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:
“Ye purs, that been to me my lives light
And saviour, as in this world down here,
Out of this tonne helpe me thurgh your might,”
—Geoffrey Chaucer (1340?–1400)
“Every living language, like the perspiring bodies of living creatures, is in perpetual motion and alteration; some words go off, and become obsolete; others are taken in, and by degrees grow into common use; or the same word is inverted to a new sense or notion, which in tract of time makes an observable change in the air and features of a language, as age makes in the lines and mien of a face.”
—Richard Bentley (1662–1742)
“All the critics who could not make their reputations by discovering you are hoping to make them by predicting hopefully your approaching impotence, failure and general drying up of natural juices. Not a one will wish you luck or hope that you will keep on writing unless you have political affiliations in which case these will rally around and speak of you and Homer, Balzac, Zola and Link Steffens.”
—Ernest Hemingway (1899–1961)
“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)