Physics Forums Insights

Table of Contents This article is written by way of a reference for my longstanding PF colleague and prolific poster of challenging Maths/geometry problems @chwala . The particular post this article will discuss is an example of one such problem which he raised on Physics Forums. We take the liberty of including the original diagram from that thread: f A deceptively simple diagram which holds a ‘…

Table of Contents This project began life in 2017 when the author had just begun experimentation with GPIO pins on a Raspberry Pi 3. At that point in time a greatly appreciated Christmas present was an “Explorer Hat” module which provided the aspirant programmer with 5 volt tolerant input and output channels (analogue and digital) , capacitive touch pads, built in light emitting diodes (hencefort…

Table of Contents In Memory of Dr. Thomas J. LeCompte (1964-2025), Detector Designer and Champion of Education and Science. Someone who shows interest in science is initially a welcome development. So are fresh ideas from unexpected quarters. In contrast, there is a scientific community that is meticulously organized down to the last detail, allowing little to no external influence. With the inve…

In her YouTube video Bell’s Theorem Experiments on Entangled Photons, Dr. Fugate shows how polarization-entangled photons violate Bell’s inequality. In this Insight, I will use quantum information theory to explain why such entangled photon-polarization qubits violate the version of Bell’s inequality due to John Clauser, Michael Horne, Abner Shimony, and Richard Holt known as the Clauser-Horne-Sh…

Table of Contents This is an update of my 2006 post (reconstructed in 2014) Relativator: The circular slide-rule for physicists. This is a circular slide-rule for doing relativistic calculations for elementary particle physics that I learned about from – an article by Elizabeth Wade ( “Artifact: Relativator”, Symmetry (FNAL/SLAC), 01/01/06, https://www.symmetrymagazine.org/article/december-2005ja…

Table of Contents In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra: [tex]\delta^j_k =\left\{\begin{array}{lcl}1&\text{ if } & j=k\\0&\text{ if }…

Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated: Before we end, let’s now briefly talk about the birth of quantum information science, a pivotal shift that began in the 1990s. This is the era when researchers stopped asking, why is quantum physics so weird? And started ask…

Table of Contents This article will build on the hints about treating the complex numbers as a branched surface, briefly described and pictured in section 4.2 of https://www.physicsforums.com/insights/views-on-complex-numbers/#The-Radish. Using a particular set of conventions, all the problems described in https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/ can be removed,…

Table of Contents Fermat’s Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity …

Table of Contents A vector space is an additively written abelian group together with a field that operates on it. Vector spaces are often described as a set of arrows, i.e. a line segment with a direction that can be added, stretched, or compressed. That’s where the term linear to describe addition and operation, and the term scalar for the scaling factor from the operating field come from. Alth…

Table of Contents Modern Video codecs are all based on similar principles. Recently, these have been complemented by AI techniques, such as super-resolution, to form hybrid codecs. The current state of the art is one of transition to have one based only on AI eventually: Codecs using only AI are several years away. For the foreseeable future, we will use conventional codecs supplemented with AI. …

[CONTENT] Contents That there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know this. Yet the tidal bulge is still used to portray why the Moon is receding the Earth. If there is no tidal bulge, some other explanation is in order. That other explanation uses gravitation as the driving force but does not result in a tidal bulge. To develop…

Table of Contents Topology as a branch of mathematics is a bracket that encompasses many different parts of mathematics. It is sometimes even difficult to see what all these branches have to do with each other or why they are all called topology. This article aims to shed light on this question and briefly summarize the content of the many branches of topology. We start with a historical review a…

Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It’s now a key player in data science, quant finance, and mathematical biology. This article is drawn from notes I wrote for an undergraduate statistical physics course a few months ago. There won’t be any mathematical rigor. Table of Contents In 1d, the term Brownian motion is …

Table of Contents PBS Space Time produces some very good videos on the foundations of quantum mechanics (QM), so let me comment on their video What If Physics IS NOT Describing Reality to provide (crucial) missing information. This comment pertains only to the first 9 min of the video, i.e., it has nothing to do with “entropic uncertainty,” so you don’t have to watch more than that before reading…

Table of Contents It took until the last century for physicists and mathematicians in the Netherlands to question the Euclidean concept of dimension as length, width, and height. Luitzen Egbertus Jan Brouwer published a ground-breaking paper On the Natural Concept of Dimension (Amsterdam, [2]) in 1913 about the mathematical definition of dimension picking up a thought from Poincaré, and Tatjana E…

Table of Contents Why do we need yet another article about complex numbers? This is a valid question and I have asked it myself. I could mention that I wanted to gather the many different views that can be found elsewhere – Euler’s and Gauß’s perspectives, i.e. various historical views in the light of the traditionally parallel development of mathematics and physics, e.g. the use of complex coord…

The “Addition of Velocities” formula (more correctly, the “Composition of Velocities” formula) in Special Relativity [tex]\frac{v_{AC}}{c}=\frac{ \frac{v_{AB}}{c}+\frac{v_{BC}}{c} }{1 + \frac{v_{AB}}{c} \frac{v_{BC}}{c}}[/tex] is a non-intuitive result that arises from a “hyperbolic-tangent of a sum”-identity in Minkowski spacetime geometry, with its use of hyperbolic trigonometry. However, I cla…

The concept of quantum superposition (or superposition for short) is very counterintuitive, as Schr##\ddot{\text{o}}##dinger noted in 1935 writing [1], “One can even set up quite ridiculous cases.” To make his point, he assumed a cat was closed out of sight in a box with a radioactive material that would decay with 50% probability within an hour. If a radioactive decay occurred, a deadly gas woul…