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NEW STRUCTURE MODELS OF HADRONS, NUCLEI AND MOLECULES PERMITTED BY HADRONIC MECHANICS, THEIR EXPERIMENTAL VERIFICATIONS AND THEIR INDUSTRIAL APPLICATIONS
Ruggero Maria Santilli
Institute for Basic Research
P. O. Box 1577, Palm Harbor, FL 34682
Tel. +1-727-934 9593; Fax +1-727-934 9275; E-address ibr@gte.net
Curriculum Vitae

The most visible and convincing experimental evidence on the mutability of the intrinsic characteristics of elementary and composite particles (called mutation and first introduced by R. M. Santilli in the original proposal (38) to built hadronic mechanics) is the lack of existence in nature of perfect rigidity. In fact, the lack of rigidity implies the necessary deformability of wavepackets and/or charge distributions. In turn, the latter implies the necessary alterability of the intrinsic magnetic moment. After one mutation is established, the mutation, in general, of spin, rest energy, charge, meanlife, parity, and other intrinsic characteristics follows via simply compatibility arguments, or via the use of the Lorentz-Santilli isotransforms.

With the apparent sole exception of Ref. (38), the notion of mutation did not exist in the physics of the 20-th century because Hamiltonian mechanics, quantum mechanics, special relativity, rotational symmetry, Poincare' symmetry and all other basic methods of the physica of the 20-th century are irreconcilably incompatible with deformations. In fact, all these methods assume particles as being dimensionless points. It is evident that points cannot be deformed. Therefore, no mutation could exist in the physics of the 20-th century.

By comparison, our iso-Hamiltonian mechanics, hadronic mechanics, isospecial relativity, isorotational symmetry, Poincare'-Santilli isosymmetry, and the other methods used in these studies have been conceived and constructed to represent extended, and therefore deformable particles, as stated in various titles of the references (see, e.g., the title of Ref. ((26) on the first isotopies of special relativity).

It should be noted that the mutation of individual characteristics depends on the physical conditions at hand. For instance, if we have the deformation of shape of an isolated charged and spinning sphere due to external fields, we do have a necessary mutation of the intrinsic magnetic moment, but there is no mutation of spin, as experimentally established in classical electromagnetism. However, if the same extended spinning charge is immersed within a hyperdense medium, the mutation of spin jointly with that of the intrinsic magnetic moment is necessary to avoid the belief of perpetual motions within physical media.

In this Part III, we shall provide various experimental evidence on mutations of particles. The first direct experimental verification of the deformability of the intrinsic magnetic moments of nucleons was announced by H. Rauch (228) in 1981 (at our Third Workshop on Lie-Admissible Formulations of hadronic mechanics, see Proceedings (73,74,75)) via a potentially historical neutron interferometric test of the 4p-spinorial symmetry of neutrons (see Refs. (229) for technical details).

Jointly, G. Eder (219) (who also participated in the same meeting) conducted various calculations for a thermal neutron beam exposed to the intense fields when passing in the vicinity of heavy nuclei, as it is the case for Rauch's experiment (see below). Eder's conclusions are that strong nuclear forces do not imply an appreciable effect due to the very small sectional area of their influence, while nuclear electric and magnetic fields do imply a measurable effect of the order of 1%, that is precisely the amount measured by Rauch and his collaborators.

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In the experiment a thermal neutron beam is first coherently split by a perfect crystal. The beam then passes through an electromagnet gap in one (or both) branches with the magnetic field. The beam is then coherently recombined by the perfect crystal as shown in Figure 1. The experimenters calibrated the field of the electromagnet to the value 7,496 G to achieve exactly two spin flips, i.e., a rotation of 4p = 720^o, as predicted by the conventional value of the neutron magnetic moment in vacuum

(1.1) m_neutron = - 1.913148 ± 0.000066 m_N.

When the neutron beam travels in empty space (namely the electromagnet gap is empty), the experimenters confirmed the exact occurrence of q = 4p, thus providing a beautiful verification of quantum mechanics in the conditions under which it is applicable, that is, when the neutrons of the beam can be all well approximated as massive points.

However, in order to avoid stray fields at the gap borders, the experimenters filled up the electromagnet gap with Mu-metal sheets. This essentially provided a test of the spinorial symmetry of neutrons under the intense electric and magnetic fields in the vicinity of Mu metal nuclei.

In all tests, Rauch and his collaborators did not find the expected angle of q = 4p = 720^o but found instead an angle of spin-flip whose median value is consistently smaller than 720^o, an effect that has been called by the author angle slow down effect. Rauch's best available experimental values are given by (228,229)

(1.2a) q = 715.87^o ± 3.8^o,

(1.2b) q_max = 719.67^o, q_min = 712.07^o.

These measurements do not contain the exact angle 720^o thus providing experimental evidence of the breaking of the SU(2)-spin symmetry.

Needless to say, the experiment is not final and it must be repeated until the deviation is at least three times the error. By remembering that measurements (1.2) date back to 1978 (see later on for comments), these improvements can be done nowadays in a variety of ways, such as conducting the tests for a large multiple of 4p that would be resolutory, provided that the experimenters fill up the electromagnet gap with Mu-metal sheets or other heavy element (in which absence the tests would have no connection or relevance for the test of mutation).

Despite this unsettled aspect, Rauch measurements (1.2) are plausible indeed. In fact, they are confirmed by various deviation from quantum mechanical values of total nuclear magnetic moments (see, later on, Section 4). Also, as recalled earlier, perfectly rigid bodies do not exist in the physical reality. Therefore, the amount of mutation is certainly open to scientific debates at this writing, but its existence is beyond credible doubt.

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Also, he possible recovering of the full 720^o angle is not sufficient to claim full confirmation of quantum mechanics in the conditions herein considered because there are several other aspects that have to be obtained. One of them is the sinusoidal character of the curve on the coherent recombination of the two split neutron beams. The experimental data shown in Figure 2 show a clear loss of such a sinusoidal character in an amount that is indeed a multiple of the error. On strict scientific grounds, this is sufficient, alone, to provide experimental evidence of mutation.

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The physical interpretation of these data is so simple to be trivial. When the gap of the electromagnet is given by the vacuum, the neutrons cannot experience any mutation (see the l.h.s of Figure 3), and the predictions of quantum mechanics are exact.

However, when the gap of the electromagnet is filled up with dense Mu-metal sheets, neutrons experience a deformation of their charge distribution that, in turn, implies a necessary alteration of their intrinsic magnetic moment, as requested by Maxwell's electrodynamics of charged, spinning and deformed spheres. Note in this case that the mutation of the intrinsic magnetic moment occurs without mutating the spin 1/2 of the neutron, evidently in view of the long range character of the acting forces.

The fact that the measured angle is consistently smaller than that expected (angle slow down effect) implies that the intrinsic magnetic moment of the neutron is decreased.

The achievement of a numerical, exact and invariant representation of experimental data (1.2) via relativistic hadronic mechanics is also elementary. Since the neutron is a spinning particle, it is natural to assume that the only possible mutation is that of the charge distribution of the neutron from its spherical shape (necessary for quantum mechanics) to a spheroidal ellipsoid, in which case

(1.3) b₁ = b₂ ≠ b₃.

The ellipsoid will then be a prolate or oblate depending, respectively, on whether

(1.4a) b₃^-2 > b₁^-2 = b₂^-2,

(1.4b) b₃^-2 < b₁^-2 = b₂^-2.

Rauch measured a deviation from the SU(2)-spin symmetry transform in the angle q of spin precession along the third axis. Such a transform is best represented via Dirac's equation according to the well known law

(1.5) y' = R(q) x y = (e^{iG₁ x G₂ x q/2}) x y,

where the Gs are the conventional Dirac gamma matrices.

The use of our covering iso-Dirac equation and related isotopic SU^(2)-spin symmetry then implies the applicability of the following isolaw from the iso-Dirac equation of Section II.5

(1.6) y^' = R^(q^) * y^ = (e^{iG^₁ x G^₂ x q^/2}) x y^ = (e^{ib₁ x G₁ x b₂ x G₂ x q/2}) x y^

where, the third expression is defined on isospaces over isofields, while the last expression is its projection on conventional spaces over conventional fields.

By using the third realization of the iso-Minkowskian metric (II.3.9) (that expressed via the characteristic quantity b) and the explicit form of the iso-Dirac gamma matrices, we obtain the expression

(1.7) q^ = b₁ x b₂ x q_715.87^o = 720^o

where the exact value of 4p for the isoangle q^ should be expected by experts in isotopies. In fact, all isotopies reconstruct as exact on isospace over isofields conventionally broken symmetries. In this case, the reconstruction of the exact SU(2)-spin symmetry requires that the isoangle be equal to the exact value 4p. In this case the deviation occurs only in the projection of the isotheory in our conventional spacetime, exactly as realized in Eq. (1.7).

The above expression immediately provides the first numerical values of the characteristic quantities

(1.8a) b₁ = b₂ = 1.003,

(1.8b) b₁^-2 = b₂^-2 = 0.994.

Next, the mutation here considered cannot possibly change the density of the hyperdense medium inside the neutron, namely, the mutation must be volume preserving. By assuming that the original sphere has a radius normalized to one, this condition implies that

(1.9) b₁^-2 x b₂^-2 x b₃^-2 = 1,

from which we obtain the numerical value of third characteristic quantity

(1.10a) b₃^-2 = 1.002,

(1.10b) b₃ = 0.994,

namely, relativistic hadronic mechanics characterizes an oblate spheroidal deformation, with a consequential decrease of the intrinsic magnetic moment, precisely as needed to represent the experimental data.

To achieve a numerical value of the mutated intrinsic magnetic moment m^ we assume that in first approximation

(1.11) m^/m = 715.87^o/720^o.

But, from Eq. (II.5.7) we have
'

(1.12) m^ = mx b₃/b₄.

Therefore, we have

(1.13a) b₃/b₄ = 715.87/720,

(1.13b) b₄ = 720 x 0.994/715.87 = 1.000

namely, the density of the thermal neutron beam is insufficient to affect the maximal causal speed, that remains the speed in vacuum (Isoaxiom II.4.1). The numerical value of the mutated intrinsic magnetic moment is then given, in average, by

(1.14) m^ = m x b₃ = -1.902 m_N.

namely, the mutation of the intrinsic magnetic moment in Rauch's experiment (228,229) is of the order of 1 %.

This completes the numerical, exact and invariant representation of all experimental data of Rauch's 4p neutron interferometric experiment as permitted by hadronic mechanics, representation that is manifestly impossible for quantum mechanics.

In summary, relativistic hadronic mechanics permits a simple, direct, numerical, exact and invariant representation of:

1) The actual, extended and nonspherical charge distributions of neutrons via the basic isounit

(1.15) I^ = Diag. (b₁², b₂², b₃², b₄²) > 0,

where b₁^-2, b₂^-2, b₃^-2 represent the semiaxes of the spheroidal ellipsoid and b₄^-2 geometrizes the density of the medium in the electromagnet gap (that is, the medium in which neutron propagate);

2) All possible deformations of these shapes via a dependence of the isounit, e.g., on the intensity of the external electric and magnetic fields originating from the nuclei of the Mu-metal nuclei;

3) The angle slow-down effect, namely, the systematic decrease of the angle of precession due to a decrease of the intrinsic magnetic moment for the physical conditions considered;

4) The necessarily oblate mutation/deformation of the charge distribution of the neutron to represent said angle slow down effect;

5) All the above exact numerical representations are obtained by reconstructing the exact SU(2)-spin symmetry on isospaces over isofield, while the same symmetry remains broken in conventional treatments.

In closing, the author feels a duty to recall rather extreme political interferences by the academic establishment against the finalization of Rauch's fundamental experiment, in documented knowledge of its paramount importance for the prediction and treatment of clean new energies so much needed by mankind. In fact, Rauch's measurements reported herein date back to 1978. Following their presentation at our meeting of 1981, Rauch and his associates were prohibited to continue the experiment at its original laboratory in Grenoble, France, under the conditions herein considered (with the electromagnet gap filled up with heavy metals). ALL repetitions of the experiment occurred since that time (they are not quoted here because useless for new knowledge) were carefully conceived and conducted in such a way as to have the thermal neutron beam move in vacuum in order to know in advance the full preservation of quantum mechanics, and this fundamental experiment has not been repeated to this day because of the persistence until today (for over two decades !) of said political obstructions by organized interests on old doctrines, despite countless solicitations for its repetition.

Due to the societal implications of the case, the author felt obliged to denounce these organized obstructions in book (60) and document them in volumes (61). It is the deep conviction of this author that, until the ethical decay in the contemporary physics community is contained, no significant research for the much needed new clean energies can be effectively conducted.

2. EXPERIMENTAL VERIFICATION VIA THE BEHAVIOR OF MEANLIVES OF UNSTABLE HADRONS WITH SPEED.

A direct experimental verification of the validity of isorelativity and its underlying iso-Minkowskian geometry and Poincare'-Santilli isosymmetry (Section II.4) in the interior of hadrons is provided by the anomalous behavior of the meanlife of unstable hadrons with speed. In fact, according to current experimental data reviewed below, such a behavior:

1) is at variance with the behavior predicted by special relativity,

(2.1a) t = t_o x g,

(2.1b) g = 1/(1 - b²)^1/2, b² = v_k x v_k/c_o x c_o,k = 1, 2, 3,

where c_o is the speed of light in vacuum;

2) confirms the behavior predicted by isospecial relativity (Isoaxiom II.4.3, Eq. (II.4.31)),

(2.2a) t = t_o x g^,

(2.2b) g^ = 1/(1 - b^²)^1/2, b^² = v_k x b_k² x v_k/c_o x b₄² x c_o,k = 1, 2, 3

3) constitutes an indirect verification of the iso-Doppler law (Isoaxiom III.4.4, Eq. (II.4.32)).

Recall that the center-of-mass behavior of a particle in an accelerator must strictly obey the laws of special relativity (because the particle moves in vacuum under external electromagnetic interactions). Yet, nonlocal interactions are known to imply deviations from such laws. The issue is therefore how nonlocal effects in the interior of hadrons can manifest themselves in their exterior behavior in a particle accelerator.

Blokhintsev and his school at the JINR in Dubna (230) pioneered the hypothesis that such nonlocal internal effects can manifest themselves via departures from the Minkowskian behavior of the meanlife of unstable particles with speed, while the center-of-mass trajectory follows Einsteinian theories exactly, and submitted certain generalized time-dilation laws. The problem was subsequently studied by several authors, including Redei (231), Kim (232), Nielsen and Picek (233) and others. This resulted in a variety of generalized time dilation laws.

In 1983, Santilli (26) submitted the isotopies of the special relativity with underlying isotopies of the Minkowskian spacetimes and the Lorentz-Poincare' symmetry as a form of geometrization of the physical medium in the interior of hadrons with isotopic law (2.2). The latter law was subsequently proved by Aringazin (192) to be "directly universal," i.e., including all possible generalizations of the time dilation law (230-233) via different expansions in terms of different parameters and with different truncations ("universality") in the fixed reference frame of the experimenter ("direct universality").

The covering character of our isorelativity now acquires its full experimental significance. Prior to the unified isotopic laws, experimenters had to test a considerable variety of different time dilation laws without having any mean for a possible selection due to the unavoidable approximation. With the universal iso-Minkowskian laws these problems are eliminated and the tests can be restricted to the unifying law (2.2).

Preceding generalized time dilation laws left basically unsolved the problem of their compatibility with the Einsteinian center-of-mass behavior, thus remaining unsettled even in the event of final experimental verifications. By comparison, the Poincare'-Santilli isosymmetry has been constructed for the purpose of yielding conventional center-of-mass trajectories, a feature achieved by preserving all ten Poincare' generators/conserved quantities and and isotopically lifting instead their Lie algebra into the form [A, B]* = AxTxB - BxTxA, where T is fixed for the hadron considered. Yet the Poincare'-Santilli isosymmetry admits generalized internal laws due to the new interactions represented by the isotopic element T. Therefore, the use of the Poincare'-Santilli isosymmetry assures the compliance of particles with Einsteinian center-of-mass behavior in particle accelerators, in a way fully compatible with nonlocal internal effects. Note that this is a fundamental point for the historical legacy on the nonlocality of the strong interactions.

The first phenomenological verification of the iso-Minkowskian geometry for the interior of hadrons has been provided by Nielsen and Picek (233) who computed deviations from the Minkowskian geometry inside pions and kaons via standard gauge models in the Higgs sector. These phenomenological studies resulted in a "deformed Minkowski metric" inside pions and kaons of the type

(2.3) m^ = Diag. [(1 - a/3), (1 - a/3), (1 - a/3), -(1 - a)],

where a is a constant with numerical values different for different mesons. It is evident that the above generalized metric is a particular case of our iso-Minkowskian metric in Eqs. (II.4.9) with numerical values in terms of the characteristic b-quantities via the the data of Ref. (233)

(2.4a) PIONS p^±: b₁² = b₂² = b₃ ² = 1 + 1.2 x 10^-3 , b₄² = 1 - 3.79 x 10^-3

(2.4b) KAONS K^±: b₁² = b₂² = b₃ ² = 1 - 2 x 10^-4 , b₄² = 1 + 6.1 x 10^-4.

Note the change in numerical value of the isotopic element in the transition from pions to kaons, that is necessary because of the change of the density. In fact, all hadrons have approximately the same size, but different rest energies, thus having different densities. Consequently any treatment of different hadrons via isorelativity requires different isounits.

The first direct experimental verification of the anomalous behavior of the meanlives of unstable hadrons with speed was reached by Aronson et al. (234) who measured a clear anomalous behavior of the meanlife of the K^o in the energy range 30-100 GeV. Subsequent experiments conducted by Grossman et al. (235) confirmed the conventional behavior of the meanlife of the same particle in the different energy range 100-350 GeV.

Nevertheless, the latter experiment (235) is afflicted by equivocal theoretical and phenomenological assumptions reviewed below, to such an extent to raise doubt as to whether tests (235) were specifically intended to recover conventional laws (as it has been the case for all neutron interferometric tests following that by Rauch outlined in the preceding section). To appraise this case, one should never forget that special relativity is clearly inapplicable in media of low density such as air or water due to insufficiencies beyond credible doubt (See Section II.4). Therefore, the belief that special relativity is exactly valid in the hyperdense media inside hadrons has no credibility, thus casting doubts on excessive theoretical and phenomenological manipulations of raw experimental data.

An exact fit of the anomalous measurements of Ref. (234) between 35 and 100 GeV was done by Cardone et al (110) by reaching the numerical values (see Figure 4 for the plot)

(2.5a) b₁² = b₂² = b₃² = 0.9023 ± 0.0004,

(2.5b) b₄² = 1.003 ± 0.0021,

(2.5c) b₁ = b₂ = b₃ = 0.949,

(2.5d) (2.5d) b₄ = 1.001,

Cardone et al (111) also achieved an exact fit via iso-Minkowskian law (2.2) of the two seemingly discordant measurements (234) and (235) for the energy range from 35 to 400 GeV for the interior of the K^o-particle, resulting in the following experimental values for the characteristic b-quantities for K^o

(2.6a) b₁² = b₂² = b₃² = 0.909080 ± 0.0004,

(2.6b) b₄² = 1.002 ± 0.007,

(2.6c) b₁ = b₂ = b₃ = 0.0954,

(2.6d) b₄ = 1.001,

(2.6e) Db_k² = 0.007, Db₄² = 0.001,

that are of the same order of magnitude of values (1.4).

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Measurements (233-235) also confirm the prediction of the iso-Minkowskian geometry in the range 35-400 GeV according to which the b₄ quantity (being a geometrization of the density of a given hadron) is constant for the particle considered (although varying from hadron to hadron), while the dependence in the velocity rests with the b_k-quantities.

Note the reconstruction of the exact Lorentz and Poincare' symmetries at the isotopic level for all anomalous time behavior of meanlives, as proved in Ref. (26). In fact, the quantity a of Eq. (2.3) was called by Nielsen and Picek (233) the Lorentz asymmetry parameter. In reality the Lorentz symmetry is exactly valid for the deformed metric (2.3), that only calls for its construction with respect to the new unit

(2.7) I^ = diag. [(1- a/3)^-1, (1- a/3)^-1, (1- a/3)^-1, - (1- a)^-1)],

and related isomathematics. In particular, note that the conventional Lorentz transformations are necessarily broken for metric (2.3). Only the Lorentz symmetry remains exact, although realized in a more general way.

In summary, all available conceptual, theoretical, phenomenological and experimental evidence establish deviations from the Minkowskian geometry inside hadrons with the sole exception of the Fermilab tests (235). A comprehensive critical analysis of the latter tests was done by Arestov et al (120) and can be summarized as follows. Arestov et al. re-examined tests [3b] by focusing the attention first on the range-energy selection rule that can be applied to re-elaborate the initial data on decays. By taking into account the results as they were done, Ref. (120) performed Monte Carlo simulations of the main features of experiment (235) via the use of the same statistics and reached conclusions dramatically different than those of ref. (235).

Attention in Ref. (235) was also given to the parameters used in Ref. (235) in the formula dN/dt for the proper time evolution. The strong correlation of said parameters causes a generally regular dependence of the parameters on entities not present in the formula, such as number of runs, energy, etc., apart from the systematic uncertainties. Therefore, the above dependence shadows the weak energy dependence that is dominant in this case, as can be seen from the large values of the correlation elements in Ref. (235).

Ref. (235) solved the problem of non-correlated fit by selecting the kaon momenta greater than 100 GeV/c. By means of that energy cut off, Ref. (235) obtained the data sample in which the CP violating terms contribute up to 1.6 %. However, it is unrealistic to look for the deviations from the Minkowskian decay law of the order of 1.6 percent. More realistic is to test the decay law for the kaons for deviations of the order of 10^-3 percent, as suggested in the fits by Cardone et al (110,111).

In fact, the assumption of 1.6 % contribution from PC violation in the data elaboration of Ref. (235) implies looking for a large energy dependence of their tau function, thus rendering it meaningless to look for more realistic deviations.

The large inefficiency (error) of tests (235) occurred because they had not been optimized for the problem at hand. Basically, the experimental design and data selection rules followed those of conventional relativistic studies in weak interactions, thus implicitly assuming special relativity in the data elaboration,. as shown in Figure 6.

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Thus, in the selected number of events, both fits achieve a good mean value of the hidden parameter determining the energy dependence in the neutral kaon decays. However, the error bars differ strongly, although both results for fitting values are still insignificant statistically even in the selected sample of events. Therefore, the 100 % error bar in the fit of Ref. (120) illustrates the insufficiency of tests (235) quite clearly, since such error permits manipulations of the selection procedure aiming at achieving a predetermined result.

In conclusion, the apparent results of tests (235) (apparent confirmation of special relativity within the hyperdense media inside the kaons) have no conception or epistemological credibility; they are far from being resolutory in their energy range of 100 to 400 GeV due to an excessive number of equivocal theoretical and phenomenological manipulations of the raw experimental data, besides having insufficient statistics and excessive error; and, even assuming that they are eventually confirmed by future tests, the same results confirm the inapplicability of the special relativity within kaons when fitted with other tests in favor of the covering isorelativity.

The exact fit of experimental data (234,235) of Refs. (110,111) constitutes experimental evidence on the following predictions of isospecial relativity:

1) Photons propagate inside kaons at speeds bigger than that in vacuum,

(2.7) c = b₄ x c_o = 1.001 x c_o,

with maximal causal speed inside kaons bigger than the local photons (as it occurs for water, Section II.4) (Isoaxiom II.4.1)

(2.8) V_Max = c_o x b₄ / b₃ = 1.001/0.953 x c_o = 1050 x c_o > c;

2) The time within kaons t^ (isotime) is different than our own time t, and it is given by
<

(2.9) t^ = t x b₄

3) The unit of isotime decreases with the increase of the density, as shown by the data in the transition from pions to kaons, thus predicting that the isotime for gravitational singularities is null.

As we shall see, the validity of the iso-Minkowskian geometry and the Poincare'-Santilli isosymmetry inside hadrons is truly fundamental for the scientific study and industrial development of new clean energies. Despite their transparent scientific and societal importance, ALL major particles laboratories in the U. S. A., Europe and Russia have refused to conduct resolutory experiments on the behavior of the meanlives of unstable particles with speed following formal petitions by the author as well as numerous other concerned scientists.

As reviewed in book (60) and documented in volumes (61), beginning in 1978, this author suggested to all major particle laboratories the conduction of said fundamental tests because necessary for scientific accountability in the use by particle laboratories of large public funds, all crucially dependent on the exact validity of special relativity within the hyperdense medium inside hadrons.

Since, on one side, new clean energies are crucially dependent on deviations from the exact validity of special relativity inside hadrons, and since, on the other side, organized interests have systematically prevented or otherwise jeopardized the experimental verification of basic physical laws within hadrons, the only possible conclusion is that, as it was the case for Rauch's fundamental interferometric experiment, no serious advancement toward new clean energies is possible without concerned people first addressing issues of scientific ethics and accountability in particle physics. Remeber, "your" environmnent is at stake.

3. EXPERIMENTAL VERIFICATION VIA THE BOSE-EINSTEIN CORRELATION.

Hadronic mechanics has been built for quantitative treatments of the nonlocal-integral character of the hadronic structure and the strong interactions at large. Therefore, the most fundamental verifications of the new mechanics are those directly dealing with nonlocal interactions.

Among various possible experimental verifications of this type, the most important is that with the Bose-Einstein correlation. We are here referring to the collision of protons and antiproton at high or low energy, their annihilation forming the so-called "fireball," and the subsequent emission of a number of unstable massive particles whose final product is a set of correlated mesons (see, e.g., review (236) and Figure 7 below).

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Evidently, the approximate validity of quantum mechanics for the Bose-Einstein correlation is beyond scientific doubt. However, any firm belief on the exact character of quantum mechanics for the event here considered is a scientific misconduct, particularly if proffered by experts in the field, because:

1) the Bose-Einstein correlation is necessarily due to nonlocal-integral effects originating in the deep overlapping of the wavepackets of protons and antiprotons;

2) The mathematical foundations of quantum mechanics (such as its topology), let alone its physical laws, are inapplicable for any meaningful representation of said nonlocal interactions (those occurring in a volume that, as such, cannot be consistently reduced to a finite set of isolated points as requested by quantum mechanics); and

3) The fundamental quantity needed for the representation of experimental data on the Bose-Einstein correlation, the two-point correlation amplitude (see below), is irreconcilably incompatible with the basic axioms of quantum mechanics.

As an example, the basic quantum mechanical axiom of expectation values of a Hermitean, thus diagonal operator A (observable) solely permits structures of the type

(3.1) C_k = S_k=1,2,3,...(s_k| x A_kk x |s_k),

as expected to be known by "experts."

By comparison, as also expected to be known by "experts," a quantitative representation of the Bose-Einstein correlation necessarily requires cross terms of the type

(3.2) C_ij = (s_i| x A x |s_j), i ≠ j,

that are impossible for the quantum axiom of expectation value.

Admittedly, there exist a number of semiphenomenological models in the literature (236) with a good agreement with the experimental data. Scientific misconduct occurs when these models are claimed to be compatible with the basic axioms of quantum mechanics. In fact, as we shall see better below, any agreement with experimental data on the Bose-Einstein correlation achieved by throwing in parameters and functions of completely unknown physical origin constitute mere adulterations for pre-meditated schemes.

Of course, the selection of the appropriate generalization of quantum mechanics for quantitative representations of the Bose-Einstein correlation must be open to scientific debate. The scientific misconduct occurs when its need is denied for personal equivocal gains. At any rate, an inspection of the huge deviations from the predictions of quantum mechanics and experimental data on the Bose-Einstein correlation indicated in Figure 9 below is sufficient to unmask said scientific misconducts.

After studying the problem for years, Santilli (112) proposed in 1992 the treatment of the Bose-Einstein correlation via relativistic hadronic mechanics for the following reasons:

i) Relativistic hadronic mechanics has been built precisely for the quantitative treatment of the nonlocal-integral interactions in general thus including those occurring in the fireball of the Bose-Einstein correlation;

ii) The basic axioms of relativistic hadronic mechanics have been built to admit the needed cross terms in the expectation values of Hermitean operators, which cross terms are merely permitted when Hermitean isotopic operator T has non-diagonal elements,

(3.3) C^_ij = (s_i| x T_ik x A_kk x T_kj x |s_j), i, j = 1, 2, i ≠ j,

iii) Relativistic hadronic mechanics reconstructs the exact Poincare' symmetry for the Bose-Einstein correlation because all nonlocal-integral effects are embedded in the generalized unit;

iv) Relativistic hadronic mechanics is the only known generalized mechanics outside the class of unitary equivalence of quantum mechanics that achieves invariance, thus avoiding the catastrophic physical and mathematical inconsistencies of Theorem II.2.1;

v) As it was the case for the behavior of the meanlife with speed, relativistic hadronic mechanics is directly universal, thus including as particular cases all possible nonunitary generalizations of quantum mechanics.

The analysis of Ref. (112) can be outlined as follows. The rigorous application of the unadulterated axioms of relativistic quantum mechanics predicts the following two-point correlation function

(3.4) C₂ = N x (1 + e^{-r2 x q2}),

where N is a renormalization constant, r is the radius of the fireball and q the relative four-momentum of the proton-antiproton system. However, the above expression is dramatically far from experimental data.

A chain of adulterations of the exact expression (3.4) were then worked out in the literature in order to achieve a fit of experimental data while still claiming exact validity of quantum mechanics (236). The first adulteration was the following one

(3.5) C₂ = N x (1 + C x e^{-r2 x q2}),

where C is an ad hoc quantity called "chaoticity parameter," and introduced without any physical motivation or origin. Expression t(3.5) also resulted in being excessively far from experimental data. Therefore, additional adulterations became necessary with expression of the type (236)

(3.6) C₂ = N x (1 + + C₁ x e^{-r₁2 x q2} + C₂ x e^{-r₂2 x q2} + ...),

It is at this point where scientific misconduct occurs whenever the above empirical expression is claimed to be compatible with quantum mechanics, particularly when the claim is ventured by "experts." In fact, it is well known to "experts" that the addition of exponential terms in expression (3.6) necessarily requires exiting from the quantum axiom of expectation values because of the need for cross terms as in Eq. (3.2).

The representation of the Bose-Einstein correlation via relativistic hadronic mechanics can be outlined as follows. First, the new mechanics permits a direct representation (i.e., a representation via the isometric itself) of the actual shape of the fireball with the characteristic quantities b₁^-2, b₂^-2, b₃^-2 representing the semiaxes of the spheroidal ellipsoid, as well as of its density of the fireball via characteristic quantity b₄^-2, resulting in the isounit, isotopic element and isometric of the type (see Section II.4 for details)

(3.7a) I^ = Diag. (b₁^-2, b₂^-2, b₃^-2, b₄^-2) = 1/T > 0,

(3.7b) T = Diag. (b₁², b₂², b₃², b₄²),

(3.7c) m^ = T x m = Diag. (b₁², b₂², b₃², - b₄²)

where m = Diag. (1, 1, 1, -1) is the conventional Minkowski metric.

However, the above diagonal expression is insufficient for the proton-antiproton correlation due to the need of the indicated cross terms. Therefore, the complete isominkowskian metric M^ is given by the above expression m^ multiplied by the following nondiagonal Hermitean matrix

(3.8) M^ = m^ x
| C₁₁ C₁₂ |
| C₂₁ C₂₂ |

where C₁₁ and C₂₂ are real valued, C₁₂ = C₂₁⁺, and the four Cs are given by all possible integrals in the inner product of wavefunction 1 for the proton and 2 for the antiproton (see Ref. (112) for brevity), thus resulting in the needed terms 11 and 22 as as occurring for quantum mechanics, plus the cross terms 12 and 21 solely admitted by hadronic mechanics, resulting in a total of four terms.

The isotopies of the conventional relativistic derivation, done for the first time by Santilli in Ref. (112), yield the following two-point isocorrelation function

(3.9) C^₂ = 1 + (K/3) x S_k=1,2,3,4 m^_kk x e ^{-q_t2 / b_k2}

where q_t is the momentum transfer needed to fit experimental data (that are expressed precisely via the momentum transfer), m^ is expression (3.7c) and K has the following form

(3.10) K = b₁² + b₂² + b₃² = 3,

where the normalization to 3 is requested to admit a consistent relativistic limit.

Note that isocorrelation function (3.9) predicts the following maximal and minimal values(112)

(3.11a) C₂^max = 1 + 1/3 + 1/3 + 1/3 - 1/3) = 1.67.

(3.11b) C₂^min = 1.

Moreover, relativistic hadronic mechanics predicts the following maximal value for the fourth characteristic quantity (density of the fireball)(112)

(3.12a) 1 + K⁴ / 3 + 3 x K² x b₄² = 1.67,>

(3.12b) b₄² = n₄^-2 = 2.33

(3.12c) b₄^-2 = n₄² = 0.429.
,p> (3.12d) b₄ = 1.526,

(312e) n₄ = 0.654.

IT SHOULD BE INDICATED THAT THE ABOVE NUMERICAL VALUE OF THE DENSITY OF THE FIREBALL COINCIDES WITH THAT NEEDED FOR THE EXACT NUMERICAL REPRESENTATION OF RUTHERFORD'S CONCEPTION OF THE NEUTRON AS A BOUND STATE OF ONE PROTON AND ONE ELECTRON AT ONE FERMION MUTUAL DISTANCE, AS PRESENTED IN PART V. Note that this is purely theoretical prediction prior to experimental verifications,. Note also that this is a "limit" density, and that the actual one for the Bose-Einstein fireball is expected to be different because it depends on the energy.

Therefore, relativistic hadronic mechanics predicts that the speed of photons inside the Bose-Einstein fireball is bigger than that in vacuum,

(3.13) c = b₄ x c_o = 1.526 x c_o,

and that the intrinsic time of the fireball (isotime) is decreased with respect to our time

(3.14) t^ = t / b₄ = 0.654 x t.

A comprehensive phenomenological study of the above prior theoretical derivation by Santilli (112) was conducted by F. Cardone and R. Mignani (113), resulting in an outstanding fit of all experimental data on the Bose-Einstein correlation reproduced in Figure 8 below. Cardone and Mignani also provided the following experimental data on the characteristic iso-Minkowskian quantities for the Bose-Einstein correlation

(3.15a) b₁ = 0.267 ± 0.054 , b₂ = 0.437 ± 0.035 , b₃ = 1.661 ,

(3.15b) b₄ = 1.653 ± 0.015.

with related values here computed because quite useful for subsequent calculations

(3.16a) b₁² = 0.071 , b₂² = 0.191, b₃² = 2.759,

(3.16b) b₄² = 2.732,

(3.16c) n₁ = 3.745, n₂ = 2.288, n₃ = 0.602,

(3.16d) n₄ = 0.605,

(3.16e) n₁² = 14.025, n₂² = 5.235, n₃² = 0.602,

(3.16f) n₄² = 0.366,

Note the very elongated character of the fireball, as indicated by the above experimental values of its semiaxes n_k², k = 1, 2, 3. Note also that the density of the fireball, b₄² = 2.732 is bigger than the limit theoretical value b₄² = 2.33, thus implying bigger local speeds of the photons, as expected from the very large energy of the proton and antiprotons.

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The above fit provide a major experimental verification of the following aspects:

I) The predictions of relativistic hadronic mechanics are confirmed with an exact fit of the experimental data;

II) The fits of experimental data provide a clear confirmation of the maximal value 1.67 and minimal value 1 of the two-point isocorrelation function;

III) The experimental fits provide a clear confirmation of the theoretical prediction (3.12b) for the value of the density of the proton-antiproton fireball, that is crucial the new structure model of hadrons with physical particles presented in these pages, the experimental value (3.16b) being greater than the theoretical value due to the relative energy of the proton and antiproton;

IV) The experimental fits confirm the nonlocal, nonpotential and nonunitary nature of the correlation at the very foundation of hadronic mechanics;

V) The fits confirm the validity of the Minkowski-Santilli isogeometry for the interior of the proton-antiproton fireball with isometrics of the type (3.8);

VI) The fits confirm the capability of relativistic hadronic mechanics of reconstructing the exact Poincare' symmetry at the isotopic level for the proton-antiproton annihilation under isounits (4.11).

VII) The fits confirm that the speed of photons within hyperdense hadronic media is bigger than the speed of photons in vacuum as per Eq. (3.13), and that the intrinsic time of the fireball is different than our time, as in Eq. (3.14).

When the above experimental verification is joined with the preceding one, it is expected that even the most resilient (or opposed?) reader will accept the evidence of the validity of hadronic mechanics in the physical conditions in which quantum mechanics cannot be exactly valid.

By combining the above experimental values with those of the preceding section, we can have the following values of the isounits of time

(3.17) I^_t(pions) = 1.004, I^_t(kaons) = 0.998 , I^_t(protons) = 0.366,

As one can see, the above data clearly indicate the decrease of the isounit of time with the increase of the density, thus implying a null isotime at the limit of a gravitational singularity.

The cosmological implications of the above numerical results are significant, because they imply the prediction by isorelativity that stars and other astrophysical bodies with different masses have different times, and, in particular, stars and other astrophysical objects that have the same mass but different densities have different times. A significant is that we are referring to predictions of a local time that is not predicted by general relativity. As an illustration, the prediction implies that the flow of time here on Earth and that on Jupiter is different in rates not predicted by general relativity, a prediction that can be one day tests when a clock can be immersed in Jupiter's gravitational field and retrieved for comparison to a twin clock on Earth.

4. EXPERIMENTAL VERIFICATIONS IN NUCLEAR PHYSICS.

4.1. THE DISTRESSING CONDITION OF NUCLEAR PHYSICS.

There is no doubt that, thanks to quantum mechanics, nuclear physics achieved truly historical discoveries during the 20-th century. However, on true scientific grounds, a discipline can be said to be exactly valid for given specific field only when that discipline represents the totality of the experimental data in an exact and invariant way via the rigorous use of the original axioms, without their adaptations to fit the data. If the discipline provides only an approximate representation of the experimental data, then any claim of "exact" validity is a scientific misconduct.

Along these lines, quantum mechanics can be claimed to be exactly valid for the structure of the hydrogen atoms (not so for heavier atoms!) because, in that particular field, the mechanics represented all experimental data in an exact and invariant way without any adulteration of its basic axioms. By the same argument, any claim that quantum mechanics is exactly valid in nuclear physics is purely political because of the well known, historical inability of the discipline to represent all nuclear data.

The first evidence on the lack of exact character of quantum mechanics in nuclear physics dates back to the 1930s where it emerged that experimental values of nuclear magnetic moments could not be exactly explained with quantum mechanics, since there were deviations of the order of a few percents for the simplest possible nucleus, the deuteron, with increasing deviations with the increase of the mass, all the way to embarrassing deviations for large nuclei, such as the Zirconium (see Figure 10 below).

Despite these deviations, quantum mechanics was continued to be claimed as being exact in nuclear physics throughout the 20-th century on grounds that the existing disparities would be solved by "deeper theories," such as quark theories, when in reality the deviations and problematic aspects increased, rather than decreased with quark conjectures, e.g., because of their inability to represent correctly even the spin of nucleons, let alone their magnetic moments.

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Additional serious disagreements between the prediction of quantum mechanics and nuclear data existed since the inception of the field and continued to increase, rather than decrease, in time. A second disparity is given by the disagreement between the predictions and experimental data in inelastic scattering of nucleons on nuclei.

Unfortunately for human knowledge, as soon as these disagreements were found, excellent fits with experimental data were quickly obtained via the adaptation of theoretical predictions with ad hoc parameters without physical motivation or origin, resulting in the claim, again, that quantum mechanics is exact. However, in reality, these adulterations and parametrization constitute a quantitative measurements of the deviations of quantum mechanics from nuclear realities, as it has been the case for the Bose-Einstein correlation and other fields.

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Perhaps the most distressing, yet suppressed, insufficiency of quantum mechanics in nuclear physics has been in its notoriously failed attempt to represent nuclear forces. Recall that a necessary condition for the applicability of quantum mechanics is that ALL interactions have to be derivable from a potential, trivially, because the mechanics can only represent systems via the Hamiltonian.

The original concept that nuclear forces were central soon resulted in being drastically disproved by nuclear reality, thus requiring the addition of non-central nuclear forces. Subsequently, there was the need to introduce exchange, van der Waals, and numerous other types of potentials in an attempt to represent nuclear forces. As of today, after about one century in keeping adding new potentials to the Hamiltonian, we are still far from an understanding,
let alone a quantitative representation of the nuclear forces, despite the fact that we have now reached the unreassuring addition of some twenty or more different nuclear potentials to the Hamiltonianbr>

(4.1) H = S_k=1,2,...,Np_k²/2m_k + V₁ + V₂ + V₃ + V₄ + V₅ + V₆ + V₇ + V₈ + V₉ + V₁₀ + V₁₁ + V₁₂ + V₁₃ + V₁₄ + V₁₅ + V₁₆ + V₁₇ + V₁₈ + V₁₉ + V₂₀ + .........

It is evident that this type of process cannot be kept indefinitely without risking condemnation by posterity. The time to stop adding potentials to the Hamiltonian in the dream of reaching a satisfactory representation of the nuclear forced passed decades ago.

In summary, the approximate character of quantum mechanics in nuclear physics is, evidently, beyond scientific doubt. However, a rather vast evidence establishes that the lack of exact character of quantum mechanics in nuclear physics is beyond credible doubt. The open scientific issue is the selection of the appropriate generalization of quantum mechanics for nuclear physics, but not its need.

Admittedly, the deviations here considered are small, as we shall see. However, the small deviations of quantum mechanics in nuclear physics directly imply new clean energy that cannot be even conceived, let alone treated via quantum mechanics. Therefore, we have a societal duty to conduct serious investigations on the applicability of broader mechanics in nuclear physics.

Santilli proposed the covering hadronic mechanics for more accurate studies of nuclear physics since the original proposal. (38) of 1978 for the following reasons.

The comparison of nuclear volumes with the volumes of the nucleons reveals that nucleons in nuclei are in conditions of mutual penetration of about 1/1000 of the volume of their charge distribution. This is sufficient to establish that, when members of a nuclear structure, nucleons are in condition of mutual penetration and overlap of their charge distributions. In turn, this experimental evidence is sufficient to establish the necessary presence of contact, nonlocal, nonlinear and nonpotential terms in the nuclear force.

Therefore, the first and perhaps most fundamental implication in the use of hadronic mechanics in nuclear physics is the truncation of keeping adding potentials to the Hamiltonian, and the separation instead of nuclear forces into a potential component represented with the Hamiltonian, plus a contact nonpotential component represented with the isounit

(4.2a) H = S_k=1,2,...,N p_k²/2xm_k + V,

(4.2a) I^ = Diag. (b₁^-2, b₂^-2, b₃^-2, b₄^-2) x e^{F(t, r, p, |s>, ...)},

where the characteristic quantities b_k^-2 = n_k², k = 1, 2, 3, permit, for the first time, a direct representation of the actual, nonspherical and deformable shape of the charge distribution of nucleons, b₄^-2= n₄² permits, also for the first time, a direct representation of the density of nuclei, and the function F permits, again for the first time, a representation of the contact, nonlocal,. nonlinear and nonpotential nuclear forces.

The broadening of the representational capability of hadronic mechanics over quantum mechanics is then evident to all readers in good faith. Note also the covering character of hadronic over quantum mechanics. In fact, at the limit when all nucleons are perfectly spherical (b_k = 1), the density of nuclei is abstracted into that of the vacuum (b₄ = 1) and all forces are of potential type (F = 0), quantum mechanics is recovered identically. Note also that hadronic mechanics recovers quantum mechanics identically for all distances bigger than one Fermi. In fact, all isounits are restricted to verify the rule

(4.3) Lim I^_{r >> 1 Fermi} = I.

The first process initiated by hadronic mechanics is then the re-interpretation of which nuclear force is truly of potential and which is of nonpotential type, a process that is under way and will be reported at some future time.

Another reason for recommending the use of hadronic mechanics in particle physics is that their basic isosymmetries, the Galilei-Santilli isosymmetry (52-53) for nonrelativistic treatment, and the Poincare'-Santilli isosymmetry (54-55) for relativistic studies, have been conceived and constructed precisely for the nuclear structure under the following conditions:

i) The generators of the spacetime isosymmetries coincide with the conventional generators of quantum mechanics, thus assuring that the total ten conserved quantities of the Galilei or Poincare' symmetry remain conserved under isotopies (for all isolated nuclei);

ii) The spacetime isosymmetry guarantees the lack of a Keplerian center, thus permitting the representation of nuclei without nuclei, thanks to their foundations on the generalized unit that represent precisely contact interactions among extended nucleons, while recovering Keplerian systems at the limit (4.3).

iii) The exact validity of the spacetime isosymmetries assures the achievement of invariant descriptions of contact nonunitary effects, thus avoiding the catastrophic inconsistencies of Theorem II.2.1.
.

4.2. EXPERIMENTAL VERIFICATIONS OF HADRONIC MECHANICS IN NUCLEAR PHYSICS.

A number of applications and experimental verification of hadronic mechanics in nuclear physics will be presented in Part IV. In this section we provide the experimental verification of hadronic mechanics via the first known exact, numerical and invariant representation of ALL nuclear magnetic moments..

The first historical hypothesis for the correct interpretation of the anomalous behavior of the nuclear magnetic moments dates back to the time of Fermi, Segre, and others in the 1940's. The hypothesis propagated to various treteases in nuclear physics in the first half of the 20-th century. For instance, in the treteases in nuclear physics by Blatt and Weisskopf (not quoted here because it is excessively known) one can read on page 31:

It is possible that the intrinsic magnetism of a nucleon is different when it is in close proximity to another nucleon.

The reader should be aware that the Santilli hypothesis on the mutation of the intrinsic characteristics of particles (38) was based precisely on this historical legacy of Fermi, Segre, Weisskopf and other founders of nuclear physics.

The study of this so simple and effective a hypothesis was abandoned in the second half of the 20-th century when researchers understood that deformations of the intrinsic characteristics of nucleons are strictly prohibited by Einsteinian doctrines, evidently because in flagrant disagreement with the Poincare' symmetry. As a result, the history of physics has now on record a truly incredible number of papers published in the past half a century in the study of nuclear magnetic moments all centrally dependent on Einsteinian theories for evident political reasons, yet ALL of which failed to reach an exact representation precisely because of the political premises of the research.

As of today, quantum mechanics has been unable to reach an exact representation of the magnetic moment of the smallest nucleus, the deuteron, since about one percent is still missing, despite all possible relativistic and other corrections, as shown, e.g., by V. V. Burov and his associates (238) at the JINR in Dubna, Russia. Rather embarrassing deviations exist for heavier nuclei.

Most unreasuringly, studies on the magnetic moment of the deuteron have been based on the use of a mixture of different states, while the magnetic moment has been measured, specifically, when the deuteron is in its ground state.

The quantitative treatment via relativistic hadronic mechanics of the above historical legacy of Fermi, Segre, Weisskopf and other founders of nuclear physics was first presented by R. M. Santilli at the meeting "Deuteron 1993" at the Joint Institute for Nuclear Research, Dubna, Russia (238) and then treated in other papers (see Ref. (114) for a comprehensive treatment of nuclear physics via hadronic mechanics). Most effective for the task herein considered is the use of the Dirac-Santilli isoequation (see Section II.5) since it provides a direct representation of the mutation of the intrinsic magnetic moment of nucleons.

We assume here a knowledge of Part II, with particular reference to the fact that, according to hadronic mechanics, the nuclear constituents are not protons and neutrons, but their isotopic image called "isoprotons" and "isoneutrons", or, collectively, "isonucleons." Since the contributions due to mutual penetrations are small, isonucleons can be assumed in first approximation to maintain the conventional spin 1/2 and charge, but experience a mutation of their magnetic moments as well as of other characteristics identified below.

This implies that isotopic treatment of nuclear magnetic moments can be obtained via the simple method of subjecting conventional treatment to a nonunitary transform representing precisely the mutation as in Eq.s (I.3.6) (technically, this means that the isorepresentation of the Poincare'-Santilli isosymmetry are "regular" and not exceptional). Moreover, the new conception of nuclei permitted by hadronic mechanics implies that each isonucleon has its own shape generally different from other isonucleons that is expressed by the characteristic functions of the iso-Minkowskian isogeometry b_k, k = 1, 2, 3.

A simple isotopy of the conventional quantum mechanical treatment of nuclear magnetic moments (available in any treteases in the field) leads to the following isotopic total nuclear magnetic moments expressed for simplicity along the third axis

(4.4a) µ^_tot = S_k=1,2,...,N (g^_k^{L^} x L^_k3 + g^_k^{S^} x S^_k3),

(4.4b) g^_k^{L^} = g_k^L x b₃ / b₄, g^_k^{S^} = g_k^S x b₃ / b₄,

where L (S) represents the angular momentum (spin, the gs are the conventional gyromagnetic factors with explicit values with conventional values

(4.5a) µ^S = µ_P g^S x S, µ^L = g^L x L,

(4.5b) g_p^L = 1, g_n^L = 0

(4.5c) g_p^S = 5.585, g_n^S = - 3.816, µ_P = 1,

L^, S^ and g^ are the isotopic expressions, and N is the total number of isonucleons.

To a good approximation the density b₄ of the isonucleons can be assumed to be the same for all these isoparticles. We select the use of value (3.16) because it represents the density of nucleons as derived from other fits. We therefore have the expression

(4.6a) b₄ = n₄^-1 = 1.652, b₄^{-14 = 0.605,}

(4.6c) g^_k^{L^} = 0.654 x b_k3 x g_k, g^_k^{S^} = 0.654 x b_k3 x g_k^S,

where we have assumed in first approximation that the isoproton and the isoneutrons experience the same mutation.

It is easy to see that the above model provides a quantitative resolution of the historical open problem of total nuclear magnetic moments. Consider first the case of the deuteron, that is a p-n bound state in triplet S-state (L = 0), the state with L = 1 being unallowed by parity (that is preserved under isotopies).

We have the following quantum mechanical (QM) and experimental values of the deuteron magnetic moment

(4.7a) µ^D_QM = g_p + g_n = 0.879 ,

(4.7b) µ^D_exp = 0.857 (for µ_p = 1)

Note that the quantum mechanical representation is in excess of the experimental value. Therefore, the exact representation requires a reduction of the above theoretical values. In turn, this implies the prediction of a prolate spheroidal deformation (in which the rotation occurs along the major semiaxis), because an oblate deformation would imply an increase of the magnetic moment (due to the rotation around the smaller semiaxis).

By comparison, we have the following deuteron magnetic moment as exactly represented by hadronic mechanics (HM) (238)

(4.8a) µ^D_HM = (b₃/b₄ x (g_p + g_n) = µ^D_exp = 0.857,

(4.8b) b₃ = n₃^-1 = 1.490,

(4.8b) b₄ = n₄^-1 = 1.652

The remaining two semiaxes of the isonucleons (evidently assumed to be a spheroidal ellipsoid due to spin) can be identified via the condition used earlier that mutations of shape must conserve the density (or volume) of the nucleon. Therefore, we have the condition

(4.9) n₁² x n₂² x n₃² = 1,

from which we obtain the value of all semiaxes of the two isonucleons in the deuteron

(4.10) n₁² = n₂² = 1.490, n₃² = 0.450.

As one can see, hadronic mechanics achieves an exact and invariant representation of the deuteron magnetic moment, by confirming the prediction that the deformation is prolate. The physical interpretation of the representation is so simple to be trivial (see Figure 12 below). The above model should be refined via different mutations of the isoproton and the isoneutron, evidently expected from their different absolute value of the magnetic moments. This study is left to the interested reader.

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The above results will be re-examined in Part VI with a deeper structure model of the deuteron in which the neutron is reduced to its constituents.The extension of the above model for an exact representation of the magnetic moment of the tritium and ALL other nuclei is straighforward and it is left to the interested reader, jointly with refinements due to D-couplings, pionic currents and other aspects here basically inessential to illustrate the exact representational capability of quantum mechanics compared to the approximate capabilities of quantum mechanics.

5. EXPERIMENTAL VERIFICATIONS IN SUPERCONDUCTIVITY.

5.1.THE DISTRESSING CONDITION OF SUPERCONMDUCTIVITY.

There is no doubt that superconductivity has made major advances in recent decades. However, there is equally no doubt that superconductrivity currently is at the stage of atomic physics in the early part of the 20-th century before the discovery of the structure of atoms. In fact, superconductivity is based on electrons bonded in Cooper pairs, yet no quantitative model exists or is actually permitted by quantum mechanics for such pairs, thus resulting in a discipline that studies systems on which there is no serious knowledge.

Superconductivity is another field in which the exact validity of quantum mechanics has been stretched well beyond its limit for various reasons. As well known, individual electrons cannot be brought to superconducting conditions because their intrinsic magnetic field interferes with the stray atomic fields in conductors, by creating in this way what we call electric resistance. Superconductivity is only reached by Cooper pairs that are deeply correlated electron pairs in singlet bonds. In particular, these electron pairs are so stable to have been detected crossing potential barriers in said bonded form. The total magnetic field of the Cooper pair is dramatically smaller than that of individual electrons (due to the antiparallel alignment of the two electrons). Therefore, Cooper pairs experience much less resistance in their hopping from one atom to another in a conductor, thus permitting superconductivity (see Figure 13).

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There is no doubt that quantum mechanics provided an excellent description of an "ensemble" of Cooper pairs each abstracted as a point, the latter condition being necessary from the very structure of the theory. However, it is equally well known that quantum mechanics has been unable to provide ANY structure model of ONE Cooper pair, trivially, because electrons repel each other according to the fundamental Coulomb law. Therefore, the belief that quantum mechanics provides a complete description of superconductivity is equivalent to the construction of atomic physics without any model at all of the atomic structure, resulting in transparent political-nonscientific misconduct.

Due to the absence of such a fundamental knowledge, researchers were forced to introduce new interactions seemingly experienced by electrons that have no counterpart in any other branch of physics. I am referring to the introduction in superconductivity of the notion called phonons and related new electron-phonon interactions. Inspection of all other branches of physics reveals that phonons exist in the sound theory, but not at the particle level, thus casting justified shadows in the actual existence of phonons beyond the level of a conceptual abstraction. Alternatively,the lack of existence of electron-phonon interactions outside superconductivity casts doubts as to whether the conjecture of phonons will survive after the achievement of deeper and more accurate theories.

Above all, the stretching of the validity of quantum mechanics for systems for which it was not built for is best manifested by the exhaustion of predictive capacities. In fact, all possibilities of increasing the superconducting temperature have been exhausted, while all advances are attempted via phenomenological trails and errors without a sound guiding theory.

As it was the case for the preceding fields, the approximate character of quantum mechanics in superconductivity is beyond doubt. Equally beyond doubt is its lack of exact character and the need for a deeper theory capable of providing q quantitative structure model of the Cooper pair, representing the various aspects in a way compatible with experiments and exhibiting novel predictive capacities for further advances.

5.2 EXPERIMENTAL VERIFICATIONS OF HADRONIC MECHANICS IN SUPERCONDUCTIVITY.

The research reported in this section was originated with Santilli's (38) hadronic bound state of one electron and one positron at short distance originated by nonlocal, nonlinear and nonpotential interactions due to deep wave overlappings (see Part IV for more details). Animalu (169,170) recognized that the strength of the new non-Hamiltonian interactions is such to overcome the Coulomb repulsion, and therefore be applicable also to the electron-electron correlation. Via the use of Santilli results (38), Animalu (loc. cit.) then applied hadronic mechanics to produce the first known structure model of the Cooper pair and built a new theory today known as Animalu isosuperconductivity. Finally, Animalu and Santilli (116) completed the structure model of the Cooper pair via hadronic mechanics.

It is assumed the reader is aware of the fact that, according to hadronic mechanicsthe constituents of the Cooper pair are "isoelectrons" and not conventional electrons. As a matter of fact, it will soon become evident that, without the isotopic interpretation of particles, a structure model of the Cooper pair is impossible, thus confirming the basic limitations of quantum mechanics.

It is evident that we can only outline here some of the main aspects of isosuperconductivity and its clear experimental verification. To avoid the "illusion" of novelty, the first step is to exit from the class of equivalence of quantum mechanics. This= task can be easily achieved via the method of nonunitary transforms of Eqs. (I.3.6).

Consider the Schroedinger equation for one electron with mass m and charge -e in the field of an identical electron

(5.1a) H x |e> = (pxp/2m + e²/r) x |e> = E x |e>,

(5.1b) p x |e> = - i D_r |e>.

where, due to insufficient symbols in HTLM, D_r represents partial derivative with respect to r. The image of the above equations under a nonunitary transform is given by

(5.2a) U x U⁺ = I^ = 1 / T ≠ I,

(5.2b) (U x U⁺)^-1 = T,

(5.2c) U x (H x |e>) = (U x H x U⁺) x (U x U⁺)^-1 x (U x |e>) = H^ x T x |e^> = E x |e^>,

(5.2d) U x (p x |e>) = (U x p x U⁺) x (U x U⁺)^-1 x (U x |e>) = p^ x T x |e^> = - i U (D_r |e>) = - i D^_r |e^> = - i I^ x D_r |e^>,

where e^ represents the wavefunction of the isoelectron, and D^_r represent partial isoderivative (Part I).

(5.3) H^ x T x |e^> = [p^xTxp^/2m^ + e²/r)xI^] x T x |e^> = E x |e^>

However, the creation of Cooper pairs requires an "external trigger' (in the labnguage of hadronic mechanics). In fact, since identical electrons repel each other, and since the new attractive non-Hamiltonian interactions only occur at short distances of the order of 1 Fermi, without an external action (called trigger) identical electrons would never form the Cooper pair.

It is evident that the "trigger" for formation of the Cooper pair requires must be constituted by positive charges. Studies of the issue have discovered that the hadronic trigger for the Cooper pair is provided by Cuprate ions. The latter are purely quantum mechanical (because they act for large distances as compared to the range of applicability of hadronic mechanics). Therefore, their interaction of Cuprate ions must be merely added to the short range hadronic state (5.3) resulting in the expression

(5.4) H^ x |e^> = [p^xTxp^/2m^ + e²/r)xI^ - z x e²/r]]xTx|e^> = E'x|e^>

where the positive charge ze is the ionic valence and the conventional quantum nature is expressed by the lack of multiplication by I^. Note that one could equivalently write structure (5.4) at the quantum level and add the hadronic effects at short range by achieving the same results.

At this point Animalu (169,170) and Animalu and Santilli (116) selected the following realization of the isounit and isotopic element:

(5.5a) I^ = e^{- (e^_up|x|e^_down) x e_down / e^_down} = 1 - (e^_up|x|e^_down) x e_down / e^_down

(5.5b) T = e^{+ (e^_up|x|e^_down) x e_down / e^_down} = 1 + (e^_up|x|e^_down) x e_down / e^_down

where e^_up and e^_down represents the wavefunction of the isoelectron with spin up and down, respectively, e_down represents the wavefunction of the ordinary electron, and (|x|) represents the volume integral between e^_down⁺ and e^_up.

Note that isounit (5.5a) provides a direct representation of the new interactions caused by deep waveoverlapping of the wavepackets of the isoelectrons that are nonlocal because represented by the volume integral (|x|), nonlinear because depending on the wavefunctions in a nonlinear way, and nonpotential because of clear contact/zero range type not representable with a Hamiltonian.

Most importantly, readers should keep in mind the short range character of the above isotopic lifting since isounit (5.5a) recovers the trivial unit I for all distances sufficiently greater than 1 Fermi (10^-13 cm) for which the volume integral (e^|x|e^) is null. Under these conditions hadronic mechanics recovers quantum mechanics uniquely and identically. Therefore, we are here presenting new correlations solely occurring at short distances where quantum mechanics is inapplicable, while recovering quantum mechanics identically for all longer distances. This point is important because it will eliminate the need for the conjecture of phonon as physical quantity beyond its value of a mere formalism.

In order to obtain an explicit structure equation for the Cooper pair, we use the following behavior

(5.6a) e_down = A x e^{- r / R}

(5.6b) e^_down = B x (1 - e^{- r / R})/r,

where the first expression is known from atomic physics, the second expression was identified in Ref. (38), and R represents the charge radius of the Cooper pair. After substitution in Eq. (5.4) and turning the isokinetic energy into a renormalization m' of the electron mass m (another standard procedure of hadronic mechanics), we obtain the differential equation

(5.7) [p²/2xm' + (z - 1)e²/r - V x e^{- r / R} / (1 - e^{- r / R}) ] x |e^> = E x |e^>,

where one recognizes the familiar Hulten potential. The solution of the above equitation was worked out in detail in the original proposal (38) of 1978 and can be summarized as follows (see Part IV for details).
at short distances the Hulten potential behaves like the Coulomb potential by therefore absorbing the latter and resulting into a very strong ATTRACTIVE force between the two IDENTICAL electrons in singlet couplings. In fact, at short distance Eq. (5.7) yields the following structure equation of the Cooper pair of isoelectrons

(5.8) [p²2xm' + - K x e^{- r / R} / (1 - e^{- r / R}) ] x |e^> = E x |e^>,

where K is the new constant (in view of the original V) absorbing the coefficient of the repulsive Coulomb force.

The solutions of the equation (5.8) yields the familiar Hulten energy spectrum(38)

(5.9) E = - (m/xKxR² / h² x n - n)² x h² / 4xm'xR², n = 1, 2, 3, ...

where h represents h-bar.

Santilli (38) identified the solution for the structure of the p^o via the introduction of the two parameters

(5.10) k₁ = h/2xm'xR² = 0.34, k₂ = m'xKxR²/h = 1 + 8.54 x 10^-2,

reviewed in Part IV. Animalu (169,170)identified the solution for the Cooper pair via the parametrization for the ground state

(5.11a) k₁ = F x R / h x c_o, k₂ = KxR/F,

(5.11b) | E_{Cooper Pair} | = 2 x k₁ x [ 1 - ( k₂ - 1 )² / 4 ] x h x c_o / R,

where F is the Fermi energy of the isoelectron. Eq. (5.11b) can be written in good approximation

(5.12) | E_{Cooper Pair} | = k₂ x T_c / q_D

where T_c is the superconducting temperature and q_D is the Debye temperature.

Animalu then worked out several examples, such as

(5.13a) Aluminum: q_D = 428^oK, T_c = 1.18^oK, k₁ = 94, k₂ 1.6 x 10^-3

(5.13b) YBa₂Cu₃O_6x: k₁ = 1.3 x z^-1/2 x 10^-4, k₂ = 1.0 x z^1/2,

where the effective valence z varies from a minimum of z = 4.66 for YBa₂Cu₃O_6.96, T_c = 91^oK, to a maximum of z = 4.33 for YBa₂Cu₃O_6.5, T_c = 20^oK. The general expression predicted by Animalu isosuperconductivity for YBa₂Cu₃O_6-x is given by [Eq. [5.15], p. 373, ref. (169)]

(5.14) T_c = 367.3 x z e^{- 13.6 / z},

and it is in remarkable agreement with experimental data (see the figures below).

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A few comments are now in order. The connection between the proposed model and the conventional theory of the Cooper pair is intriguing. As studied in ref. (169, the constant in the Hulten potential can be written

(5.15) K = h x w

where w is precisely the (average) phonon frequency. Expression (5.11b) can then be rewritten

(5.16) | E_{Cooper Pair} | = 2 x k₁ x k₃ x c_o / R x (e^{1 / NV}),

where NV is the (dimensionless) electron-phonon coupling constant. The main results of our model can therefore be reformulated in terms of the electron-phonon interactions, as expected. However, as expected, the conjecture of the phonon is replaced in our model with the new non-Hamiltonian interactions for the simple reason that phonons do not yield an attractive force between identical electrons, while our non-Hamiltonian interactions do.

The mechanism for the creation of the attraction among the identical electrons of the pair via the intermediate action of cuprate ions is a general law of hadronic mechanics according to which nonlinear, nonlocal and nonhamiltonian interactions due to wave-overlappings at short distances are always attractive in singlet couplings and such to absorb Coulomb interactions, resulting in total attractive interactions irrespective of wether the Coulomb contribution is attractive or repulsive. As noted earlier, the Hulten potential is known to behave as the Coulomb one at small distances, being must stronger than the latter and therefore absorbing the latter.

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Another main feature of the model is characterized also by a general law of hadronic mechanics, according to which bound states of particles due to wave-overlappings at short distances in singlet states suppress the atomic spectrum of energy down to only one possible level. This occurrence is called the hadronic suppression of the atomic energy spectra. In fact, the non-Hamiltonian forces would disappear for any excited state, thus resulting in conventional quantum energy levels, while the hadronic level can only one.

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The solutions for the Cooper pair also reduce the finite spectrum down to only one admissible level, that of the Cooper pair. Excited states are indeed admitted, but they imply large distances R for which nonlinear-nonlocal-nonhamiltonian interactions are ignorable, thus resulting in repulsion. Alternatively, we can say that, in addition to the conventional, quantum mechanical, Coulomb interactions among two electrons, there is only one additional system of hadronic type with only one energy level per each couple of particles.

The case of possible triplet couplings also follows a general law of hadronic mechanics. While singlets and triplets are equally admitted in quantum mechanics (that is, coupling of particles under their point-like approximation), this is no longer the case for hadronic mechanics (that is, couplings of extended particles one inside the other). In fact, all triplet couplings of particles under conditions of mutual penetration are highly unstable due to evident repulsive forces, the only stable states being the singlets.

This law was first derived in Ref. (38) via the "gear model", i.e., the illustration via ordinary gears that experience a known highly repulsive force in triplet couplings, while they can be coupled in a stable way in singlets. The possibility of applying the model to a deeper understanding of Pauli's exclusion principle is then consequential, and will be indicated later.

6. EXPERIMENTAL VERIFICATIONS IN CHEMISTRY.

6.1. THE DISTRESSING CONDITION OF QUANTUM CHEMISTRY.

Chemistry is another branch of science that achieved simply historical advances in the 20-th century thanks to quantum mechanics. Despite that, chemistry is a field where the exact validity of quantum mechanics has been stretched beyond the limit of credibility because of truly incontrovertible limitations or sheer inconsistencies.

With the understanding that the approximate validity of quantum mechanics for the description of chemical structures is beyond doubt, the sole issue open to scientific debates is the identification of the appropriate generalized of mechanics providing a more accurate description of molecular structures and chemical processes at large, while the continued belief on the terminal character of quantum mechanics in chemistry becomes a clear scientific misconduct due to the nature, dimension and implications of said limitations and inconsistencies.

A systematic study of the limitations and inconsistencies of quantum mechanics in chemistry has been conducted by Santilli in monograph (59). The identifications and resolution of these limitations and inconsistencies is too technical for the limited capacities of the htlm format of these pages. Therefore, we are regrettably forced to the sole presentation of conceptually outlines in the figures below.

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After the insufficiency of the basic axioms of quantum chemistry was proved beyond doubt, chemists were forces to initiate their adulterations. The most effective for the improvement of the representation of experimental data has been the use of the so-called screened Coulomb potentials, namely the Coulomb potential multiplied by an exponential (or other functions) of the type

(5.1) V = N x e ^{r x b} / r.

The resulting models have still been qualified as belonging to "quantum chemistry." However, the use of the above potentials implies the loss of the very notion of "quantum," since, as well known, quanta can only occur in between purely Coulomb energy levels. Moreover, screened Coulomb laws can only be reached via nonunitary transforms of the Coulomb law, as also well known. Therefore, the use of potentials of type (5.1) is concrete evidence for exiting the class of equivalence of quantum chemistry, besides suffering of the catastrophic physical and mathematical inconsistencies of Theorem II.2.1. Therefore, the qualification of models based on potentials (5.1) as belonging to "quantum chemistry" is essentially a political posture deprived of serious scientific content.

The known effectiveness of "screened Coulomb laws" is a visible evidence of the validity of hadronic chemistry for a more accurate representation of molecular structures. In fact, the new discipline is structurally nonunitary, thus including as particular cases all possible generalized potentials of type (5.1). Their treatment via the novel isomathematics then resolves the catastrophic inconsistencies of Theorem II.2.1. Despite these results, for reasons conceptually outlined in the following figures (see monograph (59) for a comprehensive treatment), hadronic chemistry would remain basically insufficient to resolve the main inconsistencies of quantum chemistry without a basically new notion of valance bonds developed by Santilli and Shillady (125,126).

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Note that nuclei cannot participate in molecular bonds evidently due to their extreme distances (for the particle world). Therefore, as universally admitted, molecular bonds are due to the bonding of valence electrons. At this point the insufficiencies of quantum chemistry appear in their full light because quantum mechanics cannot provide any ATTRACTIVE force between IDENTICAL valence electrons due to the repulsive Coulomb force, as it was the case for the Cooper pair in superconductivity (Section 5).

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On technical grounds, the origin of this large inconsistency is due to the inability by quantum mechanics to restrict the valence bond to TWO electrons. This is a general, well known problem in chemistry, since all experimental data establish that correlation solely occurs in pairs, while molecular models in chemistry generally have no restriction at all, thus implying the inconsistency of this figure. It is regrettable for human knowledge that the existence of the above inconsistency is generally suppressed in technical papers, conference presentations and Ph. D. courses in chemistry.

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FIGURE 19: A view of another major inconsistency of quantum chemistry: the prediction that all substances are paramagnetic, in dramatic disagreements with reality. The prediction is here illustrated with the hydrogen molecules that is known to be diamagnetic. Nevertheless, when the current quantum chemical model of the hydrogen molecule is completed within an intense external magnetic field, it predicts a total magnetic polarization solely possible for paramagnetic substances, thus in dramatic contradiction with reality.

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FIGURE 20: A conceptual view of the birth of hadronic mechanics, superconductivity and chemistry: extended wavepackets of electrons in conditions of deep mutual penetration into a singlet quasi-particle state. According to quantum chemistry, valence electrons can only be abstracted as massive points and, consequently, the physical conditions of this figure do not exist. But point-like wavepackets cannot exist in nature, as well known. It then follows that, whenever the mutual distances are such to render ignorable wave overlappings (as it occurs for the structure of the H atom - see Figure 16), quantum mechanics is exactly valid. However, when the mutual distances are such to imply deep mutual penetrations of the wavepackets of particles (as it occurs in particle physics, superconductivity and chemistry), we have contact, zero range, nonlocal-integral, nonlinear and nonpotential interactions that are beyond any hope of serious treatment via quantum mechanics.

A pillar of quantum mechanics, superconductivity and chemistry is the fact that the new contact forces due to weep wave-overlappings in singlet couplings results to be STRONGLY ATTRACTIVE, thus permitting basically new structure models in various branches of sciences that are inconceivable for quantum mechanics. The new strongly attractive contact forces were first identified by Santilli in his original proposal (38) of 1978 to build hadronic mechanics. The same forces were then discovered to be applicable with great success to superconductivity by Animalu (1169) in 1993. Finally, the use of the new forces for the introduction of a basically new notion of valence bond was developed by Santilli and Shillady (125,126) (see monograph (59) for a comprehensive presentation).

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6.2. EXPERIMENTAL VERIFICATIONS OF HADRONIC MECHANICS IN CHEMISTRY.

FIGURE 21: A schematic view of the Santilli-Shillady isochemical model of the hydrogen molecule (125,126,59), here depicted at absolute zero degrees temperature and in the absence of any rotation. The model has achieved the first known exact and invariant representation of ALL characteristics of the hydrogen molecules from first unadulterated principles of hadronic chemistry. The exact representation of the binding energy and other molecular data is due to the introduction of the new Santilli-Shillady strong valence force originating from to the deep overlappings of the wavepackets of valence electrons in singlet coupling, that is so strongly attractive to overcome the repulsive Coulomb force (see the case of the Cooper pair in the preceding Section 5).

Such a strong valence bond can only occur for pairs, thus avoiding the inconsistency of Figure 20. In fact, the bond creates a quasiparticle called isoelectronium that has charge -2 but spin and magnetic moment zero. As a result, a third electron with spin 1/2 cannot form any stable correlation/.bond with such a quasiparticle state with spin zero. Moreover, said strong valence bond implies that electrons pairs orbit in the two H atoms in opposite directions as shown in the figure, thus preventing any net total magnetic polarity, and avoiding the inconsistency of Figure 19.

It should be indicated that the isoelectronium cannot be a fully stable particle in view of the uncertainty principle and other laws. In any case, in the event the isoelectronium would be a stable particle, molecular binding energies would be prohibitively large.

It should be finally mention that the isoelectronium has permitted the first known quantitative interpretation of Pauli's seclusion principle (59). This basic principle is accepted in quantum mechanics without any quantitative explanation for the following reasons. For an electron to be able to "exclude" another electron with the same characteristics in the same energy level, there has to be some form of interaction. The sole interactions admitted by quantum mechanics, those of potential type, are grossly inapplicable for an understanding of Pauli's principle because they would imply large departures from spectral lines and other disagreements with experiments (since they would grant additional energy to the electrons that does not exist in nature). Hadronic mechanics has permitted the first quantitative interpretation of Pauli's exclusion principle because the interactions occurring in this case, as represented with the isounit, HAVE NO POTENTIAL, thus being consistent with experimental data. Note the exclusion of triplet couplings that is another basic law of hadronic (but not of quantum!) mechanics.

To state it differently, the existence of Pauli's exclusion principle in nature is, perhaps, the strongest individual evidence on the existence of contact nonpotential forces in the ultimate layers of nature, and the consequential validity of hadronic mechanics as their sole invariant description known at this writing.

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FIGURE 22: A schematic view of the Santilli-Shillady isochemical model of the water molecule that has achieved, for the first time, an exact representation of all molecular characteristics without adulteration of the basic axioms of hadronic chemistry (125,126,59). The model is too complex to be reviewed in this page. An intriguing aspect is that, while the water molecule is only one for quantum chemistry, for the covering hadronic chemistry the same molecule may acquire a variety of different configurations with different physical and, therefore, chemical properties, mostly as yet unexplored. This confirms that our quantitative understanding of water, rather than having reached a final character, is just at its initiation.

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FIGURE 23: A schematic view of the first important prediction of hadronic chemistry: the new chemical species of Santilli magnecules (127,239,59). It consists of clusters of individual atoms such as H, C, O, etc., dimers (incomplete molecules) such as HO, CH, etc., and ordinary molecules such as H2, CO2, H2O, etc., bonded together under a new attractive force originating from the toroidal polarization of the orbits of peripheral atomic electrons due to very strong external magnetic fields. Santilli magnecules are detected via clearly identified peaks in Gas Chromatographic Mass Spectrometers that remain un-identified by the computer search among all known molecules, while having no InfraRed signature at their atomic mass unit (amu). A review of the rather large experimental verifications on the existence of Santilli magnecules in gases, liquids and solids, is presented in monograph (59).

As an illustration of the need to exercise scientific caution before venturing judgments without the prior acquisition of a serious knowledge of the new hadronic chemistry, it is generally believed that "the hydrogen molecule is diamagnetic and, therefore, it cannot experience a magnetic bond." Such a view is scientifically vacuous because the new bond in Santilli magnecules occurs at the level of individual atoms, and NOT at the level of molecules. As such, the new magnetic bond can occur for ALL natural elements irrespective of whether diamagnetic or paramagnetic.

Another judgment deprived of scientific foundations is the belief that "individual atoms cannot be bonded in clusters unless they are bonded via valence couplings into molecules." This belief, also due to lack of technical knowledge of the experimental evidence in the new chemical species, is immediately disproved by calculations showing that one unbounded atom can have a magnetic bond much stronger than that of the same atom when valence bonded to another. This is due to the fact that, in the former case there is the additional availability of the polarized intrinsic magnetic moment of peripheral electrons (that is very large for particle standards). The latter bond is absent when the same atom is under a valence bond to another because the isoelectronium has no measurable magnetic field, as indicated earlier.

The need to exercise scientific caution before venturing technically unsubstantiated beliefs comes into full light by noting that the magnetic bond of isolated atoms has a fundamental role for the development of new clean burning combustible fuels so much needed by our society. As an illustration, magnecular clusters rich in "isolated" hydrogen atom can effectively replace hydrocarbons while being dramatically cleaner (patented and international patents pending) because, when the clusters decompose under combustion, we have the formation of H2 with the release of large energy (105 Kcal/mole) as part of the combustion itself. Therefore, questions and scientific discussions are welcome, solicited and appreciated. However, the venturing of technically unsubstantiated objections in the new science herein reported is de fact opposition against the search of new clean energies and fuels for which main purpose hadronic mechanics, superconductivity and chemistry have been built.

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FIGURE 24: Another intriguing prediction of hadronic chemistry: a hydrogen atom with fractional Bohr's orbits (58). The new atom is predicted from the photodisintegration of the H-molecule via the expulsion of one proton, in which case the two strongly correlated/bonded valence electrons can only orbit around the remaining proton. Since the charge is now -2e, and Bohr's orbit is inversely proportional to the square of the charge, the orbit of this anomalous hydrogen atom is predicted to have radius a/4, where a is the conventional Bohr radius. Note that hadronic mechanics enters solely in the study of the deeply correlated/bonded electrons, while the indicated fractional charge is purely quantum mechanical, since it is due to long range Coulomb interactions. Also, it should be noted that the above anomalous H-atom is not stable because the strong correlation/bond of two valence electrons is unstable in the conditions considered, and decays into isolated electrons, one of which is expelled free.

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7. EXPERIMENTAL VERIFICATIONS IN ASTROPHYSICS AND COSMOLOGY.

7.1. THE DISTRESSING CONDITION OF ASTROPHYSICS AND COSMOLOGY.

There is no doubt that astrophysics and cosmology also achieved historical advances in the 20-th century. However, it is equally true that astrophysics and cosmology have been afflicted by a real scientific obscurantism because of the systematic adaptation of the universe to organized interests on Einsteinian doctrines, rather than adapting the doctrines to the universe, as any serious scientific process would require.

The first dominant reason for the distressing condition of the field is the widespread belief on the "universal constancy of the speed of light,"

(7.1) c_o = universal constant,

that is a well known, central pillar for the validity of Einsteinian doctrines. However, in the physical reality, the speed of electromagnetic waves is a local variable with a rather complex functional dependence on the light frequency w and various other characteristics of the medium in which it propagates,

(7.2) c = c(w, ...) = c_o / n₄(w, ...) = c_o x b₄(w, ...),

where n₄ = 1/b₄ is the familiar index of refraction.

The local character of the speed of electromagnetic waves was discussed in Section II.4. Due to its relevance for astrophysics and cosmology, let us review it again. It has been experimentally established since Newton's times that the speed of light in media of low density, such as air, water, etc., varies from medium to medium and it is smaller than the speed of light in vacuum

(7.3) c < c_o for low density media.

Speeds c > c_o have been experimentally measured by A. Enders and G. Nimtz (240) in the tunneling of photons between certain guides (see review (241) for additional references and details). Speeds c > c_o have also been identified in astrophysical events (242-244) (see also the recent data 246)). A comprehensive review of all speeds c > c_o can be found in Ref. (247). Therefore, we shall write in general

(7.4) c > c_o for special and hyperdense media.

When faced with the experimental evidence such as the refraction of light (see Figure 25 below), a rather universal posture (intended, or implying in any case salvaging Einsteinian doctrines) is that such a local variation is only "apparent" because the decrease of the speed of light is due to the scattering of photons among the atoms of the medium, thus implying a longer travel. In this way, the universal constancy of the speed of light (7.1) is salvaged because photons would travel in vacuum, and Einsteinian doctrines are consequently preserved. However, such a political posture has no scientific credibility for the following reasons:

1) The local character of the speed of light has also been established for electromagnetic waves, e.g., of one meter in wavelength, in which case said reduction to photons is a pure nonscientific nontechnical nonsense due to the excessive size of the wavelength that prevent any meaningful reduction to photons.

2) The existence of electromagnetic waves propagating at speeds bigger than that of light in vacuum is today an experimental reality (240-247), in which case the reduction of such superluminal propagation to photons scattering the atoms of the medium is an additional nonscientific nontechnical nonsense.

3) Even assuming that, somehow, the "universal constancy of the speed of light" could be made compatible with these local values smaller and bigger than the speed in vacuum, special relativity remains grossly inapplicable within physical media for the various reasons identified in Section II.4, e.g., the violation of the principle of causality within physical media when "the local speed of light" is assumed as the maximal causal speed (e.g., because electrons can travel faster than light in water), the violation of the relativistic law of addition of speeds of light in the event "the speed of light in vacuum" is assumed as the maximal causal speed within physical media (because the sum of two speeds of light in water does not yield the speed of light in water), and numerous other serious inconsistencies.

4) Assuming that both the "universal constancy of the speed of light" and special relativity could be salvaged, somehow, within physical media, the reduction of light to photons remains grossly unable to represent the local dependence of the speed on the frequency and other characteristics as occurring, e.g., in the spectral decomposition of light by a crystal.

5) The essentially political nature of the reduction of the propagation of light within physical media to photons scattering among atoms is finally established by the lack of any q treatments published in refereed journals providing a QUANTITATIVE-NUMERICAL explanation of ALL the behavior of light within physical media.

The widespread posture on the "universal constancy of the speed of light" and the universal validity of Einsteinian doctrines within physical media becomes truly paradoxical when one notes that most physical media are not transparent to light, in which case the use of light for any geometric treatment is pure nonsense, thus establishing the need for fundamentally new notions to characterize the maximal causal speeds within physical media NOT based on the speed of light.

The scientific reality is that Einsteinian doctrines are inapplicable to physical media (the term "violation" would not be appropriate and would actually be a form of lack of respect toward the memory of Albert Einstein because the doctrines were solely conceived for the vacuum, and their applicability was stretch