hi Aleksandra, [cc: cosmo-media public mailing list]

wt., 7 mar 2023 o 09:31 Boud Roukema <...> napisał(a):

...

I assume this is your blog: https://medium.com/@szymula.aleksandra You're welcome to ask me some questions - email would probably be the simplest.

Yes, that is exactly the blog. Thank you very much for giving me this opportunity.

These are the questions I'd like to include in this interview:

1. For a good start, what is exactly the concept of infinity?

There are many definitions of infinity [1]. The two infinities that are generally used in practice in cosmology are, informally speaking, \aleph_0, the amount of natural numbers (counting numbers) [2], and 2^{\aleph_0}, the amount of real numbers [3]. In simple words, these two infinities are each the size of a certain set of things. There's an easy proof of why these two infinities are different, related to writing down numbers in the decimal system.

[1] https://en.wikipedia.org/wiki/Infinity

[2] https://en.wikipedia.org/wiki/Countable_set

[3] https://en.wikipedia.org/wiki/Cardinality_of_the_continuum

2. In your opinion, what is the most mind-bending idea related to the

infinite universe, and how does it challenge our understanding of the nature of existence?

2a. The infinitely repeating identical worlds paradox is fairly mind-bending :).

In a spatially infinite universe, any physical sequence of events with a tiny probability that is allowed by our known laws of physics would have a probability of 1 of occurring somewhere. That doesn't mean that it's certain, just that it's very likely. If the Universe were really infinite, then it would very likely happen somewhere that a planetary system almost identical to ours forms, with an Earth almost identical to ours, and life evolves in almost exactly the same way as it has evolved here, and the Internet evolves and the Fediverse evolves, just like these events have taken place here. In some cases, the events will diverge in a few tiny ways, and gradually diverge more and more. This must be almost certain (the probability is 1) if the Universe is really infinite.

You can read some modern descriptions about this paradox infinite universe in [4] or [5].

2b. Our understanding of the nature of existence is quite limited, so I don't see the infinitely repeating identical worlds paradox as a challenge to it. Infinities imply surprising things. It would be a lot simpler if our Universe were finite - as Ellis & Brundrit mention [4].

[4] Ellis & Brundrit 1979, https://ui.adsabs.harvard.edu/abs/1979QJRAS..20...37E

[5] Garriga & Vilenkin 2001, https://ui.adsabs.harvard.edu/abs/2001PhRvD..64d3511G

3. Is the universe infinite in terms of space and time, or is there an

ultimate boundary?

We don't know if the Universe is infinite or not. So far, we have no significant evidence of it being finite. In both finite and infinite models of the Universe, we normally assume that there are no spatial boundaries.

How does this idea challenge traditional concepts of time and space?

The Newtonian cosmological model of infinite space has lots of problems. General-relativistic models make it a lot easier to have spatially finite models.

4. Can we ever truly comprehend the vastness of the universe?

Unlikely. :)

And what are some of the most interesting phenomena that suggest its infinite nature?

I don't see any evidence of the Universe being infinite. Our current standard model, if interpreted literally, is of an infinite universe, but the standard model is not really taken seriously as a complete model - it's just a fairly good model of all of our observations.

5. Now, how do you approach the task of visualizing or representing the

infinite universe? How has technology aided in our exploration ability?

Either a finite or infinite universe is represented cognitively through a lot of work using 2-dimensional analogies, drawing diagrams, making calculations, and developing symbolic mathematical skills and intuition of differential geometry and of the topology of 3-dimensional manifolds.

My guess is that by "technology" you mean software. The best software for cosmology is FOSS (free and open source software), since when the software is *not* free-software-licensed, we're not allowed to understand the software or correct bugs or improve it. FOSS helps for playing around with calculations, both with numerical calculations (with numbers) and for symbolic algebra (SageMath, Maxima).

6. There are many theories about how our universe works and all of them

sound intriguing, as well as confusing. Since there is so many concepts, how do various theories of the universe, such as the Big Bang, the parallel universe, the multiverse hypothesis, or the concept of fractal universe, contribute to our understanding of its infinite nature? How do these theories relate to each other?

The Hot Big Bang model is the standard model of the Universe developed to match general relativity to three observations - the expansion of the Universe, the cosmic microwave background, and nucleosynthesis - roughly from 1917 to becoming widely accepted from the 1960s to the early 1990s.

The next level of detail is the LambdaCDM model - roughly from the 1980s to becoming well accepted by the 2000s. This is currently the standard cosmological model.

Parallel universes and multiverse models are speculation that are nowhere near having any observational support.

A fractal structure of the spatial distribution of galaxies is to some degree a fair approximation on some scales - it's unlikely to change standard cosmology last time I checked it.

7. I mentioned the multiverse universe theory, and I have to say that is

one of my favorite concepts. Based on that I have to ask, what is the most compelling evidence for the multiverse theory, and how does it relate to the infinite universe concept?

I don't work on multiverse theory, so I couldn't say. Max Tegmark got quite famous for this and might want to talk about that. :)

8. What implications does the infinite universe have on the search for

extraterrestrial life?

Completely irrelevant. We're only searching for extraterrestial life in a finite part of the Universe. The most interesting would be signs of extraterrestial life within a few parsecs, since in that case two-way communication within our lifetimes could be possible.

9. Can we ever hope to travel to other parts of the universe given its

infinite nature?

We have no evidence that the Universe is spatially infinite, but even if we did, that would be irrelevant for space travel.

However, space travel by humans is a low priority. The current scientific priority is handling the climate emergency [6]. If there is not too much debris in Low Earth Orbit (LEO) once we get into a stable maximums of 2 deg C post-industrial warming (I'm being optimistic), maybe in the 2050s or 2070s or so, then planning on sending some space arks on multi-decade (or multi-century) journeys to neighbouring stellar systems *might* become realistic and ethically justified.

[6] https://web.archive.org/web/20230320135908/https://report.ipcc.ch/ar6syr/pdf...

(10). Finally, what is the most promising avenue for exploring the infinite universe?

The most interesting thing is looking for evidence that our Universe is finite, rather than infinite. Space in the standard cosmological model has both curvature and topology: either positive curvature (like a 2-sphere) or a multiply connected topology (like a 2-torus) would be examples where our Universe would be spatially finite. One of the recently discovered methods of detecting signs of cosmic topology is topological acceleration [7][8] - by observing the movements of galaxies carefully enough, we could, in principle, detect signs of the global shape of the Universe - curvature and topology.

What do you hope to achieve throughout your research?

It would be great to discover evidence of topological acceleration. :) However, that's not guaranteed. What is more likely is that the modelling work and observations and observational analyses needed to get there will lead to many related, possibly unexpected, side discoveries in the details of the formation of galaxies and the structure of the Universe.

[7] https://ui.adsabs.harvard.edu/abs/2007A%2526A...463..861R

[8] https://arxiv.org/abs/2201.09102

All of the above information is public - the latest observational and theoretical work can all be found on ArXiv [9]. If you see a press release about a "new" result or idea and there's no corresponding research paper about it on ArXiv, then it's unlikely to be serious research.

In principle cosmology can be self-taught - i.e. without attending university lectures - there's a huge amount of open-access information. However, in practice, university education is unavoidable. Good students generally take quite a bit of time (several years) to work through the standard material. Proposing new hypotheses in cosmology requires first understanding standard cosmology.

[9] https://arxiv.org/list/astro-ph.CO/recent

Cheers Boud