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Four Postulates of Quantum Mechanics Are Three.
Gabriele Carcassi1, Lorenzo Maccone2, Christine A Aidala1
1Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA.
Physical Review Letters
|April 2, 2021
Summary
This study logically derives the tensor product rule, a fundamental concept in quantum mechanics, from basic postulates. This work reduces the number of necessary postulates for quantum mechanics by one.
Area of Science:
- Quantum Mechanics
- Foundations of Physics
- Mathematical Physics
Background:
- The tensor product postulate is a cornerstone of quantum mechanics, defining the Hilbert space of composite systems.
- Existing formalisms often rely on this postulate or equivalent hidden assumptions.
- A need exists to simplify and logically ground the postulates of quantum mechanics.
Purpose of the Study:
- To provide a natural definition for composite systems in quantum mechanics.
- To logically derive the tensor product rule from more fundamental postulates.
- To reduce the number of axiomatic postulates in quantum mechanics.
Main Methods:
- Defined a composite system as a set containing its component systems.
- Utilized the state postulate and measurement postulate of quantum mechanics.
- Employed logical deduction to derive the tensor product rule.
Main Results:
- Successfully derived the tensor product rule from the state and measurement postulates.
- Demonstrated that the tensor product postulate is not independent.
- Showed a natural definition of composite systems leads to the tensor product structure.
Conclusions:
- The tensor product rule can be logically derived, reducing the axiomatic burden of quantum mechanics.
- This work offers a more parsimonious and logically coherent foundation for quantum mechanics.
- The definition of composite systems as sets naturally incorporates the tensor product structure.
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