Problematic aspects of string theories and their possible resolution

Abstract

We identify new, rather serious, physical and axiomatic inconsistencies of the current formulation of string theories due to the lack of invariant units necessary for measurements, lack of preservation in time of Hermiticity-observability, and other shortcomings. We propose three novel reformulations of string theories for {\it 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 formulation on curved manifolds, the reduction of macroscopic irreversibility to the most primitive level of vibrations of the universal substratum (ether), or the treatment of multi-valued biological structures. We then identify three corresponding {\it classical} formulations of string theories for {\it 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 Poincar\'e 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 matter and antimatter in the universe; and identically null total characteristics of time, energy, linear and angular momentum, charge, etc.