions by various authors, isomechanics remained incomplete for a decade due to the lack of a consistent isotopy of the linear momentum. This insufficiency prevented the isotopic formulation of the angular momentum with consequential lack of consistent applications to concrete physical or chemical problems, including the impossibility to treat the neutron synthesis.

This impasse was resolved by Santilli in memoir [9] of 1996 thanks to the discovery of the isodifferential calculus that finally permitted the correct definition of the *isolinear isomomentum* written as a projection in ordinary spacetime

(50) p* ×* ψ(t, r) = - i*×*∂*_{r*}ψ*(t,r) = - i I*_{r*} ∂_{r} ψ*(t, r)

with consequential fundamental isocommutator rules

(51a) [p*_{i}, p*_{j}]* = [r*_{i}, r*_{i}]* = 0,

51b) [p*_{i}, r*_{i}]* = - i* ×* δ*_{ij} = i I* δ_{ij}

which expressions are defined on a *Hilbert--Myung-Santilli isospace* [zzz over Santilli isofields [9[ (see also Ref. [10]).

Following the above discovery, the applications and experimental verifications of hadronic mechanics in general and of isomechanics in particular, literally exploded, as partially reviewed in the next section.

By noting the crucial presence of the isoderivative (14b) in Eq. (50), the history of the isolinear isomomentum illustrates the truly fundamental role of the isodifferential calculus for the new physics, include the neutron synthesis, and illustrates the reason the isodifferential calculus is considered as being at the foundation of the "New Sciences for a New Era" [46].

As indicated earlier, isomechanics is intended for the representation of closed-isolated bound stems of extended particles/wavepackets inn conditions of mutual overlapping with conventional as well as non-linear, non-local and non-Hamiltonian internal forces (Figures 2 and 5).

This representation is possible thanks to the use of the conventional Hamiltonian H for the representation of conventional interactions, plus the use of the isotopic element T* for the representation of all non-Hamiltonian interactions.

The consistency of the representation is assured by the anti-commutativity of the Lie-Santilli isocommutators that, as such, allows the conservation of conventional, total physical quantities, such as the conservation of the total energy

(52) idA/dt = H×*H - H×*H = 0.

The remaining nine conventional total conservation laws are also assumed by the Lie-Santilli isotheory because, in the transition from the Lie to the Lie-Santilli isotheory, the generators remains the same and only their associative product is lifted in an associativity-preserving form.

We should recall that isomechanical models can be easily constructed via the simple non-unitary transform of conventional quantum models [50]

(53a) UU^{†} ≠ I, A → A* = UAU^{†},

(53b) 1 → I* = U I U^{†},

(53c) AB → U(AB)U^{† = A* T* B*, T* = (UU†)-1,}

(53d) [A, B] → [A*, B*]*, etc.

The Schrodinger-Santilli isoequation and underlying Hilbert-Myung-Santilli isospace can also be easily constructed via the non-unitary transformation of the conventional quantum mechanical formulations

(54a) U(H ψ) U^{†} = H* T* ψ* = U(E ψ) U^{†} = E ψ*,

(54b) U <ψ | A | ψ>: U^{†}

= <'ψ* | T* A* T* |ψ*&ht; I*,

(54c) H* = U H U^{†}, ψ* = U ψ U^{†}

where in Eq. (54b) one can see the new vacuum isoexpectation values of the iso-Hilbert space with isostates ψ* [40].

Therefore, when applicable, *the lifting of a conventional quantum mechanical model of a bound state into the coveting hadronic model is easily achieved via the identification of all non-Hamiltonian interactions with non-unitary transform (53aa).*

The invariant of isomechanics was first proved in Ref.[50] via he reformulation of a conventional non-unitary transformation on a Hilbert space into the *isounitary* isotransformations on the Hilbert-Myung-Santilli isospace

(55a) U U^{†} = I* ≠ I,

(55a) U = U* T*^{1/2}, U* ×*U*^{†} = U*^{†} ×* U = I*

under which we have the following invariances

(56a) I* → I*' = U* ×*I* ×* U*^{†} = I*,,

(56b) A* ×* B* → U* ×* ( A* ×* B*) ×* U*^{†} = A*' ×* B*',

namely, we have the *invariance of the numerical values of the isotopy of and, equivalently, of the isotopic element under isounitary transforms,* By remembering that I* = 1/T* represents all non-Hamiltonian interactions, properties (56) confirm the prediction of the same numerical values under the same conditions at different times.

*RELATIVISTIC ISOMECHANICS*

Following the above preparatory studies, while visiting in the summer of 1995 the Joint Institute for Basic Research, Dubna, Russia,Santilli achieved in Ref. [34] 9see also monographs [40] and and memoir [50]) below) the relativistic representation of the synthesis of the neutron from the hydrogen atom that will be reviewed later on in this nomination.

Said solution was based on the first known construction of the isotopies of the spinorial covering of the Poincare' symmetry and its use for the characterization of the isotopies of Dirac's equation, today known as the *Dirac-Santilli isoequation* that can be written in the form according to the full use of isomathematcs

(57) [γ*^{μ}(p*_{μ} - i*×*e*×*A*_{μ}) - (i*×*m*×*c)*] ×* ψ*(x*) = 0,,

where the *Dirac-Santilli isogamma matrices* incorporate all non-Hamiltonian interactions via the non-unitary transform

(58) γ*^{μ} = U_{4x4}γ^{μ}U^{†}_{4x4},

and verify the anti-isocommutator rules

(59) {γ*^{μ}, γ*^{ν}}* = γ*^{μ} T* γ*^{ν} + γ*^{ν} T* γ*^{μ} = η*^{μν}

where the isometric is restricted to have the topology (+, +, +, -) but possesses otherwise the most general possible functional dependence on all needed local variables as in Eq. (6), i.e.,

(60) η*^{μν} = η*^{μν}(x, v, ω, E, ξ, τ, ψ, ∂ψ, ...)

which unrestricted dependence is necessary fir serious studies of interior problems.

Eqs. (57) are based on the sole isotopies of the four-dimensional Minkowski spacetime for the orbital motion, Eqs. (21)-(26). In his typical style of studying first the most general case, and then working out particular cases, Santilli presented in Refs. [34,zzzzzz,50) the most general isotopies. those of the Minkowski spacetime for the orbital motion as well as those of the internal degrees of freedom for the spin. Regrettably, we cannot review the latter isotopies because excessively advanced for the level of this nomination.

Note the remarkable appearance of the isometric η* of the Minkowski-Santilli isospacetime in the anti-isocommutators of the γ* matrices, thus confirming the deep interconnection between geometry and dynamics that exists at the conventional level and persists in full under isotopies.

As it is well known, the conventional Dirac equation represents the structure of the Hydrogen atom with the electron at large distance from the proton which is considered as external (top view of Figure 2). By contrast, * the Dirac-Santilli isoequation represents the electron, this time, immersed within the proton, thus being mutated into the isoelectron* (bottom view of Figure2).

Detailed presentations of relativistic isomechanics are available in monographs [40] and in memoir [50].

*MAIN FEATURES OF ISOMECHANICS*

To properly appraise this nomination without misunderstandings due to lack of knowledge of the new sciences, we review the following most salient features of isomechanics [40]:

1. Isomechanics is a non-unitary "completion" of quantum mechanics respectively according to the celebrated argument by Einstein, Podolsky and Rosen on the lack of completion of quantum mechanics.

2. The basic axioms of isomechanics are the same as those of quantum mechanics, to such an extend that all distinctions between the two mechanics disappear at the abstract, realization-free level, at which level both mechanics can be presented with the same symbols, only subjected to different realizations.

3. Isomechanics is solely valid at one Fermi mutual distances and recovers conventional mechanics identically for mutual distances sufficiently bigger than one Fermi. This feature is assured by the fact that, a condition for the isodifferential calculus to recover conventional calculus, Eq. (14a), is that the non-Hamiltonian interactions must be represented with an exponential form as presented in Eq. (6a) and that, in turn, for sufficiently ;large mutual distances, the integral in the exponent of REq. (6a) is null;l, thus eliminating all non-Hamiltonian effects. In turn, this feature illustrates again the enormous importance of Santilli isodifferential calculus in the 'New Sciences fora New Era.'

4, All quantities that are observable in quantum mechanics (essentially self-adjoint) remain observable for isomechanics because the conditions of Hermiticity and iso-Hermiticity coincide [40].

5. Isomechanics is the only known mechanics allowing a consistent treatment of bound states of particles with non-linear interactions. This is due to the fact that non-linear quantum mechanical models can only be described via Schroedinger equations of the type

(61) H(r, p, ψ, ...) ψ = E ψ,

that, as such violate the superposition principle, by therefore prohibiting a consistent identification of the constituents.

By contrast, isomechanics has bee constructed in such a way to embed all non-linear (as well as, more generally, all non-Hamiltonian) interactions in the isounit or, equivalently, in the isotopic element, by therefore implying the following identical reformulation n-n0linear equations (40)

(62) H(r, p, ψ, ...) ψ = H'(r, p) ×'* ψ* = H'(r, p) T*(ψ, ...) ψ* = E ψ*,

which does verify the superposition principle on isospaces over isofields, thus allowing the characterization of the individual constituents of the bound states.

To illustrate again the unity of Santilli's conception of isomechanics, note that the "particles" emerging from the regaining of the superposition principle under non-linear interactions are not ordinary particles, but they are, necessarily, isoparticles characterized by the isoaxioms..

6, The ultimate significance of isomathematics in the resolution of the inconsistencies of non-linear, non-local and non-unitary theories is that of allowing the reconstruction of locality, linearity and unitarity when formulated on isospaces over isofields, resulting in new notions today known as * Santilli isolocality, isolinearity, isolocality and isounitarity.*

7. An important advance permitted by that isomathematcs is the remove of the singularity at the origin r = 0 of the Dirac distribution thanks to the *Dirac-Myung-Santilli isodelta isofunction* [9,10]

(63) δ*(r) = ∫ e^{ikT*(r, ...)r} dk,

and the conversion of divergent convergent series, such as the canonical one

(64) A(w) = I + w (AH - HA)/1! + ..., w > 1,

into strongly convergent isoseries, e.g., of the isocanonical type,

(65) A(w) = I* + w (AT*H - HT*A)/1! + ..., |T*| << w

Consequently, the time currently needed for computer calculations of molecular data can be reduced by at least 1,000 times [9,14,15].

The proper appraisal of this no requires the knowledge that properties (63)-(65) have allowed A. O. E. Animalu and Santilli the construction of the first and only known *relativistic scattering theory without divergencies* [51] which is a central pillar of relativistic isomechanics. This discovery is of such a historical significance to deserve alone a nomination.

*Figure 11. A most important implications of Santilli's discoveries is that Feynman diagrams depicted in the l.h.s of this pictures, while remaining exactly valid for quantum electrodynamics, are only approximate for the scattering of hadrons due to inevitable non-linear, non0-local and non-Hamiltonian effects due to deep overlapping depicted in the r.h.s of this figure. In particular, A. O. E. Animalu and R. M. Santilli [51] have shown that the divergencies of relativistic scattering theory are due precisely to the point0-like abstraction of particles which is inherent in Feynman diagrams, and such divergencies are removed when the actual size of particles and their densities are admitted and represented via isomathematics s, isosymmetries and isorelativities. *

On a historical note, the (late) mathematician H. C.Myung and Santilli had realized in 1982 [9] that hadronic mechanics at large and isomechanics in particular removes the divergencies of quantum mechanics. Santilli then visited P. A. M. Dirac in 1983 while he had retired in Tallahassee, Florida. Dirac strongly supported the modification of quantum mechanics in such a way to avoid the ongoing removal of infinities by subtracting infinities which is implied by conventional divergencies, for which advocacy Dirac was strongly criticized, and and discredited (sic!), by physicists of the time at Harvard University, MIT and similar places.

As recalled by Santilli (see Vol. IV of Refs. [43]), after listening to Santilli's presentation of the main ideas of properties (63)-(65), Dirac walked for minutes in total silence near the table of the presentation, and then told Santilli *"Please send me papers on hadronic mechanics," *that Santilli did on his way to Cambridge, Massachusetts. Unfortunately. a search done later on revealed that Dirac never saw these papers because his health deteriorated and then died. There is no doubt that. in the event Dirac could have collaborated with Santilli, the history of physics would have changed.

** 8. EXPERIMENTAL VERIFICATIONS.**

We now review the main experimental verifications of isosymmetries, isorelativities and isomechanics, not only to establish the credibility of the new sciences, but also to identify the numerical values of the characteristic n-quantities for the interior of hadrons whose value will be crucial to achieve a representation of the synthesis of the neutron from the hydrogen atom.

**8.1,Experimental verification in water**

Since special relativity is believed to be valid for whatever conditions exist in the universe, light propagating in water is widely reduced to photons for the intent of recovering special relativity at the level of photon propagating in inter-molecular vacuum.

However, such an *ad hoc* adaptation of nature to a preferred theory is afflicted by numerous inconsistencies outlined in Figure 12 that are resolved by Santilli isorelativity. We here merely indicate that, since water is homogeneous and isotropic, all characteristic n-quantities majesty have the same value, in which case they can be factorized out of invariant (30), and the maximal causal speed in water is c.

Thew latter feature avoids the violation of causality for electrons traveling in water faster than light (Cherenkov light), and establishes quite clearly the necessity to differentiate, in general, the speed of light from the maximal causal speed., which coincide only for homogeneous, isotropic and transparent media, by keeping in mind that physical media are generally opaque to light, to requiring a new concept the maximal causal speed.

The violation in water of the relativistic sum of speeds is also resolved by isorelativity via IsoAxiom III because, in the latter case, the sum of two isospeeds of light in water yields the isospeed of light in water,

(66) V_{tot} = (c/n_{4} + c/n_{4}) / [1 + (c^{2} / n_{4}^{2}) / ( n_{4}^{2} / c^{2}) ] = c/n_{4}

The above property also clarifies the important feature according to which ordinary speeds, including the speed of light c, are *not* invariant under the Lorentz-Santilli isosymmetry thus mandating the use of isospeeds for any consistent elaboration in interior conditions.

The verification of IsoAxiom IV on the isovariation of length is outlined in Figure 12. The validity of the remaining isoaxioms is outlined below.

The reader should be aware that the geometric deviations in water of the geometry of the vacuum, despite water being homogeneous and isotropic, not only occurs for all physical media, but are magnified when considering inhomogeneous and anisotropic media such as those in the interior of hadrons, nuclei and stars [40-43] (see also the general review "New Sciences for a New Era) [46]).

*Figure 12. As it is well known, Albert Einstein obtained a fully justified Nobel Prize for his hypothesis of the photon for the quantized 'absorption' of light by matter. Einstein never suggested the reduction to photons of light 'propagating' through a physical medium, such as water, because such a reduction is manifestly inconsistent for infrared, radio, and other waves with larger wavelength that admit the same phenomenology of visible light. The reduction to photons for light propagating in water has been propagated by Einstein followers for clear non-scientific reasons, resulting in a century-old scientific obscurantism in the field that has been finally dispelled by Santilli [14-34]. In fact, said reductioT is afflicted by a host of generally ignored inconsistencies, such as: A) the impossibility of representing the angle of refraction of light (since photons will scatter in all directions at the point of impact with the water surface); B) The impossibility to represent the reduction of the speed of light by about 1/3 (the scattering of photons among the water molecules can at best represent the reduction of the speed of light by a few percentages); C) The impossibility to represent the propagation of light along a straight beam illustrated in this figure (because photons will scatter in all directions and certainly not propagator along a straight line); and other inconsistencies. Additional inconsistencies have never been resolved quantitatively, such as electrons traveling in water at speeds bigger than the local speed of light (Cherenkov light), the violation of the relativistic sum of speeds (because the sums of two light speeds in water does not yield the speed of lighter in water), and other departures from the axioms of special relativity. Santilli has identified these inconsistencies in details and shown that isorelativity resolves them all in a coordinated and consistent way [24-43]. Finally, Santilli has shown the impossibility of a serious formulation in water of the basic axioms of special relativity, including the impossibility of even formulated an experiment to test the constancy of the speed of light in water due to the lack of inertial reference frames caused by water resistance. In view of the above plethora of inconsistencies, Santilli adopted the original Lorentz conception of light as an electromagnetic wave created and propagated by the ether as a universal substratum with a locally variable speeds depending on the characteristic of the medium.*

*Figure 13. Santilli has shown that special relativity is unable to provide a quantitative representation of the fact that objects submerged in water appear to have dimensions bigger than those occurring in the outside. Such a difference is readily represented via the Minkowski-Santilli isogeometry [36] and isorelativity [22-26] and, in particular, via the general rule of isotopies for preserving not only the original, axioms but also the original numeric values [40] under which we have L _{ext} I = L_{int} I*. But for water I* > 1, Consequently L_{int} > L_{ext}, an occurrence known as Santilli isogeometric effect. * Santilli has then proved that the difference between internal and external dimensions occurs for all physical media and constitutes clear evidence that the geometries within physical media must be suitable coverings of the conventional geometries for the vacuum.

*8.2. Experimental verification in air*

According to a widespread posture implemented for one full century, nature must be adapted to verify special relativity. Consequently, the redness of *direct* (rather than scattered) Sunlight at Sunset is interpreted as being due to the absorption of blue light by our atmosphere.

The above posture has resulted in another century-old scientific obscurantism because, in reality, it is well known that the absorption of light by a transparent medium is proportional to the wavelength, with blue light being most penetrating and red light being quickly absorbed by the medium, as established, for instance, by the penetration of light in seawater according to which only blue light survives at 20 meters undersea.

In fact, the sky is blue, rather than red, when the Sub is at the Zenith because red light is absorb din the relatively short vertical propagation for about 60 miles in our atmosphere. Yet, for the intent of adapting nature to special relativity, there has been a century-old belief that red light survives when propagating for about 6,000 miles (sic) in our atmosphere along a tangent at the equator, and blue light is absorbed !

In monographs [24] of 1991 Santilli dispelled this additional obscurantism, identified these inconsistencies in detail, noted the necessity of covering geometries for a consistent representation of the inhomogeneity and anisotropy of our atmosphere, and submitted the hypothesis that light loses (gains) energy, thus decreasing (increasing) its frequency, when propagating within a medium at low (high) temperature *without any relative motion between the source, the medium and the observer.* Since these predictions were based on isorelativity, the frequency shifts were called *isoredshift* (*isoblueshift*), and *isoshifts* in general.

These predictions were uniquely and unambiguously characterized by IsoAxioms V on the Doppler-Santilli isoshift, that was first proposed in paper [31] of 1983 and then elaborated in detail in monographs [34]. Recall that the characteristic n-quantities have an arbitrary functional dependence on all needed local variables according to Eqs. (6b), thus admitting the expansion on the distance d covered by light (whose numeric value is, in general, much smaller than other terms, such as the speed or the frequency of light, and we can write

(67) n_{4}^{2}/n_{k}^{2} ≈ ± cKd/v,

where K is a positive constant in first approximation. Under this expansion, IsoAxioms IV becomes (for the case of null angle of aberration)

(68) ω_{e} = ω_{o} (1 ± β*) ≈ ω_{o} (1 ± v/c ± Kd+ ....).

where the first term is the conventional Doppler shift and the second term is the Santilli isoshift.

Since no physics laboratory was interested in testing the isoshift hypothesis despite numerous proposals by Santilli dating back to 1991 (due to its departure from special relativity), Santilli had no other choice than that of doing the measurements himself by achieving very clear experimental confirmations of his isoshifts,. not only for individual laser light (Figure 14), but also for the entire spectrum of Sunlight [52-57] (Figures 15, see also the general review "New Sciences for a New Era" [46]).

*Figure 14. A view in the top of the 'IsoShift testing Station' built by Santilli at the laboratory of the Institute for Basic Research in 19xxxxx. the bottom-left view reproduces the first measurement of the isoredshift and the bottom-right view reproduces the first detection of the isoblueshift, both measurement being done with a blue laser light, all frequency shift achieved without any relative motion between the source, the medium and the observer, that were that had been first predicted in monograph [zzzz].*

*Figure 15. the left view reproduced the familiar redness of the Sun at Sunset where one can see the increase of the redness with the decrease of the elevation, thus with the increase of the travel of Sunlight in our atmosphere., The right-view reproduces one of numerous measurements conducted in the U.S.A. as well as in Europe establishing that the redness of the Sun at Sunset is Santilli isoredshift [zzz] *

The historical significance of isoshifts (68) is that they apply to cosmology and provide a clean experimental verification of Zwicky's hypothesis of tired light, by actually deriving Hubble's law

(69) z = Hd

from the primitive Lorentz-Poincare'-Santilli isosymmetry without any expansion of the universe [52-57] (see Figures 16).

Additionally, Santilli [58] has proved that isoshifts (68) provide the only known experimentally verified on Earth of the anomalies behavior of the redshift of individual galactic stars, thus resolving the notorious obscurantism in cosmology with the complete elimination of the never ending chain of hyperbolic conjectures all conceived to impose the validity of special relativity for the large scale structure of the universe (Figure 17).

*Figure 16. Santilli has conducted decades of mathematical, theoretical and experimental studies [24-57] to honor the view by Einstein, Hubble, Zwicky, Hoyle, Fermi, de Broglie, and other illustrious scientists who died without accepting the conjecture of the expansion of the universe. A reason is that Hubble's law z = Hd clearly implies the 'radial' character of the cosmological redshift in all possible directions from Earth (see the sculpture in the l.h.s. of this figure), and consequential return to the Middle Ages with Earth at the center of the universe. Additionally, Santilli has proved that the conjecture of the expansion of the universe and its inherent conjecture of the acceleration of the expansion are afflicted by catastrophic inconsistencies. In fact (see the r.h.s of this figure), the two galaxies G _{1} and G_{2} are at double distance from Earth E and, therefore, must have double speed according to the expansion of the universe, thus having a relative acceleration. However, Santilli has shown that there exist an infinite number of observers in the universe, such as galaxy G, for which G_{1} and G_{2} have the same distance, thus having no relative acceleration and establishing the inconsistency of the conjecture of the expansion of the universe and its inherent acceleration beyond scientific doubt. Note that these inconsistencies also apply to the externally implausible conjecture of the expansion of space itself. Hubble's law has been represented since the 1940s with the conjecture of the expansion of the universe, z = Hd = v/c, again the very authoritative view by Einstein, Hubble, Zwicky, Fermi, de Broglie et al.,for the studios, but unspoken, intent to impose the validity of special relativity for the large scale structure of the universe. This has created an additional, century-old, scientific obscurantism that has been dispelled by Santilli along Galileo's teaching, that via experiment on Earth establishing that the redness of the Sun at Sunset (l.h.s of Figure 15) is a visual evidence that the cosmological redshift according to which galactic light loses energy to the cold intergalactic medium without any relative motion, namely, the cosmological redshift is Santilli's isoredshift. These discoveries have confirmed Zwisky hypothesis of 'tired light' by providing an exact representation of the cosmological redshift of all galaxies, including those at the edge of the known universe, without the implausible conjecture of galactic speeds bigger than the speed of light, or the equally implausible conjecture of the expansion of space itself. [52-57].*

*Figure 17. The adaptation of the universe the verification of special relativity has created an additional scientific obscurantism, this time via the conjecture that galaxies are filled up with a mysterious and invisible substance e called 'dark matter.' Santilli has shown that such a conjecture has never represented, even minimally, the data for which it was proffered, namely the deviation of the redshift of individual galactic stars from the redshift of a galaxy as a whole (l.h.s of this figure). By contrast, isoshifts (68) provide a numerically exact and time invariant representation of the experimental data. It is known that the conjecture of dark matter was ventured for the studious, but also untold intent to derail attention from the existence of a medium in the interior of galaxies which is visible via telescopes (see the r.h.s of this figure) within which special relativity is inapplicable in favor of then covering isorelativity. In fact (see the r.h.s. of this figure), said medium is very cold in the periphery of galaxies, thus causing an isoredshifts in addition to the cosmological redshift, while being very hot in the vicinity of the galactic centers, thus causing isoblueshift with ensuing, first and only known exact representation of experimental data [58].*

* 8.3. Experimental verifications via the mean life of unstable hadrons*

As recalled in Section 2, the "point-like" quarks were propagated for the specific intent of maintaining special relativity in the interior of hadrons. This additional adaptation of nature to a preferred theory has caused an additional scientific obscurantism, this time in the small scale structure of the universe, particular in view of the widespread ignorance of opposing physical evidence.

This is due to Santilli's stressing the lack of existence in nature of "point-like wavepackets" [5], as a result of which, whether quarks exist or not, hadrons are composed by a hyperdense medium constitutes by the total mutual penetration of the wavepackets of the constituents, resulting in this way in the existence of internal non-linear, non-local and non-Hamiltonian effects simply beyond d any hope of representation via special relativity.

By noting that the center of mass ofd hadrons must obey special relativity when isolated in vacuum as it is the case in particle accelerators,, D. I. Blokhintsev [59] argued in 1964 that non-local effects within unstable hadrons should manifest themselves in the outside via deviations from the axiom of time dilation of special relativity.

Numerous generalizations of said axioms of Einstein';s time dilation law were proposed (see, e.g., L. B. Refdei [60] et al.). A. K. Aringazin [61] ;roved in 1989 that Santilli's time isodilation law (42) is universal because it contains all possible generalizations via different expansions in terms of different parameters and the use of different truncations. Besides, Santilli's time isodilatation law is the only one derivable from a symmetry, thus assuring the time invariance of numerical predictions.

S. H. Aronson et. al. [62] tested the conventional axiom of time dilation by measuring the behavior of the mean life of unstable kaons with energy between 10 and 100 GeV, by reporting clear deviations. A counter-experiment was commissioned by Einstein followers and conducted by N. Grossman et al. [63] at FERMILAB by claiming verification of the conventional time dilation, although for energies between 100 and 400 GeV.

F. Cardone et al. [64,65] showed that Santilli isodilation law on Santilli's iso-Minkowskian spaces provides an excellent fit for both tests [62,63] reported in Figure 18. Yu. Arestov et al. [66] proved the universality of Santilli iso-Minkowskian geometry for the fit of the experimental data on the behavior of the mean life of unstable hadrons with speed.

Finally, Santilli showed in Vol. IV of Refs. [42] that the slightest change in the theoretical elaboration of the experimental data by N. Grossman et al. [63], whether in form factors or in the various theoretical assumptions, implies a deviation from the conventional time dilation law for energies ranging from 100 to 4009 GeV which deviations are even bigger than those presented by Aronson et al [62].

Refs. [64,65] identified the following numerical values of the characteristic quantities for the fit of experimental data [62,63] within the Minkowski-Santilli isogeometry

(70) n_{1}^{2} = n_{2}^{2} = n_{3}^{2} = 1.0111 ± 0.0004

(71) n_{4}^{2} = 0.9987 ± 0.0007

The most important implication of this exact fit is that *the ,maximal causal speed within the hyperdense medium inside kaons is bigger than c,*

(72) V_{max} = c (n_{k}/n_{4} = 1.0061 c, k = 1, 2, 3.

As we shall see below, the superluminal character of causal speeds within hyperdense hadronic media, first conjectured by Santilli in 1981 [47], and first proved experimentally in Refs. [64.65]. is a systematic property verified by all fits of experimental data without apriory theoretical assumptions, for all experimental data dealing with the structure of hadrons, thus including the synthesis of the neutron from the hydrogen atom (see also the general review "New Sciences for a New Era) [46]).

*Figure 18. F. Cardone et al. [64,65] have shown that the conventional time dilation law is violated by the behavior of the mean life of unstable hadrons with speed even under the assumption that the experimental claims by N. Grossman et al. [63] are correct. This important result was proved by showing that the Minkowski-Santilli isogeometry [36] provides an exact fit for both tests [62,63], including the deviations detected from 10 to 100 Gev (see the l.h.s of this figure) as well as the fit of all data from 10 to 400 GeV (r.h.s of this figure). *

**8.4. Experimental verification with the Bose-Einstein correationb**

The experimental data on the Bose-Einstein correlation on the annihilation of proton and (apparent) antiprotons have been systematically assumed as verifying special relativity. This has created an additional scientific obscurantism because the two-point correlation function can at beast admit *two* free parameters, while the fit of the experimental data requires *four* free parameters (called the "chaoticity parameters").

In Ref.[67] of 1992, Santilli has shown that, in reality, the four arbitrary parameters used in the fit of the experimental data are clear evidence of the deviation of the Bose-Einstein correlation from special relativity. Ref.[67] then shows the exact character of isorelativity, and achieves an exact fit of the experimental data characterized by:

1) The space characteristic quantities representing the elongated fireball of the p-p* annihilation, and

(73)   n_{1} = 3.745,   n_{2} = 2.288,   n_{3} = 0.602

2) The forth characteristic quantity rep[resenting the density of the fireball (see Figure 19)

(74)   n_{4} = 0.604

(see Ref. [67] for the statistical errors and other data).

The above data confirm the superluminal character of the maximal causal speed in the interior of the Bose-Einstein fireball. F. Cardone and R. Mignani provided in Ref. [68] of 1998 an independent confirmation of all results by Santilli in memoir [67] of 1992 (see also the general review "New Sciences for a New Era) [46]).

*Figure 19. The excellent fits at high energy (left) and at low energy (right) achieved by Santilli [66] for the experimental data of the Bose-Einstein correlation in which the space characteristic functions acquire the direct physical meaning of representing the semiaxes of the proton-antiproton fireball, while the fourth characteristic quantity represent its energy. F. Cardone and R. Mignani provided in p aper [67] of 1998 an independent verification of Santilli's results [66] of 1992. *

**8.5. Experimental verifications with nuclear magnetic moments**

As it is well known in serious scientific circles, a theory can be claimed to be exactly valid for given conditions if and only if it represents the entirety of the experimental data from first principles without manipulations [42].

The above conditions are evidently met for the quantum representation of the hydrogen atom, but clear evidence establishes that quantum mechanics *cannot* be exactly valid in nuclear physics for numerous reasons, including the inability by said theory to achieve a representation of the magnetic moment of the simplest nucleus, the deuteron, with truly embarrassing deviations for large nuclei. This insufficiency has been studiously ignored by academia by creating an additional scientific obscurantism.

*Figure 20. A view of the minimal and maximal values of nuclear magnetic moments between the so-called Schmidt limits characterizing deviations from quantum mechanical predictions via the use of conventional values of the magnetic moments of protons and neutrons. The nuclear physics community has ignored these deviations from quantum laws, and actually imposed the exact validity of quantum mechanics for about one century,thus creating an additional scientific obscurantism with very serious implications for energy related issues that have been established by Santilli research in nuclear physics.*

Among other reasons indicated earlier and reviewed below, Santilli developed the isotopies of Lie's theory [7,40] for the intent of honoring the view of Enrico Fermi [3] according to which the anomalous character of nuclear magnetic moments is due to *deformations* of the charge distribution of protons and neutrons under strong nuclear forces, with consequential *alteration* (now called *mutation*) of conventional quantum mechanical values (figure 20).

To achieve a representation of nuclear magnetic moment along Fermi';s teaching, Santilli used in Ref. [69] the isotopies SO*(3) of the rotational symmetry SO(3) [16,29,40]

(75) [J_{i},J_{j}]* = J_{i}T*J_{j} - J_{j}T*J_{i} = ε_{ijk} J_{k}, i, j, k = 1, 2, 3,

with realization of the isotopic element representing Fermi's hypothesis

(76) T* - Diag. (1/m_{1}^{2}, 1/m_{2}^{2}, 1/m_{3}^{2}

The above isosymmetry preserves conventional eigenvalues (under conventional realization of the generators)

(77a) J_{3} T* ψ* = k ψ*, k = 0, ± 1, ...

(77b) J*^{2*} T* ψ* = (J_{1}T*J_{1} + J_{2}T*J_{2} + J_{3}T*J_{3})T*ψ* = Kψ,* K = 0, 1, ...

while admitting an internal degree of freedom originating from the condition of isounitarity

(78a) Det T* = 1, m_{1}^{2}m_{2}^{2}m_{3}^{2} = 1,

(78b) m_{1}^{2} = m_{2}^{2} = m^{2}, m_{3}^{2} = 1/m^{2}

The use in Ref.[69] of the Dirac-Santilli isoequation (57] then yielded the mutation of the magnetic moment of nucleons

(79) &mu' = μ (n_{3}/n_{4}) = μ/mn4

The use of value (74) for the characterization of the density of nucleons, then allowed in Ref. [69] the first and only known achievement of the numerically exact and time invariant representation of the anomalous magnetic moment of the deuteron via the use of the isotropic degree of freedom of the rotational symmetry.

This hidden degree of freedom was then used by Santilli for the achievement in Ref., [70] of the first and only known exact representation of anomalous anomalous magnetic moments of of all stable nuclei (see also the general review "New Sciences for a New Era) [46]).

*Figure 21. A pictorial view of Fermi's [3] hypothesis on the origin of the anomalous character of nuclear magnetic moments (namely, the inability of their derivation via quantum mechanics) as being due to the deformability of protons and neutrons under strong nuclear forces, with consequential deformation of their intrinsic magnetic moments due to their spin. This very plausible a hypothesis, remained ignored by the nuclear physics community since the 1940s, and its study has been opposed, thus creating an additional scientific obscurantism this time in nuclear physics for the unspoken but evident reason that the study of Fermi's hypothesis requires a structural generalization of quantum mechanics from the current abstraction of protons and neutron as dimensionless points, to their representation as extended, thus deformable charge distributions. In complete oblivion to non-scientific academic stands, Santilli has honored Fermi's memory by achieving the first and only known exact representation of the anomalous magnetic moment, firstly, of the deuteron [69] and that of all stable nuclei [70] by therefore confirming the historical intuition of 1968 [3-4] of embedding the shape and deformability of protons and neutrons in the isotopic element, Eqs. (6).*

**8.6. Experimental verifications with nuclear spins**

As it is well known and admitted by serious scholars, quantum mechanics *cannot* be exactly valid in nuclear physics because of the additional failure to achieve a consistent representation of the spin of the deuteron, with embarrassing insufficiencies for the spin of bigger nuclei.

In fact, the spin of the deuteron is 1, but the sole stable, quantum mechanical, bound state between two particles with spin 1/2, the proton and the neutron, is the singlet within spin 0. Consequently, for close to one century the spin of the *ground stated* of the deuteron has been represented via *excited orbital states,* with bigger problems for bigger nuclei. Rather than admitting a basic insufficiencies in nuclear spins, the nuclear physics community has imposed the exact validity of quantum mechanics in nuclear physics, resulting in an additional scientific obscurantism.

The origin of this additional insufficiency of 20th century knowledge is the known abstraction of nuclear constituents to dimensionless points while, in reality, protons and neutrons are in conditions of partial mutual penetration (Figure 3), thus being ideally suited for representation )(6) thanks to the covering isomathematics, isorelativity and isomechanics.

In fact, the spin of extended nuclear constituents is characterized by the isotopic SU*(2) isosymmetry [29,30,40]

(80) [S_{i},S_{j}]* = S_{i}T*S_{j} - S_{j}T*S_{i} = ε_{ijk} S_{k}, i, j, k = 1, 2, 3,

with realization of the isotopic element

(81) T* - Diag. (1/1q_{1}^{2}, 1/q_{2}^{2}

SU*(2) preserves conventional eigenvalues (under conventional expression of the generators) as it was the case for the isotopies of the rotational symmetry,

(82a) S_{3} T* ψ* = k ψ*, k = ± ½...

(82b) S*^{2*} T* ψ* = (S_{1}T*S_{1} + S_{2}T*S_{2} + S_{3}T*S_{3})T*ψ* = Kψ,* K = ¾, ...

while admitting an internal degree of freedom originating from the condition of isounitarity

(83) Det T* = 1, q_{1}^{2} = 1/q_{2}^{2} = λ

resulting in a hidden degree of freedom which constitutes a concrete realization of the theory of hidden variables [30].

A. A. Bhalekar and R.M. santilli [71] have used this degree of freedom and achieved the first and only known exact representation of nuclear spins.

*Figure 22. A table on the numerical val;use of the spin of stable nuclei whose exact and time invariant representation has been missing for about one century, until achieved buy A. A. Bhalekar t and R. M. Santilli in memoir [71]*

*8.7.. Expeerimental vrification in chemistry*

As it is well known, atoms are neutral in their natural state. Consequently, no conventional interaction can be credibly claimed to be responsible for molecular bonds. Additionally, serious scholars admit that, according to quantum mechanics and chemistry, the electrons of covalence bonds should *repel* each other, and certainly not achieve a stable bond, since they have the same charge.

in monograph [72], Santilli has identified the above insufficiencies of quantum chemistry, as well as additional ones, such as the loss of the very notion of the quantum of energy for the use of the so-called "screened Coulomb potential," namely, the multiplication of the Coulomb potentialV(r) - e^{2}/r by an arbitrary function f(r) which is then fitted from the experimental data.

Additionally, quantum chemistry implies the prediction that all substances are paramagnetic evidently due to the lack of a strong covalence bond with ensuing possibility that orbitals can be oriented with a sufficiently strong magnetic field. Therefore, monograph [82] has established the relevance of *isochemistry* with particular reference to the need for a *new interaction* which is responsible for molecular structures.

The use of the non-linear, non-local and non-Hamiltonian interactions resulting from the deep wave overlapping of covalence electrons in singlet coupling O)see Figure 23), has permitted the achievement of the first known numerically exact and time invariant representation from unadulterated first principles of the binding energy and other experimental data of the hydrogen molecule [73] and of the water molecule [74], thus confirm this time n chemistry the validity of isomathematcs, isosymmetries and isomechanics, this time, in chemistry (see also the Nobel nomination [75] and the review "New Sciences for a New Era" [46]).

*Figure 19. An illustration of the notion at the foundation of this nomination, namely, the deep mutual penetration and overlapping of the wavepackets of valence electrons in singlet coupling, with ensuing non-linear, non-local, and non-Hamiltonian interactions whose quantitative treatment requested Prof. Santilli to conduct decades of studies, first, for the construction of the new isomathematics [1-3], and then the construction of the novel isomechanics [7] and isochemistry [9].*

**9. NON-RELATIVISTIC REPRESENTATION OF THE NEUTRON MASS, MEAN LIFE AND CHARGE RADIUS **

Santilli states: *I simply cannot accept that the permanently stable proton and electron "disappear" at the time of the synthesis of the Hydrogen atom into the neutron and certain hypothetical quarks "appear" by academic fiat and, then, at the time of the spontaneous decay of the neutron, certain hypothetical quarks "disappear" while the permanently stable proton and electron "reappear" again by academic fiat. Under these evident doubts, I have studied the most plausible hypothesis that the proton and the electron are actual physical constituents of the neutron in our spacetime, not in their conventional quantum mechanical states, but in generalized states due to the total penetration of the wavepacket of the electron within the hyperdense proton, for which I have suggested the names of "isoproton,"* here denoted p*, * and "isoelectron," * here denoted e*, * which new states are technically realized as irreducible isorepresentation of the Lorentz-Poincare'-Santilli isosymmetry. Hence, I have studied the representation of "Rutherford's compression" of the Hydrogen atom into a neutron inside a star via a non-unitary transform of the conventional structure of the Hydrogen atom* (HA)

(29) HA = (e^{-}_{↑}, p^{+}_{↓})_{qm} → U(e^{-}_{↑}, p^{+}_{↓})U^{†} = (e*^{-}_{↑}, p^{+}_{↓})_{hm} = n, UU^{†} ≠ I,

where qm stands for elaboration via quantum mechanics and hm stands for elaboration via hadronic mechanics and its fundamental isosymmetries.

Note the assumption of one single non-unitary transform used for the regular isotopies of Lie's theory (rather than two non-unitary transforms as used for the covering Lie-admissible theory) because the synthesis of the neutron is reversible over time due to its spontaneous decay, thus requiring antisymmetric brackets, although with non-Hamiltonian internal effects represented by the Lie-Santilli isotheory.

The transition from protons p and electrons e in vacuum to their corresponding states p* and e* when in conditions of total mutual penetration is called a *mutation* according to terminology introduced in 1967 [1] and today fully appropriate in order to distinguish these studies from known deformations. Note also that the proton is about 2,000 times heavier than the electron. Therefore, Santilli assumes in model (29) that the proton is not mutated, and only the electron experiences a mutation.

Santilli then selects the following realization of the fundamental isounit (15)

(30) I* = 1/T* = UU^{†} = Diag. (1, 1, 1) exp{ [r e^{- r / R} / (1 - e^{- r / R})] ∫ e^{*-}_{up} x p^{+}_{down} d^{3}r} =

= exp{[|e) / |e*)] ∫ e*^{-}_{up} p^{+}_{down} d^{3}r},

where |e) and |e*) represent the wave-functions (in first approximation) of the electron in the Hydrogen atom and when immersed inside the proton, respectively. Note the emergence of non-linear, non-local/integral and non-Hamiltonian interactions represented by the isounit, exactly as desired.

By recalling representation (15) of the actual size and shape of particles via the n^{2}-quantities, note that in isounit (30) Santilli assumes that the proton charge distribution is perfectly spherical with radius of 1 Fermi abstracted to 1. The inclusion of the actual non-spherical shape due to the spin of the proton is expected to provide only contributions of higher order.

Note also that, by central assumption, the isounit recovers the unit for null values of the integral, that is, when there is no appreciable overlapping of the wavepackets of the electron and the proton. This implies that, by conception, excited states of the neutron recover conventional quantum states of the Hydrogen atom. Note finally that the value of the isounit I* = 1/T* is much bigger than 1, the value of the isotopic element T* is, consequently, much smaller than 1, and model (29) admit *no divergencies* with rapidly convergent perturbative series as in Eq. (17).

Via the use of the above non-unitary transform, Santilli maps the conventional Schrodinger equation of the Hydrogen atom into the isoequation (22) of hadronic mechanics (with h-bar = 1)

(31) H |e) = [(-1/m)∂_{k}∂_{k} - e^{2}/r] |e) = E |e) →

→ U[H |e)]U^{†} = U[(-1/m)∂_{k}∂_{k} - e^{2}/r] |e)U^{†} =

= [(-1/m)∂*_{k}∂*_{k} - e^{2}/r] (UU^{†})^{-1} |e*)

where m is the usual reduced mass, ∂* = I*∂ represents Santilli's isoderivative [16], and is the sum over the k-indices.

Under the approximation that the neutron is fully stable (since the 15 minutes mean-life is very large for particle standards), and therefore the orbit of the electron within the proton is stable, Santilli assumes that the isounit can be approximated into a constant. By replacing expression (30) into (31), we have

(32a) [- (1 / m') Δ + V_{Coulomb} + V_{Hulten}] |e*) =

= [- (1 / m') Δ - e^{2}/r - K e^{- r / R} / (1 - e^{- r / R}) ] |e*) = E' |e*),

(32b) m' ≈ m / | I*^{2}|

By reducing the above equation to the radial form and by adding the constraints for the 15 minutes mean-like and the charge radius of the neutron, we have the following *Santilli non-relativistic structure model of the neutron with physical constituents* first achieved in Ref. [390] of 1990

(33a) [(1/r^{2}(d/dr)r^{2}(d/dr) + (4 π^{2}m')(E + N e^{- r / R} / (1 - e^{- r / R}) ] |e*) = 0,

(33b) τ_{n} = 2 λ^{2} | e^{*}(0)|^{2} α E_{e*}/h = 10^{3} sec,

(33c) R_{n} = 10^{-13 } cm,

that do indeed admit physically and mathematically consistent solutions for the representation of the rest energy, mean-like and charge radius of the neutron we cannot possibly review here for brevity (see Ref. [30] with first detailed solutions available in Section 5 of Ref. [5] and reviews [23,25]).

The following comments are here in order. The conventional Coulomb potential of the Hydrogen atom is absorbed in Eq. (33) by the Hulten potential since it is known to behave like the Coulomb potential at short distances, said absorption merely implying a shift of the constant N; the Coulomb binding energy is ignored in first approximation because much smaller than the Hulten binding energy; and the solution for the rest energy of the neutron is given by

(34) E_{n} = E_{p} + E_{e*} - | E' | = 939 MeV, E_{e*} = 1.293 MeV, E' ≈ 0.

Non-expert in the field should not be surprised at the fact that E' ≈ 0 because we are dealing with a binding mechanism caused by contact interactions that, as such, have *no* potential energy by assumption.

*Figure 23. An illustration of Rutherford's conception of the neutron as a "compressed hydrogen atom," as well as of Santilli's conception of the excited states of the neutron as being the conventional quantum states of the hydrogen*

Recall that, unlike the Coulomb potential, the Hulten potential admits a *finite* number of energy levels. Intriguingly, Eqs. (33) admit one and only one energy level, the neutron, since all excited states imply the transition from hadronic to quantum mechanics. Hence, the excited states of the above structure model of the neutron are given by the conventional states of the Hydrogen atom (Fig. 6).

Santilli calls this single energy level the *hadronic mass spectrum suppression* to emphasize the transition from the *classification* of hadrons where a mass spectrum is indeed needed, and the *structure* of individual hadrons preventing the joint study of different hadrons. In fact, when the hadronic constituents are assumed as being physical particles in our spacetime generally produced in the spontaneous decays with the lowest mode, different hadrons have emerged as having different constituents and, therefore, different structures [10,23,25].

It is important to identify the mechanism used by Santilli for the achievement of a consistent synthesis of the neutron and appraise its implications for particle physics for discussions at this workshop. Recall that the missing energy of 0.782 MeV cannot be provided by the relative kinetic energy of the proton and the electron when dealing with quantum mechanics, that is, when the proton and the electron are assumed as being point-like particles.

Note that the crucial consistency of model (33) is due to the increase of the value of the electron energy of the electron, from 0.511 MeV to 1.293 MeV (see also Eq. (32b)), which is called *mass isorenormalization* to stress that we are not dealing with a conventional renormalization. The new isorenormalization was fully identified by Santilli in the originating memoir [5], Section 5, Eq. (5.11.4a), p. 836 (with the notation ρ for I*).

This new isorenormalization is inherent in all non-unitary coverings of quantum mechanics or, equivalently, whenever considering dynamics of extended particles or wavepackets within physical media, and it is today technically and invariantly treated via the transition from the Lorentz-Poincare' symmetry to the covering Lorentz-Poincare'-Santilli isosymmetry [9].

Discussions are invited at this workshop on the implications of Santilli's mass isorenormalization for all high energy scattering processes since they all imply a hyperdense scattering region in which special relativity and quantum mechanics cannot be consistently defined, let alone directly tested. Specifically, an open problem suggested for discussions at the workshop is whether the Higgs boson should or should not be subjected to Santilli's mass isorenormalization.

**II.5. Non-relativistic representation of the neutron spin**

Santilli's main contentions for the representation of the spin of the neutron are the following [31] (Fig. 7):

I. Under quantum mechanical treatment, the proton is a massive point in which case Pauli and Fermi had no other option than that of conjecturing the existence of the hypothetical neutrino. However, when the proton is represented as it is in nature, i.e., as an extended particle permitted by the covering hadronic mechanics, there is the emergence of the *orbital* motion of the electron within the proton which is completely absent in the quantum treatment.

*Figure 24. A historical consequences in the transnsition from the point-0like abstraction of the proton to the representation of its actual dimension is the emergence of the angular momentum of the electron within the spinning proton, first identified by Santilli, which allows the representation of the spin of the neutron without the conjecture of the hypothetical neutrinos. *

II. Rather than being constituted by ideal isolated point-like quarks, the proton is in reality one of the densest objects measured by mankind to date due to the total mutual penetration of the wavepackets of its constituents. When compressed inside such a hyperdense medium, the electron is constrained to rotate with an angular momentum equal to the proton spin, otherwise the electron would experience very large resistive and/or repulsive forces when orbiting inside the proton against its spin, which forces would prohibiting any synthesis.

III. As it is well known, half-odd-integer angular momenta are known to be impossible for quantum mechanics (they violate causality). However, it is easy to see that half-odd-integer angular momenta M are fully admitted by hadronic mechanics thanks to the new degrees of freedom offered by the three-dimensional isounit of the Lie-Santilli O*(3) isosymmetry [31].

It then follows that *the total angular momentum of the isoelectron is null and the spin 1/2 of the neutron coincides with that of the proton*

(35) J_{n} = J_{p} - J_{e*} + M_{e*} = J_{p}, J_{e*} = M_{e*} = 1/2, J^{tot}_{e*} = 0.

For details on the derivation via the Lie-Santilli isoalgebras O*(3), we refer for brevity to Ref. [31] or reviews [23,25,48].

**II.6. Non-relativistic representation of the neutron magnetic moment**

A notorious insufficiency of the standard model, as well as of quantum mechanics at large for the structure of hadrons, is the inability to represent the anomalous magnetic moment of the neutrons as well as of hadrons at large.

Santilli contends that this insufficiency is due to the to the representation of the the proton as a massive point, in which case quantum mechanics can solely use the conventional magnetic moments of the proton and the electron, resulting in deviations between the prediction of the theory and experimental data.

However, when the proton is represented as an extended particle, the exact representation of the anomalous magnetic moment of the neutron is simple and immediate, because the missing contribution is the magnetic moment of the *orbital* motion of the electron inside the proton.

Simple calculations then yield the exact representation first achieved in Ref. [31] of 1990 (see reviews [23,25,48])

(36a) μ_{n} = μ_{p} + μ_{e*,Intrinsic} - μ_{e*,Orbital} = -1,913 μ_{N},

(36b) μ_{p*} = μ_{p} = + 2.793 μ_{N}, μ_{e*} = μ_{e} = - 1.001 μ_{B} = 1,837.987 μ_{N}, μ_{p} + μ_{e*} = 1,835 μ_{N},

(36c) μ_{e*Orbital} = +1.004 μ_{B}, μ_{e*Total} = 3 x 10^{-3} μ_{B}, μ_{n} = -1,913 μ_{N}.

This completes our review of Santilli's non-relativistic representation of the neutron characteristics. Note that the small value of the total magnetic moment of the isoelectron is fully in line with the small value of its total angular momentum (that is null only in first approximation due to the assumed lack of mutation of the proton).

**II.7. Relativistic representation of the synthesis of the neutron from the Hydrogen atom**

Of course, the non-relativistic representation of the neutron synthesis was merely preparatory to the full relativistic treatment on which Santilli conducted comprehensive studies over three decades, including: the isotopies of Lie's theory [4-6]; the geometrization in 1983 [37] of inhomogeneous and anisotropic physical media via the isotopies of the Minkowskian spacetime with conventional metric η = Diag. (1, 1, 1, -1) and isotopic line element

(37a) x*^{2} = x^{μ}T*_{μ}^{ρ} η _{ρν} x^{ν} = x^{μ} η*_{μν} x^{ν} ,

(37b) η * = T*η , I* = 1/T*, μ, ν, ρ = 1, 2, 3, 4;

its universal isosymmetry achieved in the same 1983 paper [37]; the isotopies of all aspects of the conventional Poincare' symmetry resulting in the *Lorentz-Poincare'-Santilli isosymmetry* [9]; the isotopies of Galileo's and Einstein's special relativities [38]; the isotopies of the Minkowski geometry [39]; and the study of other aspects (see monographs [13] for comprehensive treatments).

Following these preparatory studies, Santilli proposed in Refs. [33,34] of 1993 the isotopies of the spinorial covering of the Poincare' symmetry, and then the isotopies of Dirac's equation, today known as the *Dirac-Santilli isoequation* that we write in the form

(38a) [γ*^{μ}(p*_{μ} - ieA_{μ}) - (imc)*] T* |e*) = 0,

(38b) γ*^{μ} = U_{4x4}γ^{μ}U^{†}_{4x4},

(38c) γ*^{μ} T* γ*^{ν} + γ*^{ν} T* γ*^{μ} = η*^{μν}

where the γ* are called the *Dirac-Santilli isogamma matrices.*

Eqs. (38) are based on the isotopies of the four-dimensional Minkowski spacetime for the orbital motion and the isotopies of the two-dimensional unitary space for the spin, with related fundamental isounits

(39a) I*_{orb} = 1/T*_{orb} = Diag. (n_{1}^{2}, n_{2}^{2}, n_{3}^{2}, n_{4}^{2}) = U_{4x4} U^{†}_{4x4},

(39b) I*_{spin} = 1/T_{spin} = Diag. (s_{1}^{2}, s_{2}^{2}) = U_{2x2} U^{†}_{2x2}.

Eq. (38a) permitted Santilli to achieve the relativistic, invariant, and exact representation of *all* characteristics of the neutron in its synthesis from a Hydrogen atom inside a star, and not solely the representation of the mass via a mass spectrum linked to other hadrons according to quark conjectures.

Note the remarkable appearance of the isometric η* of the Minkowski-Santilli isospacetime, Eqs. ( 33), in the isoanticommutators of the γ* matrices, thus confirming the deep interconnection between geometry and dynamics that exists at the conventional level and persists in full under isotopies.

*Figure 24. An illustration of the behavior of the energy of nuclear beta decay (on the left) and its interpretation by Santilli as being due to the dependence of the nucleus-electron interactions from the direction of emission of the electron, without any need to conjecture the hypothetical neutrino. *

As it is well known, the conventional Dirac equation represents the electron at large distance from the proton considered as external. By contrast, the Dirac-Santilli isoequation represents the electron, this time, immersed within the proton, thus being mutated into the isoelectron.

The most important outcome of the model is that *a necessary condition for the exact and invariant relativistic representation of the synthesis of the neutron from the Hydrogen atom inside a star is that the isoelectron must orbit with a tangential superluminal speed.* In fact the fit of all characteristics of the neutron requires that the isoelectron tangential speed is given by

(40) V_{e*} = c/n_{4} > c, n_{4} = 0,605.

There is no violation of special relativity here because such a theory cannot be even defined within the hyperdense medium inside the proton. Additionally, the speed limit c set by special relativity solely holds for point-like particles moving in empty space under action-at-a distance interactions derivable from a potential energy.

These special relativity conditions are inapplicable for the speed of the isoelectron inside the proton because, in this case, the particle is accelerated by contact interactions having no potential energy under which the maximal causal speed is arbitrary, as anticipated by Santilli since 1981 [40], now characterized by the Lorentz-Poincare'-Santilli isosymmetry, and verified in all fits of particle experiments without the a priory assumption of relativistic quantum mechanics (Vol. IV of Refs. [14 and Chapter 5 of Refs. [23,25]).

Note incidentally that maximal causal speed (40) is referred to a particle with *real mass* in spacetime. As such, *the isoelectron is not a tachyon.* For interior conditions, Santilli has introduced the notion of *isotachyon* with imaginary mass which is a hypothetical particle outside the interior light cone with speed bigger than the local maximal causal speed (see monographs [13] for technical treatments).

**II.8. Santilli etherino**

As indicated earlier, under the a priory assumption of the exact validity of quantum mechanics and the consequential approximation of the proton as a massive point, the Pauli-Fermi *emission* at the time of the synthesis of the neutron from a proton and an electron is unavoidable, to our knowledge.

However, Santilli contends that, when the proton is represented with its actual extended dimensions thanks to the covering hadronic mechanics, the missing energy of 0.782 MeV and the structure equations of the neutron offer no possibility of identifying additional energy for the creation of the hypothetical neutrino. Additionally, under the indicated conditions, the emission of the neutrino would *violate,* rather than verify, the conservation of the total angular momentum due to the necessary emergence of a constrained angular momentum of the isoelectron when immersed inside the hyperdense proton.

*Figure 25. A picture of Don Carlo Borghi, the Italian Priest and physicists of the University of Milan, who initiated experimental tests for the laboratory synthesis of the neutron from the hydrogen atom. Said experiments were so strenuously opposed by the Italian as well as by the world wide physics community, that Don Borghi had to do his experiment in Brazil. The unspoken reason to oppose an experiment (sic!), is that said synthesis violates Einstein's special relativity as well as quantum mechanism thus confirming the scientific obscurantism denounced in this nomination various times.*

*Figure 26. A view in the left of the klystron used by Don Borghi for the first tests of the synthesis of the neutron from the hydrogen, and a view in the right of the evidence of nuclear transmutations of substances placed in the outside of the klystron that could only be explained by a neutron flux originating from the interior of the klystron.*

Additionally, Santilli contends that we have a similar situation for nuclear beta decays (Fig. 9). In fact, when the nuclei and their constituents are represented via quantum mechanics, the only possibility of explaining the bell-shaped behavior of the energy of the beta decay is that via the emission of the hypothetical neutrino, as well known.

However, when nuclei and their constituents are represented via the covering hadronic mechanics, the bell-shaped behavior of the energy of the emitted electron is easily explained as being dependent on the direction of emission of the electron because of the dependence of its energy on the *attractive* Coulomb interaction between the electron and the nucleus, resulting in an energy emission which is maximal for the radial emission and minimal for the tangential one.

In summary, while working on the synthesis of the neutron from a proton and an electron, Santilli was forced to dismiss the Pauli-Fermi hypothesis of the neutrino as a physical particle in our spacetime. In his words: *I was quite embarrassed in writing my papers of the 1990s on the structure of the neutron because, on one side, my devotion for my mentors Pauli and Fermi forced me to maintain the presence of the neutrino in the r.h.s. of the reaction while, on the other side, I knew that the emission of the neutrino was inconsistent with the fusion process.*

Santilli further states: *I had a reverence for the original Pauli-Fermi hypothesis of "one" neutrino and "one" anti-neutrino. However, I simply cannot accept the recent series of implausible neutrino conjectures ventured for the specific intent of maintaining the validity of the standard model for all of particle physics, such as: first, the multiplication of neutrino into three different particles without well identified physical distinctions; then the further multiplication of neutrinos due to color, again, without clearly identified physical distinctions; then the conjecture that these neutrinos have mass; then the conjecture that they "oscillate"; and so on. Under such a chain of far reaching conjectures, I simply cannot accept that the hypothetical numerous neutrinos and anti-neutrinos exist as physical particles in our spacetime.* Hence, Santilli was forced to search for an alternative to the neutrino hypothesis.

Following decades of studies of the problem, Santilli's main contention is that the missing energy of 0.782 MeV cannot originate from the interior of a star because, at the initiation of the production of light, small stars synthesize from the primordial Hydrogen atoms about 10^{30} neutrons *per second* with bigger stars synthesizing neutrons at the rate of up to 10^{50} per seconds. Santilli contends that, in the event the missing energy originates from their interior, stars would never initiate producing light because they would *lose* from 10^{30} to 10^{50} MeV *per seconds,* thus becoming cold.

As indicated earlier, in the event the missing energy is provided by the relative kinetic energy between protons and electrons, their synthesis is rendered impossible by the extremely low value of the cross section of their scattering, while hypothetical neutrinos cannot possibly be the source of the missing energy due to their virtually null cross section with protons and electrons.

Santilli agrees with Pauli and Fermi on the need for a third unknown particle in the synthesis of the Hydrogen atom into the neutron. However, he contends that the primary function of this particle is to *supply the missing energy,* without any need for a contribution to the spin. Also, the missing particle should appear in the *left hand side* of the reaction, rather than in its right hand side as per Eq. (26).

In view of the above aspects, Santilli has submitted in Ref. [41] of 2007 the hypothesis of the *etherino* represented with the symbol "a" (from the Latin "aether") delivering the missing 0.782 MeV energy to the proton and the electron according to the reaction

(41) p^{+} + a + e^{-} → n.

In particular, the etherino is *not* suggested to be a particle, but rather a *longitudinal impulse* originating from the ether as a universal substratum with extremely high energy density for the characterization and propagation of electromagnetic waves as well as particles.

Santilli contends that, contrary to a rather popular belief, the ether as a universal substratum *does not* cause any violation of Einstein special relativity in vacuum because the absolute reference frame hypothetically at rest with the universal substratum cannot be identified in our laboratory.

Participants to this workshop should keep in mind the remark of Ref. [41] that the Hilbert space of quantum mechanics *cannot* represent exchanges of energy between the ether and our world, while such exchanges are indeed quantitatively representable via the covering iso-Hilbert space of hadronic mechanics.

*Figure 27. A view in the left of the klystron used by Don Borghi for the first tests of the synthesis of the neutron from the hydrogen, and a veiw in the right of the evidence of nuclear transmutations of substances placed in the outside of the klystron that could only be explained by a neuyrin flux originatging from the interior of the klystron.*

A topic of discussion at our workshop is the open problem that, apparently, a longitudinal impulse from the universal substratum may interpret data on the so-called "neutrino experiments" without any need for the existence of the neutrino. In any case, it is difficult for several physicists to accept the idea that particles such as the neutrinos today believed to possess mass according to the standard model could possibly traverse entire planets and stars without collisions. By contrast, a longitudinal impulse propagating in the universal substratum can indeed traverse entire planets and stars without conjecturing implausible physical events.

Yet an additional aspect to be discussed at the workshop is the contention that an energy input from the ether is needed for stars not only at their initiation of production of light, but also at the time of their death, because nuclear syntheses are insufficient to represent the immense energy of supernovae by a factor believed by some to be of about 1,000,000 for the very reason that, at the time of the supernovae explosions, all primary nuclear syntheses have been exhausted by central assumption.

A further suggestive aspect open for discussion at the workshop is *Santilli's revival of the steady state cosmology with continuous creation of matter* which is implicit in the etherino hypothesis, especially when combined with recent experimental evidence that the universe is not expanding [42].

**II.9. Laboratory synthesis of the neutron from a Hydrogen gas**

The first laboratory synthesis of the Hydrogen atom into the neutron was conducted in 1965 by the Italian priest-physicist Don Carlo Borghi (Fig. 10) and his colleagues and published later on in Refs. [43,44]. With reference to Fig. 11, a klystron was filled up with Hydrogen gas, maintained in its ionized state by an electric discharge and traversed by a microwave. The klystron was surrounded by fissionable substances that apparently showed nuclear transmutations following several hours of operation.

With reference to Fig. 12, the laboratory synthesis of the neutron was confirmed by Santilli [45-47] in 1997 via the use of a klystron with transparent walls (to visually assure proper internal events) filled up with a Hydrogen gas and solely exposed to a 10 kW DC arc between internal Tungsten electrodes. Three different neutron detectors were placed in the vicinity of the klystron. Apparently, the tests confirmed that a particle with zero charge and the dimension of the order of 1 Fermi (as necessary to traverse walls) had apparently been produced inside the klystron.

It should be noted that Don Borghi assumed that the synthesis of ionized Hydrogen gas into the neutron was done by the microwave, while Santilli assumed that said synthesis is achieved by the DC electric arc for which reason he solely used a DC internal discharge. As we shall see in the next section, this principle of the synthesis of the Hydrogen into the neutron has resulted to be important for nuclear syntheses without harmful radiations.

** II.10. The hypothesis of the neutron**

Both Don Borghi and Santilli agree that the emitted particle is not necessarily the neutron, but an intermediate state with the mass, size and charge of the neutron but zero spin, called *neutron* and denoted with the symbol ñ. Santilli reported that unequivocal detections of true neutrons by all three neutron detectors occurred only under the addition of special events he called "triggers", e. g., when the Hydrogen was contaminated with air resulting in an explosion at the activation of the electric arc.

In fact, Santilli had to evacuate the lab three different times when testing with the indicated trigger due to all neutron detectors entering into maximal sonic and vibrational alarms (see Fig. 13)

Experimentalists interested in doing truly basic tests may be interested in knowing that the R. M. Santilli Foundation has research funds available for the systematic rerun of the above tests for the laboratory synthesis of the neutron from a Hydrogen gas due to its relevance for new clean nuclear energies as well as for all of science.

** II.11. The apparent new class of nucleoids**

Santilli [45-47] has reported cases in which neutron detectors showed no signal following the activation of the arc in the klystron, but clear detections did occur later on when the detectors were at large distance from the klystron. In one case, Santilli reported that the neutron detector manufactured by Polimaster entered into sonic and vibrational alarm, about 15 minutes following its exposure to the operating klystron while being miles away from the klystron.

The sole rational explanation of this occurrence is that the experimental set up produced neutroids ñ, rather than neutrons n, which was absorbed by the nuclei of the plastic casing of the detector that, as such, became unstable with a mean-life of about 15 minutes. Therefore, Santilli submitted the following:

*HYPOTHESIS II,11: In addition to the well known class of tabulated nuclides, there exists an additional class of anomalous nuclides, submitted with the name of nucleoids, characterized by the absorption of a neutroid ñ by a conventional nuclide N according to the reaction (where A is the atomic number, Z the nuclear charge, J the spin, and M the mass)*

(42) N(A, Z, J, M) + ñ(1, 0, 0, 1.008) ⇒ N^{*}(A + 1, Z, J, M + 1.006).

The study of Santilli's apparent new class of nucleoids is an important task of this workshop due to their evident relevance for new nuclear energies.

**REFERENCES**

[1] H. Rutherford, Proc. Roy. Soc. A, ** 97**, 374 (1920)

. [2] J. Chadwick, Proc. Roy. Soc. A, **136**, 692 (1932).

[3] E. Fermi, * Nuclear Physics,* University of Chicago Press (1949).

[4] R. M. Santilli, "Embedding of Lie-algebras into Lie-admissible algebras," Nuovo Cimento {\bf 51}, 570 (1967),

http://www.santilli-foundation.org/docs/Santilli-54.pdf

[5] R. M. Santilli, "On a possible Lie-admissible covering of Galilei's relativity in Newtonian mechanics for nonconservative and Galilei form-non-invariant systems," Hadronic J. Vol. 1, 223-423 (1978),

http://www.santilli-foundation.org/docs/Santilli-58.pdf

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http://www.santilli-foundation.org/docs/santilli-73.pdf

[7] R. M. Santilli, * Foundation of Theoretical Mechanics,* Volumes I (1978) [37a], and Volume II (1982) [7b], Springer-Verlag, Heidelberg, Germany,

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http://www.santilli-foundation.org/docs/Santilli-36.pdf

[9] H. C. Myung and R. M. Santilli, "Modular-isotopic Hilbert space formulation of the exterior strong problem," Hadronic Journal {\bf 5}, 1277-1366 (1982)

http://www.santilli-foundation.org/docs/Santilli-201.pdf

[10] M. Nishioka, "Expansion of the Dirac-Myungf-Santilli Delta Function to Field Theory," Lettere Nuovo Cimento Vol. 39, pages 369-372 (1984),

http://www.santilli-foundation.org/docs/Santilli-202.pdf

[11] R. M. Santilli, "Isonumbers and Genonumbers of Dimensions 1, 2, 4, 8, their Isoduals and Pseudoduals, and "Hidden Numbers" of Dimension 3, 5, 6, 7," Algebras, Groups and Geometries Vol. 10, 273 (1993)

http://www.santilli-foundation.org/docs/Santilli-34.pdf

[12] R. M. Santilli, "Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures, P. Vetro Editor, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, 7-82 (1996)

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[13] D. S. Sourlas and G. T. Tsagas, *Mathematical Foundation of the Lie-Santilli Theory,* Ukraine Academy of Sciences 91993),

http://www.santilli-foundation.org/docs/santilli-70.pdf

[14] J. Lohmus, E. Paal, and L. Sorgsepp, *Non-associative Algebras in Physics,* Hadronic Press, Palm Harbor, 1994),

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[15[ J. V. Kadeisvili, ''An introduction to the Lie-Santilli isotopic theory," Mathematical Methods in Applied Sciences {\bf 19}, 1349 (1996),

http://www.santilli-foundation.org/docs/Santilli-30.pdf

[16] Chun-Xuan Jiang, *Foundations of Santilli Isonumber Theory,* Inter- national Academic Press (2001),

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[17] Raul M. Falcon Ganfornina and Juan Nunez Valdes, * Fundamentos de la Isdotopia de Santilli,* International Academic Press (2001),

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English translation Algebras, Groups and Geometries Vol. 32, pages 135-308 (2015),

http://www.i-b-r.org/docs/Aversa-translation.pdf

[18] B. Davvaz, *Hyperings Theory and Applications,* International Academic Press (2007),

http://www.santilli-foundation.org/docs/Davvaz.pdf

[19] S. Georgiev, *Foundation of the IsoDifferential Calculus,* Volumes I, II, III, IV, V and VI, Nova Academic Press (2015 on).

[20] C-Xu. Jiang, * Foundations of Santilli IsoMathematucs, With Applications to New Cryptograms, Fermat's Theorem and Goldbach's Conjecture,* in press.

[21] R. M. Sanrtilli, "Galileo-isotopic symmetry," ICTP communication No. IC/91/253 (1991),

http://www.santilli-foundation.org/docs/Santilli-147.pdf

[22] R. M. Sanrtilli, "Galile-isotopic relativity," ICTP communication No. IC/91/265 (1991),

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[23] R. M. Sanrtilli, "The notion of non-relativistiuc isoparticles," ICTP communication No. IC/91/265 (1991),

http://www.santilli-foundation.org/docs/Santilli-145.pdf

[24] R. M. Santilli, *Isotopic Generalizations of Galilei and Einstein Relativities,* Vols. I and II(1991), International Academic Press

http://www.santilli-foundation.org/docs/Santilli-01.pdf

http://www.santilli-foundation.org/docs/Santilli-61.pdf

[25] R. M. Santilli, *Isorelativity for matetr and its isodual for antimatter,* to appear..

[26] A. K. Aringazin, A. Jannussis, F. Lopez, M. Nishioka and B. Vel-janosky, *SantilliÕs Lie-Isotopic Generalization of Galilei and Einstein Relativities,* Kostakaris Publishers, Athens, Greece (1991),

http://www.santilli-foundation.org/docs/Santilli-108.pdf

[27] R. M. Sanrtilli, "Rotational isotopic symmetries," ICTP communication No. IC/91/261 (1991),

http://www.santilli-foundation.org/docs/Santilli-148.pdf

[28] R. M. Santilli, ''Isotopies of Lie Symmetries," I (basic theory) and II (isotopies of the rotational symmetry), Hadronic J. Vol. 8, 36 and 85 (1985),

http://www.santilli-foundation.org/docs/santilli-65.pdf

[29] R. M. Santilli, "Isotopic Lifting of the SU(2) Symmetry with Applications to Nuclear Physics," JINR rapid Comm. Vol. 6. 24-38 (1993),

http://www.santilli-foundation.org/docs/Santilli-19.pdf

[30] R. M. Santilli, "Isorepresentation of the Lie-isotopic SU(2) Algebra with Application to Nuclear Physics and Local Realism," Acta Applicandae Mathematicae Vol. 50, 177 (1998),

http://www.santilli-foundation.org/docs/Santilli-27.pdf

[31] R. M. Santilli, "Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles," Lettere Nuovo Cimento {\bf 37}, 545 (1983),

http://www.santilli-foundation.org/docs/Santilli-50.pdf

[32] R. M. Santilli, "Lie-isotopic Lifting of Unitary Symmetries and of Wigner's Theorem for Extended and Deformable Particles," Lettere Nuovo Cimento Vol. 38, 509 (1983),

http://www.santilli-foundation.org/docs/Santilli-51.pdf

[33] R. M. Sanrtilli, "Lie-isotopic generalizaiton of the Poincare' symmetry, classical formulation,"," ICTP communication No. IC/91/45 (1991),

http://www.santilli-foundation.org/docs/Santilli-140.pdf

[34] R. M. Santilli, "Nonlinear, Nonlocal and Noncanonical Isotopies of the Poincare' Symmetry," Moscow Phys. Soc. Vol. 3, 255 (1993),

http://www.santilli-foundation.org/docs/Santilli-40.pdf

[35] R. M. Santilli, "Recent theoretical and experimental evidence on the synthesis of the neutron," Communication of the Joint Institute for Nuclear Research, Dubna, Russia, No. E4-93-252 (1993).

[36] R. M. Santilli, "Isominkowskian Geometry for the Gravitational Treatment of Matter and its Isodual for Antimatter," Intern. J. Modern Phys. D {\bf 7}, 351 (1998),

http://www.santilli-foundation.org/docs/Santilli-35.pdf

[37] R. M. Santilli, "Direct universality of isospecial relativity for photons with arbitrary speeds" in {\it Photons: Old problems in Light of New Ideas,} V. V. Dvoeglazov Editor Nova Science (2000),

http://www.santilli-foundation.org/docs/Santilli-24.pdf

[38] R. M. Santilli, "Compatibility of Arbitrary Speeds with Special Relativity Axioms for Interior Dynamical Problems," American Journal of Modern Physics, in press (2016)

http://www.santilli-foundation.org/docs/ArbitrarySpeeds.pdf

[39] R. M. Santilli, "Rudiments of isogravitation for matter and its isodual for antimatter," American Journal of Modern Physics Vol. 4(5), pages 59-75 (2015)

http://www.santilli-foundation.org/docs/isogravitation.pdf

[40] R. M. Santilli, * Elements of Hadronic Mechanics,* Vol. I and Vol. II (1995) [15b], Academy of Sciences, Kiev,

http://www.santilli-foundation.org/docs/Santilli-300.pdf

http://www.santilli-foundation.org/docs/Santilli-301.pdf

(41) R. M. Santilli, * The Physics of New Clean Energies and Fuels According to Hadronic Mechanics,* Special issue of the Journal of New Energy, 318 pages (1998)

http://www.santilli-foundation.org/docs/Santilli-114.pdf

42] R. M. Santilli, *Hadronic Mathematics, Mechanics and Chemistry,*, Vol. I [a], II [b], III [c], IV [d] and [e], International Academic Press, (2008),

http://www.i-b-r.org/Hadronic-Mechanics.htm

[43] J. V. Kadeisvili, "Direct universality of the Lorentz-Poincare'-Santilli isosymmetry for extended-deformable particles, arbitrary speeds of light and all possible spacetimes" in {\it Photons: Old problems in Light of New Ideas,} V. V. Dvoeglazov Editor Nova Science (2000,

http://www.santilli-foundation.org/docs/Santilli-25.pdf

[44] A. K. Aringazin and K. M. Aringazin, "Universality of Santilli's iso-Minkowskian geometry" in {\it Frontiers of Fundamental Physics,} M. Barone and F. Selleri, Editors Plenum 91995),

http://www.santilli-foundation.org/docs/Santilli-29.pdf

[45] J. V. Kadeisvili, *SantilliÕs Isotopies of Contemporary Algebras, Geometries and Relativities,* Ukraine Academy of Sciences, Second edition (1997),

http://www.santilli-foundation.org/docs/Santilli-60.pdf

[46] I. Gandzha and J Kadeisvili, *New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli,* Sankata Printing Press, Nepal (2011),

http://www.santilli-foundation.org/docs/RMS.pdf

[47] R. M. Santilli, "Can strong interactions accelerate particles faster than the speed of light?" Lettere Nuovo Cimento {\bf 33}, 145 (1982)

www.santilli-foundation.org/docs/Santilli-102.pdf

[48] R. M. Santilli, "Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B 121, 443 (2006), \\ http://www.santilli-foundation.org/docs//Lie-admiss-NCB-I.pdf

[49] R. M. Santilli, *Isodual Theory of Antimatter with Applications to Antigravity, Grand Unifications and Cosmology,* Springer (2006). http://www.santilli-foundation.org/docs/santilli-79.pdf

[50] R. M. Santilli, ``Relativistic hadronic mechanics: non-unitary axiom-preserving completion of quantum mechanics" Foundations of Physics Vol. 27, p.625-739 (1997) http://www.santilli-foundation.org/docs/santilli-79.pdf

[51] . M. Santilli and A. O. E. Animalu, "Nonunitary - isounitary Lie-isotopic and Lie-admissible scattering theories of Hadronic Mechanics," Papers, I, II, II, IV and V

http://www.santilli-foundation.org/docs/Isoscattering-I.pdf

http://www.santilli-foundation.org/docs/Isoscattering-II.pdf

http://www.santilli-foundation.org/docs/Isoscattering-III.pdf

http://www.santilli-foundation.org/docs/Isoscattering-III.pdf

http://www.santilli-foundation.org/docs/Isoscattering-V.pdf

[52] R. M. Santilli, "Experimental Verifications of IsoRedShift with Possible Absence of Universe Expansion, Big Bang, Dark Matter, and Dark Energy," The Open Astronomy Journal {\bf 3}, 124 (2010),

http://www.santilli-foundation.org/docs/Isoredshift-Letter.pdf

[[53] R. M. Santilli, "Experimental Verification of IsoRedShift and its Cosmological Implications," American Institute of Physics Conference Proceedings Vol. 1281, pp. 882-885 (2010)

http://www.santilli-foundation.org/docs/Santilli-isoredshift.pdf

[54] R. M. Santilli, "Experimental verifications of isoredshift with possible absence of universe expansion, big bang, dark matter and dark energy," The Open Astronomy Journal {\bf 3}, 124 (2010), available as free download from

http://www.santilli-foundation.org/docs/Santilli-isoredshift.pdf

[55] R. M. Santilli, G. West and g. Amato, "Experimental Confirmation of the IsoRedShift at Sun at Sunset and Sunrise with Consequential Absence of Universe Expansion and Related Conjectures, " Journal of Computational Methods in Sciences and Engineering, Vol. 12, pages 165-188 (2012)

http://www.santilli-foundation.org/docs/Confirmation-sun-IRS.pdf

[56] G. West and G. Amato, "Experimental Confirmation of Santilli's IsoRedShift and IsoBlueShift," contributed paper to the {\it Proceedings of the San Marino Workshop on Astrophysics and Cosmology for Matter and Antimatter,} Republic of San Marino, September 5 to 9, 2011, in press (2012),

http://www.santilli-foundation.org/docs/Confirmation-IRS-IBS.pdf

[57] H. Ahmar, G. Amato, J. V. Kadeisvili, J. Manuel, G. West, and O. Zogorodnia, "Additional experimental confirmations of Santilli's IsoRedShift and the consequential lack of expansion of the universe,"Journal of Computational Methods in Sciences and Engineering, Vol. 13, page 321 (2013),

http://www.santilli-foundation.org/docs/IRS-confirmations-212.pdf

[58] R. M. Santilli, "Representation of galactic dynamics via isoshifts without universe expansion, dark matter and dark energy," American Journal of Modern Physics Vol. 4, pages 26-43, 2015

http://www.thunder-energies.com/docs/dark-matter-2015.pdf

[58] [59] D. I. Blochintsev, Phys. Rev. Lett. 12, 272 (1964).

[60] L. B. Redei, Phys.Rev. 145, 999 (1966).

[61] A. K. Aringazin, Hadronic J. 12 71 (1989).

[62] S. H. Aronson et al., Phys. Rev. D 28, 495 (1983).

[63] N. Grossman et al.,Phys. Rev. Lett. 59, 18 (1987).

[64] F. Cardone, R. Mignani and R. M. Santilli Lie-isotopic energy dependence of the K¯S lifetime, J. Phys. G: Nucl. Part. Phys. 18 [1992], L141-L152.

[65] F. Cardone and R. Mignani, Nonlocal approach to the Bose-Einstein correlation, Univ. of Rome Preprint No. 894, July 1992.

[66] Yu. Arestov, R. M. Santilli and V. Solovianov, "Experimental evidence on the isominkowskian character of the hadronic structure," Foundation of Physics Letters Vol. 11, pages 483-492 (1998)

http://www.santilli-foundation.org/docs/Santilli-52.pdf

[67] R. M. Santilli, ``Nonlocal formulation of the Bose-Einstein correlation within the context of hadronic mechanics," Hadronic J. {\bf 15}, 1-50 and 81-133 (1992),\\ http://www.santilli-foundation.org/docs/Santilli-116.pdf

[68] F. Cardone and R. Mignani, ``Nonlocal approach to the Bose-Einstein correlation, Euop. Phys. J. C 4, 705 (1998). see also ``Metric description of hadronic interactions rom the Bose-Einstein correlation," JETP Vol. 83, p.435 (1996)\\ http://www.santilli-foundation.org/docs/Santilli-130.pdf

[69] R. M. Santilli, ``A quantitative isotopic representation of the deuteron magnetic moment," in {\it Proceedings of the International Symposium 'Dubna Deuteron-93,} Joint Institute for Nuclear Research, Dubna, Russia (1994),

http://www.santilli-foundation.org/docs/Santilli-134.pdf

[70] R. M. Santilli, ``Nuclear realization of hadronic mechanics and the exact representation of nuclear magnetic moments,' R. M. Santilli, Intern. J. of Phys. Vol. 4, 1-70 (1998)

http://www.santilli-foundation.org/docs/Santilli-07.pdf

[71] A. A. Bhalekar and R. M. santilli, "Exact and Invariant Representation of Nuclear Magnetic

Moments and Spins According to Hadronic Mechanics," American Journal of Modern Physics, in press (2016)

http://www.santilli-foundation.org/docs/nuclear-MM-spins.pdf

[72] R. M. Santilli, *Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels,* Kluwer Academic Publishers (2001),

http: //www.santilli-foundation.org/docs/Santilli-113.pdf

Russian translation by A. K. Aringazin

http://i-b-r.org/docs/Santilli-Hadronic-Chemistry.pdf

[73] R. M. Santilli and D. D. Shillady,, "A new isochemical model of the hydrogen molecule," Intern. J. Hydrogen Energy Vol. 24, pages 943-956 (1999)

http://www.santilli-foundation.org/docs/Santilli-135.pdf

[74] R. M. Santilli and D. D. Shillady, , "A new isochemical model of the water molecule," Intern. J. Hydrogen Energy Vol. 25, 173-183 (2000)

http://www.santilli-foundation.org/docs/Santilli-39.pdf

[75], J. Fewldman, "Second Nomination of Prof., R. M. Santilli for the 2016 Nobel Prize in Chemistry,"

http://nobelprizeweb.com/index.php/nominations-3

[49] R. M. Santilli *Il Grande Grido - - Ethical Problem of Einstein followers in the U.S.A: An Insider's View,* (1984) and *Documentation of Il Grande Grido,* Vols. I, II and III (1985)m Alpha Publishing

http://www.scientificethics.org/IlGrandeGrido.htm

1985-2008 update

http://www.scientificethics.org/Santilli-ethical-decay.htm

2008-2016 update

http://www.i-b-r.org/