Cosmology - What are the problems with the theory of Eternal Return?

Question

I have been thinking of Niestzche's Eternal return theory and how it could be possible that everything we do and our entire history and the universe will be repeated exactly the same again, and again with no end.

Here's how I want to imagine it:

Since time is directly tied to space (which makes up the universe) - earning it the name space-time, what if the space-time is a sphere for us because we are 3d but like a 2d circle for a 4d being, what if every move and action we make is already predestined and practically printed into this sphere - like a record cd but with images instead. And therefore the past and the big bang itself is therefore our future as it comes after our future and the universe's future end?

Are there any problems with the theory of Eternal Reccurrence and/or evidence that suggests that our exact history and us as we experience life will never repeat?

Answer 1

Poincare's recurrence theorem shows that certain systems will, after some arbitrarily long period of time, return to a state identical (or practically identical) to the initial state. Defining the "initial state" is kind of arbitrary too so what it actually says is that in these certain types of systems all states will eventually reoccur.

Whether or not this applies to our universe is a different issue. Perhaps it will collapse before this arbitrarily long time? Perhaps some other cosmic event might stifle the process during this arbitrarily long period of time. I just thought this might be kind of interesting to you.

In From Eternity to Here, Sean Carrol discusses Poincare's recurrence theorem and likens it to the theory of eternal return. Though Niestzche likely didn't believe this literally to be the case. He was more talking about the idea that we ought live as though this were true as to guide ourselves into living a life that we would want to live again and again and again- a good and fulfilling life.

Check here for more details.

Answer 2

In 1949 Kurt Godel proposed a solution to Einstein's general relativity equations that allowed for closed time-like trajectories. It is known now to be one instance of cosmological dust models. Einstein apparently was not enthusiatsic; details and the story are easily found e.g. in Yourgau's book (2005).

On a more grand scale Roger penrose has proposed his Conformal cyclic cosmology which is what its name precisely says: the future time-like infinity of each previous iteration being identified with the Big Bang singularity of the next. It has been exposed in series of papers found at the arxiv.

The idea of creating a cycle or a return by matching beginning with end has been explored at some length by the greeks stoics (see Hahm's Book): they imagined a universal conflagration in which everything is reduced to ashes and then gradually a world develops, people appear, thing happen until a great fire reduces evrything to ashes...

A problem with such a construction is that it leaves no room for an external observer who could state that a return occurs. The ancient thinkers discussed at some length are the items (people included) exactly the same or indeed materially the same or only approximately.

Nietzsche of course knew about the ancient theory but apparently had an impressive experience of "deja vu": experiencing being different from knowing he started advertising it as his own discovery. Actually in the same decade Auguste Blanqui and Gustave Le Bon proposed an other kind of eternal return, based on exhaustion of combinations allowed by atoms.

[Refs]: Yourgrau, Palle (2005). A world without time: the forgotten legacy of Gödel and Einstein. New York: Basic Books.

David E. Hahm. The Origins of Stoic Cosmology. Ohio State University Press, 1977.

Auguste Blanqui, L'eternite par les astres, 1872

Answer 3

Currently, astrophysics says that spacetime is expanding at an increasing rate. This means that parts of the universe that were connected to us are now moving away at faster than the speed of light, and these parts are going to get closer and closer. In a few trillion years, there will be nothing visible except the local cluster of galaxies. There's a good discussion in Krauss, "The Universe from Nothing" of the "Big Rip".

If this is true, there will be no recurrence. The matter in the Universe can never come back together. The Universe will expand forever.

Krauss suggests that there may be infinitely many other Universes, in which case it's theoretically possible that an exact duplicate might come about, but that isn't certain. There are an infinite number of integers, all different. There's a larger infinite number of real numbers, all different. There's no reason to think this is different with Universes.