# Light-Like Separation

novice_hack
Is it possible for all the events in a field to be light-like separated from each other? What would such a field be like?

Gold Member
2022 Award
What do you mean by "events in a field"?

Events in relativity are points of the space-time manifold. A field is a function of events, ##f(x)## (where ##f## can be all kinds of quantities, scalars, vectors, tensors, or various kinds of spinors or also operators of all these kinds when it comes to QFT, and ##x## are coordinates, ##(x^0,x^1,x^2,x^3)##).

martinbn, Nugatory and Ibix
novice_hack
Ok. I suppose I meant: can all the spacetime intervals between events be light-like?

Homework Helper
Ok. I suppose I meant: can all the spacetime intervals between events be light-like?
The set of events comprising a light-like geodesic would have that property.

However, if you included any additional event not on that trajectory then it seems clear that such an event would have space-like separation from some events on the trajectory and a time-like separation from others.

Note that you must be talking about flat space-time since the "spacetime interval" between events is ambiguous otherwise.

vanhees71 and Ibix
Mentor
Ok. I suppose I meant: can all the spacetime intervals between events be light-like?
The spacetime interval is defined along a path. It requires more than just specifying a pair of events. It requires specifying the path from one to the other. So the question really is not well formed.

vanhees71