# Minkowski space

1. In Minkowski space, coordinates which satisfy

$$x^2 = t^2 - X^2 > 0$$

are in the region of spacetime that is time-like.

2. If it's

$$x^2 = t^2 - X^2 < 0$$

the region is space-like.

3. But if

$$x^2 = t^2 - X^2 > 0$$

then its "trajectory of light-like particles".

I have understood the first two points about time- and space-like regions but I could not get the third one about "light-like particles".

My confusion is - why just light-like particles? There are many other particles at quantum level.

• In the future, please use MathJax, not HTML markup, to display math. Thanks. – G. Smith Apr 6 '19 at 22:38

The reason why only massless particles are able to travel between two events separated by a light-like distance is that it requires you to travel at exactly the speed of light. You can see this by considering the equation $$t^2-x^2=0$$, this means that $$x=\pm t$$. These equations are with the units such that the speed of light $$c=1$$. Thus the particle taking this trajectory is travelling at the speed of light.