Ultimate Explanations of the Universe by Michael Heller

eliminate the beginning from the history of the universe is the concept of closed time: a sequence of events recurring an infinite number of times; a history heading nowhere but only endlessly reiterating what has already occurred an infinite number of times; an unending chain of births, deaths, and renewed births; the hopelessness of the impossibility of wresting free from an inexorable loop. Nonetheless this idea has been resurging quite often, both in our none too strictly controlled imagination as well as in the history of human ideas.
    In Antiquity the Stoics reduced the idea of eternal returns to its logical extreme. The history of the world was cyclical: after each cycle the world returned to its original state ( apokatastasis ), passing through a phase of destruction by fire and then starting a process of ordering itself anew ( diakosmesis ). In each cycle exactly the same structure was reconstructed, down to its most minute detail: “After the passage of centuries the same Socrates will be teaching in the same Athens, and in the streets of the same cities the same people will be going through the same suffering.” 1
    Every so often this doctrine is self-renewed and arises out of its own ashes. A contribution to its popularity in the modern period has come from Friedrich Nietzsche, who was very fond of it and treated it as a sort of religious message. He also tried to find a scholarly justification for it, albeit rather ineptly. In his opinion, the world should be envisaged as “a particular number of foci of force” and therefore “had to go through a calculable number of combinations, as if in a game of dice, in the grand game of existence.” Hence the world was a sequence of identical combinations “which had already been repeated an infinite number of times and which continued to play out their game ad infinitum .” 2
    You might think that today the idea of looped time could persist only in literary visions and science fiction. But the history of science turns out to be stranger than fiction.
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    4.2   Kurt GÖdel’s Universe
    Quite out of the blue it turned out that the general theory of relativity lends fairly strong support to the concept of closed time. The first solution of Einstein’s equations involving closed time-like curves was discovered in 1924 by Cornelius Lanczos, who was later Einstein’s assistant. 3 It was rediscovered in 1937 by Willem Jacob van Stockum, a Dutchman who was killed in action during the Second World War, as a pilot fighting for the Allies. 4 This solution (now known as van Stockum’s dust) describes a space-time with a cylindrical symmetry, in which matter in the form of dust rotates around an axis of symmetry. This fact physically distinguishes the axis of symmetry, as a result of which the space-time is not isotropic. Van Stockum’s solution has one other feature, apart from closed time-like curves, for which it is hard to give a physical interpretation: the density of the dust particles increases with distance away from the axis of rotation.
    In spite of their exotic properties, neither Lanczos’ nor van Stockum’s solution attracted much notice. It was not until Kurt Gödel’s discovery of another solution in 1949 that people’s attention was turned, 5 most probably thanks to the fact that Gödel was already a well-known personality and also because from the very start he promoted his solution as a cosmological model. Gödel’s solution entailed closed time-like curves, and understandably the possibility of a return to one’s own past stirred up a sensation. To reach a closed time-like curve in Gödel’s world you would have to have an unrealistically immense store of energy available to accelerate your spaceship appropriately, but what was that in view of the prospect of conquering time? Let’s take a closer look at Gödel’s solution. 6
    Gödel’s universe is filled with matter consisting of dust with a constant density, just like the