Note that the trigonometric functions are related to the hyperbolic functions via

48 cos ity = cosh ty and sin ity = i sinh ty, and, hence, if cosh ty = y , sinh ty = Yv/c. From Space and Time, an address delivered in Cologne in 1908. Translation from Lorentz, etal. (1913) (see also Galison (1979)).

Thus, for example, we can write the Lorentz transformation x' = y (x — vt), t' = y(t — vx/c2) as ds2 = dx2 + dy2 + dz2, whereas, in Minkowski's spacetime, the line element is given by ds2 = dx2 + dy2 + dz2 - c2dt2.

domain. A number of detailed refutations of this point of view have appeared in print subsequently, and it seems clear that, while the contributions of Poincare and Lorentz were hugely significant, it was Einstein who took the fundamental leap needed to create the new theory. Max Born, a contemporary of Einstein and protege of Minkowski, put it like this:

Relativity actually ought not to be connected with a single name or with a single date. It was in the air about 1900 and several great mathematicians and physicists -Larmor, Fitzgerald, Lorentz, Poincare, to mention a few - were in possession of many of its contents. In 1905 Albert Einstein based the theory on very general principles of a philosophical character, and a few years later Hermann Minkowski gave it final logical and mathematical expression. The reason Einstein's name alone is usually connected with relativity is that his work of 1905 was only an initial step to a still more fundamental 'general relativity', which included a new theory of gravitation and opened new vistas in our understanding of the structure of the

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