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Feynman Paths and Weak Values
1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Quantum particle trajectories are re-examined. Bohmian trajectories represent the average of many Feynman paths, not individual particle paths, clarifying quantum phenomena like the two-slit experiment.
Area of Science:
- Quantum mechanics
- Foundations of physics
Background:
- Recent resurgence in interest regarding quantum particle trajectories.
- Exploration of connections between Dirac's formulation, Feynman path integrals, and the Bohmian approach.
Purpose of the Study:
- To elucidate the relationship between Dirac's ideas, Feynman paths, and the Bohm approach.
- To provide a novel interpretation of Bohmian trajectories in quantum mechanics.
Main Methods:
- Utilizing the weak value of momentum, identified as Feynman's transition probability amplitude.
- Analyzing the ensemble average of stochastic Feynman paths.
Main Results:
- Established that Bohmian trajectories are the average of an ensemble of individual stochastic Feynman paths.
- Demonstrated that these trajectories represent mean momentum flow, not individual particle paths.
Conclusions:
- Bohmian trajectories are statistical averages, not deterministic paths of single quantum particles.
- This interpretation offers a clearer explanation for experimental results, such as the two-slit experiment.
- Reconciles different formalisms in quantum mechanics through the weak value of momentum.
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