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:
“The world goes by my cage and never sees me.”
—Randall Jarrell (1914–1965)
“While you are divided from us by geographical lines, which are imaginary, and by a language which is not the same, you have not come to an alien people or land. In the realm of the heart, in the domain of the mind, there are no geographical lines dividing the nations.”
—Anna Howard Shaw (1847–1919)
“Is it not possible that an individual may be right and a government wrong? Are laws to be enforced simply because they were made? or declared by any number of men to be good, if they are not good? Is there any necessity for a man’s being a tool to perform a deed of which his better nature disapproves?”
—Henry David Thoreau (1817–1862)
“My bad head cannot adjust itself to the way things are.... If I want to depict spring, it has to be in wintertime; if I want to describe a beautiful landscape, I must be enclosed within walls; and I have said a hundred times that if I were put in the Bastille, there I would paint a picture of liberty.”
—Jean-Jacques Rousseau (1712–1778)
“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)