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Fundamental theories of physics

Concise Description of the CA Interpretation

Gerard ’t Hooft

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Even if we still face problems in formulating concise theories that explain the resolution of various apparent paradoxes, one may simply assume such a theory to exist, and that it will one day be found. This leads to the CA (Cellular Automaton) Interpretation. We now formulate the rules. The universe has a wave function, which, in terms of the classical degrees of freedom, collapses continuously, yet fully in agreement with Schrödinger’s equation. We formulate how to look at various notoriously ‘quantum mechanical’ phenomena, such as superposition, exponential decay, and the double slit experiment. What can we say about the ‘quantum computer’? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-319-41285-6_5

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Even if we still face problems in formulating concise theories that explain the resolution of various apparent paradoxes, one may simply assume such a theory to exist, and that it will one day be found. This leads to the CA (Cellular Automaton) Interpretation. We now formulate the rules. The universe has a wave function, which, in terms of the classical degrees of freedom, collapses continuously, yet fully in agreement with Schrödinger’s equation. We formulate how to look at various notoriously ‘quantum mechanical’ phenomena, such as superposition, exponential decay, and the double slit experiment. What can we say about the ‘quantum computer’? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We wrap up the main outcomes of our investigations. Even if not all questions and issues could be addressed as precisely and persuasively as one would wish, we do find that the assumption of an underlying theory describing a single, definite world with completely deterministic evolution laws, can be maintained and pursued further. In the more distant future, it is hoped that the Cellular Automaton Theory will enable us to select credible models for grand unification an quantized gravity; in the mean while, the Cellular Automaton Interpretation will be helpful in visualizing what we are actually doing when we are involved with quantum mechanical calculations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
When investigating theories at the tiniest conceivable scales in nature, quantum logic is taking over from logic in the minds of almost all researchers today. Dissatisfied, the author investigated how one can look at things differently. This report 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, may be viewed as a quantum mechanical approach to analyse a system that could be classical at its core. We then explain how these apparently heretic thoughts can be reconciled with Bell's theorem and the usual objections voiced against the notion of 'super determinism'. Our proposal would eradicate the collapse problem and the measurement problem.
An outline is given of the interpretation of quantum mechanical expressions if one assumes that what is called Quantum Mechanics today, refers to an underlying reality as in Chap. 2 , even if many authors claim to have evidence to the contrary, as is usually brought forward. If there exists a sub-microscopic classical world of real things, is that the same classical world as the world of large things such as planets, rocks and people? How does the notion of probability enter into quantum mechanics? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Many body physics is concerned with macroscopic systems consisting of a very large number of microscopic particles (N ≈ 10 20 ). In this case the direct dynamical treatment of the complete system is impossible. A quite useful and frequently applied approximation consists in the neglection of terms which are relatively small as the volume of the systems tends to infinity, the particle density remaining constant. For the concise theoretical description of the typical many body phenomena such as phase transitions and spontaneous symmetry breakdown the use of the thermodynamical limit is even necessary, since no existing theory for the finite systems shows these effects. As a general rule one can say that a quantum system behaves like a thermodynamical system only in the infinite-volume limit. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.