  A deterministic reformulation of quantum mechanics can bypass the usual
philosophical interpretations of probability and stochasticity that are found
in the literature. This can be obtained with the ontological formulation of
quantum mechanics, obtained by writing the Hamiltonian of a quantum system in a
way to render it mathematically equivalent to a deterministic system. Such
deterministic models are thought to consist of elementary cells - cellular
automata - inside which the quantities describing the dynamics oscillate in
periodic orbits, extending and replacing the quantum-mechanical classical
language based on harmonic oscillators. Here we show that the structure of the
cellular automata sets find a clear physical interpretation with the
infinite-components equation published by Majorana in 1932, also known as the
Majorana Tower: the cellular automata are elementary building blocks generated
by the Poincar\'e group of spacetime transformations with positive-defined
energy down to the elementary building blocks of the fabric of spacetime.
Interestingly, the mathematical approach here considered presents close
relationships with those used for the distribution of prime numbers in the
P\'olya-Hilbert conjecture for the Riemann Hypothesis.
