13 research outputs found
Randomness in Classical Mechanics and Quantum Mechanics
The Copenhagen interpretation of quantum mechanics assumes the existence of
the classical deterministic Newtonian world. We argue that in fact the Newton
determinism in classical world does not hold and in classical mechanics there
is fundamental and irreducible randomness. The classical Newtonian trajectory
does not have a direct physical meaning since arbitrary real numbers are not
observable. There are classical uncertainty relations, i.e. the uncertainty
(errors of observation) in the determination of coordinate and momentum is
always positive (non zero).
A "functional" formulation of classical mechanics was suggested. The
fundamental equation of the microscopic dynamics in the functional approach is
not the Newton equation but the Liouville equation for the distribution
function of the single particle. Solutions of the Liouville equation have the
property of delocalization which accounts for irreversibility. The Newton
equation in this approach appears as an approximate equation describing the
dynamics of the average values of the position and momenta for not too long
time intervals. Corrections to the Newton trajectories are computed. An
interpretation of quantum mechanics is attempted in which both classical and
quantum mechanics contain fundamental randomness. Instead of an ensemble of
events one introduces an ensemble of observers.Comment: 12 pages, Late
Semiclassical properties and chaos degree for the quantum baker's map
We study the chaotic behaviour and the quantum-classical correspondence for
the baker's map. Correspondence between quantum and classical expectation
values is investigated and it is numerically shown that it is lost at the
logarithmic timescale. The quantum chaos degree is computed and it is
demonstrated that it describes the chaotic features of the model. The
correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy