# 1: Special Relativity


• 1.1: A Need for a New Model
In the world of Newtonian Mechanics, it was assumed that measured lengths and time intervals were observer-independent. A meter stick, for example, is one meter long for everybody, and something that lasts for one second will last one second for everybody. The discovery that the speed of light is the same regardless of the observer's state of motion, however, changed that. Let's use some thought experiments to see why.
• 1.2: The Spacetime Interval
In Newtonian mechanics, the length of an object is invariant. That is, if you use a different coordinate system to mark locations, the result you get for the length does not change. In Special Relativity, however, it is a combination of distance and time that is invariant from one coordinate system to another. We call this the spacetime interval.
• 1.3: Natural Units
If we define a particular unit of length to be the distance that light travels in one second (i.e. a light-second), then the speed of light can be written as 1 light-second/second. We call this system of units natural units. The advantage of natural units is that it allows you to drop every instance of c from equations; the downside is that if you want numbers that are not in natural units, then you need to figure out how to reinstate all of the factors of c .
• 1.4: Spacetime Diagrams
A spacetime diagram is used for plotting and visualizing events and worldlines.
• 1.5: Four-Momentum
In Newtonian mechanics, position in space can be indicated with a three-dimensional vector. In Special Relativity, however, events are indicated using four coordinates: x=(t,x,y,z).
• 1.6: Index Notation
The metric is a function or matrix that can be used to determine the distance between two points. It can be thought of as defining the rules of geometry.
• 1.0: A Muon Anomaly
Muons created in the upper atmosphere often reach the ground even though a simple classical calculation shows that they shouldn't.
• 1.7: Video Resources

Thumbnail: Artist concept of Gravity Probe B orbiting the Earth to measure space-time, a four-dimensional description of the universe including height, width, length, and time. (Public Domain; NASA).

This page titled 1: Special Relativity is shared under a not declared license and was authored, remixed, and/or curated by Evan Halstead.