Is history repeating itself?

Alexander Vilenkin

The idea that history repeats itself is a commonplace notion, often expressed through sayings such as man is the only animal that trips twice over the same stone. However, that is not what we are addressing here, as such repetitions are always partial—events never recur in exactly the same way. Here, we will discuss whether it is possible for history to repeat itself in such way that events unfold exactly as they did before.

In principle, there are two ways history could repeat itself:

·         In time: According to theories of cyclical time—accepted by various civilizations—time repeats itself. Greek astronomers like Hipparchus and Ptolemy calculated that the cycle of the precession of the equinoxes (the wobble of the Earth's axis) lasted about 36,000 years (one degree every 100 years). Believing that the position of the stars determined human destiny, some concluded that every 36,000 years—when the stars returned to the same positions—history would repeat itself exactly, and the same people would be born again. Although Saint Augustine rejected this theory in The City of God, some Scholastics revived it, and the Church was forced to condemn their ideas as heretical. I discussed cyclical time in two previous blog posts: Cyclic Time and Linear Time and Is Time Infinite?

It is interesting to note that those who developed this astrological theory of historical repetition made several glaring errors: a) The cycle of the precession of the equinoxes does not last 36,000 years, but rather 25,772 years—approximately one degree every 72 years. b) And what about the planets? Astrologers believed that their position also influenced human life; however, their periods are not submultiples of the cycle of the precession of the equinoxes. Consequently, at the start of the next cycle, the planets would occupy positions completely different from those at the start of the previous cycle, thus their influence would not recur with that of the stars.

·         In space: In this case, repetitions would take place, not in time, but in space. Identical histories could—simultaneously or otherwise—exist in different parts of the universe. There are two distinct proposals regarding this scenario:

George Ellis

1.      The proposal by George Ellis and G.B. Brundrit: It begins with the assumption that the space of our universe is infinite. Then the number of planets in the universe would also be infinite. From this, they deduce that the number of planets harboring life is likewise infinite. However, the number of distinct life forms cannot be infinite, because the number of DNA variants must be finite. Therefore, when distributing a finite number of variants across an infinite number of inhabited planets, each variant must be repeated an infinite number of times.

2.      The proposal by Joan Garriga and Alexander Vilenkin: It also begins with the assumption that the space of our universe is infinite. Then the universe could be divided into an infinite number of causally disconnected regions (regions unable to influence one another)—each containing a finite amount of energy, according to the decoherent histories interpretation of quantum mechanics. So the number of life histories that could emerge within these regions would be finite. A finite number of histories distributed across an infinite number of regions would imply infinite repetitions of each history.

Francisco José Soler Gil

In an article published on arXiv—and subsequently published with some modifications in the journal Theoria—Francisco José Soler Gil and I responded to the two aforementioned theories by putting forward, among others, the following arguments:

·         Regarding the Ellis and Brundrit theory:

1.      It is doubtful that the universe is spatially infinite.

2.      Even if it were, the probability of life existing on a planet could be zero. It would suffice for the number of planets with life in the universe to be finite; thus, their probability would equal a finite number divided by infinity.

3.      Even if there were an infinite number of planets with life, the number of their histories would be a higher order of infinity (the infinity of trajectories, which, according to Cantor, is greater than the infinity of numbers and greater than the infinity of the continuum). Consequently, the probability of a specific history occurring in that universe would be zero, and there would be no repetition of histories.

·         Regarding the Garriga and Vilenkin theory:

1.      It is doubtful that the universe is spatially infinite.

2.      Quantum mechanics cannot be applied—just like that—to cosmology, because it is incompatible with General Relativity.

3.      The presence of black holes in a region would increase the number of possible histories, potentially rendering it infinite, which undermines the main argument of this proposal.

Our article was discussed on Phys.org. Anyone wishing to gain a deeper understanding of the two proposals and our responses can consult one of the versions of our article, linked above, or the Phys.org article.

The same post in Spanish

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Manuel Alfonseca