hadronic mathematics, mechanics and chemistry - Institute for Basic ...

HADRONIC MATHEMATICS, MECHANICS AND CHEMISTRY 3
1.1.2 The Mathematical Origin of the Imbalance
The origin of this scientific imbalance was not of physical nature, because it was
due to the lack of a mathematics suitable for the classical treatment of antimatter
in such a way as to be compatible with charge conjugation at the quantum level.
Charge conjugation is an anti-homomorphism. Therefore, a necessary condition
for a mathematics to be suitable for the classical treatment of antimatter
is that of being anti-homomorphic, or, better, anti-isomorphic to conventional
mathematics.
Therefore, the classical treatment of antimatter requires numbers, fields, functional
analysis, differential calculus, topology, geometries, algebras, groups, symmetries,
etc. that are anti-isomorphic to their conventional formulations for matter.
The absence in the 20-th century of such a mathematics is soon established
by the lack of a formulation of trigonometric, differential and other elementary
functions, let alone complex topological structures, that are anti-isomorphic to
the conventional ones.
In the early 1980s, due to the absence of the needed mathematics, the author
was left with no other alternative than its construction along the general
guidelines of hadronic mechanics, namely, the construction of the needed mathematics
from the physical reality of antimatter, rather than adapting antimatter
to pre-existing insufficient mathematics. 1
After considerable search, the needed new mathematics for antimatter resulted
in being characterized by the most elementary and, therefore, most fundamental
possible assumption, that of a negative unit,
−1, (1.1.1)
and then the reconstruction of the entire mathematics and physical theories of
matter in such a way as to admit −1 as the correct left and right unit at all levels.
In fact, such a mathematics resulted in being anti-isomorphic to that representing
matter, applicable at all levels of study, and resulting in being equivalent
to charge conjugation after quantization. 2
1 In the early 1980s, when the absence of a mathematics suitable for the classical treatment of antimatter
was identified, the author was (as a theoretical physicist) a member of the Department of Mathematics at
Harvard University. When seeing the skepticism of colleagues toward such an absence, the author used to
suggest that colleagues should go to Harvard’s advanced mathematics library, select any desired volume,
and open any desired page at random. The author then predicted that the mathematics presented in
that page resulted in being fundamentally inapplicable to the classical treatment of antimatter, as it did
indeed result to be the case without exceptions. In reality, the entire content of advanced mathematical
libraries of the early 1980s did not contain the mathematics needed for a consistent classical treatment
of antimatter.
2 In 1996, the author was invited to make a 20 minutes presentation at a mathematics meeting held in
Sicily. The presentation initiated with a transparency solely containing the number −1 and the statement