[Cosmo-media] blogger introduction to cosmology questions

[Boud Roukema]

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/IPCC_AR6_SYR_SPM.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