I would like to learn about the angle between space-like vectors and time-like vectors. Is there anyone who can help me repeatly, please?
robphy said:Angle measure is usually defined as the ratio of arc-length on a "circle" to the radius. With two future-timelike vectors, one can use the intercepted arc-length of a unit hyperbola to define the angle between two future-timelike vectors. (This is called the rapidity.)
The angle between a space-like and a time-like vector is not well-defined in the context of special relativity. This is because the concept of "angle" relies on the notion of a Euclidean space, which does not apply to the non-Euclidean spacetime of relativity.
No, the angle between two spacetime vectors cannot be measured in the same way as angles in Euclidean geometry. However, there are other mathematical techniques that can be used to compare the orientations of different vectors in spacetime.
The distinction between space-like and time-like vectors is crucial in understanding the behavior of objects in relativity. Space-like vectors represent distances and lengths, while time-like vectors represent intervals of time. The angle between them can indicate the relative motion of objects and how events are perceived by different observers.
No, the angle between space-like and time-like vectors can vary. In fact, in some cases, it can be imaginary or undefined. This is because the angle is determined by the inner product of the two vectors, which can be complex or non-existent depending on the nature of the vectors.
The angle between space-like and time-like vectors is relative and can change depending on the observer's reference frame. This is known as the relativity of simultaneity, where two events that are simultaneous in one frame of reference may not be simultaneous in another frame. Therefore, the angle between the space-like and time-like vectors may also change.