Could the Universe's Infinite Nature Align with Thermodynamics?

[collinsmark]

I suspect there's not enough available information to assign probabilities to any of the imagined "possibilities" regarding whether the universe is infinite or not. ["Possibilities" such as a) vast, yet closed, finite universe with slightly positive curvature, b) flat and infinite, c) flat and finite (e.g., torus shaped), d) open and infinite with a slightly negative curvature.]

Here's a tale of caution regarding probabilities which involve infinity. It's a purely mathematical story and doesn't even touch on the physical unknowns that are pertinent to this thread. If it's even on topic at all, it doesn't become on-topic until 13:30 or so of the second video.





Forgive me if this isn't on topic. This isn't exactly my area of expertise.

 

[Hornbein]

Hi @Hornbein:

I am puzzled by the statement that seems to imply that a finite universe has a curvature Ω_k which gets larger as the universe expands. Ω_k is inversely proportional to the radius R of the finite universe. Since the radius gets bigger over time, Ω_k gets closer to zero, that is closer to flatness. I think that the statement that the critical density (assumed to be greater than 1) approaches 1 (and then is larger as the size is smaller) is also incorrect. This was the case for Ω_Λ = 0, but not so for the currently best fit where Ω_Λ ~= 0.7.

Regards,
Buzz

I don't understand it. I just quote experts. There are discussions on this topic elsewhere at PF, I would suppose under Cosmology.

 

[Buzz Bloom]

Hi @collinsmark:

Wikipedia has a very clear explanation of the paradox.

https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)​

It is an excellent example that the probability distribution of a variable depends on the method used to define an instance of the variable. A different method results in a different distribution.

I do not think this paradox is applicable to the topic of calculating the distribution of a cosmological variable, but I could be mistaken. I would be only moderately surprised if it should be found out that the recent strange difference in results between two methods of calculating H₀ is an example of this paradox.

Regards,
Buzz

 

[Evo]

Sorry, we really do not allow philosophy at PF, with the exception in Quantum Physics, at the mentors discretion in that forum, it's a fine line.

So thanks again to everyone for keeping the thread from going off the rails, but alas, time to close it before people outside of PF find the thread and begin quoting unicorns and fairies.