Physics

Learning Objectives Gain confidence and experimental care in making accurate measurements. Understand the relationship between force and spring…

Introduction One interesting problem when dealing with a vehicle of a certain mass is to determine what is required to get the maximum acceleration while…

Servo-constraint was invented by Henri Beghin in his Ph.D. thesis in 1922. For details see the celebrated monograph in rational mechanics by Paul Appell.To…

From Exploring Black Holes by John Wheeler and Edwin Taylor. The relations below apply to any object falling radially toward a static, spherically symmetric…

Introduction Much has lately been said regarding this paradox that first appeared in one of W. Lewin's MIT lecture series on YouTube (see References [1]).…

Introduction: Why Rindler Motion? When students learn relativity, it's usually taught using inertial (constant velocity) motion. There are lots of reasons…

This is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 14. Free quantum fields.The next chapter is 16. Renormalization. 15.…

The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 12. Gauge fixing.The next chapter is 14.…

 A Short Proof of Birkoff's Theorem derived the Schwarzschild metric in units of ##G = c = 1##:\begin{equation} ds^2 = -\left(1 - \frac{2M}{r}\right)dt^2…

The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 10. Gauge symmetries.The next chapter is…

Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…

Macromolecules Paper overview A joint computational-experimental paper that I worked on was just published in MacroLetters, a journal that covers all…

This is chapter 4 of a series on Mathematical Quantum Field Theory.The previous chapter is 3. Fields.The next chapter is 5. Lagrangians.  4.…

The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 1. Geometry.The next chapter is 3. Fields  2.…

Why I'm a Bohmian and Questioning Orthodox QM Many people here know that I am a "Bohmian", i.e. an adherent of a very non-orthodox interpretation of quantum…

Introduction This article won't contain much about physics that typical readers of this site don't already know. However, deconstructing improper physics…

In terms of wavelength, peak solar radiation occurs at about 500 nm.  Interestingly, this is well within the range of human vision.  When solar radiation…

Introduction In introductory physics, the optics unit often teaches about virtual and real images, focal lengths, indexes of refraction, etc. Some questions…

Purpose The purpose of this Insights article is to give the reader a brief introduction to the principles behind diffraction-limited focusing. The reader…

Introduction: The purpose of this Insight is to explain permanent magnets in a way that is in agreement with advanced textbooks on the subject, and that…

 When we left off in part 2, we were looking at the metric for the Schwarzschild geometry in Kruskal-Szekeres coordinates:$$ ds^2 = \frac{32…

This is a little note about quantum amplitudes. Even though quantum probabilities seem very mysterious, with weird interference effects and seemingly nonlocal…

Every quantum physicist knows that all particles are either bosons or fermions. And the standard textbook argues that this so does not depend on the number…

The fundamental interactions of the Standard Model are described by Yang-Mills theory. This is a gauge theory, which means the following: (1) Choose a…

 It is familiar that Einstein gravity may be formulated in terms of a vielbein field together with a "spin connection", subject to the constraint…

Introduction Let us start with a familiar situation. Take a familiar part of a road, for example, the one from your home to work. How long will it take…

The Schwarzschild Metric A Lagrangian that can be used to describe geodesics is [itex]F = g_{\mu\nu}v^\mu v^\mu[/itex], where [itex]v^\mu = dx^\mu/ds[/itex]…

Introduction Purpose and scope In late high school physics courses and first-year university courses, the phenomenon of acoustical 'beats' (digital audio)…

Consider a problem about the curve of fastest descent in the following generalized statement. Suppose that we have a Lagrangian system $$L(x,\dot x)=\frac{1}{2}g_{ij}(x)\dot…

Here we present some useful kinematic fact which is uncommon for textbooks in mechanics. Consider a convex rigid body (RB) rolling without slipping…

Introduction I recently wrote a post on my blog about a fairly esoteric idea regarding sound propagating through light. This inspired me to write an…

If we violate a Bell inequality, we know we have quantum entanglement, and it used to be thought that these two notions were one and the same.At least,…

In discussions on the internet (including a number of Wikipedia pages) and in books and articles for non-experts in particle physics, there is considerable…