Do cyclic models of the universe

[_heretic]

I have a question as to the actual nature of cyclic models of the universe (e.g. Roger Penrose's Conformal Cyclic Cosmology or the Ekpyrotic universe) - essentially where the universe has no beginning or end it simply goes through cycles eternally in both time directions. So in these situations would the entire history of the universe be considered to be mathematically an countably infinite or uncountably infinite as a set? That is, would each cycle (e.g. big bang to big crunch) be classed as an element of a countably infinite set or an uncountably infinite one?

Furthermore, if the set of these cycles was countably infinite would that mean that each cycle (i.e one in which there is an Earth and this post of the Physics Forums) could only ever occur **once** in the entire history of the universe. (?) Or would it mean that each cycle could have identical "looking" cycles later on. i.e at time N1 we encounter cycle A in which there is an Earth with this post on the Physics Forums, and later, at time N2 we encounter cycle B in which there is a situation functionally the same as in cycle A: Identical planet with identical post on identical network which, for all intents and purposes, is then the same as cycle A (?)

Thanks in advance!

 

[_heretic]

Anyone?

 

[twofish-quant]

So in these situations would the entire history of the universe be considered to be mathematically an countably infinite or uncountably infinite as a set? That is, would each cycle (e.g. big bang to big crunch) be classed as an element of a countably infinite set or an uncountably infinite one?

Countably infinite since you can map everything to integers.

Furthermore, if the set of these cycles was countably infinite would that mean that each cycle (i.e one in which there is an Earth and this post of the Physics Forums) could only ever occur **once** in the entire history of the universe. (?) Or would it mean that each cycle could have identical "looking" cycles later on. i.e at time N1 we encounter cycle A in which there is an Earth with this post on the Physics Forums, and later, at time N2 we encounter cycle B in which there is a situation functionally the same as in cycle A: Identical planet with identical post on identical network which, for all intents and purposes, is then the same as cycle A (?)

It's called Poincaire recurrence, but if you have the universe a situation in which you have countably infinite universes in a non-infinite phase space (i.e. you have infinite universes but the number of possible universes is finite) then mathematically things will repeat.

Yes this does lead to weird things which bothers people.

 

[_heretic]

Thanks for the info twofish-quant Just to clarify though, in terms of universe cycles what would the phase space be likely measuring? e.g. Possible energies at the big bang?

 

[sardar]

I find the concept of cyclic models of the universe to be fascinating and thought-provoking. These models propose that the universe undergoes infinite cycles, with no beginning or end. In terms of mathematical sets, the entire history of the universe in these models would be considered uncountably infinite, as there is no limit to the number of cycles that could occur.

In terms of whether each cycle would be considered an element of a countably or uncountably infinite set, it would depend on the specific model and how it defines a cycle. For example, in Roger Penrose's Conformal Cyclic Cosmology, each cycle would be considered an element of an uncountably infinite set as it is defined as a complete and self-contained universe. In contrast, the Ekpyrotic universe model proposes that each cycle is a result of a collision between two branes, which could potentially be a countably infinite set.

Regarding the question of whether each cycle could only occur once or if there could be identical cycles, it again depends on the specifics of the model. In some cyclic models, each cycle is considered unique and would only occur once. However, in other models, there could be identical cycles, especially if the conditions for each cycle are the same.

Overall, the concept of cyclic models of the universe raises many interesting questions and challenges our understanding of the universe and its origins. It is an area of ongoing research and debate in the scientific community, and I am excited to see where future studies and observations will take us in understanding the nature of our universe.