True wavefunctions and antiparticles of Klein-Gordon equation: $\hbar$-conjugation, elimination of $CPT$-invariance, and anti-gravitation

Abstract

While revisiting Klein-Gordon relativistic quantum equation for spin-0 particles, we predicted that $\hbar$ reverses its sign for negative energies, and formulated a universal symmetry rule, whereby all the parameters that couple particles to external fields reverse their sign along with $\hbar$ at a particle$\leftrightarrow$antiparticle transformation; this in particular implies anti-gravitation between matter and antimatter. Our results suggest that the $\hbar$-conjugation principle and related invariance may replace $CPT$-invariance in general relativistic quantum mechanics.