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Time, the arrow of time, and Quantum Mechanics (1804.01383v1)

Published 4 Apr 2018 in quant-ph

Abstract: It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition, time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. We explain these statements in terms of the author's favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as `vector space analysis', and expand on these ideas.

Citations (7)

Summary

  • The paper introduces a deterministic cellular automaton framework that bridges classical causality with quantum phenomena.
  • It argues that embedding an inherent arrow of time is essential for establishing causal relationships in physical theories.
  • It critically evaluates Bell's theorem and retro-causality, suggesting that quantum probabilities may emerge from underlying deterministic processes.

Determinism, Quantum Mechanics, and the Arrow of Time: A Critical Examination

In this paper, Gerard 't Hooft presents a sophisticated examination of the fundamental nature of time, causality, and quantum mechanics through the lens of deterministic models, specifically cellular automata. The overarching argument posits that time, marked by its characteristic ordering of events, is a fundamental construct necessary for the development of viable physical theories. The research further explores how quantum mechanics, despite its counterintuitive nature and the ongoing debates over its interpretation, can be approached from a deterministic perspective.

Defining Time and Its Role in Physical Theories

The paper argues that any comprehensive model of the universe requires a well-defined notion of time characterized by an arrow pointing from past to future. This temporal ordering is essential for establishing causal relationships, as it allows for sequential event explanations. 't Hooft underscores that time reversibility, often assumed in classical mechanics, is not inherently necessary for such models, and the arrow of time can be conceptually embedded even at localized scales.

Quantum Mechanics and the Deterministic Cellular Automaton Model

Quantum mechanics traditionally challenges deterministic interpretations due to its inherent probabilistic nature. However, the paper reinvigorates the discussion on determinism through what the author refers to as the "Cellular Automaton (CA) Interpretation" or "vector space analysis." This interpretation attempts to reconcile quantum mechanics with deterministic laws by modeling quantum phenomena as manifestations of underlying classical systems described through cellular automata.

Using the CA framework, the paper argues that quantum mechanics might emerge as a statistical realization of deterministic processes at the deepest levels, involving large ontological bases realized in Hilbert space. This approach posits that the probabilistic behavior observed in quantum experiments, such as those involving EPR/Bell-type setups, can be accounted for by deterministic variables at Planck-scale resolutions.

Bell's Theorem and the Free Will Debate

The paper critically engages with Bell's theorem, which places significant constraints on local hidden variable theories, by asserting that the usual assumptions about causality and free will might be challenged within the deterministic CA framework. It argues that settings chosen by experimental observers like Alice and Bob—whether characterized by free will or not—are in fact ontologically correlated with the state of particles emitted by the source. Such correlations resurface the idea of 'retro-causality,' albeit as a natural consequence of deterministic equations that work both forwards and backwards in time.

Theoretical and Practical Implications

The exploration of deterministic models for explaining quantum mechanics reveals potential avenues for theoretical developments that could reshape our understanding of the universe's foundational mechanics. The CA interpretation offers an alternative narrative to the Copenhagen interpretation and many-world theories, suggesting instead that our classical intuitions about reality—as filtered through complex mathematical transformations—might still hold relevance.

Furthermore, the paper implies future research trajectories that involve identifying suitable classical algorithms or cellular automata capable of reproducing quantum statistical results. The potential for classical information loss mechanisms to translate into effective quantum models is a provocative area for ongoing investigation, with broader implications for fields such as quantum computing and cosmology.

Conclusion

Gerard 't Hooft's paper proposes a thought-provoking paradigm shift towards reconciling quantum mechanics with deterministic principles via the cellular automaton framework. Although controversial, this perspective heralds novel ways of conceptualizing the intersection between quantum physics and classical reality, challenging foundational assumptions about time, causality, and the probabilistic nature of quantum states. As such, it invites deeper inquiry into the fundamental laws governing our universe, questioning the permanence of quantum mechanics as the ultimate theoretical framework.

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