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by means of supernovae, he perused clearly identified standard candles whose real brightness—that which one would perceive near the star—can be derived from other properties accessible from afar. Since the brightness as seen from Earth decreases with the distance to the object, the difference between real and observed brightness allows one to compute the distance. For Hubble, standard candles were not supernovae but Cepheids: variable stars for which Henrietta Leavitt had noticed a close relationship between their brightness and pulsation rates. Hubble found numerous Cepheids in some of the known nebulae, and from their pulsation rate he could determine first the real brightness and then the distance of the host nebulae—with the exceedingly surprising finding that nebulae lie far outside the Milky Way. Thus, nebulae are diffuse simply for the reason that they themselves consist of innumerable but very distant stars. Nebulae are nothing but galaxies of their own. By his observations, Hubble extended the understanding of the cosmos far beyond the borders of the Milky Way.

Moreover, the puzzle of escape velocities was now solved by the finding that more distant objects, independent of their kind, move away more rapidly than closer ones. Quantitatively, Hubble found a linear relationship between the escape velocity and the distance, a simple proportionality. The unflattering conclusion that we are so unpopular in the universe that not even galaxies can stand to be around us can easily be evaded by assuming a uniform expansion of the entire universe, of space itself. Galaxies do not move away from us or any other point; space between them and us expands. At a given moment in time, each piece of a line between Earth and a galaxy is increased by the same factor, making the change of the total length proportional to the distance. Moreover, observations found easy qualitative agreement with the cosmological solutions of general relativity—and that without assuming a cosmological constant. (Only very precise observations during recent years had revealed, as already mentioned, an acceleration of the expansion caused by dark energy. This again requires a special, déjà-vu contribution behaving in a way similar to that of a cosmological constant.) One could trust the theory, even when it was applied over such large cosmological distances. Here lies the birthplace of modern cosmology.

Alas, the solutions had a grave flaw: As one followed them backward in time, all of them gave infinitely high values for the matter density of the universe a finite time ago, a time when all of space had withered down to a single point. At that point, the infamous singularity, Einstein’s equations lose all their sense; the point itself falls outside the physics described by the theory. And yet attempts have often been made to interpret the singularity as the starting point of the universe, as it were a scientific proof for a linear worldview. But based solely on the classical theory, such bold conclusions are not allowed; the singularity clearly shows that the theory cannot be applied at that point.

Only an extension of the theory can help here, rendering it still able to describe expanding solutions but without running into a singularity. Only such a theory can show whether the instant of the classical singularity can play the role of an initial point, or whether physical time extends beyond the singularity—before the big bang. Since its early days, quantum theory has been seen as a crucial component of such an extension of general relativity; but this enterprise could be tackled only very slowly because of substantial mathematical complications. Early versions of quantum cosmology gave pictures of how a nonsingular beginning could appear, but properties of the singularity as a temporal boundary of space-time were not questioned; physicists merely attempted to cover up, as it were, the singular behavior behind the uncertainty of quantum theory. Such ideas were developed in the 1980s, in particular by Jim Hartle and Stephen Hawking on one side and Alex