The Cellular Automaton Interpretation of Quantum Mechanics (1405.1548v3)

Abstract: When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will always involve states in Hilbert space, controlled by operator equations. Returning to classical, that is, non quantum mechanical, descriptions will be forever impossible, unless one accepts some extremely contrived theoretical constructions that may or may not reproduce the quantum mechanical phenomena observed in experiments. Dissatisfied, this author investigated how one can look at things differently. This book is an overview of older material, but also contains many new observations and calculations. Quantum mechanics is looked upon as a tool, not as a theory. Examples are displayed of models that are classical in essence, but can be analysed by the use of quantum techniques, and we argue that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analyse a system that could be classical at its core. We explain how such thoughts can conceivably be reconciled with Bell's theorem, and how the usual objections voiced against the notion of `superdeterminism' can be overcome, at least in principle. Our proposal would eradicate the collapse problem and the measurement problem. Even the existence of an "arrow of time" can perhaps be explained in a more elegant way than usual. Discussions added in v3: the role of the gravitational force, a mathematical physics definition of free will, and an unconventional view on the arrow of time, amongst others.

• The paper introduces the deterministic Cellular Automaton Interpretation to recast quantum mechanics without reliance on inherent randomness.
• It presents an ontological basis where classical permutations resolve the wave function collapse and Schrödinger's cat paradox.
• The work also discusses challenges in integrating quantum field theory and gravitational interactions within a deterministic framework.

Essay on "The Cellular Automaton Interpretation of Quantum Mechanics"

The paper under review, authored by Gerard 't Hooft and presented as a comprehensive manuscript, lays the groundwork for the so-called Cellular Automaton Interpretation (CAI) of quantum mechanics. This interpretation posits a radical yet methodically constructed view that challenges conventional quantum orthodoxy by recasting quantum mechanics as a mathematical toolkit ultimately founded upon deterministic principles.

Overview and Key Concepts

The CAI postulates that the universe evolves deterministically, governed by classical laws akin to cellular automata. This stands in stark contrast to the traditional probabilistic view inherent in the Copenhagen interpretation of quantum mechanics. The paper suggests that quantum probabilities are not fundamental but arise due to our incomplete knowledge, similar to how statistical mechanics provides a macroscopic view of a system with limited information about its microscopic states.

The Ontological Basis

A pivotal aspect of the CAI is the ontological basis, a special basis in Hilbert space wherein all states are deterministic, and evolution corresponds to classical permutations among these states. This proposition aligns closely with classical logic, and the states are termed "ontological," effectively rejecting the notion of inherent randomness in nature. While typical quantum descriptions such as the position or momentum basis are non-ontological due to inherent uncertainties, the CAI seeks to identify ontological states where variables exhibit classical commutativity.

Key Results and Implications

One of the most profound implications of the CAI, as outlined by 't Hooft, is the resolution of the wave function collapse problem. In this interpretation, the universe is always in one specific ontological state, thereby naturally selecting a single outcome without requiring hypothetical wave function collapses. Similarly, the infamous Schrödinger's cat paradox finds a resolution through the realization that macroscopic classical states — like those representing a dead or alive cat — naturally align with the ontological states, preserving the classical logic without invoking superpositions at macroscopic scales.

Furthermore, the CAI elegantly sidesteps the challenges posed by Bell's theorem and the associated inequalities. By voiding the assumption of counterfactual definiteness, the CAI proposes that the outcomes of measurements are not predetermined independently of the measurement settings. The universe's ontological states inherently incorporate all correlations required by quantum entanglement, reflecting a deterministic yet non-local structure where information about the entire system is intricately linked.

Future Prospects and Challenges

While the CAI presents a coherent alternative framework for understanding quantum mechanics, several challenges remain before it can claim complete congruence with the full breadth of empirical data. Notably, aligning this interpretation with established quantum field theories, especially with considerations of special relativity, presents significant technical hurdles. The concept of second quantization within this deterministic framework, particularly for fermionic particles, represents a promising stride toward rectifying the Hamiltonian's boundedness from below, a crucial enabler for stability and realistic particle physics descriptions.

Moreover, integrating gravitational interactions and addressing the problematic hierarchy of scales remain open issues needing exploration. Insights from the CAI may also lead to refined models that cohere better with experimental observations or suggest novel avenues of empirical inquiry, potentially making it a tool for theoretical innovation in the quest for a unified physical theory.

Conclusion

In summary, Gerard 't Hooft's exposition of the Cellular Automaton Interpretation proposes a striking alternative to the mainstream understanding of quantum mechanics. By positing a fundamentally deterministic universe reflected through a cleverly constructed ontological basis, this interpretation endeavors to demystify quantum phenomena while preserving the predictive power of standard quantum mechanics. As the search for a deeper understanding of quantum gravity and the fabric of spacetime continues, the insights from CAI offer intriguing possibilities for both theoretical advancements and empirical verification. However, substantial work remains to fully integrate this interpretation with quantum field theory and explore its empirical ramifications comprehensively.