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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“Indeed, I thought, slipping the silver into my purse ... what a change of temper a fixed income will bring about. No force in the world can take from me my five hundred pounds. Food, house and clothing are mine for ever. Therefore not merely do effort and labour cease, but also hatred and bitterness. I need not hate any man; he cannot hurt me. I need not flatter any man; he has nothing to give me.”
—Virginia Woolf (1882–1941)
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—Henry David Thoreau (1817–1862)
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—Henry David Thoreau (1817–1862)
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—Ralph Waldo Emerson (1803–1882)