For this entry, let's take a much-needed break from ongoing national happenings and embark on a cosmological journey into the Alice-in-Wonderland realm of metaphysics by featuring and discussing (or rather, summarizing) a pair of YouTube videos produced by the online outfit Disculogic collectively titled "Post Eternity: Part 1" and "Post Eternity: Part 2."
Disculogic itself is a YouTube channel dedicated to videos exploring matters related to cosmology, astronomy, and theoretical physics with an eye toward "later" getting into AI, the philosophy of science, futurism, and transhumanism (no, that's not some WOKE gibberish). The videos really are "out there" on topics such as "Before the Big Bang," "4 Levels of the Multiverse," "Arrow of Time," "Black Holes," "Infinity," "Ekpyrotic Universe," and "Conformal cyclic cosmology."
The two videos featured and discussed in this entry are Post Eternity Part 1: The Universe Repeating Itself (Poincaré Recurrence) and Post Eternity Part 2: Boltzmann Brains.
The videos were made about three years ago and are each nearly 20 minutes long. And the New Agey fusion music that accompanies both is evocative and appropriate to the topic.
Note: The video title pages have the "Post Eternity" Parts 1 and 2 reversed from the written titles, perhaps because the two videos were initially intended to be shown in reverse order.
The summary text and concluding references and links are from the YouTube webpages with their descriptions. The explanatory text is my own paraphrasing of what the narrator is relating in each video. About that narrator, I couldn't determine who he is, but he sounds like the fellow, Anton Petrov, from the What Da Math? astronomy and mathematics educational video series.
Post Eternity Part 1: The Universe Repeating Itself (Poincaré Recurrence)
YouTube webpage description first video:
Is it possible for the universe to go through a cosmic Poincaré Recurrence? In other words, can the universe repeat itself? Will the same history happen again at some distant future? If the universe is closed and isolated, which indicates that it’s probably qualified for experiencing a Poincaré Recurrence in cosmic scale, will the entire history of our universe happen for an infinite number of times? If cosmic Poincaré Recurrence can take place, does it mean that the entropy of the entire universe will decrease at some point? Isn’t that the violation of the second law of thermodynamics?
The video opens by featuring a profound paragraph in a book by Nietzsche ruminating on eternal recurrence. Below is a screenshot of the paragraph below and, because I find it so profound, below that is the actual text of the paragraph.
What if, some day or night, a demon were to steal after you in your loneliest loneliness and say to you: "This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence -- even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again -- and you with it, speck of dust!"
--Friedrich Nietzsche, "Eternal Recurrence," Die fröhliche Wissenschaft (The Gay Science), 1882
The notion of de Sitter space is the fundamental concept as to why the Universe as we know it could undergo eternal cycles of recurrence.
For starters, the idea of de Sitter space and its opposite, anti de Sitter space, are based upon highly abstract mathematical known as manifolds that are used in mathematical treatments of general relativity, i.e., the four-dimensional fabric of space-time.
One type of manifold is the Riemannian and a special "pseudo" case is the Lorentzian. It has mathematical properties used in describing the curvative of spacetime. Let's just say that de Sitter space is a type of Lorentizan manifold with constant positive scalar curvature which, per Wikipedia, "is directly applicable to a maximally symmetric vacuum solution of Einstein's field equations with positive cosmological constant." For its part, the cosmological constant, Λ, is related to dark energy.
Again, per Wikipedia (sorry), a de Sitter universe is spatially flat and ignores matter so that the positive cosmological constant (dark energy) dominates the dynamics of that universe.
Given that the cosmological constant is positive, this universe expands at an accelerating rate forever, eventually "faster" than the speed of light itself (remember that it's spacetime itself expanding, so the speed of light limit is not being violated).
All matter and electromagnetic radiation in such a universe become ever-more-diluted until, eventually, a true de Sitter space is reached in any informational-bounded (i.e., observable) region -- and at this point, Poincare Recurrence becomes not only possible but inevitable.
That is, everything repeats.
How? Well, let's dive a bit into the video. For starters, above and below are two images showing the characteristics of pure de Sitter space.
These characteristics -- or, if you prefer, assumptions -- are necessary to explain how Poincaré Recurrence can occur in an infinitely expanding Universe. With them, as the narrator explains, given enough time, a very improbable thermal fluctuation WILL generate a new universe.
3D visualization of quantum (vacuum state) fluctuations of the quantum chromodynamics (QCD) vacuum
Here I need to make a big upfront admission: I don't understand the difference between a quantum fluctuation and a thermal fluctuation and what it means experimentally.
Difference between quantum and thermal fluctuations; Source: Physics Stack Exchange (link above)
OK, having admitted that ...
Here are the key points summarized from the video:
de Sitter space does not apply to the Observable Universe as we see it right now but that which may have dominated the very early cosmos and which may be the correct description of a far future version of it.
The Observable Universe has a cosmic horizon, and all the degrees of freedom are bounded within it. The implication is that such a bounded universe ends in a de Sitter space condition as a result of accelerating expansion and dilution. Such an observable universe is eternal but finite. This observable universe is a closed and functionally isolated system that is a causal patch of a larger "total" Universe.
It is here we have to introduce the concept of entropy (disorder) At time = 0, the entropy of the Universe is in low (lowest) state, a fact that gives rise to the Arrow of Time, although how this entropy came into place in a hypothetical initial cycle (i.e., before any subsequent recurrences) is unknown.
Regardless of why that initial low entry exists, any closed system is characterized by a bounded entropy, i.e., a finite system that can experience Poincaré Recurrences. Even with an infinite Universe, given the eventual dilution of matter and electromagnetic energy in our inflating Observable Universe into de Sitter space, it too becomes a closed system.
Our Observable Universe has an estimated 10^80 baryonic ("matter") subatomic particles in it. That's an inconceivable number you can state in many ways such as in the above video screenshot image, but I'll say as 100 quadrillion sextillion sextillion sextillion. But for as large as is that number, it's still finite (and, by the way, nowhere near a googol, 10^100, much less a googolplex, 10^10^100).
All 10^80 baryons in the Observable Universe will return to their initial condition at the time of the Big Bang given a mindboggling but still finite period of time -- i.e., in the Poincaré Recurrence time -- and resulting in a new Big Bang. This is distinct from the less likely but NOT zero probability case that every elementary particular will return to its EXACT previous state so that the EXACT conditions of the Big Bang will be there to restart our EXACT Universe.
To be clear, the "total" Universe does not have to reach its initial state as a whole. Instead, different parts of this Universe could fluctuate into its very early stages, i.e., revert to a low entropy state and undergo a thermal fluctuation. For our purposes, it would be our Observable Universe that underwent this fluctuation.
Here are three additional assumptions that go into this de Sitter-based Poincaré Recurrence:
With these assumptions, then Poincaré Recurrence is inevitable. What's more, as the Universe reaches its maximum entry (disordered) state and dies (i.e., the heat death), if we wait long enough -- an incomprehensible time but not infinity -- then a thermal fluctuation would cause the inflation field to start a new cycle of inflation, reheating, Standard Cosmology, and, eventually, heat death -- i.e., the process repeats.
Such fluctuations outside the thermal equilibrium state are exceedingly rare, and those large enough to start a new Universe are extremely rare.
Poincaré Recurrence time for the Observable Universe in exponential notation.
But due to their non-zero probabilities, no matter how improbable, they WILL eventually happen.
What's more, at any given point in time, an infinite number of Poincaré Recurrences may have already happened. More importantly, these very rare event low entropy fluctuations (Poincaré Recurrences) do not violate the Second Law of Thermodynamics.
The implications of this are similar to a multiverse in a bounded system. Given a huge amount of time, EVERYTHING will eventually happen with every possible event fluctuating back to its similar prior state or even the exact same state.
We could therefore think of each closed system as a multiverse but in the sense that each closed universe has the potential of creating every accessible state.
For a closed universe, it is limited to its own physical constants, and therefore its number of states is effectively nothing compared to a multiverse that is capable of creating universes with different physical constants. That is, it can only generate different universes with different initial conditions but not different physical laws.
The philosophical implications of a cosmic scale Poincaré Recurrence:
After you die, if there's a non-zero probability that a Poincaré Recurrence will take place, and create every possible state, then there is a guarantee that you will be included in some of those universes. The same, exact you including your cells, molecules, and every elementary particle down to the quantum state.
The physical and mental configurations of every person will be created endlessly.
And if every possible state of you can exist at some point, then there would be many states in which you are advanced enough to extend your life indefinitely.
But what doesn't have an answer is if you die and then after an inconceivably long time, you are reborn due to Poincare Recurrence, would that be the EXACT version of you that was born before??
To answer that question, we have to answer the question: What IS consciousness?? And THAT, dear children, remains a mystery no matter what any atheist or know-it-all confidently declares.
On a personal note, I would like to relive my lost New Jersey childhood life and world -- even given that I won't recall anything from this (or any other) time.
Of note, this video's YouTube page includes a list of the following two relevant arXiv electronic preprint articles with awesome titles:
Information Loss in Black Holes and/or Conscious Beings
Author: Don N. Page
Disturbing Implications of a Cosmological Constant
Authors: Lisa Dyson, Matthew Kleban, and Leonard Susskind
This is actually related somewhat to the Ethan Siegel piece I reposted in this entry that considers expanding models of the Universe to answre the question [direct link to Siegel piece]: How Much Of The Unobservable Universe Will We Someday Be Able To See?
And here is the second part of this Post Eternity series ...
Post Eternity Part 2: Boltzmann Brains
I'm not going to go into great detail for this video. Here is a description of the second video:
Boltzmann brain is another bizarre consequence of laws of physics. It’s a configuration of matter, similar to our brains; a statistical fluctuation risen out of thermal equilibrium, a conscious observer created by a sudden decrease in entropy, having false memories of a grand structure exactly like our universe.
Given enough time, every single possibility allowed by the physical laws in our most likely closed universe must eventually occur, including one with a fluctuated brain, sitting in the middle of nowhere, having the exact same thoughts that you are having right now.
Boltzmann brains are speculative and inevitable at the same time. There is a serious chance that you might be indeed one of those brains, experiencing your false memories within a fake universe which is nothing but a delusion.
"At last -- by chance -- the quantum tangles emitted a knot of structure sufficiently complex to reflect, not just the universe outside, but its own inner state.
"It was a spark of consciousness: not descended from the grunting, breeding humans of the Afterglow, but born from the random quantum flexing of a singularity."
--Stephen Baxter, The Gravity Mine, 2000
This video's YouTube page includes a list of the following two relevant arXiv electronic preprint articles:
Are there Boltzmann brains in the vacuum
Authors: Matthew Davenport and Ken D. Olum
Why Boltzmann Brains Are Bad
Author: Sean M. Carroll
OK, I'm going to wrap up this entry. I might not post another entry before I head off to Fort Lauderdale / Deerfield Beach for a desperately needed few days in a lovely seaside near-tropical place no where near D.C. It's possible my next entry won't be before the weekend (I assume I'll have hotel internet access).