dorsal/arxiv
View SchemaUncertainty and information in classical mechanics formulation. Common ground for thermodynamics and quantum mechanics
| Authors | Adrian Faigon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311153 |
| URL | https://arxiv.org/abs/quant-ph/0311153 |
Abstract
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. Wave mechanics and Schrodinger equation appear without additional assumptions by choosing the representation for delta-q in the case the motion is not trajectory describable. The Cramer-Rao inequality serves that purpose. For a particle hidden from direct observation, the position uncertainty determined by the enclosing boundaries leads to thermodynamics in a straightforward extension of the presented formalism. The introduction of uncertainty in classical mechanics formulation enables the translation of mechanical laws into the wide ranging conceptual framework of information theory. The boundaries between classical mechanics, thermodynamics and quantum mechanics are defined in terms of informational changes associated with the system evolution. As a direct application of the proposed formulation upper bounds for the rate of information transfer are derived.
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"abstract": "Mechanics can be founded on a principle relating the uncertainty delta-q in\nthe trajectory of an observable particle to its motion relative to the\nobserver. From this principle, p.delta-q=const., p being the q-conjugated\nmomentum, mechanical laws are derived and the meaning of the Lagrangian and\nHamiltonian functions are discussed. The connection between the presented\nprinciple and Hamilton\u0027s Least Action Principle is examined.\n Wave mechanics and Schrodinger equation appear without additional assumptions\nby choosing the representation for delta-q in the case the motion is not\ntrajectory describable. The Cramer-Rao inequality serves that purpose. For a\nparticle hidden from direct observation, the position uncertainty determined by\nthe enclosing boundaries leads to thermodynamics in a straightforward extension\nof the presented formalism.\n The introduction of uncertainty in classical mechanics formulation enables\nthe translation of mechanical laws into the wide ranging conceptual framework\nof information theory. The boundaries between classical mechanics,\nthermodynamics and quantum mechanics are defined in terms of informational\nchanges associated with the system evolution. As a direct application of the\nproposed formulation upper bounds for the rate of information transfer are\nderived.",
"arxiv_id": "quant-ph/0311153",
"authors": [
"Adrian Faigon"
],
"categories": [
"quant-ph"
],
"title": "Uncertainty and information in classical mechanics formulation. Common ground for thermodynamics and quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0311153"
},
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