A brief history of space (4/4)

Sequel of the preceding post A Brief History of Space (3/4) : From Descartes to Schwarzschild

Cosmology developed rapidly after the completion of general relativity by Albert Einstein, in 1915. In this theory, the Universe does not reduce to a space and a time which are absolute and separate; it is made up of the union of space and time into a four dimensional geometry, which is curved by the presence of matter.

Albert Einstein (here in 1910) developed the theory of relativity and was awarded the 1921 Nobel prize for physics. Image by © Hulton-Deutsch, Collection/CORBIS

It is in fact the curvature of space-time as a whole which allows one to correctly model gravity, and not only the curvature of space, such as Clifford had hoped. The non-Euclidean character of the Universe appeared from then on not as a strangeness, but on the contrary as a physical necessity for taking account of gravitational effects. The curvature is connected to the density of matter. In 1917, Einstein presented the first relativistic model for the universe. Like Riemann, he wanted a closed universe (one whose volume and circumference were perfectly finite and measurable) without a boundary; he also chose the hypersphere to model the spatial part of the Universe.

Einstein static universe in a space-time diagram.

At any rate, Einstein’s model made the hypothesis of a static Universe, with the radius of the hypersphere remaining invariable over the course of time. In truth, the cosmological solutions of relativity allow complete freedom for one to imagine a space which expands or contracts over the course of time: this was demonstrated by the Russian theorist Alexander Friedmann, between 1922 and 1924.

At the same time, the installment of the large telescope at Mount Wilson, in the United States, allowed for a radical change in the cosmic landscape. In 1924, the observations of Edwin Hubble proved that the nebula NGC 6822 was situated far beyond our galaxy. Very rapidly, Hubble and his collaborators showed that this was the case for all of the spiral nebulae, including our famous neighbor, the Andromeda nebula: these are galaxies in their own right, and the Universe is made up of the ensemble of these galaxies. The “island-universes” already envisaged by Thomas Wright, Kant and Johann Heinrich Lambert were legitimized by experiment, and the physical Universe seemed suddenly to be immensely enlarged, passing from a few thousand to several dozen million light-years at the minimum. Beyond this spatial enlargement, the second major discovery concerned the time evolution of the Universe. In 1925, indications accumulated which tended to lead one to believe that other galaxies were systematically moving away from ours, with speeds which were proportional to their distance. Continue reading

A brief history of space (3/4) : from Descartes to Schwarzschild

Sequel of the preceding post A Brief History of Space (2/4) : From Ptolemy to Galileo

At the beginning of XVIIth century, the way was open for new cosmologies, constructed on the basis of infinite space. Until then, the notion of space was conceived in the cosmological and physical order of nature, and not as the “background” of the figures and geometric constructions of Euclid. In other terms, physical space was not mathematicized. It became so thanks to René Descartes (1596 – 1650), who had the idea of specifying each point by three real numbers: its coordinates. The introduction of a universal system of coordinates which entirely criss-crossed space and allowed for the measurement of distances was a reflection of the fact that, for Descartes, the unification and uniformization of the universe in its physical content and its geometric laws was a given. Space is a substance in the same class as material bodies, an infinite ether agitated by vortices without number, at the centers of which were held the stars and their planetary systems.

A portrait of René Descartes

This new conception of the cosmos upset philosophical thought and led it far from the initial enthusiasm of the atomists and Giordano Bruno: “The absolute space which inspired the hexameters of Lucretius, the absolute space which that had been a liberation for Bruno, was a labyrinth and an abyss for Pascal.”[5] As for the scholars, they did not allow themselves to be discouraged by these moods and irresistibly moved towards the infinite universe.

The Descartes system of the world using vortices

The tendency toward the radical geometrization of an infinite space, initiated by Descartes, was consummated by the Englishman Isaac Newton (1642-1727). Newton postulated an absolute space, encompassing not only the background space of mathematics and the physical space of astronomy, but also that of metaphysics, since space was the “sensorium of God.” Physical space, finally identified with geometrical space, was necessarily Euclidean (the only one known at the epoch), without curvature, amorphous and infinite in every direction. At the heart of this immobile framework, Newton explained celestial mechanics in terms of the law of universal attraction, from now on considered responsible for gravitation and the large scale structure of the Universe. With Newton, cosmology took root for more than two centuries in the framework of an infinite Euclidean space and an eternal time.

Newton around 1700

All the problems are not resolved in Newtonian cosmology, far from it. On the question of the distribution of stars in space, for example, Newton believed that they must occupy a finite volume since, he argued, if they occupied an infinite space, they would be infinite in number, the force of gravitation would be infinite, and the universe would be unstable. Newton moreover supposed that the stars were uniformly spread within a finite mass|like a galaxy, for example. But a problem of instability remained: since each celestial body is attracted by every other one, at the least movement, at the least mechanical perturbation, all the bodies in the universe would fall towards a unique center, and the universe would collapse. Newton’s universe is therefore only viable if it does not admit motion on the large scale: its space is rigid and its time immobile. Continue reading