When going through the questions and comments of the recent Zodiac series, I found a lot of questions regarding the spacetime interval and realised I didn’t go into it in any great detail in last years relativity series. Silly me!
When I discussed the spacetime interval in the past, I explained it in the mathematical form as opposed to the important role it plays in our collective understanding of reality.
Einstein’s Relativity demonstrates that two observers in deep space or even the earth don’t always collect the same data on a particular event. Both observers may not agree on time, distance or sequence of events despite measuring everything perfectly. Both sets of data individually are entirely consistent despite being different and neither of them is wrong!
So what can both observers agree on? Causality! Causality in the way of the spacetime interval is what defines our entire reality. If two people are playing catch with a ball on the back of a moving pickup truck, they throw the ball to one another at a certain velocity. If the truck drives by someone at the side of the road and someone is watching, they will measure the ball going at its own speed plus the speed of the moving truck!
This is probably the best example I can give as to how the same event can have two different and correct outcomes depending on the position of the observers.
Depending on coordinate systems on a graph, the interval can be positive, zero or negative. In other words an interval between two events can be time-like or distance-like. It depends really on what the two observers cannot agree on. As space and time are linked, the further away one travels, the further back in time they go.
The speed of light is an important factor. It doesn’t change for any observer regardless of velocity or position. If you are in a car travelling at the speed of light and you turn the headlights on, the light will travel at the speed of light outward. In the same way, in a vacuum we can’t slow light down either.
The spacetime interval between events has been extremely well tested and stood up to every scrutiny ever thrown at it despite how counter intuitive it is. At this stage it is universally accepted and gives us the real facts of a situation two observers can’t agree on individually. Almost like a mathematical umpire which keeps reality present at all times.
The bottom line really is, time isn’t responsible for causality. Causality is responsible for time! The spacetime interval is the realest thing we have in humanity really!