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A deterministic reformulation of quantum mechanics can bypass the usualphilosophical interpretations of probability and stochasticity that are foundin the literature. This can be obtained with the ontological formulation ofquantum mechanics, obtained by writing the Hamiltonian of a quantum system in away to render it mathematically equivalent to a deterministic system. Suchdeterministic models are thought to consist of elementary cells - cellularautomata - inside which the quantities describing the dynamics oscillate inperiodic orbits, extending and replacing the quantum-mechanical classicallanguage based on harmonic oscillators. Here we show that the structure of thecellular automata sets find a clear physical interpretation with theinfinite-components equation published by Majorana in 1932, also known as theMajorana Tower: the cellular automata are elementary building blocks generatedby the Poincar\'e group of spacetime transformations with positive-definedenergy down to the elementary building blocks of the fabric of spacetime.Interestingly, the mathematical approach here considered presents closerelationships with those used for the distribution of prime numbers in theP\'olya-Hilbert conjecture for the Riemann Hypothesis.

Majorana Tower and Cellular Automaton Interpretation of Quantum Mechanics down to Planck Scales