### Posts

### I Know the Math Says so, but Is It Really True?

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I'm sure anyone who has hung out long enough here on Physics Forums has encountered threads that go something like this (I'll use an example based on threads…

### Understanding Precession in Special and General Relativity

The Absolute Derivative
In relativity we typically deal with two types of quantities: fields, which are defined everywhere, and particle properties, which…

### Exploring Fermi-Walker Transport in Kerr Spacetime

In the last two posts in this series, we developed some tools for looking at Fermi-Walker transport in Minkowski spacetime and then applied them in Schwarzschild…

### Learning Fermi-Walker Transport in Schwarzschild Spacetime

In the first post in this series, we introduced the concepts of frame field, Fermi-Walker transport, and the "Fermi derivative" of a frame field, and developed…

### Fermi-Walker Transport in Minkowski Spacetime

This is the first of several posts that will develop some mathematical machinery for studying Fermi-Walker transport. In this first post, we focus on Minkowski…

### How to Better Define Information in Physics

When I ask questions about the conservation of information I frequently get the reply, “It depends on what you mean by information.” So, I researched…

### How to Solve Einstein’s Field Equations in Maxima

A few months ago, pervect pointed me to a post by Chris Hillman which is an introduction to the usage of Maxima for General Relativity. Maxima is a free…

### The Schwarzschild Geometry: Physically Reasonable?

In the last article, we looked at various counterintuitive features of the Schwarzschild spacetime geometry, as illustrated in the Kruskal-Szekeres…

### The Schwarzschild Geometry: Spacetime Diagrams

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…

### The Schwarzschild Geometry: Coordinates

At the end of part 1, we looked at the form the metric of the Schwarzschild geometry takes in Gullstrand-Painleve coordinates:$$
ds^2…

### The Schwarzschild Geometry: Key Properties

Not long after Einstein published his Field Equation, the first exact solution was found by Karl Schwarzschild. This solution is one of the…

### Exploring General Relativity as a Gauge Theory

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…

### The Revival of Newton-Cartan Theory in General Relativity

It's a calculation which you can find in any textbook on General Relativity (GR): when gravity is weak and does not vary with time, and when particles…

### Learn about the Big Bang and the Expansion of the Universe

The "ordinary Big Bang and expansion" (no inflation, no dark energy)
Einstein's General Relativity allows a solution (FLRW metric) where an empty Universe…

### Radius of the Observable Universe in Light-years Is Greater than Its Age

The radius of the observable universe is about 46 billion light-years, which is considerably greater than its age of about 14 billion years. The radius…

### Can We Tell Whether the Universe Is Rotating?

If you believe wholeheartedly in Mach's principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing…