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:

Interval of Events in Minkowski Spacetime
Interval of Events in Minkowski Spacetime

Last update: 2014.

Table of Contents

 About This Book

 Introduction of Space

 Introducion of Frame of Reference

 Introducion of Time

 Introduction of Speed

 Newton's Laws of Motion

 Introduction of Special Relativity

 Time Dilation in Special Relativity

 Length Contraction in Special Relativity

 The Relativity of Simultaneity

 Introduction of Spacetime

Minkowski Spacetime and Diagrams

What Is Minkowski Spacetime?

 Events Interval and Relations

 What Is Lorentz Transformation?

 What Is Minkowski Diagram?

 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

 Multiple Reference Frames in Minkowski Diagram

 References

 PDF Printing Version