World Lines As A Tool To Describe Events
A one-dimensional line or curve can be represented by the coordinates as a function of one parameter. Each value of the parameter corresponds to a point in spacetime and varying the parameter traces out a line. So in mathematical terms a curve is defined by four coordinate functions (where usually denotes the time coordinate) depending on one parameter . A coordinate grid in spacetime is the set of curves one obtains if three out of four coordinate functions are set to a constant.
Sometimes, the term world line is loosely used for any curve in spacetime. This terminology causes confusions. More properly, a world line is a curve in spacetime which traces out the (time) history of a particle, observer or small object. One usually takes the proper time of an object or an observer as the curve parameter along the world line.
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Famous quotes containing the words world, lines, tool, describe and/or events:
“I have defeated them all.... I was left with some money to battle with the world when quite young, and at the present time have much to feel proud of.... The Lord gave me talent, and I know I have done good with it.... For my brains have made me quite independent and without the help of any man.”
—Harriet A. Brown, U.S. inventor and educator. As quoted in Feminine Ingenuity, ch. 8, by Anne L. MacDonald (1992)
“There is something to be said for government by a great aristocracy which has furnished leaders to the nation in peace and war for generations; even a Democrat like myself must admit this. But there is absolutely nothing to be said for government by a plutocracy, for government by men very powerful in certain lines and gifted with the “money touch,” but with ideals which in their essence are merely those of so many glorified pawnbrokers.”
—Theodore Roosevelt (1858–1919)
“And if thou wilt make me an altar of stone, thou shalt not build it of hewn stone: for if thou lift up thy tool upon it, thou hast polluted it.”
—Bible: Hebrew Exodus 20:25.
“So, if we must give a general formula applicable to all kinds of soul, we must describe it as the first actuality [entelechy] of a natural organized body.”
—Aristotle (384–323 B.C.)
“One cannot be a good historian of the outward, visible world without giving some thought to the hidden, private life of ordinary people; and on the other hand one cannot be a good historian of this inner life without taking into account outward events where these are relevant. They are two orders of fact which reflect each other, which are always linked and which sometimes provoke each other.”
—Victor Hugo (1802–1885)