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:
“When will the world learn that a million men are of no importance compared with one man?”
—Henry David Thoreau (1817–1862)
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Let rigid Cato read these lines of mine.”
—Robert Herrick (1591–1674)
“The first tool I step on
Turned into a weapon.”
—Robert Frost (1874–1963)
“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.)
“The prime lesson the social sciences can learn from the natural sciences is just this: that it is necessary to press on to find the positive conditions under which desired events take place, and that these can be just as scientifically investigated as can instances of negative correlation. This problem is beyond relativity.”
—Ruth Benedict (1887–1948)