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 of light, speed, light and/or causality:
“For myself and my loved ones, I want the heat, which comes at the speed of light. I don’t want to have to hang about for the blast, which idles along at the speed of sound.”
—Martin Amis (b. 1949)
“No speed of wind or water rushing by
But you have speed far greater.”
—Robert Frost (1874–1963)
“The earth had a single light afar,
A flickering, human pathetic light,
That was maintained against the night,
It seemed to me, by the people there,
With a Godforsaken brute despair.”
—Robert Frost (1874–1963)
“Any important disease whose causality is murky, and for which treatment is ineffectual, tends to be awash in significance.”
—Susan Sontag (b. 1933)