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The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non relativistic context and this opened up the interesting possibility that lead to the…
The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the…
Quantum field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even…
Effective field theories (EFTs) are widely considered by physicists to be explanatory and to be the appropriate frameworks for modelling various phenomena at different scales. At the same time, they are known to be approximate, restricted,…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…
We propose a simple experiment to explore magnetic fields created by electric railways and compare them with a simple model and parameters estimated using easily available information. A pedestrian walking on an overpass above train tracks…
The theoretical framework of electromagnetism played a foundational role in Einstein's development of special relativity. To support conceptual understanding, we present a fully special relativistic computer simulation that visualizes…
Electromagnetism, being much less intuitive than mechanics, where a lot of sources of misconceptions have been documented, has in addition to the common sources of misconceptions borrowed from mechanics other sources related to the abstract…
Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
The existence of the zero point electromagnetic field in the dark is a trivial property of classical electromagnetism. Splitting the total, genuine electromagnetic field into the sum of a conventional field and a zero point field is…
In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We…
It is regrettable that the quantum length of an object is rarely if ever discussed, because it provides an ideal pedagogical paradigm for understanding how a physicist uses classical intuition to define quantum properties and how such…
The theory of transport of charged particles in cosmic magnetic fields is at the very center of the investigation of non-thermal phenomena in the universe, ranging from our local neighborhood to supernovae, clusters of galaxies or distant…
The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a…
The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. Much attention has been devoted to the blow-up estimate, especially in two dimensions, for the…
We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region…
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes.…
Entanglement is one of the most fascinating concepts of modern physics. In striking contrast to its abstract, mathematical foundation, its practical side is, however, remarkably underdeveloped. Even for systems of just two orbitals or sites…