system
Given the following post, respond as if you're commenting on Reddit:
human
Is there any meaning to rotation around the time axis in spacetime?

If spacetime is a four-dimensional object, and you can rotate around the three spatial axes, how would you interpret rotation around the time axis?
gpt
Rotations which leave the time coordinate unchanged only mix spatial coordinates with each other, so these would be standard spatial rotations.

Where things get interesting is if you mix spatial and time coordinates. For example, you could rotate an object in the xt-plane (meaning transform the coordinates of a four-vector while leaving its magnitude invariant). This would correspond to a Lorentz boost. This is how you change between inertial reference frames, and it's a hyperbolic rotation. You can also think of it as a rotation by an imaginary angle in the xt-plane.