The Cellular Automaton Interpretation of Quantum Mechanics

Gerard 't Hooft

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First annotation on Sep 10th, 2025.

Preface

The discovery of the laws of quantum mechanics has severely affected the way investigators now think about 'reality'. Even authorities such as Richard Feynman were baffled: "I think I can safely say that nobody today understands quantum mechanics"
Some critical readers were wondering where the complex numbers in quantum mechanics should come from, given the fact that we start off from classical theories. The answer is simple: complex numbers are nothing but man-made inventions, just as real numbers are. In Hilbert space, they are useful tools whenever we discuss something that is conserved in time (such as baryon number), and when we want to diagonalize a Hamiltonian. Note that quantum mechanics can be formulated without complex numbers, if we accept that the Hamiltonian is an anti-symmetric matrix. But then, its eigen values are imaginary. We emphasise that imaginary numbers are primarily used to do mathematics, and for that reason they are indispensable for physics.
Gravitation is a destabilizing force. Causing masses to attract one another, it generates greater masses and thus even stronger attraction. This may lead to gravitational implosion. In contrast, electric as well as magnetic charges act repulsively (if they have equal signs), which makes electromagnetism a lot more stable than gravity as a force system.
In contrast, the classical, ontological states are very asymmetric in time, because, as we stated, these are directly linked to the underlying classical degrees of freedom.