Related papers: Non-Cartesian Thinking
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
We discuss the work-kinetic energy theorem and the mechanical energy conservation theorem in the context of general physics courses. The motivation is the fact that all modern texts on introductory mechanics show the same conceptually…
We emphasize the usefulness of the Lie brackets in the context of classical and quantum mechanics. By way of examples we show that many dynamical systems, especially the ones with (gauge) constraints, can equally be treated in their time…
Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive…
Care making only clock-specific assertions about elapsed-time, and other ``space-time smart'' strategies from the perspective of a selected inertial map-frame, open doors to an understanding of anyspeed motion via application of the metric…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
We use a reinforcement learning approach to reduce entropy production in a closed quantum system brought out of equilibrium. Our strategy makes use of an external control Hamiltonian and a policy gradient technique. Our approach bears no…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…
Let us consider a reference frame for which the pseudo-Euclidean geometry is valid (prefered frame). The equations of Maxwell in empty space have a simple form and are derived from a Lagrangian. In a medium magnetic permeability and…
It is well-known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in quantitative problem-solving process can…
This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line…
Various 'optimistic' attempts have been made to reasonably explain the undeniable effectiveness of mathematics in its application to physics. They range over retrospective, historical accounts of mathematical applicability based on…
Symmetries have proven useful in machine learning models, improving generalisation and overall performance. At the same time, recent advancements in learning dynamical systems rely on modelling the underlying Hamiltonian to guarantee the…
We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the…
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
We present a matrix formalism, inspired by the Minkowski four-vectors of special relativity, useful to solve classical physics problems related to both mechanics and thermodynamics. The formalism turns out to be convenient to deal with…
The ability to categorize problems based upon underlying principles, rather than contexts, is considered a hallmark of expertise in physics problem solving. With inspiration from a classic study by Chi, Feltovich, and Glaser, we compared…
The study rederives the fundamental equations of fluid flow and examines the inherent relationship between momentum conservation and mechanical energy conservation. It is shown that the material derivative of velocity is to depict the…