Special Relativity: Law of causality

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Causality

As humans, we have the tendency to explore events in greater depth and detail. To be more specific, we strive to find the causes and consequences for all events in the universe. However, in the scientific world, there are some restrictions for these answers. These were derived from Einstein's special relativity which highlighted how the speed of light in a vacuum was the universal speed limit. For the sake of simplicity, this concept is typically illustrated with a light cone.


WHAT IS THE LAW OF CAUSALITY?

The light cone is a diagram built in Minkowski space, using Non-Euclidian geometry. It captures a very important concept of causality, by restricting space to 2 dimensions [x and y plane in the diagram] and taking time to be the third dimension [z plane in the diagram]. An event J is assumed to occur at the origin. This framework is precisely what is shown below.


Since nothing travels faster than the speed of light, the light cone provides two results. Firstly, any event that could have caused J must have occurred inside or on the past light cone. Secondly, any event that J could cause, must be located inside or on the future light cone. 

Equally importantly, any event outside this light cone, can neither cause the event J, nor can it be caused by event J. This is because, the signal would have to travel faster than light for such a scenario, which is, as previously established, impossible.


While this seems like a trivial concept, and not very helpful in our daily lives, this light cone is truly essential when we are dealing with more prominent events in the universe. For example, astrophysicists rely on this very concept to predict the locality of events, when light from those events has just reached the earth. In fact, most of what we see in the night sky is simply the light reaching our eyes, billions of years after it was emitted by those stars. 

Learn more about the derivation and reasoning behind the universal speed limit, and about special relativity in its entirety, through this oversimplified presentation.

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