“From which stars have we fallen to meet each other here?”

— Friedrich Nietzsche

Last update Oct. 1, 2023. History

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Friedrich Nietzsche 655

German philosopher, poet, composer, cultural critic, and cl… 1844–1900

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“Consider an event, for example the outburst if a nova… Suppose this event is observed from two stars in line with the nova, and suppose further that the two stars are moving uniformly with respect to each other in this line. Let the epoch at which these stars passed by each other be taken as the zero of time measurement, and let an observer A on one of the stars estimate the distance and epoch of the nova outburst to be x units of length and t units of time, respectively. Suppose the other star is moving toward the nova with velocity v relative to A.”

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Let an observer B on the star estimate the distance and epoch of the nova outburst to be x<nowiki>'</nowiki> units of length and t<nowiki>'</nowiki> units of time, respectively. Then the Lorentz formulae, relating x<nowiki>'</nowiki> to t<nowiki>'</nowiki>, are<center><math>x' = \frac {x-vt}{\sqrt{1-\frac{v^2}{c^2}}} ; \qquad t' = \frac {t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}</math></center>
These formulae are... quite general, applying to any event in line with two uniformly moving observers. If we let c become infinite then the ratio of v to c tends to zero and the formulae become<center><math>x' = x - vt ; \qquad t' = t</math></center>.
The Structure of the Universe: An Introduction to Cosmology (1949)