World Lines in General Relativity
The use of world lines in general relativity is basically the same as in special relativity, with the difference that spacetime can be curved. A metric exists and its dynamics are determined by the Einstein field equations and are dependent on the mass distribution in spacetime. Again the metric defines lightlike (null), spacelike and timelike curves. Also, in general relativity, world lines are timelike curves in spacetime, where timelike curves fall within the lightcone. However, a lightcone is not necessarily inclined at 45 degrees to the time axis. However, this is an artifact of the chosen coordinate system, and reflects the coordinate freedom (diffeomorphism invariance) of general relativity. Any timelike curve admits a comoving observer whose "time axis" corresponds to that curve, and, since no observer is privileged, we can always find a local coordinate system in which lightcones are inclined at 45 degrees to the time axis. See also for example Eddington-Finkelstein coordinates.
World lines of free-falling particles or objects (such as planets around the Sun or an astronaut in space) are called geodesics.
Read more about this topic: World Line
Famous quotes containing the words world, lines, general and/or relativity:
“Things of this world are in so constant a flux, that nothing remains long in the same state.”
—John Locke (1632–1704)
“Called as partners in Christ’s service,
Called to ministries of grace,
We respond with deep commitment
Fresh new lines of faith to trace.
May we learn the art of sharing,
Side by side and friend with friend,
Equal partners in our caring
To fulfill God’s chosen end.”
—Jane Parker Huber (b. 1926)
“In former times and in less complex societies, children could find their way into the adult world by watching workers and perhaps giving them a hand; by lingering at the general store long enough to chat with, and overhear conversations of, adults...; by sharing and participating in the tasks of family and community that were necessary to survival. They were in, and of, the adult world while yet sensing themselves apart as children.”
—Dorothy H. Cohen (20th century)
“By an application of the theory of relativity to the taste of readers, to-day in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!”
—Albert Einstein (1879–1955)