THE R.M. SANTILLI FOUNDATION
PROMOTING BASIC SCIENTIFIC ADVANCES AND SCIENTIFIC ETHICS


  September 4, 2011

INFORMAL SUGGESTIONS ON THE REPLACEMENT OF SUPERSYMMETRIES, DARK MATTER AND ALL THAT

Ruggero Maria Santilli
The Institute for Basic Research, Florida, U.S.A.
basicresearch@i-b-r.org

Dear Colleagues,

According to widespread views, recent experiments at CERN have disproved the validity of supersymmetries, dismissed the existence of the hypothetical dark matter, and stimulate a call for a more appropriate theory
http://www.bbc.co.uk/news/science-environment-14680570
http://www.scientificamerican.com/article.cfm?id=beautiful-theory-collides
http://www.sciforums.com/showthread.php?t=106674

Our group has independently reached the same conclusions. In fact, we have established experimentally the redshift of light propagating within physical media without any relative motion, thus achieving a numerical representation of the dynamics of galactic stars via the mere loss of energy by light to the innergalactic medium without any need for hypothetical conjectures. Additionally, we have identified decades ago serious structural inconsistencies of the supersymmetric theories, and presented other views fully aligned with the indicated recent trend. The astrophysical implications will be discussed at our forthcoming meeting

San Marino Workshop on Astrophysics and Cosmology for Matter and Antimatter
September 5 to 9, 2011
http://www.workshops-hadronic-mechanics.org/

Workshop Aim
http://www.workshops-hadronic-mechanics.org/workshop_aim.html

Experimental Confirmation of Santilli IsoShifts
http://www.workshops-hadronic-mechanics.org/isoshifts.php

In view of the above, I have been asked by various colleagues to outline my views in the replacement of supersymmetries, dark matter and all that, which I do below.

INITIAL DYNAMICAL CONSIDERATIONS
My first suggestion is to resist the temptation of studying the problem at the sole phenomenological level, but first examine the ultimate dynamical foundations, and study phenomenology only thereafter.

Supersymmetries can be connected to time evolutions of a (Hermitean) operator A characterized by a combination of Lie and Jordan products

(1) i dA/dt = (A, H) = m [A, H] + n {A, H} = m (AB - BA) + n {AB + BA}

where m, n, m \pm n are non-nu scalars (see below for matrices) and the product AB is associative.

Time evolutions of type (1) are a particular case of the Lie-admissible and Jordan-admissible time evolutions I introduced in the mid 1960s as part of my thesis for the graduate school (see the first paper [1] and others of that period in my CV) which I wrote in the infinitesimal form

(2) i dA/dt = (A, H) = p AH - q HA = m [A, H] + n {A, H}, p = m + n, q = n - m

as well as in the exponentiated / finite form

(3) A(t) = U(t) A(0) W^+(t) = [exp(i H q t)] A(0) [exp(- i t p H)].

with corresponding classical counterparts here ignored for brevity.

Hence, on dynamical grounds, supersymmetric structures of type (1) are a particular case of the (p, q)-deformations of Lie algebras. As an incidental note, my late fried Larry Biedenharn knew paper [1] well, but for some reason elected to launch in 1986 the smaller class of q-deformations (with p = 1) without its quotation, an occurrence that caused my dubbing as "the most plagiarized physicists of the 20th century" due to the enormous number of papers in q-deformation without quotation of their origination in my 196 paper.The irony is that, by 1986, I had abandoned the field because of very serious structural inconsistencies identified below.

I should recall that a nonassociative algebra with product (A, B) is called Lie-admissible (Jordan-admissible) when the attached totally antisymmetric product [A, B]* = (A, B) - (A) (totally symmetric product {A, B}* = (A, B) + (B, A)) verifies all Lie axioms (all Jordan axioms).

My first objective was to replace the notorisous time-reversal invariant character of quantum mechanics with a covering irreversible mechanics. To do that, I had to break the symmetry of the Lie product under anti-Hermiticity, [A, B] = - [A, B]^+. After years of search during my graduate studies, Lie-admissible algebras turned out as being the best for such a physical objective, as it is still the case today, since Lie-admissible algebras are "structurally irreversible, in the sense that A, B) \ne - (A,B)^+. Copnsequently, time evolutions are distinctly different for motions forward and backward in time.

A second objective was the representation of interactions not derivable from a potential that, when combined with irreversibility, demand the :nonconservation of the energy. Lie-admissible algebras also assure that property since we generally have the energy releases to the environment of the type

(4) i dH/dt (H, H) = f(t) \ne 0.

Another objective was to indicate that Jordan's dream of physical applications, while notoriously impossible for Jordan algebras per se, becomes possible in broader Jordan-admissible algebras. In this way, rather than being useless in physics, Jordan algebra have a very deep role, particularly for the characterization of the irreversible component of scattering processes, that is still vastly unexplored to this day (see comments below).

In summer 1967 I left my chair in nuclear physics at the Avogadro Institute in Torino Italy, and moved with my young family to the University of Miami in Coral Gables, Florida, to discover that Lie-admissible/Jordan admissible algebras were completely unknown in the U. S. scientific community of the time, with the sole exception of the late mathematician Marvin Tomber (who subsequently became a good fiend of mine I still miss). Since I had a family to feed and shelter, I was forced to abandon the study of Lie-admissible/Jordan-admissible mechanics and pass to write Phys. Rev. papers which I did for a decade.

UNIVERSAL COVERING OF SUPERSYMMETRIES
When I became a member of Harvard University in 1977, I was requested by David Peaslee of the DOE to resume the study of Lie-admissible and Jordan-admissible mechanics which I did with great appreciation (I had met David during my preceding stay at MIT from 1974 to 1977 and informed him about the implications of the new irreversible mechanics, particularly for new energy processes, since they are notoriously irreversibe).

My first observation was that time evolution of supersymmetries or, equivalently, of (p, q)-deformations of Lie algebras, is characterized by a nonunitary transform. The second observation was that the action of such a transform on the dynamics produces the most general known algebra as commonly understood in mathematics (see the origination memoirs [2.3] of April 1978 subsequently formulated more rigorously in the monographs at Springer-Verlag [4] I wrote when at MIT, and initially released as MIT preprints, to be finalized when I was at Harvard, all works done under DOE support I keep appreciating)

(5) i dA/dt = (A, B)* = P(A, B)Q^+ = ARS - BSA = (ATB - BTA) + (AJB + BJA) =

= [A, B]* + {A, B}*, PP^+ \ne I, QQ^+ \ne I, PQ^+ \ne I,

(6) A(t) = [exp(i H S t)] A(0) [exp(- i t R H)]

with Lie-isotopic particularization ("isotopic" being referred to the verification of all abstract Lie axioms)

(7) i dA/dt = ATB - BTA) = [A, B]*

(8) A(t) = [exp(i H T t)] A(0) [exp(- i t T H)]

where now R, S, T, J, R \pm N are nonsinguar ooperators or matrices but otehrwise possess a totally unrestricted, non-linear non-local integro-differential and non-Hamiltonian functional dependence on all possible variables, including time t, coordinates r, velocities v, accelerations a, wavefunctions \psi, their derivatives, etc.

I also realized in the original memoirs [2,3] that the product (A,B)* of Eqs. (5) is "directly universal" in the sense of admitting all possible produces of an algebras (universality) without the need of transformations (direct universality). In fact, the algebra with product (A, B)* admits as particular cases: associative, Lie, Jordan, Lie-isotopic, Jordan-isotopic,, supersymmetric, Kac-Moody, nilpotent,flexible and any other possible algebras (defined as a set of elements equipped with a bilinear composition verifying the right and left distributive and scalar laws over a field of characteristic zero ).

Therefore, I proposed in memoirs [2.3] the construction of an irreversible covering of quantum mechanics (QM) under the name ofhadronic mechanics (HM), and proved in Section 5 of memoir [3] its application to particle physics via the representation, for the first time to my knowledge, of "all" characteristics of the \pi^o meson in its synthesis from an electron and a positron, e^+ + e^- => \pi^0

Colleagues should be aware that this result is impossible via QM because the rest energy of the \pi^0 is 133 MeV "bigger" than the sum of the rest energies of the electron and positrons, thus demanding a "positive binding energy" under which the Schroedinger equation becomes inconsistent. Section 5 of Ref. [3] essentially showed that a nonunitary lifting of the Schroedinger equations resolved the insufficiency of quQM thanks to the admission of "non, non, non" interactions due to total wave overlapping of the constituents, followed by the known annihilation.

I called the new mechanics "hadronic" for its primary intent of being applicable in the interior of hadrons, thus the interior of nuclei, stars, quasars and black holes, under the condition of recovering QM uniquely and identically for all exterior dynamics in vacuun, trivially achieved for R = S = T = I. More generally, HM recovers QM automatically, by constructioon, for all "exterior dynamical probles" (point-partices and elm waves propagating in empty space, thus solely admitting potential interactions) and solely applies for "interior dynamiocal probens" (extended, therefore deformable and nonspherical particles and elm waves propagating within physical media, thus admitting potential as well as "non, non, non" interactions).

The general Lie-admissible and Jordan-admissible equations (5), (6) were suggested for the treatment of irreversible events, while the simpler Lie-isotopic equations (70, (8) were suggested for reversible processes with "non, non, non" internal interactions, as it is the case for the synthesis of the \pi^0, the neutron and otehr hadrons. The rudiments of the Lie-admissible and Lie-isotopic coverings of Lie's theory (nowadays known as Santilli Lie-admissible and Lie-isotopic theories) were proposed in the first memoir [2] to as an evident necessary premise for phenomenological elaborations.

By recalling that special relativity and quantum mechanics are reversible over time, a widespread v20th century iew was that irreversibility is only "apparent" (sic!) because, when irreversible systems are reduced to their elementary constituents, irreversibility "disappears" (sic!), and one recovers nice QM particles in reversible conditions. By contrast, the first exercise I requested to my graduate students was the proof of the following

NO REDUCTION THEOREM: An irreversible system cannot be consistently reduced to a finite number of elementary constituents all in reversible conditions and, vice versa, a finite number of elementary particles all in reversible conditions cannot possibly characterize an irreversible system.

Lagrange and Hamilton proposed their historical equations with external terms (truncated during the 20th century to achieve compatibility with special relativity and quantum mechanics, but assued at the foundation of my works [4,10,11]) precisely to represent the irreversibility of nature. The above theorem implies that, rather than "disappearing" to fix things, irreversibility originates at the most ultimate and elementary level of nature, e.g., for a spaceship during reentry in atmosphere, irreversibility originates from the "non, non, non" interactions caused by the mutual penetration of the peripheral electron orbitals of the spaceship with corresponding electron orbitals of our atmosphere.

A point important to prevent embarking physics into another generation of experiments doomed to failures from their inception, is that the irreversibility of high energy inelastic scattering processes simply does not "disappear" with the reduction of the scattering region to nice hypothetical quarsks and other intermediate hypothetical particles all in reversible conditions and, consequently, said irreversibility must be addressed to prevent the waste of anotehr generation of studies.

THE LABORIOUS JOURNEY FOR MATURITY
The abiove steps released in April 1978 [2,3] were the initiation of a long journey that remains mostly unknown to colleagues in supersymmetries, dark matter and the like, to their peril. To prevent the indicated risk of another generation of failed efforts, I believe it is important that the scientific process underlying the construction of HM be subjected to collegial scrutiny because the problems apply to ALL nonunitary generalizations of QM, thus including most supersymmetric models, quantum gravity, etc.

As indicated above, the basic dynamical equations of HM are directly universal. Consequently, the Lie-admissible and Jordan-admissible characters are preserved under the most general known (non singular) nonunitary transforms, e.g.,

(9) P[(A, B)*]Q^+ = A' R' B' - B' S' A'

(10) A' = PAQ^+ , B' = PBQ^+,

(11) R' = (PQ^+)^-1 (PRQ^+) (PQ^+)^-1 ,

(12) S' = (PQ^+)^-1 (PSQ^+) (PQ^+)^-1

The first crucial point for the replacement of supersymmetries is that, even though algebraically magnificent, transformations (9) are a total disaster from a physical viewpoint. This is due to the fact that in an interior problem (think at the interior of a high energy scattering region) all conventional potential interactions are represented with the usual Hamiltonian H, while all "non, "non, non" interactions are represented with the R and S operators. Consequently, the maps R => R' and S => S' of Eqs. (11), (12), represent the transition from one event to another, e.g, from the Higgs boson to the neutralino or whatever else.

The second point important for the replacement of supersymmetries is the following. We physicists are accustomed to what I have called "the majestic axiomatic structure of quantum mechanics" because it assures: the preservation over time of the numerical value of the units used in measurement; the same numerical predictions under the same conditions at different times; the preservation of Hermiticity (thus observability) under the time evolution of the theoryl and other features crucial for physical consistency particularly needed in the conduction of experiments. Most colleagues assume that these majectic properties are preserved for whatever generalized theory we like! Unfortunately, this is not the case, as expressed by the following

INCONSISTENCY THEOREM (see Ref. [5] with large preecding literature): When formulated via the mathematics of quantum mechanics (Hilbert spaces over a field of complex numbers, etc.) nonunitary time evolutions are afflicted by the following inconsistencies:

1) Lack of preservation over time of the numerical value of the units used for measurements (from the very definition of a nonlinear transform);

2) Lack of prediction of the same numerical values under the same conditions at different times;

3) lack of preservation over time of Hermiticity, with consequential loss of observability (Lopez lemma); and others.

Any theory that deviates from the unitary character of the time evolution of QM, and is treated with the QM formalism, is afflicted by the above inconsistencies. This is the case also for supersymmetries since they generally require a deviation from the conventional unitary characterization of Lie's theory. This is a reason I had anticipated the recent experimental dismissal of supersymmeytries at CERN.

The resolution of the above catastrophic inconsistencies required indeed a long series of trials and errors over decades. In fact, the Lie-admissible / Jordan-admissible branch of HM reached maturity only recently in the 2006 memoir at Il Nuovo Cimento [6] thanks to the construction of a new mathematics specifically constructed for the scope at hand.

I cannot possibly review in an informal email the new mathematics and its resolution of the catastrophic inconsistencies (see the letures for the general physics audience of Level II in the WLS [9]). However, I believe that it is important to convey at least some central points. We all know how to formulate potential interactions in a way invariant over time. The new task is that of formulating in a way equally invariant over time interactions that are not representable with a Hamiltonian by central assumption. The results of decades of studies of this problem is the following.

The new "non, non, non" interactions are represented in HM by the R and S operators. The ONLY possible way to achieve the needed invariance is to embed them in generalized units since the units are the basic invariant of all possible theories. This simple condition led to the formulations of TWO new mathematics, first achieved in the mathematical memoir [7] of 1996, one with generalized unit (fw meaning forward)

(13) I^fw(t, r, v, a, \[so, \partial\psi,...) = 1 / S

with all products ordered to the right, representing motion forward in time, and a second mathematics with generalized unit (bw meaning backard

(14) bw^I(t, r, v, a, \psi, \partial\psi, ...) = 1 / R

and all products ordered to the left, representing motion backward in time. The difference of the above two units assures irreversibility. The entire mathematics of QM had to be reconstructed twice, one for motion forward and the second for motion backward in time. Let us recall that, despite their irreversibility, the total energy is conserved in deep inelastic scattering processes. Therefore, I have to recall for the non-expert in the field that Lie-admissible time evolutions elaborated with the old mathematics of Lie's theory evidently imply the non-conservation of the energy because i dH/dt - H(R + S)H \ne 0. However, when Lie-admissible theories are elaborated with their own mathematics, the total energy is indeed conserved because the term HRH computed with respect to the generalized unit bw^I = 1/R yields the same numerical results of the term HSH computed with respect to the generalized unit I^fw = 1/S, and we can write

(15) i dH/dt = (H, H)* = HRH_{1/R} - HSH_{1/S} = 0.

This occurrence can be best illustrated by nothing that the elaboration of Lie;\'s theory with the Lie-admissible mathematics is the same nonsense as elaborating Lie-admissible theories with Lie's mathematics.

The invariant formulation of the original parametric (p, q)-deformations of QM, Eqs. (2), (3), was achieved in the 1997 paper [8]. The invariant formulation of the universal, operator, (R, S)- Lie-admissible / Jordan-admissible equations required several additional years of work, and was achieved in the 2006 memoir [6].

The theoretical conclusion of my fifty years of studies in irreversibility are the following:

1) A broadening - covering of QM is unavoidable because the No Reduction Theorems prohibits the representation of interior structural problems via the riversible linear formalism of QM. The historical value of supersymmetries is their manifestation of such an inevitable advance.

2) The sole true broadenings of QM are those characterized by "non" unitary time evolutions, since all remaining presumed broadenings in reality belong to the unitary class of equivalence of QM.

3) The only axiomatically consistent nonunitary broadening of QM that bypasses the inconsistency theorems is HM in its various branches [9]. In view of the direct universality of Lie-admissible / Jordan-admissible algebras, any claim of novelty over HM is vacuous.

I should indicate that most irreversible processes can be studied in good first approximation via the simpler Lie-isotopuc formalism of HM, and then pass to a full Lie-admissible / Jordan-admissible treatment. as An illusytrtation, the propaghation of light within physical media can be consistently studied via the Kie-isotopuc formalism becaiuse the additional Jordan-isotopic contribition solely represent the dispersion of the beam considered.

Colleagues interested in acquitting a technical knowledge of the field, may first listen to the series of lectures [9], then inspect the detailed presentation in Ref.s [10] with upgrade and experimental verifications in monographs [11].

I should indicate that a large number of mathematicians, theoreticians and experimentalists have contributed to the study of Lie-admissible / Jordan-admissible and their Lie-isotopic particularization (see the 50 pages long bibliography in Vol. I of Ref. [11]).

I can only mention here the initiation in the 1990s by John Ellis and his group at CERN [12] of irreversible, Lie-admissible studies of the structure of astrophysical bodies. It is unfortunate that, for some reason, John did not continued these studies, thus preventing astrophysics from passing to the inevitable higher level of direct compatibility with thermodynamical laws 6]. The continuation of these stiudies would also have promoted a bigger awareness at CERN of the need serious consideration of irreversible contributions in the notoriously irreversible, high energuy particle experiments.

I finally mention the work by Steven Adler [13] who, immediately following the the appearance of memoirs [2.3], essentially proposed the study of the Lie-admissible covering of supersymmetries. Hence, even though supersymmetries were identified as particular cases of Lie-admissible algebras in Refs. [2.3], the origination of the proposal of this email (replace supersymmetries with Lie-admissible theories) can be identified as being due to Steven Adler in 1978. It is also unfortunate for particle physics, as well as for his people and for the IAS in Princeton, that, for some reason, Steven too halted his research in the field immediately following the appearance of the imortnt paper [13]. In fact, by knowing Steven's capability, had him continued the research in the field, particle physics would be nowadays at a much more advanced stage.

EXPERIMENTAL IMPLICATIONS
The most important lesson that should be gained from the recent experimental dismissal at CERN of supersymmetries and related conjectures is that particle physics laboratories should hereon no longer spend public money in testing theories that are catastrophically inconsistent on dynamical grounds, particularly when the theory to be tested is unable to predict the same numerical values under the same conditions at different times. The inconsistency theorems for nonunitary extensions of quantum theory have been published in various refereed journals and, therefore, the fact that they are not widely spoken, does not void hereon their existence.

Once the axiomatic consistency of a nonunitary theory has been verified by theoreticians, experimentalists have to face a number of rather radical and simply unavoidable departures from conventional, 20-th century, experimental settings, such as:

1) Absence of new particles.
The continued 20th century process of trying to predict new particles and then attempting their experimental verifications is halted by Lie-isotopic or Lie-admissible formulations because they provide a more detailed representation of processes without any need for new particles. The best illustration is the first known, quantitative, time invariant representation of "all" characteristics of the neutrons in its synthesis from a proton and an electron in the core of stars (see review [14] for both nonrelativistic and relativistic derivation and original literature quoted therein). This representation is another case for which HM was proposed [2,3] because QM provides no quantitative treatment due to the fact that the mass of the neutron is bigger than the sum of the masses of the proton and the electron, thus calling for a "positive binding energy" which is anathema for QM. In Ref. [15] I was forced to introduce the "etherino" under repeated stressing that it does not refer to a new hypothetical particle but solely represent the "process" of transferring the missing energy, spin and other quantities from the environment to the neutrinos. Quarks are reduced to what they are, mathematical representation necessary for the excellent SU(3)-color Mendeleev-type classification of hadron. The point is that quarks cannot be even defined in spacetime, thus stimulatig a "necessary return to sanity in physics" (as stated by Karl Popper following the appearace of Refs. [2.3]). It is hoped that the recent experimental disproof at CERN on supersymmetries signals the end of the now futile search for new hypothetical particles.

2) Mutation of intrinsic characteristics.
Lie-isotopic and Lie-admissible formulations require a revision of the numerical value of the masses of hypothetical particles mediating high energy scattering processes, because nonunitary interactions imply new renormalization (called mutations) of all intrinsic characteristics of particles, beginning with their mass, but also including spin and other characteristics. In plain language, I exclude that an electron in the core of a black hole has the same characteristics as those when rotating in vacuum around a proton in the hydrogen structure (that would imply perpetual motion within physical media!). To conduct studies that may resist the test of time, I have to identify the most general possible deviations of conventional intrinsic characteristics in interior conditions and make final selection depending on experimental result, rather than preset theologies. In short, the very value of the mass of the Higgs boson, let alone its existence, is in doubt once we admit the reality of "non, non, non" interactsions in the interior of the scattering region due to the absence in nature of "point-like wavepackets," as onfirmed by 96% of the experimental results at CERN analyzed so far. This second implication is best identified by the covering scattering theory of hadronic mechanics studied in details at the 2011 Nepal International Conference on Lie-admissibille Treatment of Irreversible processes (see the five papers by Santilli and Animalu in Proceedings [16]).

3) Frequency shifts without relative motion. My former colleague at Harvard, Halton Arp, discovered in the 1970s quasars physically connected to associated galaxies, yet with dramatically different cosmological redshift [17], thus providing evident of clear violations of Einstein special relativity in cosmology (under which validity, quasars and galaxies should have been separated billions of years ago). The isotopies of spacetime symmetries (known as the Galilei-Santilli (GS) or the Lorentz-Poincare'-Santilli (LPS) isosymmetries [10], see also Lecture IIIA of WLS [9]) predict the existence of a redshift of the frequency of light propagating within physical media at low temperature without any relative motion 9first proposed in Ref. [18] of 1991) by providing a time invariant, causal and numerical representation of the different redshifts in Arp's associated quasars-galaxies [19]. Following two decades of dismissal by laboratories around the world to test my 1991 predictions of anomalous shift, I conducted the experiment myself in a 60 feet long pressure tube [20] (see also Ref.s [21,22]). This anomalous shift has now been independently verified as merely consisting in the release of energy by light to the medium at low temperature (IsoRedShift), or in the gain of energy by light from the medium when at high temperature (IsoBlueShift) [23,24]. This provides a numerically exact and time invariant representation of the dynamics of galactic stars as due to energy loss by light to the innergalactic medium, without any need for the hypothetical dark matter (that, debides derailing tye attention from the evident departure from special relativity, has not represented the intended data in clear terms). The redness of the Sun at Sunset has been experimentally established as being due to IsoRedShift in our atmosphere without any relative motion, thus eliminating the universe expansion, acceleration of the expansion and the big bang (all mandating a return to the Middle Ages with Earth at the center of the universe to maintain the validity of special relativity in cosmology). The elimination of dark energy is based on the IsoBlueShift of light and its implication that the total energy of the universe is about 80 times that believed until now, without any need of the hypothetical dark energy (that, in any case, according to Einstein gravitation, would imply the contraction rather than the acceleration of the expansion of the universe)/ All these and other advances studied at our forthcoming meeting http://www.workshops-hadronic-mechanics.org/ suggesting a much needed return to sanity in astrophysics and cosmology.

4) Arbitrary speeds of light.
Another implication of the LPS isosymmetry is the prediction of completely arbitrary speeds of light within physical media in a fully causal and time invariant way [18,10]. This prediction has been experimentally confirmed by the pioneering tests conducted by Enders and G. Nimtz [25,26] via the transmission of elm waves at speed bigger than c when propagating within certain guides, thus within a physical medium. The same preduction of arbitrary speeds bigger than c has been confirmed by ALL fits of experimental data in particle physics (see Vol. IV of Ref. [11]). It should be noted that this aspects is achieved by preserving the quantized "absorption" of light for suitable frequencies as stated by Einstein, but on the impossibility of reducing any elm waves to photons during its "propagation" within a physical medium because excessive insufficiencies, such as inability to represent quantitatively: the angle of refraction; the reduction by anput 1/3 of the speed; the propagation along a straight line with minimal diffusion; the diffraction; etc., besdes the inability of reducing to photons elm waves with large wavelength that mandates a return to the Maxwellian conception of light as a wave with local speed C = c/n.

5) Surpassing special relativity.
Even though not admitted for some reason, supersymmetries do imply a structural surpassing of special relativity because the application of their time evolution to relativity axioms implies their broadening. The replacement of supersymmetries with Lie-isotopic or Lie-admissible theories renders mandatory the surpassing of special relativity within physical media (only!) in favor of a covering formulation. By recalling that no change of light is conceivably possible without an alteration of spacetime, the most fundamental implication of the studies herein considered is that the presence of matter (or energy) implies a structural change of spacetime characterized by the mutation of the Minkowski metric into the most general known symmetric metric in (3+1)-dimensions under the universal Lorentz-Poincare'-Santilli isosymmetry that that provides the invariance as particular cases Minkowskian, Riemannian, Finslerian and any otehr geometry ion (3+1)-dimension (Lecture IIIA [9], and refs. [10,18]). All aspects considered above, as well as in the about 20,000 pages of publications to date, are a mere consequence of this primitive geometric aspect. Einstein stated quite clearly that his theory was valid under the following three conditions: A) for point particles and elm waves; B) moving in empty space; and C) referred to inertial systems. By maintaining the exact validity of special relativity under these conditions (e,g., for atomic structures, particles in accelerators, etc.), it is time for physics laboratories to admit that the violation of any one of conditions A, B, C implies the inapplicability of special relativity as technically discussed by experimentalists at the forthcoming San Marino meeting. This implies that special relativity in its 20th century formulation is nowhere exact for the interior of hadrons as well as of high energy particle experiments (see Vol.IV of Refs. [11] for numerous experimental fits). Even at the astrophysical level, the above evidence implies that special relativity (also in its 20th century formulation) is nowhere applicable in the universe, because intergalactic and innergalactic spaces are physical media, while matter stars, quasars and black holes constitute physical media of high density. The inapplicability of special relativity for antimatter stars, quasars and black holes is established by numerous evdience, such as the lack of any distinction between neutral matter and antimatter and otehr insufficiencies [27]. After all, to prevent the abuse of the name of Albert Einstein, colleagues are expected to admit that antimatter was discovered years following the formulation of special relativity. What the physics community does not appear to have understood (with due numerous exceptions) and, if so, not to have appreciated to its peril, is that, rather than abusing the name of Albert E Einstein for conditions dramatically beyond those of the original conception and experimental verification, I have honored Albert Einstein by preserving his axioms at the abstract level and broadening the conditions of their applicability via broader "realizations" permitted by new mathematics specifically built in His Honor.

REFERENCE

[1] R. M. Santilli, Nuovo Cimento {\bf 51}, 570 (1967), available in free download from the link\\ http://www.santilli-foundation.org/docs/Santilli-54.pdf

[2] R. M. Santilli, " Hadronic J. {\bf 1}, 223-423 (1978), available in free pdf download from \\ http://www.santilli-foundation.org/docs/Santilli-58.pdf

[3] R. M. Santilli, Hadronic J. {\bf 1}, 574-901 (1978), available in free pdf download from \\ http://www.santilli-foundation.org/docs/Santilli-73.pdf

{4] R. M. Santilli, {\it Foundation of Theoretical Mechanics,} Volume I (1978) [10a], and Volume II (1982) [10b], Springer-Verlag, Heidelberg, Germany, available as free download from\\
http://www.santilli-foundation.org/docs/Santilli-209.pdf \\ http://www.santilli-foundation.org/docs/santilli-69.pdf
[5] R. M. Santilli, Intern. J. Modern Phys. {\bf 14}, 3157 (1999, available as free download from\\ http://www.santilli-foundation.org/docs/Santilli-104.pdf

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

[7] R. ~M.~Santilli, Rendiconti Circolo Matematico Palermo, Suppl. {\bf 42}, 7-82 (1996), available as free download from\\
http://www.santilli-foundation.org/docs/Santilli-37.pdf

[8] R. M. Santilli, Found. Phys. {\bf 27}, 1159 (1997), available in free pdf download from the link \\ http://www.santilli-foundation.org/docs/Santilli-06.pdf

[9] J.Pace, Chairman, World Lecture series
http://www.world-lecture-series.org/

[10] R. M. Santilli, {\it Elements of Hadronic Mechanics}, Vol. I and II (1995), Second Edition, Academy of Sciences
http://www.santilli-foundation.org/docs/Santilli-300.pdf\\
http://www.santilli-foundation.org/docs/Santilli-301.pdf

[11] R. M. Santilli, {\it Hadronic Mathematics, Mechanics and Chemistry,}, Vols. I, II, III, IV, and V, international academnioc press, (2008), http://www.i-b-r.org/Hadronic-Mechanics.htm

[12] J. Ellis, N. E. Mavromatos and D. V. Nanopoulos in Proceedings of the Erice Summer School, 31st Course: From Superstrings to the Origin of Space-Time, World Scientific (1996).

[13] S. Adler, Phys. Rev. 17, 3212 (1978)

[14] J. V. Kadeisvili, "The Rutherford-Santilli neutron." html version http://www.i-b-r.org/Rutherford-Santilli-neutron.htm free pdf downloadhttp://www.i-b-r.org/Rutherford-Santilli-II.pdf "> http://www.i-b-r.org/Rutherford-Santilli-II.pdf

[15] R. M. Santilli "The etherino and the neutrino hypothesis," Found. Phys 2007; 37, 670, http://www.santilli-foundation.org/docs/EtherinoFoundPhys.pdf

[16] C. Corda, Editor, Proceedings of the Third International Conference on the Lie-admissible Treatment of irreversible processes,Kathmandu University, Ne[pal, 2011
http://www.santilli-foundation.org/docs/Nepal-2011.pdf

[17] H. Arp, Frontiers of Fundamental Physics, Barone M. and Selleri F. editors. Plenum 1994.

[18] R. M. Santilli, {\it Isotopic Generalizations of Galilei and Einstein Relativities,} Vol.~I (1991) [12a] and Vol. ~II (1991) [12b], Hadronic Press, Palm Harbor, Florida, available in free pdf download from\\
http://www.santilli-foundation.org/docs/Santilli-01.pdf\\
http://www.santilli-foundation.org/docs/Santilli-61.pdf

[19] R. Mignani, "Quasars redshifts in iso-Minkowski spaces," Physics Essay 1992; 5, 531, http://www.santilli-foundation.org/docs/Santilli-31.pdf

[8] R. Mignani, "Quasars redshifts in iso-Minkowski spaces," Physics Essay 1992; 5, 531,
http://www.santilli-foundation.org/docs/Santilli-31.pdf

[20] R. M. Santilli, The Open Astronomy Journal, 2010, Vol. 3, page 1-43m
http://www.santilli-foundation.org/docs/Santilli-isoredshift.pdf

[21] R. M. Santilli, Contributed paper in the Proceedings of the International Conference on Numerical Analysis and Applied Mathematics,Rhodes, Greece, September 19-25, 2010, T. E. Simos, Editor, AIP Conference Proceedings Vol. 1281, pp. 882-885 (2010) http://www.santilli-foundation.org/docs/Isoredshift-Letter.pdf

[22] R. M. Santilli, Contributed paper in Cosmology, Quantum Vacuum, and Zeta Functions, Diego Saez-Gomez, Sergei Odintsov Sebastia Xambo Editors, Springer, 2011.
http://www.santilli-foundation.org/docs/Isominkowskian-Geom.

[23] R. Anderson, "Confirmation of Santilli IsoRedShift and IsoBlueShift,"
http://www.santilli-foundation.org/icnf.html

[24] G. West and G. Amato, "Independent experimental confirmation of Santilli IsoRedShift and IsoBlueShift," to ppears as lecturte in WLS [9] as well as in the proceedings of the 2011 San marino Workshop.

[25] A. Enders and G. Nimtz, "On superluminal barrier traversal," Journal Phys 1. France 2 (1992), 1693-1698.

]26] G. Nimta, D"Do evaniscent modes violate relativistic causalituy?" Lectures Notes in OPhysics, Springer-Verlag, Berlin-Heidelberg (2006).}

[27] R. M. Santilli, {\it Isodual Theory of Antimatter with Applications to Antigravity, Grand Unifications and Cosmology,} Springer (2006).

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