**Herong's Notes on Physics** - Version 3.21, by Dr. Herong Yang

What Is Minkowski Spacetime?

This section provides a quick introduction on Minkowski spacetime, a 4-dimentional spacetime coordinate system used with a frame of reference to mathematically describe the special theory of relativity.

**What Is Minkowski Spacetime?**?
Minkowski spacetime is a 4-dimentional spacetime coordinate system named after the mathematician Hermann Minkowski.
Minkowski spacetime is the most convenient coordinate system used with a frame of reference
to mathematically describe the special theory of relativity.

Minkowski spacetime has the following main assumptions:

4 axes (t,x,y,z) are mutually orthogonal.

The distance (or interval), s, between two points (or events) is defined as:

s = sqrt(-(c*dt)**2+dx**2+dy**2+dz**2) #1: Minkowski interval # c is the speed of light # dt, dx, dy, and dz are coordinate differences of the two points

Notice that the time component has a negative sign different than space components in the definition. This is an important contribution from Hermann Minkowski in constructing spacetime mathematical models. Distance is no longer a non-negative number. It is not even a real number in case where (c*dt)**2 > (dx**2+dy**2+dz**2).

If we simplify a Minkowski spacetime by dropping y and z dimensions and scale the time axis as c*t, we can illustrate the interval of two events as shown in the diagram below:

*Last update: 2014.*

Table of Contents

Introducion of Frame of Reference

Introduction of Special Relativity

Time Dilation in Special Relativity

Length Contraction in Special Relativity

The Relativity of Simultaneity

►Minkowski Spacetime and Diagrams

What Is Lorentz Transformation?

Constancy of Speed of Light in Minkowski Diagram

Time Dilation in Minkowski Diagram

Length Contraction in Minkowski Diagram

Relativity of Simultaneity in Minkowski Diagram

Invariant Spacetime Interval in Minkowski Diagram