A Minkowski flune is a four-dimensional space that follows the rules of Minkowski spacetime, with some dimensions being spacelike and some being timelike.
The metric of the Minkowski flune with one time coordinate t and three space coordinates x, y, z is .
Causal structure[]
Causality comes from the metric of the Minkowski flune by looking at the length of the vector between two points[1]:
- If it is real, the two points are timelike separated
- If it is zero, the two points are lightlike separated
- If it is imaginary, the two points are spacelike separated
If a direction for the future is chosen (typically positive t), these can be sorted into other classes.
If timelike vectors have the time component positive, they lie in the future, and if they have the time component negative, they lie in the past. This means that it is possible to travel to a timelike separated event, or have something travel to you from a timelike separated event, depending on whether it lies in the past or future.
If lightlike vectors have the time component positive, they lie on the future light cone, and if they have the time component negative, then they lie on the past light cone. It is also possible for one to be the zero vector. This means that the only way to communicate with a lightlike seperated event is using light.
All spacelike vectors lie elsewhere, meaning that it is impossible to communicate with spacelike separated events without travelling faster than light.