Space dimensions are orthogonal one to each other. But what about time in the Minkowski diagram?
At first sight, time seems to be orthogonal to space. But we have to consider that each Minkowski diagram is an observer's diagram. Thus, an object that is not moving with regard to the observer will describe a vertical worldline in the Minkowski diagram of the observer. However, from the point of view of another observer (inertial frame) the worldline described by the object might be inclined. Even the worldline of the observer himself which is the y-axis might be sloped from the point of view of other observers.
The conclusion seems to be that time is not orthogonal to space. Or is there an error?