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 SantilliThe Institute for Basic Research, Florida, U.S.A. basicresearch@ibr.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
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
Workshop Aim
Experimental Confirmation of Santilli IsoShifts
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
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 nonnu scalars (see below for matrices) and the product AB is associative.
Time evolutions of type (1) are a particular case of the Lieadmissible and Jordanadmissible 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 qdeformations (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 qdeformation 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 Lieadmissible (Jordanadmissible) 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 timereversal invariant character of quantum mechanics with a covering irreversible mechanics. To do that, I had to break the symmetry of the Lie product under antiHermiticity, [A, B] =  [A, B]^+. After years of search during my graduate studies, Lieadmissible algebras turned out as being the best for such a physical objective, as it is still the case today, since Lieadmissible 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. Lieadmissible 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 Jordanadmissible 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 Lieadmissible/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 Lieadmissible/Jordanadmissible mechanics and pass to write Phys. Rev. papers which I did for a decade.
UNIVERSAL COVERING OF SUPERSYMMETRIES
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 SpringerVerlag [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 Lieisotopic 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, nonlinear nonlocal integrodifferential and nonHamiltonian 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, Lieisotopic, Jordanisotopic,, supersymmetric, KacMoody, 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" (pointpartices 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 Lieadmissible and Jordanadmissible equations (5), (6) were suggested for the treatment of irreversible events, while the simpler Lieisotopic 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 Lieadmissible and Lieisotopic coverings of Lie's theory (nowadays known as Santilli Lieadmissible and Lieisotopic 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
As indicated above, the basic dynamical equations of HM are directly universal. Consequently, the Lieadmissible and Jordanadmissible 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 Lieadmissible / Jordanadmissible 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 nonexpert in the field that Lieadmissible time evolutions elaborated with the old mathematics of Lie's theory evidently imply the nonconservation of the energy because i dH/dt  H(R + S)H \ne 0. However, when Lieadmissible 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 Lieadmissible mathematics is the same nonsense as elaborating Lieadmissible 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) Lieadmissible / Jordanadmissible 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 Lieadmissible / Jordanadmissible 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 Lieisotopuc formalism of HM, and then pass to a full Lieadmissible / Jordanadmissible treatment. as An illusytrtation, the propaghation of light within physical media can be consistently studied via the Kieisotopuc formalism becaiuse the additional Jordanisotopic 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 Lieadmissible / Jordanadmissible and their Lieisotopic 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, Lieadmissible 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 Lieadmissible covering of supersymmetries. Hence, even though supersymmetries were identified as particular cases of Lieadmissible algebras in Refs. [2.3], the origination of the proposal of this email (replace supersymmetries with Lieadmissible 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
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, 20th century, experimental settings, such as:
1) Absence of new particles.
2) Mutation of intrinsic characteristics.
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 GalileiSantilli (GS) or the LorentzPoincare'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 quasarsgalaxies [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.workshopshadronicmechanics.org/ suggesting a much needed return to sanity in astrophysics and cosmology.
4) Arbitrary speeds of light.
5) Surpassing special relativity.
REFERENCE
[1] R. M. Santilli, Nuovo Cimento {\bf 51}, 570 (1967), available in free download from the link\\ http://www.santillifoundation.org/docs/Santilli54.pdf
[2] R. M. Santilli, " Hadronic J. {\bf 1}, 223423 (1978), available in free pdf download from \\
http://www.santillifoundation.org/docs/Santilli58.pdf
[3] R. M. Santilli, Hadronic J. {\bf 1}, 574901 (1978), available in free pdf download from \\
http://www.santillifoundation.org/docs/Santilli73.pdf
{4] R. M. Santilli, {\it Foundation of Theoretical Mechanics,} Volume I (1978) [10a], and Volume II (1982) [10b], SpringerVerlag, Heidelberg, Germany, available as free download from\\
[6] R. M. Santilli, ''Lieadmissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B {bf 121}, 443 (2006),
http://www.santillifoundation.org/docs/LieadmissNCBI.pdf
[7] R. ~M.~Santilli, Rendiconti Circolo Matematico Palermo, Suppl. {\bf 42}, 782 (1996), available as free download from\\
[8] R. M. Santilli, Found. Phys. {\bf 27}, 1159 (1997), available in free pdf download from the link \\ http://www.santillifoundation.org/docs/Santilli06.pdf
[9] J.Pace, Chairman, World Lecture series
[10] R. M. Santilli, {\it Elements of Hadronic Mechanics},
Vol. I and II (1995), Second Edition,
Academy of Sciences
[11] R. M. Santilli, {\it Hadronic Mathematics, Mechanics and Chemistry,}, Vols. I, II, III, IV, and V, international academnioc press, (2008),
http://www.ibr.org/HadronicMechanics.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 SpaceTime, World Scientific (1996).
[13] S. Adler, Phys. Rev. 17, 3212 (1978)
[14] J. V. Kadeisvili, "The RutherfordSantilli neutron." html version
http://www.ibr.org/RutherfordSantillineutron.htm free pdf downloadhttp://www.ibr.org/RutherfordSantilliII.pdf "> http://www.ibr.org/RutherfordSantilliII.pdf
[15] R. M. Santilli "The etherino and the neutrino hypothesis," Found. Phys 2007; 37, 670,
http://www.santillifoundation.org/docs/EtherinoFoundPhys.pdf
[16] C. Corda, Editor, Proceedings of the Third International Conference on the Lieadmissible Treatment of irreversible processes,Kathmandu University, Ne[pal, 2011
[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\\
[19] R. Mignani, "Quasars redshifts in isoMinkowski spaces," Physics Essay 1992; 5, 531,
http://www.santillifoundation.org/docs/Santilli31.pdf
[8] R. Mignani, "Quasars redshifts in isoMinkowski spaces," Physics Essay 1992; 5, 531,
[20] R. M. Santilli, The Open Astronomy Journal, 2010, Vol. 3, page 143m
[21] R. M. Santilli, Contributed paper in the Proceedings of the International Conference on Numerical Analysis and Applied Mathematics,Rhodes, Greece, September 1925, 2010, T. E. Simos, Editor, AIP Conference Proceedings Vol. 1281, pp. 882885 (2010)
http://www.santillifoundation.org/docs/IsoredshiftLetter.pdf
[22] R. M. Santilli, Contributed paper in Cosmology, Quantum Vacuum, and Zeta Functions,
Diego SaezGomez, Sergei Odintsov Sebastia Xambo Editors, Springer, 2011.
[23] R. Anderson, "Confirmation of Santilli IsoRedShift and IsoBlueShift,"
[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), 16931698.
]26] G. Nimta, D"Do evaniscent modes violate relativistic causalituy?" Lectures Notes in OPhysics, SpringerVerlag, BerlinHeidelberg (2006).}
[27] R. M. Santilli, {\it Isodual Theory of Antimatter with Applications to Antigravity, Grand
Unifications and Cosmology,} Springer (2006).
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