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Santilli's Isodual Mathematics and Physics for Antimatter American Journal of Modern Physics 2014; X(X): XX-XX Published online MM DD 2014 (http://www.sciencepublishinggroup.com/j/ajmp) doi: 10.11648/j.XXXX.2014XXXX.XX ISSN: 2326-8867 (Print); ISSN: 2326-8891 (Online) Santilli’s Isodual Mathematics and Physics for Antimatter P. M. Bhujbal Department of Physics, Nutan Adarsh Arts, Commerce and Smt. Maniben Harilal Wegad Science College, Umrer-441203, India. Email address: [email protected] (P. M. Bhujbal) To cite this article: P. M. Bhujbal. Santilli’s Isodual Physics for Antimatter. American Journal of Modern Physics. Special Issue: Issue II: Foundations of Hadronic Mechanics. Vol. X, No. X, 2014, pp. XX-XX. doi: 10.11648/j.XXXX.2014XXXX.XX Abstract: In this paper, we study the isodual branch of hadronic mechanics achieved by the Italian-American scientist R. M. Santilli following decades of research. We show that, thanks to the background isodual mathematics (whose knowledge is assumed), Santilli’s isodual theory of antimatter appears to be the only axiomatically consistent and time invariant theory permitting a {\it classical} representation of {\it neutral} (as well as charged) antimatter whose operator image is equivalent to charge conjugation, thus verifying all known experimental data in the field. We then show the important prediction of {\it gravitational repulsion} between matter and antimatter, with particular reference to the prediction that light emitted by antimatter, known as {\it isodual light,} experiences gravitational repulsion when in the field of matter. We finally point out that recent detections of antimatter galaxies via Santilli telescope with concave lenses may eventually result to be the first experimental evidence of antigravity. Keywords: antimatter, isodual light, antigravity PACS: 03.65.Ta; 14.60.Cd; 29.30.-h 1. Introduction identify a map which possesses the main After being conjectured by A. Schuster in 1898, mathematical structure of charge conjugation, yet it is antimatter was predicted by P. A. M. Dirac [1] in the applicable at all levels, and not solely at the operator late 1920's in the negative-energy solutions of his level. celebrated equation. Dirac himself soon discovered The main characteristic of charge conjugation is that particles with negative-energy do not behave in a that of being antiautomorphic (where the term physical way and, for this reason, he submitted his “automorphic" is referred to the map of a given space celebrated “hole theory," which subsequently onto itself). After studying a number of possibilities, restricted the study of antimatter to the sole level of Santilli has selected a map which is anti-isomorphic second quantization [2]. This occurrence created an (where the term “isomorphic" is referred to a map imbalance in the physics of this century because from one space onto another of equivalent matter is described at all levels of study, from topological characteristics to be identified later on) Newtonian mechanics to quantum field theory, while applicable at all levels of study, and given by the antimatter is solely treated at the level of second following isodual map here generically expressed to quantization. an arbitrary quantity Q (i.e. a function, or a matrix or an operator) To initiate the study for the future removal of d d d † † † this imbalance in due time, Santilli presented a theory Q(x, φ, …) à Q (x , φ , …) = −Q (−x , −φ , …) (1) of antimatter which has been conceived to begin at which, for consistency, must be applied to the totality the purely classical Newtonian level, and then to of the mathematical structure of the conventional admit corresponding images at all subsequent levels theory of matter, including numbers, fields, spaces, of study [3] in which the guiding principle is to geometries, algebras, etc. This results in a new mathematics, called isodual mathematics, which is at 2 P. M. Bhujbal.: Santilli’s Isodual Mathematics and Physics for Antimatter the foundation of the classical isodual theory of been identified in [8-10]. The need for a systematic antimatter of this paper. study aiming at a resolution of these issues is then The isodual map was first proposed by Santilli beyond scientific doubts. [4] in 1985 and then remained ignored for several The isodual theory emerged from the years. According to it the isoduality can be identification of negative units in the antiparticle represented as + l à ld = - l. The first hypothesis component of the conventional Dirac equation and on the isodual theory of antimatter appeared for the the reconstruction of the theory with respect to that operator version in 1993 [5] which also contains an unit. Isoduality therefore provides a mere initial study of the equivalence between isoduality reinterpretation of Dirac's original notion of and charge conjugation. The prediction of the isodual antiparticle, while leaving all numerical predictions theory that antimatter in the field of matter under electroweak interactions essentially unchanged. experiences antigravity was first submitted in 1994 Santilli was able to construct the isodual theory of [6] which also proposed an experiment for the antimatter which characterizes antimatter at all measure of the gravity of elementary antiparticles in possible levels, from Newtonian mechanics to second the gravitational field of earth. The experiment quantization on the basis of his isodual mathematics essentially consists of comparative measurements [11-13]. under the gravity of collimated, low energy beams of In particular, isodual mathematics permitted the positrons and electrons in horizontal flight on a tube first known geometrically consistent representation of with sufficiently high vacuum as well as protection the gravitational field of a neutral antimatter body via from stray and patch fields and of sufficient length to the Riemann-Santilli isodual geometry defined over permit a definite result, e.g. the view by the naked isodual fields [11, 13]. eye of the displacements due to gravity of the It should be stressed that the isodual theory of positron and electron beams on a scintillator at the antimatter requires, for consistency requirement, the end of the flight. conjugation of all physical quantities of matter as Theoretical and experimental studies on the well as, most importantly, all their units of isodual theory of antimatter were conducted at the measurements. Consequently, antimatter evolves International Workshop on Antimatter Gravity and along a time moving backward, the td = - t, and has Anti-Hydrogen Atom Spectroscopy, held in Sepino, negative-definite energy Ed = - E along Dirac's Italy, in May 1996 [7]. original conception [14]. The historical The motivations for the classical isodual theory inconsistencies are resolved via the joint conjunction of antimatter are rather numerous. First, there is the of the related units; in fact, negative time and need indicated earlier to achieve a full equivalence in negative energy referred to negative units of time and the treatment of matter and antimatter beginning at energy are as causal as our positive time and energies the classical level. In fact, far away galaxies and referred to positive units of time and energy. quasars may well be made up of antimatter. The Eventually, in this paper the author tried to focus absence of a classical theory of antimatter therefore on some important features of Santilli’s Isodual implies the evident impossibility of quantitative Physics for antimatter based on Santilli’s Isodual studies of this important astrophysical issue. Mathematics. Second, the current gravitational treatment of antimatter is afflicted by a number of problematic aspects. Current theories are based on only one map 2. Salient Features of Santilli’s from classical to operator settings, the naive or Isodual Mathematics symplectic quantization. Therefore, conventional The Newton's equations, Galileo's relativity and classical representations of antimatter via positive Einstein's special and general relativities were energies do not yield antiparticles under quantization, conceived before the discovery of antimatter and but conventional particles with the mere reversal of therefore no classical representation of “neutral” the sign of the charge. antimatter could be generated since at that time only Third, there is a fundamental incompatibility conjugation from matter to antimatter was the change between current theories of gravitation and unified of sign of the charge [15], which created one of the gauge theories of electroweak interactions which is biggest scientific imbalance in the history because due precisely to antimatter. In fact, current throughout the 20th century matter was studied at all gravitational theories characterize antimatter via a possible levels, from Newtonian mechanics to second positive-definite energy-momentum tensor, while quantization, while antimatter was solely studied at electroweak theories characterize antiparticles via the particle level. In essence, the prevalent stand still negative energy states. Additional motivations have adopted is that, since Einstein's special and general American Journal of Modern Physics 2014; X(X): XX-XX 3 relativities do not provide a proper description, atmosphere. The widely accepted “interpretation” of antimatter does not exist in the universe in any the Tunguska explosion as being due to a (matter) appreciable amount. The sole generally admitted comet has no scientific credibility due to the exception is that of man made antiparticles created in impossibility of such an origination
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