# Does the invariance of interval hold only for events that occur in inertial reference frames?

For example, if we have two frames that have constant relative velocity, would the interval be the same between any two events? Or should we impose the condition that the particle must not accelerate between these two events?

Non-inertial frames involve coordinates that are accelerating, that is, the coordinates themselves are changing, and so for them the interval is not, in general, invariant. For example, the metric in Rindler coordinates with constant proper acceleration $$\alpha$$ in the $$x$$ direction is $$ds^2 = -(\alpha x^2)dt^2 + dx^2 + dy^2 + dz^2$$. Such coordinate systems are harder to work with than inertial frames.