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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum fermions from classical bits.

Christof Wetterich1

  • 1Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 20, 2021
PubMed
Summary
This summary is machine-generated.

A novel probabilistic cellular automaton demonstrates equivalence to relativistic quantum field theory. This finding suggests quantum mechanics may emerge from classical statistics, opening avenues for probabilistic classical computing.

Keywords:
generalized Thirring model for fermionsprobabilistic cellular automataquantum mechanics from classical statistics

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Area of Science:

  • Quantum Field Theory
  • Statistical Mechanics
  • Computational Physics

Background:

  • Relativistic fermionic quantum field theories describe fundamental particle interactions.
  • Cellular automata are discrete dynamical systems with applications in modeling complex phenomena.
  • Classical statistical systems, like the Ising model, are foundational in understanding emergent behavior.

Purpose of the Study:

  • To establish an equivalence between a simple probabilistic cellular automaton and relativistic fermionic quantum field theory.
  • To explore the emergence of quantum mechanical concepts from classical statistical systems.
  • To investigate the potential for probabilistic classical computing.

Main Methods:

  • Development of a simple probabilistic cellular automaton.
  • Mapping fermion occupation numbers to classical bits or Ising spins.
  • Analysis of the automaton's deterministic evolution and probabilistic initial conditions.
  • Establishing equivalence to a generalized Ising model.

Main Results:

  • Demonstrated equivalence between the probabilistic cellular automaton and a relativistic fermionic quantum field theory with interactions.
  • Showcased that quantum concepts like wave functions emerge naturally from the probabilistic information.
  • Revealed that quantum mechanics can be viewed as a specific instance of classical statistics.

Conclusions:

  • A direct link exists between simple probabilistic cellular automata and complex quantum field theories.
  • Quantum mechanics may be fundamentally rooted in classical statistical principles.
  • This framework offers a new perspective for developing probabilistic classical computing paradigms.