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:
“Thank God for tea! What would the world do without tea? How did it exist?”
—Sydney Smith (1771–1845)
“Indeed, I believe that in the future, when we shall have seized again, as we will seize if we are true to ourselves, our own fair part of commerce upon the sea, and when we shall have again our appropriate share of South American trade, that these railroads from St. Louis, touching deep harbors on the gulf, and communicating there with lines of steamships, shall touch the ports of South America and bring their tribute to you.”
—Benjamin Harrison (1833–1901)
“One of the great reasons for the popularity of strikes is that they give the suppressed self a sense of power. For once the human tool knows itself a man, able to stand up and speak a word or strike a blow.”
—Charles Horton Cooley (1864–1929)
“Language was not powerful enough to describe the infant phenomenon. “I’ll tell you what, sir,” he said; “the talent of this child is not to be imagined. She must be seen, sir—seen—to be ever so faintly appreciated.”... The infant phenomenon, though of short stature, had a comparatively aged countenance, and had moreover been precisely the same age—not perhaps to the full extent of the memory of the oldest inhabitant, but certainly for five good years.”
—Charles Dickens (1812–1870)
“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.)