Related papers: Simple circuit theory and the solution of two elec…
The equilibrium conditions for charges and currents, apparent in exact solutions of the field equations, lead one to regard the Hermitian theory of relativity as the theory of a field endowed with two sources: electromagnetic and colour…
The Block Universe idea, representing spacetime as a fixed whole, suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This view is however based on time-reversible…
Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with its environment in a controllable fashion. The total…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
These lectures were addressed to nonspecialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on…
The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball,…
One of the challenges of constructing a successful cyclic universe scenario is to be able to incorporate the second law of thermodynamics which typically leads to Tolman's problem of ever shrinking cycles. In this paper we construct a…
An exhaustive analysis of the leaky tank car problem is presented, pointing out its intriguing physical properties, which well serve to students and teachers for illustrating standard Newtonian mechanics in a highly non-standard fashion.…
This work establishes a Space-Time Connectivity Theorem for normal currents. In analogy to classical results by Federer and Fleming as well as a recent theorem for integral currents by the second author, this result allows one to witness…
We present an elementary proof concerning reciprocal transmittances and reflectances. The proof is direct, simple, and valid for the diverse objects that can be absorptive and induce diffraction and scattering, as long as the objects…
The 2nd law of thermodynamics is used to shed light on present-day puzzles in cosmology. The universal law, given as an equation of motion, describes diverse systems when consuming free energy via various mechanisms to attain stationary…
We present two methods for describing, from a pedagogical point of view, the solutions of Einstein's equations applied to a homogeneous and isotropic universe. In the first method, we define an effective gravitational potential of the…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
A particle switching between two sides of a symmetric system in interaction with a continuum exhibits a telegraph-like time development without the need of the Born-Bohr principle of reduction on eigenstates of the measuring equipment. The…
Whoever has to learn or to teach thermodynamics is confronted with conceptual difficulties which are specific to this field of physics ([1],[2]). It seems that they can be eliminated by inserting relativity in the thermodynamic theory. The…
We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These…
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
In contemporary physics space and time are intertwined entities so that kinematical and dynamical quantities are expressed in the four-dimensional space-time. This formulation seems to contradict our every-day experience and perception…
This presentation intends to illustrate the specific capabilities of an e$^+$e$^-$ sub-TeV collider to provide answers on the basic issues in physics: origin of mass, hierarchy of masses, cosmological problems. Some foreseeable scenarios…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…