Related papers: Non-Cartesian Thinking
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities;…
We present and discuss a selected set of problems of classical mechanics and thermodynamics. The discussion is based on the use of the impulse-momentum equation simultaneously with the centre-of-mass (pseudo-work) equation or with the first…
Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving…
Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…
The classic brachistrochrone problem is standard material in intermediate mechanics. Many variations exist including some accessible to introductory students. While a quantitative solution isn't feasible in introductory classes, qualitative…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act…
A new general framework is presented for implementing complex a priori knowledge, having in mind especially situations where the number of available training data is small compared to the complexity of the learning task. A priori…
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
Scientists who study how the brain solves problems have recently verified that, because of stringent limitations in working memory, where the brain solves problems, students must apply facts and algorithms that have previously been well…
Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the…
We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make…
Literature analyzes the way in which Newton's second law can be used when non-inertial rotating systems are used. However, the treatment of the work and energy theorem in rotating systems is not considered in textbooks. In this paper, we…