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 felt my cheek
Alter, to see the shadow pass away,
Whose grasp had left the giant world so weak
That every pigmy kicked it as it lay;”
—Percy Bysshe Shelley (1792–1822)
“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)
“The veto is a President’s Constitutional right, given to him by the drafters of the Constitution because they wanted it as a check against irresponsible Congressional action. The veto forces Congress to take another look at legislation that has been passed. I think this is a responsible tool for a president of the United States, and I have sought to use it responsibly.”
—Gerald R. Ford (b. 1913)
“As Cuvier could correctly describe a whole animal by the contemplation of a single bone, so the observer who has thoroughly understood one link in a series of incidents should be able to accurately state all the other ones, both before and after.”
—Sir Arthur Conan Doyle (1859–1930)
“It is clear to everyone that astronomy at all events compels the soul to look upwards, and draws it from the things of this world to the other.”
—Plato (c. 427–347 B.C.)