In the last post, I wrote a short fictional dialogue, where two colleagues, Edwin and Friedrich, discussed possible scenarios for the future of the universe.
In this post, I want to come back to that topic to explore a bit of the science behind those ideas.
1. Cyclic Universe and Eternal Return
The idea is simple: if time is infinite and the number of possible configurations of particles is finite, then the configurations must repeat themselves after a certain time, just like a pendulum goes back to the same position after one full period.
Poincaré made the eternal return formal with his recurrence theorem, stating that certain systems will, after a sufficiently long but finite time, return to a state very close to the initial state. The time elapsed until the recurrence is known as the Poincaré recurrence time.
In a 1994 paper, Don Page estimated that the Poincaré recurrence time for a black hole with the mass of the entire universe would be
But Friedrich’s idea of eternal return in my post was following another line. He was playing with the cyclic universe hypothesis. If the universe is like a balloon inflating and shrinking forever, then in one of these cycles, everything should repeat just by chance.
A cyclic nature of the universe would depend on the amount of dark matter. If it’s big enough, it could eventually trigger a Big Crunch.
The cyclic universe hypothesis, however, has been knocked out by evidences that the universe expansion is accelerating, not slowing down. But still assuming that the universe is cyclic, is it reasonable to expect an eternal return?
If we lived in a classical universe, it would be enough to have the same initial positions and speeds for all particles in the universe to have everything repeating in a new cycle. That’s not easy at all. The slightest deviation in the initial conditions of a single particle could render different histories.
This happens to the double pendulum in the movie. At time 0, there are two double pendulums with almost same positions and speeds. After only 7 s, they evolve through completely different pathways.
To make things worse for the eternal return hypothesis, we don’t live in a classical universe. We are surrounded by quantum phenomena happening at random. The pendulum is not only oscillating, but it’s taking small hits all the way through.
Finally, to put the last nail in the eternal return’s coffin, the distribution and the number of particles that would condense out of each Big Bang could change completely from one cycle to another.
For all those points, eternal return seems to be one of those ideas to be left in a 19th century museum.
2. Life in a Forever-Expanding Universe
Edwin’s scenario was a forever-expanding universe. This matches better our current understanding of a universe in accelerated expansion.
The last stars should burn out in 100 trillion (1014) years. The black holes should evaporate through Hawking radiation in 10100 years. After that time, a final thermodynamical equilibrium may be reached. This state is known as the heat death, a situation where no thermodynamical free energy is available anymore (temperature is the same everywhere).
In fact, some local temperature gradients should still occur due to vacuum fluctuations. In these fluctuations, pairs of virtual particles pops out of vacuum and quickly annihilate each other. During their brief existence, however, they may interact with real particles nearby doing work. This happens, for instance, in the Casimir effect.
Edwin guesses that life could exist even in the heat dead universe. It would be based on an extremely slow-motion chemistry taking place in residual interstellar clouds, fueled by occasional quantum vacuum fluctuations.
But there was a flaw in Edwin’s reasoning. He didn’t take into account that matter may not be stable in the long run. Proton half-life is about 1033-36 years. After that, these particles should decay into positrons and γ-photons.
Thus, all atoms and molecules will disintegrate as soon as their protons start to die out, leaving the universe as a gazpacho of photons and leptons (electrons, positrons, and others), much before the evaporation of the black-holes ends.
Pity. I was quite a fan of Edwin’s frozen semi-eternal beings, but they can’t exist out of this blog.
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