Related papers: Ehrenfest's Theorem Revisited
The purpose of this article is to provide a novel approach and justification of the idea that classical physics and quantum physics can neither function nor even be conceived one without the other - in line with ideas attributed to e.g.…
Elementary Cycles Theory is a self-consistent, unified formulation of quantum and relativistic physics. Here we introduce its basic quantum aspects. On one hand, Newton's law of inertia states that every isolated particle has persistent…
Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
Newton's force law $\frac{d {\bf P}}{dt} = {\bf F}$ is derived from the Schr\"odinger equation for isolated macroscopic bodies, composite states of e.g., $N\sim 10^{25}, 10^{51}, \ldots$ atoms and molecules, at finite body temperatures. We…
The framework of entropic dynamics (ED) allows one to derive quantum mechanics as an application of entropic inference. In this work we derive the classical limit of quantum mechanics in the context of ED. Our goal is to find conditions so…
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the…
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states…
The objective of this second part of the work is to present heuristic derivations of the three classical tests of general relativity. These derivations are based on the Einstein equivalence principle and use Newtonian physics as a…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
With the aid of simple analytical computations for the Ehrenfest model, we clarify some basic features of macroscopic irreversibility. The stochastic character of the model allows us to give a non-ambiguous interpretation of the general…
There is a belief that the Ehrenfest theorem holds true universally. We demonstrate that for a classically nonrelativistic particle constrained on an $N-1$ ($N\geq 2$) curved hypersurface embedded in $N$ flat space, the theorem breaks down.
Unimodular quantum cosmology admits wavepacket solutions that evolve according to a kind of Schr\"odinger equation. Though this theory is equivalent to general relativity on the classical level, its canonical structure is different and the…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
Einstein's dream of describing elementary particles as solutions of a classical field theory is severely limited by our current understanding of Nature. Quantum theory is inconsistent with any local realistic theory such as evolving…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\h \to 0$ asymptotics, it is not yet clear how to explain within standard quantum…
Classical and quantum mechanical descriptions of motion are fundamentally different. The universality of free fall (UFF) is a distinguishing feature of the classical motion (which has been verified with astonishing precision), while quantum…