True wavefunctions and antiparticles of Klein-Gordon equation: $\mathrm{\hslash }$-conjugation, elimination of $CPT$-invariance, and anti-gravitation

While revisiting Klein-Gordon relativistic quantum equation for spin-0 particles, we predicted that $\mathrm{\hslash }$ 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 $\mathrm{\hslash }$ at a particle$\leftrightarrow$antiparticle transformation; this in particular implies anti-gravitation between matter and antimatter. Our results suggest that the $\mathrm{\hslash }$-conjugation principle and related invariance may replace $CPT$-invariance in general relativistic quantum mechanics.