A timelike vector is a type of vector in the context of special relativity that represents the direction and magnitude of an object's movement through time. It has a positive magnitude and is always pointing in the direction of increasing time.
A null vector is a type of vector in the context of special relativity that represents the direction and magnitude of an object's movement through space. It has a magnitude of 0 and is always perpendicular to timelike vectors.
In the context of special relativity, the concept of orthogonality refers to vectors being perpendicular to each other. Since a null vector has a magnitude of 0, it cannot have a direction in space and therefore cannot be perpendicular to a timelike vector which is always pointing in the direction of increasing time.
This property is significant because it is a fundamental principle in special relativity that the speed of light is constant in all reference frames. If a timelike and null vector were orthogonal, it would imply that the speed of light can change depending on the reference frame, which goes against the principles of special relativity.
The concept of timelike and null vectors not being orthogonal is a fundamental principle of special relativity, which is a theory that explains the relationship between space and time. It is essential to understanding how objects move and interact in the universe and has been confirmed by numerous experiments and observations.