Search Results

Alon Amit: "There are some things that break my heart more thoroughly than reading nonsensical conclusions from Gödel's Theorems to the limitations of physics published by eminent scientists, but they …

To build intuition for the Planck constant $\hbar$, which I understand is the purpose of the OP, I would start by noting that $\hbar$ is not a dimensionless number: it has dimensions of energy $\times …

The article by J.-L. Dorier in On the Teaching of Linear Algebra suggests the answer to your question will be different for the UK and for continental Europe: In an attempt to answer your questio …

The physical motivation for the Laplace transform is causality. Consider the linear input-output relation $$f_{\text{output}}(t)=\int_{0}^\infty R(t-t')f_{\text{input}}(t')\,dt'.$$ Causality dictates …

Early applications of $e^{i\omega t}$ in the context of electromagnetism were understood as a mathematical device: the physical fields are real, and the complex exponential is a convenient method to i …

I can recommend Leonard Susskind's Theoretical Minimum: A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology … So I started a series of courses on modern physics at Stanford University where I am a professor of physics. …

The Algebra of Grand Unified Theories, by John Baez and John Huerta may well be to your liking: A full-fledged treatment of particle physics requires quantum field theory, which uses representations … This brings in a lot of analytical subtleties, which make it hard to formulate theories of particle physics in a mathematically rigorous way. …

This is an interesting line of research in modern physics, whether Nature at its most fundamental level is described by real or by complex numbers. … The physics question is then whether unpaired Majorana fermions appear in Nature, since this would imply the fundamental equations are real rather than complex. …

Perhaps to resolve this issue it helps to work out a simple example. Take a region $D$ consisting of the strip $|x|<1$, $0<y<1$, and a $y$-independent conductivity profile $$\sigma(x)=\begin{cases} 1 …

strictly speaking, the answer to your question is "no"; but if you insist, you can modify the Euler-Lagrange equation by adding a nonzero right-hand-side to incorporate friction: $$\frac d{dt} \left( …

Since this question is still open, I take the liberty of pointing to a recent survey of the status of the Mpemba effect, Pathological Water Science -- Four Examples and What They Have in Common, which …

This line of thought seems to be the essence of the research program of Gerard 't Hooft, as exposed in a series of papers culminating in the monograph The Cellular Automaton Interpretation of Quantum …

This question has been explored in the context of global positioning systems, which need to account for general relativity. The traditional Minkowski coordinates $(t,x,y,z)$ of flat space-time do not …

The Poincaré-von Zeipel method in celestial mechanics relies on canonical transformations of the Hamiltonian to separate fast and slow degrees of freedom in a solar system. See, for example, A note on …

Fermionic modular categories and the 16-fold way classifies the topological phases of the fractional quantum Hall effect. The Laughlin states (Abelian anyons at filling factor $1/Q$, $Q$ odd) are disc …