Math in the Physical Sciences

Modern Physics and Mathematics

Did Einstein’s theories change our concept of dimensions?

Yes, our ideas about dimensions changed dramatically thanks to Einstein’s theories, not to mention the mathematics involved in producing those theories. In particular, one can’t distinguish space and time as elements in the description of events. Instead, they are joined in what is called the fourth dimension—also called a four-dimensional manifold known as space-time (see above).

Although it sounds like something out of the television show Star Trek, spacetime events in the universe are described in terms of the four-dimensional continuum. Simply put, each observer locates an event by three spacelike coordinates (positions) and one timelike coordinate. The choice of the timelike coordinate in space-time is not unique; hence, time is not absolute but is relative to the observer. The strange effects go on: In general, events at different locations that are simultaneous for one observer will not be simultaneous for another observer. (For more information about dimensions, see “Geometry and Trigonometry.”)



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