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:
“‘Where is the world?’ cries Young, at eighty. ‘Where
The world in which a man was born?’”
—George Gordon Noel Byron (1788–1824)
“Scholars and artists thrown together are often annoyed at the puzzle of where they differ. Both work from knowledge; but I suspect they differ most importantly in the way their knowledge is come by. Scholars get theirs with conscientious thoroughness along projected lines of logic; poets theirs cavalierly and as it happens in and out of books. They stick to nothing deliberately, but let what will stick to them like burrs where they walk in the fields.”
—Robert Frost (1874–1963)
“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.
“Write about winter in the summer. Describe Norway as Ibsen did, from a desk in Italy; describe Dublin as James Joyce did, from a desk in Paris. Willa Cather wrote her prairie novels in New York City; Mark Twain wrote Huckleberry Finn in Hartford, Connecticut. Recently, scholars learned that Walt Whitman rarely left his room.”
—Annie Dillard (b. 1945)
““The ideal reasoner,” he remarked, “would, when he had once been shown a single fact in all its bearings, deduce from it not only all the chain of events which led up to it but also all the results which would follow from it.””
—Sir Arthur Conan Doyle (1859–1930)