Related papers: Correspondence principle and evolution of physics
Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental…
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
It is argued that quantum mechanics follows naturally from the assumptions that there are no fundamental causal laws but only probabilities for physical processes that are constrained by symmetries, and reality is relational in the sense…
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Born's Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the…
In this paper we generalize the ideas of de Broglie and Bohm to the relativistic case which is based on the relativistic Schr\"odinger equation. In this regard, the relativistic forms of the guidance equation and quantum potential are…
A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse,…
The quantum dynamics of a classically chaotic model are studied in the approach to the macroscopic limit. The quantum predictions are compared and contrasted with the classical predictions of both Newtonian and Liouville mechanics. The…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and the Liouvillian dynamics of a nonlinear oscillator coupled to a…
I discuss the physical basis of classical mechanics, such as expressed commonly using the framework of Newton's Principia. Newton's formulation of the laws of motion is seen to have quite a few ambiguities and shortcomings. Therefore I…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent…
The correspondence principle is important in quantum theory on both the fundamental and practical levels: it is needed to connect theory to experiment, and for calculations in the technologically important domain lying between the atomic…
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…
At present, whenever we work in newtonian mechanics we consider momentum to be a three-dimensional vector or a 4-dimensional one when we work in relativistic mechanics. However, this mathematical vector model has barely 200 years and its…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
The procedure used to "do physics" in the macroscopic world is familiar: You take an object, start it off with a particular position and velocity, subject it to known forces (say gravity or friction, or both), and follow its trajectory. You…
No, but the paper argues that Bohr understood his correspondence principle, or at least an aspect of that principle expressed by the notion of rational generalization, as grounded in Hankel's principle of permanence, adapted to new…