Classical mechanics without absolute space
نویسندگان
چکیده
منابع مشابه
Classical Mechanics in Hilbert Space , Part 2
We continue from Part 1. We will illustrate the general theory of Hamiltonian mechanics in the Lie group formalism. We then obtain the Hamiltonian formalism in the Hilbert spaces of square integrable functions on the symplectic spaces. We illustrate this general theory with several concrete examples, two of which are the representations of the Lorentz group and the Poincaré group with interacti...
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Quantum-like evolution laws for observables can be derived from classical Hamiltonian equations with the only additional assumption that the phase space is non-commutative. The derivation is possible for Hamiltonians that are polynomial functions in position and momentum variables, and supports the use of phase space distributions functions in both quantum and classical theories that rely on ex...
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متن کاملClassical Mechanics
here xi = (xi1, . . . , xid) are coordinates of the i-th particle and ∂xi is the gradient (∂xi1 , . . . , ∂xid); d is the space dimension (i.e. d = 3, usually). The potential energy function will be supposed “smooth”, i.e. analytic except, possibly, when two positions coincide. The latter exception is necessary to include the important cases of gravitational attraction or, when dealing with ele...
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Whereas one can conceive of a relational classical mechanics in which absolute space and time do not play a fundamental role, quantum mechanics does not readily admit any such relational formulation. Newtons mechanics is formulated against a backdrop of what he called absolute space and time. However, absolute position and velocity appear to be unobservable, and there is a long tradition, be...
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ژورنال
عنوان ژورنال: Physical Review D
سال: 1995
ISSN: 0556-2821
DOI: 10.1103/physrevd.52.7322