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Path integral implementation of relational quantum mechanics
1Qualcomm, San Diego, CA, 92121, USA. jianhao.yang@alumni.utoronto.ca.
Scientific Reports
|April 22, 2021
Summary
This study advances relational quantum mechanics by clarifying measurement probability calculations and implementing relational probability amplitude via path integrals. This framework explains quantum phenomena like the double-slit experiment and entanglement entropy.
Area of Science:
- Quantum Physics
- Foundations of Quantum Mechanics
Background:
- Relational quantum mechanics posits that relationships between systems, not independent properties, are fundamental.
- A prior framework derived quantum probability, Born's Rule, Schrödinger Equations, and measurement theory.
Purpose of the Study:
- To extend the relational quantum mechanics framework.
- To provide a concrete implementation of relational probability amplitude.
- To clarify connections with quantum reference frame theory.
Main Methods:
- Extending path integral formulation to implement relational probability amplitude.
- Utilizing influence functionals for calculations.
- Analyzing the relationship with quantum reference frame theory.
Main Results:
- Clarified concepts for calculating measurement probability.
- Provided a physical interpretation of relational probability amplitude.
- Successfully explained the double-slit experiment and calculated entanglement entropy.
- Offered new insights into the path integral formulation.
Conclusions:
- The extended relational quantum mechanics framework offers a more complete description of quantum phenomena.
- The path integral implementation provides a powerful tool for relational quantum mechanics.
- Integration with quantum reference frame theory is necessary for a complete relational formulation.
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