# 3: Spacetime

- Page ID
- 21800

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

- 3.1: Vector Rotations
- As a lead-in to the full exposition of special relativity, we take a look at some basics of vector transformations.

- 3.2: Position 4-Vector
- If our universe really is a 4-dimensional place, then vectors should have 4 components. It's amazing how much this "simple" idea explains.

- 3.3: Velocity and Acceleration 4-Vectors
- Just as in non-relativistic mechanics, we extend the mathematics of position vectors in relativity by considering their rates of change. If we are careful to measure these rates using correct measurements of time, the 4-vectors of velocity and acceleration constructed are powerful tools in relativistic calculations.

- 3.4: Momentum 4-Vector
- We wrap-up our construction of 4-vectors with the one that pertains to relativistic dynamics.

- 3.5: General Relativity
- Here we make a brief foray into Einstein's extension of his special theory. The details of this theory are too mathematically complex for this course, but we'll get an idea of the basic concepts.