Speed of Light and Causality
Straight lines passing the origin which are steeper than both photon world lines correspond with objects moving more slowly than the speed of light. If this applies to an object, then it applies from the viewpoint of all observers, because the world lines of these photons are the angle bisectors for any inertial reference frame. Therefore any point above the origin and between the world lines of both photons can be reached with a speed smaller than that of the light and can have a cause-effect-relationship with the origin. This area is the absolute future, because any event there happens later compared to the event represented by the origin regardless of the observer, which is obvious graphically from the Minkowski diagram.
Following the same argument the range below the origin and between the photon world lines is the absolute past relative to the origin. Any event there belongs definitely to the past and can be the cause of an effect at the origin.
The relationship between of such pairs of event is called timelike, because they have a time distance greater than zero for all observers. A straight line connecting these two events is always the time axis of a possible observer for whom they happen at the same place. Two events which can be connected just with the speed of light are called lightlike.
In principle a further dimension of space can be added to the Minkowski diagram leading to a three-dimensional representation. In this case the ranges of future and past become cones with apexes touching each other at the origin. They are called light cones.
Read more about this topic: Minkowski Diagram
Famous quotes containing the words speed, light and/or causality:
“Among the laws controlling human societies there is one more precise and clearer, it seems to me, than all the others. If men are to remain civilized or to become civilized, the art of association must develop and improve among them at the same speed as equality of conditions spreads.”
—Alexis de Tocqueville (1805–1859)
“To recover a buried treasure without having it disappear miraculously in the process, one must be entitled to it, and also be willing—really willing deep in his heart—to share it with the poor and helpless. Buried money, especially silver, gives off a bright glow which comes right up through the earth and can be seen as a dim light on nights when the weather is misty or there is a gentle rain.”
—Administration in the State of Ariz, U.S. public relief program (1935-1943)
“Any important disease whose causality is murky, and for which treatment is ineffectual, tends to be awash in significance.”
—Susan Sontag (b. 1933)