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:
“We are better advised and more educated than any other generation of parents. Yet this deluge of literature and advice can also leave us feeling overwhelmed and inadequate. Where is the joy of bringing a child into the world if we are always afraid of making a mistake?”
—Neil Kurshan (20th century)
“Was seiz’d by the spirit that trails in the lines underfoot,
The rim, the sediment that stands for all the water and all the land
of the globe.
Fascinated, my eyes reverting from the south, dropt, to follow those slender windrows,
Chaff, straw, splinters of wood, weeds, and the sea-gluten,
Scum, scales from shining rocks, leaves of salt-lettuce, left by the tide,”
—Walt Whitman (1819–1892)
“The General Order is always to manoeuver in a body and on the attack; to maintain strict but not pettifogging discipline; to keep the troops constantly at the ready; to employ the utmost vigilance on sentry go; to use the bayonet on every possible occasion; and to follow up the enemy remorselessly until he is utterly destroyed.”
—Lazare Carnot (1753–1823)
“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)