Related papers: Classical mechanics with lapse
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
In loop quantum cosmology, polymer quantization is applied to gravity and Schrodinger quantization to matter. This approach misses interesting cosmological dynamics coming from the polymer quantization of matter. We demonstrate this in…
The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
The paper reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics…