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Published on: May 30, 2014
Quantum probability and Hilbert's sixth problem.
1Centro Vito Volterra, Università di Roma Tor Vergata 00133, Rome, Italy accardi@volterra.uniroma2.it.
Summary
Quantum mechanics unifies probability and mechanics, creating a new probabilistic model. This paper surveys quantum probability
Area of Science:
- Mathematical Physics
- Quantum Mechanics
- Probability Theory
Background:
- Hilbert's sixth problem aimed to axiomatize mechanics and probability.
- The advent of quantum mechanics intertwined these two fields.
- A new probabilistic model emerged alongside the classical one.
Purpose of the Study:
- To present a unified axiomatization addressing Hilbert's challenge.
- To survey the framework of quantum probability.
- To demonstrate how quantum probability accounts for mechanics and probability.
Main Methods:
- Review of quantum probabilistic axiomatization.
- Deductive analysis of foundational principles.
- Integration of quantum mechanics with probability theory.
Main Results:
- Successful axiomatization encompassing mechanics, probability, and quantum mechanics.
- Demonstration of quantum probability as a unifying framework.
- Resolution of Hilbert's challenge within quantum probability.
Conclusions:
- Quantum probability provides a comprehensive axiomatization for mechanics and probability.
- The framework successfully integrates classical and quantum principles.
- This approach fulfills the objectives of Hilbert's sixth problem.
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