Light Cones

https://en.wikipedia.org/wiki/Light_cone
Image courtesy of Wikipedia.

The above image is a light cone, another concept introduced by Einstein. It is not a physical object, but rather a representation of how we observe events in space-time. A light cone deals very much with the concept of causality and simultaneity.

To further understand a light cone, we must construct one. Below is a representation of the set up for this. We have coordinate axes representing spatial directions (the horizontal lines), with the vertical axis being the “ct” axis, or the speed of light multiplied by time. You, the observer, are located at the red dot in the center of this coordinate system.

Light cone 3

Now, imagine you shine a flashlight. Congratulations! You have created an event. Light, in a light cone, propagates at a 45 degree angle with respect to the spatial axes. The event you created moves “upwards” through space-time, creating something we call the future cone. Any events in the cone are affected by the flashlight being switched on.

 

Light Cone 4

 

Events outside of the cone, say closer to the spatial axis, cannot effect events inside. This region is often referred to as “elsewhere”. Why is this? Basically, it is because the speed of light is our universal speed limit, and in order to breach the future cone, an event’s signal would need to be transmitted to you at a speed faster than light.

 

 

Light Cone 5

We can draw a similar cone in the “downwards” direction. This one is called the “past cone” and represents events affecting you, the observer, at the origin. Like before, any event that occurs outside the past cone cannot effect/reach events inside of the cone. We can describe every event in the universe by it’s own light cone.

 

 

 

When discussing light cones, it is important to remember these ideas:

  1. Time-like separation: anything inside the past or future cone are said to behave “time-like”, meaning they occur in the same place but at different times.
  2. Space-like separation: areas outside of the past and future cone are said to behave “space-like”, occurring at the same time but in different locations.
  3. Light-like: occurs at the portion of the diagram that denotes light, the yellow 45 degree line. Simply put: this means that light can be transmitted between two events.

LET’S MOVE ON TO PUTTING THIS TOGETHER WITH TIME DILATION!

Spacetime Diagrams