Relativity

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}…

If you try learning general relativity, and sometimes special relativity, on your own, you will undoubtedly run into tensors. This article will outline…

Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsMost people who have spent any time at all studying GR are familiar with the…

This Insight was inspired by the discussion in "electric field seen by an observer in motion", which tries to understand the relation between two expressions:…

The "twin paradox" is often discussed in the introductory treatment of special relativity. Under "twin paradox" we understand the fact that if two twins…

Introduction This article is essentially an addition to the previous one on (mainly) inelastic collisions to include the particular case of inelastic…

Definition and summary Abstract from Poisson and Israel (1990), "Internal structure of black holes": "The gravitational effects associated with the radiative…

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

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…

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

 A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then…

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

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

 Combining electromagnetism with relativity and quantum mechanics led to QED. Last time we saw the immense struggles with the continuum this…

This Insight is a follow-up to my earlier tutorial Insight (Spacetime Diagrams of Light Clocks). I gave it a different name because I am placing more…

Newtonian limit and spacetime curvature It's a calculation that you can find in any textbook on General Relativity (GR): when gravity is weak and does…

Introduction In this article, I will discuss some experiments in the 19th and early 20th centuries that looked at how the velocity of a light source affects…

 This is the first in a 5-part series of Insights that will introduce blockworld (aka "block universe”) and use it to address a puzzle…

Why a rigid rod can't send faster-than-light signals One common proposal for achieving faster-than-light (FTL) communication is to use a long, perfectly…

 The title question of this article is one that often comes up in PF threads, and I would like to give my take on it. This will be the first…

I was bothered for a long time by the reasons for the relativistic validity of the work-kinetic energy relation ##\Delta E=Fd##, which holds without any…

Bell spaceship paradox — setup Bell describes two spaceships that start out at rest relative to each other with an elastic string between them, one…