A generalization of Jaynes' principle: an information-theoretic interpretation of the minimum principles of quantum mechanics and gravitation
2000
By considering the "kinetic-energy" term of the minimum principle for the Schr\"{o}dinger equation as a measure of information, that minimum principle is viewed as a statistical estimation procedure, analogous to the manner in which Jaynes ({\it Phys. Rev.},{\bf 106}, 620, 1957) interpreted statistical mechanics. It is shown that the entropy formula of Boltzmann and Jaynes obey a property in common with the quantum-mechanical kinetic energy, in which both quantities are interpreted as measures of correlation. It is shown that this property is shared by the key terms in the minimum principles of relativistic quantum mechanics and General Relativity. It is shown how this principle may be extended to non-Riemannian nonEuclidean spaces, which leads to novel field equations for the torsion.
Keywords:
- Correspondence principle
- Analytical mechanics
- Problem of time
- Quantization (physics)
- Relativistic mechanics
- Mathematical analysis
- Principle of maximum entropy
- Quantum statistical mechanics
- Hamilton–Jacobi–Einstein equation
- Quantum mechanics
- Mathematics
- Mathematical physics
- Relativistic quantum mechanics
- Physics
- Imaginary time
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