It is impossible for two events to happen simultaneously.

For millenia everyone assumed that time was the same for everyone, and so we could talk about two events happening at the same time. We could talk about things happening at the same time in two different cities or countries. Even now we routinely use a standardized time around the world and even on space missions, but it simply isn't true.

And it is all due to the effects of relativity.

Instead of confusing my readers with time distortion and the phenomena of Lorentzian spacetime right away, let me begin with a simple challenge that involves no physics at all.

Suppose that Bob sits at a table, and is given two markers - checker pieces work great for this - and is told to place them such that they are the same distance from him.


Now suppose that is friend Carol sits down beside him, and is given the same challenge. She must place the same two markers at equal distance from herself. However she has the added challenge that they must also still be at equal distances from Bob.


Is it possible to arrange the two markers such that they satisfy both requirements? In fact it is possible, but only if Bob and Carol are on opposite sides of the table. If they are seated next to each other, as shown here, then it is not possible.

And if we add a third member, Alice, to our group, then there are no such points.

Although it is easy to prove that this is impossible, it is an instructive exercise in understanding spacetime to actually get two markers and try this experiment. Try to arrange the markers so that they are equal distances from multiple observers located around the table.

So what does this have to do with the theory of relativity?

Quite a lot actually. If we replace the table with four-dimensional spacetime, which is what we live in, and replace each marker with an event (ie a point in space and time), then the distance from an observer to an event represents how much time that particular observer experiences before they encounter that event.  If each event emits a signal, then the distance to the observer determines how long it will take each signal to reach them.

Therefore if we want two events to happen simultaneously, then we need to position them at the exact same distance from the observer. But as the previous thought experiment proves, these two events will only be simultaneous for a single observer. 

In the diagrams, Bob will observe the two events happening at the exact same time, while Carol will see the event at the red marker happen earlier than the event at the blue marker.

And when we include our third observer, we see that the three friends will not even agree on which order the events happened in, as Carol insists that red is first and Alice insists that blue happened first.


In the real world, this means that if Alice and Carol are each travelling in the opposite direction from each other, then they will see the two events happen in different orders, while Bob (who is moving at a different speed from his two friends) will see them happen at the exact same time.

This is not an illusion, or some mathematical oddity. This is simply the nature of spacetime itself.

And that is why there is no such thing as simultaneity.