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, speed, light and/or causality:
“No speed of wind or water rushing by
But you have speed far greater.”
—Robert Frost (1874–1963)
“Wait, Kate! You skate at such a rate
You leave behind your skating mate.
Your splendid speed won’t you abate?
He’s lagging far behind you, Kate.”
—David Daiches (b. 1912)
“What is lawful is not binding only on some and not binding on others. Lawfulness extends everywhere, through the wide-ruling air and the boundless light of the sky.”
—Empedocles 484–424 B.C., Greek philosopher. The Presocratics, p. 142, ed. Philip Wheelwright, The Bobbs-Merrill Co., Inc. (1960)
“It is known that Whistler when asked how long it took him to paint one of his “nocturnes” answered: “All of my life.” With the same rigor he could have said that all of the centuries that preceded the moment when he painted were necessary. From that correct application of the law of causality it follows that the slightest event presupposes the inconceivable universe and, conversely, that the universe needs even the slightest of events.”
—Jorge Luis Borges (1899–1986)