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Non-Deterministic Semantics for Quantum States.

Juan Pablo Jorge1, Federico Holik2

  • 1Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina.

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Summary
This summary is machine-generated.

This study reveals the failure of truth functionality in quantum mechanics, introducing non-deterministic semantics for quantum states. This approach offers a new logical framework for quantum and post-quantum theories.

Keywords:
non-deterministic semanticsquantum statestruth functionality

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Area of Science:

  • Quantum mechanics
  • Foundations of physics
  • Mathematical logic

Background:

  • The principle of truth functionality is a cornerstone of classical logic.
  • Quantum mechanics exhibits behaviors that challenge classical logical principles.
  • Existing formalisms struggle to fully capture the non-deterministic nature of quantum states.

Purpose of the Study:

  • To investigate the failure of truth functionality within the quantum formalism.
  • To import N-matrix theory and non-deterministic semantics into the foundations of quantum mechanics.
  • To develop a logical framework for arbitrary probabilistic theories and post-quantum models.

Main Methods:

  • Describing quantum states as valuations linked to infinite non-deterministic truth tables.
  • Applying N-matrix theory and non-deterministic semantics to quantum states.
  • Constructing a similar framework for probabilistic theories based on orthomodular lattices.

Main Results:

  • A natural interpretation of quantum states via non-deterministic semantics is established.
  • The failure of truth functionality in quantum mechanics is explicitly demonstrated.
  • A method for applying logical techniques to study post-quantum models is provided.

Conclusions:

  • Non-deterministic semantics offers a viable interpretation for quantum states.
  • The developed logical framework extends to broader probabilistic theories.
  • This work opens new avenues for exploring quantum foundations using logical tools.