Lorentzian manifold

Lorentzian manifold is based on general relativity. When you board the airplane, it is necessary to avoid delaying your flight. All passengers need to have their seats before their flight. If some of them stopped other passengers to board, they would be delayed to take them off.

When a passenger had baggage, he would stop near his seat. His move must be slow. This is not efficient. You can't stop the flow.

γ(t) is causal sets. t∈[a,t]

Moreover, L(t) is arc length.

p and q are two points such as a seat (green) and a passenger (red).

p,q∈M

C(p,q)

M×M→Ｒ∪∞

This is called strong causality condition.

All passengers can't stop the flow, so you need to choose passengers who have baggage first. They move slowly to have their seats. Other passengers wait for having their seats. Therefore, nobody needs to stop before having a seat.