Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of ordinary (...) fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications. (shrink)

In this note we outline the history of q-deformations, indicate their physical shortcomings, suggest their apparent resolution via an invariant Lie-admissible formulation based on a new mathematics of genotopic type, and point out their expected physical significance.

We identify new, rather serious, physical and mathematical inconsistencies of the current formulation of noncanonical or nonunitary string theories due to the lack of invariant units necessary for consistent measurements, lack of preservation in time of Hermiticity-observability, and other shortcomings. We propose three novel reformulations of string theories for matter of progressively increasing complexity via the novel iso-, geno-, and hyper-mathematics of hadronic mechanics, which resolve the current inconsistencies, while offering new intriguing possibilities, such as: an axiomatically consistent and invariant (...) inclusion of gravity, the reduction of macroscopic irreversibility to the most primitive level of vibrations of the universal substratum (ether), or the treatment of multi-valued, irreducible, biological structures. We then identify three corresponding classical formulations of string theories for antimatter via the novel anti-isomorphic isodual mathematics. We finally outline the intriguing features of the emerging new cosmologies (including biological structures, as it should be for all cosmologies), such as: universal invariance (rather than covariance) under a symmetry isomorphic to the Poincaré group and its isodual; equal distributions of matter and antimatter in the universe (as a limit case); continuous creation; no need for the missing mass; significantly reduced dimensions; possibility of experimental identification of antimatter in the universe; identically null total characteristics of time, energy, linear and angular momentum, charge, etc.; and other intriguing features. (shrink)

The most majestic scientific achievement, of this century in mathematical beauty, axiomatic consistency, and experimental verifications has been special relativity with its unitary structure at the operator level, and canonical structure at the classical levels, which has turned out to be exactly valid for point particles moving in the homogenenous and isotropic vacuum (exterior dynamical problems). In recent decades a number of authors have studied nonunitary and noncanonical theories, here generally calleddeformations for the representation of broader conditions, such as extended (...) and deformable particles moving within inhomogeneous and anisotrophic physical media (interior dynamical problems). In this paper we show that nonunitary deformations, including, q-, k-, quatum-, Lie-isotopic, Lie-admissible, and other deformations, even thoughmathematically correct, have a number of problematic aspects ofphysical character when formulated on conventional spaces over conditional fields, such as lack of invariance of the basic space-time units, ambiguous applicability to measurements, loss of Hermiticity-observability in time, lack of invariant numerical predictions, loss of the axions of special relativity, and others. We then show that the classical noncanonical counterparts of the above nonunitary deformations are equally afflicted by corresponding problems of physical consistency. We also show that the contemporary formulation of gravity is afflicted by similar problematic aspects because Riemannian spaces are noncanonical deformations of Minkowskian spaces, thus having noninvariant space-time units. We then point out that new mathematical methods, calledisotopies, genotopies, hyperstructures and their isoduals, offer the possibilities of constructing a nonunitary theory, known asrelativistic hadronic mechanics which: (1) is as axiomatically consistent as relativistic quantum mechanics, (2) preserves the abstract axioms of special relativity, and (3) results in a completion of the conventional mechanics much along the celebrated Einstein-Podolski-Rosen argument. A number of novel applications are indicated, such as a geometric unification of the special and general relativity via the isominkowskian geometry in which the two relativities are differentiated via the invariant basic unit, while preserving conventional Riemannian metrics, Einstein's field equations, and related experimental verifications; a novel operator form of gravity verifying the axioms of relativistic quantum mechanics under the universal isopoincaré symmetry; a new structure model of hadrons with conventional massive particles as physical constituents which is compatile with composite quarks and with established unitary classifications; and other novels applications in nuclear physics, astrophysics, theoretical biology, and other fields. The paper ends with the proposal of a number of new experiments, some of which may imply new practical applications, such as conceivable new forms of recycling nuclear waste. The achievement of axiomatic consistency in the study of the above physical problems has been possible for the first time in this paper thanks to mathematical advances that recently appeared in a special issue of theRendiconti Circolo Matematico Palermo, and in other journals identified in the Acknowledgements. (shrink)

By using a language as accessible to as broad an audience as possible, in this paper we identify serious insufficiencies of the neutrino and quark hypotheses for the synthesis of the neutrons from protons and electrons inside stars according to the familiar reaction ${{\rm p}^+ + \bar {\nu} + {\rm e}^-\rightarrow {\rm n}}$ . We introduce, apparently for the first time, the hypothesis that the energy and spin needed for the synthesis of the neutron originate either from the environment or (...) from the ether conceived as a universal medium with very high energy density via an entity here called etherino, denoted with the letter “a” (from the Latin aether), carrying mass and charge 0, spin ${1\over 2}$ and 0.78 MeV energy according to the synthesis ${{\rm p}^+ + {\rm a} + {\rm e}^-\rightarrow {\rm n}}$ . We identify the compatibility ${{\rm p}^+ + {\rm a} + {\rm e}^-\rightarrow {\rm n}\rightarrow {\rm p}^+ + {\rm e}^- + \bar \nu}$ and the incompatibility condition ${{\rm p}^+ + {\rm a} + {\rm e}^-\rightarrow {\rm n}\rightarrow {\rm p}^+ + {\rm e}^- + \bar{{\rm a}}}$ of the neutrino and etherino hypotheses, the latter representing the possible return of missing features to the ether, without being necessarily in conflict with neutrino experiments. We review the new structure model of the neutron and hadrons at large with massive physical constituents produced free in the spontaneous decays as permitted by the covering hadronic mechanics. We show its compatibility with the standard model when interpreted as only providing the final Mendeleev-type classification of hadrons. We point out basically new clean energies predicted by the new model. We indicate new experiments confirming the above studies although in a preliminary form. Finally, we conclude with the proposal of new experiments suggested for the much needed search of new clean energies. (shrink)

The objective of this paper is to present an outline of a number of criticisms of the quark models of hadron structure which have been present in the community of basic research for some time. The hope is that quark supporters will consider these criticisms and present possible counterarguments for a scientifically effective resolution of the issues. In particular, it is submitted that the problem of whether quarks exist as physical particles necessarily calls for the prior theoretical and experimental resolution (...) of the question of the validity or invalidity, for hadronic structure, of the relativity and quantum mechanical laws established for atomic structure. The current theoretical studies leading to the conclusion that they are invalid are considered, together with the experimental situation. We also recall the doubts by Einstein, Fermi, Jordan, and others on the final character of contemporary physical knowledge. Most of all, this paper is an appeal to young minds of all ages. The possible invalidity for the strong interactions of the physical laws of the electromagnetic interactions, rather than constituting a scientific drawback, represents instead an invaluable impetus toward the search for covering laws specifically conceived for hadronic structure and strong interactions in general, a program which has already been initiated by a number of researchers. In turn, this situation appears to have all the ingredients for a new scientific renaissance, perhaps comparable to that of the early part of this century. (shrink)