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

Events Interval and Relations

This section provides a quick introduction of 3 categories of event relations in Minkowski spacetime: lightlike events, spacelike events and timelike events.

From previous section, we learned that the interval (or distance) of two events in Minkowski spacetime is defined as:

s = sqrt(-(c*dt)**2+dx**2+dy**2+dz**2) #1: Minkowski interval

If we take square on both sides, we get a simpler formula:

s**2 = -(c*dt)**2 + dx**2+dy**2+dz**2 #2: taking square of #1 # Relation of interval, time and space.

With this formula, we can divide relations of two events into 3 categories:

- Lightlike Events - Two events with a zero interval square: s**2 = 0.
- Spacelike Events - Two events with a positive interval square: s**2 > 0.
- Timelike Events - Two events with a negative interval square: s**2 < 0.

If we draw a light cone for a given event A, the relation of another event B with A can be stated as below:

**A and B are lightlike, if B is on the light cone of A.**
The interval square between A and B is zero: s**2 = 0, or dx**2+dy**2+dz**2 = (c*dt)**2.
In this case, Bob at event B can "instantly see" event A, if B is in the future.
This is because information (light) from event A arrives at event B at the same moment when Bob opens his eye.

**A and B are spacelike, if B is outside the light cone of A.**
The interval square between A and B is greater than zero: s**2 > 0 or dx**2+dy**2+dz**2 > (c*dt)**2.
In this case, Bob at event B will never affected by event A, even if B is in the future.
Or we can say that B is separated from event A with too much space and too less time to be affected by A.

**A and B are timelike, if B is inside the light cone of A.**
The interval square between A and B is less than zero: s**2 < 0 or dx**2+dy**2+dz**2 < (c*dt)**2.
In this case, Bob at event B can be affected by event A, if B is in the future.
Or we can say that B is separated from event A with less space and enough time to be affected by A.
Amy from event A can take a high speed train to arrive at event B and meet Bob.

*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

►Events Interval and Relations

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