from the new theory of electrons'. In 1906, Poincare developed a Lorentz-invariant form of the inverse square law and the astronomical consequences were studied by de Sitter in 1911. Poincare's analysis had revealed a whole family of possible gravitation theories indexed by an integer n, the simplest corresponding to n = 1. For this theory, de Sitter calculated an advance in the perihelion of Mercury of 7'' .15 per century, but arbitrary multiples of this could be realized simply by taking larger values of n. Moreover, any advance of this magnitude could be incorporated easily into Seeliger's zodiacal light hypothesis by reducing the mass of the inner matter ellipsoid a little.

Special relativity has not changed much since its inception, except in one important regard: the creation of the concept of spacetime by Hermann Minkowski, Einstein's mathematics teacher during his ETH days. Given what has been said previously, it will perhaps come as no surprise that one of the key ingredients in Minkowski's four-dimensional picture of the Universe was provided by Poincare, who showed in 1906 that a Lorentz transformation was equivalent mathematically to a rotation (through an imaginary angle) about the origin in a four-dimensional space with coordinates x, y, z, and ict, where i = „J— 1.

Quoted from Roseveare (1982), p. 159.

Thus, for example, we can write the Lorentz transformation x' = y (x — vt), t' = y(t — vx/c2) as where f = cosh-1 y is a real quantity.47 Poincare was searching for those quantities that remained invariant under the Lorentz transformation, and his geometrical interpretation revealed this. In particular, it follows immediately that the 'distance' x2 + y2 + z2 — c2t2 between any point and the origin remains fixed. However, Poincare did not believe that it would be worth while to translate relativity theory into this geometrical framework.

Minkowski took a radically different view. He saw the four-dimensional picture as representing an observer-independent reality, which he called 'The Absolute World':

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere

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