A Brief Summary with Examples — Dualities are equivalences between distinct descriptions (or formulations) of the same physical system. These descriptions are frequently referred to as “duality frames” and are often complementary to each other. As remarked in my first article about dualities (see link below), their significance for developing contemporary fundamental physics cannot be overstated.

How a Concept Known as “Duality” Reshapes Our View of the World, Provides Insights into Previously Inscrutable Areas of Physics, and Unexpectedly Unifies Disparate Branches of Contemporary Mathematics — One of the most profound insights of modern physics is called duality. Dualities were at the core of several breakthroughs in fundamental physics, considerably changing how physicists think about fundamental principles. …

How to Show That the Famous Jones Polynomial Invariant Has Its Origin in Physics — This article will provide a detailed account of Witten’s derivation, based on the Chern-Simons theory, of the skein relation obeyed by the Jones polynomials (in my last article, linked below, I provided only the rationale underlying the derivation). But first, let me first provide a quick review of topological quantum…

Is Gravity Just an Average of the Behavior of Unknown “Atoms” of Spacetime? — Emergent gravity is an idea in quantum gravity according to which the fabric of spacetime is not fundamental but emerges as a coarse-graining approximation of underlying (still unknown) microscopic degrees of freedom (similarly to a gas emerging from a large sampling of atoms or molecules). …

The Space-Time Approach to Quantum Mechanics — The American theoretical physicist Richard Feynman is one of the best-known scientists in the world (see this link). Feynman made several contributions to theoretical physics. These include: a new formulation of quantum mechanics using path integrals, the theory of quantum electrodynamics (including the development of his famous pictorial representations known…

The Catastrophic Consequences of Living in a Universe with a False Vacuum — A vacuum is a space with as little energy in it as possible. However, a vacuum is not entirely empty. It contains quantum fields. Quantum fields are obtained after the quantization of classical fields, which are functions of spacetime coordinates (such as, for example, the electromagnetic field). …

An Introduction to Geometrodynamics — In Albert Einstein’s original formulation of general relativity (his theory of gravity), the fundamental field is the metric tensor g and the theory is covariant in spacetime. Covariance (more precisely general covariance) “consists of the invariance of the form of physical laws under arbitrary coordinate transformations.” …

Deriving Einstein’s Famous Mass-Energy Equivalence Formula — The mass-energy equivalence formula E = mc² defines a relationship between the mass m and the energy E of a body in its rest frame (the rest frame is the frame of reference where the body is at rest). …

Why Moving Objects are Shortened — Length contraction is the relativistic phenomenon where the length of a moving object is measured to be shorter than in its rest frame. It occurs only in the direction of motion, and its effect is significant only when the object is moving at speeds close to the speed of light. The Miracle Year …