The real question is why would such a universe appear to evolve from a low entropy past following a small set of laws.
The real question is why would such a universe appear to evolve from a low entropy past following a small set of laws.
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You could say we exist in a simulation and the entities outside the simulation can pause the simulation or pre-compute the simulation so that it’s static but then you’re just kicking the can down the road because they would need their own notion of time to observe the simulation they created.
Time isn't required to differentiate two states just as time isn't required to differentiate two static regions of space. The features of the thing can do the differentiation. Whether you consider all of block spacetime as a single entity or subdivided in various ways is a matter of convention. But regions of this block spacetime can be grouped by way of their apparent dynamical connection. I.e. the appearance of evolution following laws connects some regions with others sequentially.
What gives space meaning is coordinates, which allow multiple things to exist separately from each other. Likewise you need another coordinate to differentiate “snapshots” of the universe. So in that sense time is necessary to differentiate two states. But i understand we’re talking about a more fundamental notion of time so i get what you’re saying.
Perhaps a better way to put it is time is necessary for events to happen. Let’s say you could view the universe from the outside, ok great but what can you do with that? You still need time to do things even if you’re outside the universe. Otherwise it would literally be frozen and meaningless.
That’s my issue with these timeless theories is people imagine viewing the universe as a static 4D object but they still talk about it as if things are happening outside the universe and you need time for events to happen.
If time doesn’t exist then a “gods eye view” is meaningless because nothing could happen from that perspective either. It’s also a strong statement about the origins of reality because if time doesn’t exist then reality could not have been created through any process. God or otherwise.
We normally understand a process as a sequence of static events. Time here is really just defining a dependency relation between configurations and some indexical. But a dependency relation doesn't need to be constituted by something that has change as an essential property. Dependency is just matter of an orientation through the state space. Orientation rather than change could be fundamental. With orientation comes trajectories through this structure which could plausibly ground processes. The indexical doesn't matter from the perspective of the subjective evolution of time. What's the difference between a process evolving over essential time and a process "unwound" along a trajectory? Plausibly nothing relevant to consciousness.
An analogy is that of stirring a vat of alphabet soup and noticing that there is a fair number of single-letter words popping into view ("A", "I"), a smaller number of two-letter words, an even smaller number of three-letter words ... a very very small chance of a twenty-letter word ... and a vanishingly small chance of the 189819-letter monster <https://en.wiktionary.org/wiki/Appendix:Protologisms/Long_wo...> popping into view. The stirring doesn't stop just because a multiletter word appears, so multiletter words are quickly broken up and even valid single-letter words get hidden behind the "B"s and "Q"s and other letters in the soup.
Boltzmann brains will fluctuate out of existence on the order of a small multiple of the light-crossing time of the brain-matter that fluctuated into existence. As the brains are human, they won't even have a chance to react. Although their false memories are encoded however true memories exist in our own brains, they'll have no time to have a reminiscence or notice their lack of sensory organs. (Which is probably good, since they would quickly suffer and die from lack of pressure and oxygen).
A Boltzmann-brain with a full encoding of a life worth of false memories (from never-existing sensory input) is a much larger number of letters. Also, in a cold universe, the stirring is slower, and the letters sparser. Boltzmann brains are tremendously unlikely except in a verrrrrrrrry big volume of spacetime. But with a sufficiently big volume of spacetime, or one with an energetic false vacuum, one should expect a lot of Boltzmann brains. This view puts some limits on our own cosmos's vacuum, since we don't see lots of Boltzmann brains (or even much less complicated but RADAR-detectable and/or eclipsing strucures) fluctuating into brief existence in our solar system.
Boltzmann brains are low-entropy. A persisting Boltzmann brain (fluctuating into existence and staying in existence for a long time) is much lower entropy still. This poses problems for hypotheses that the entire early universe fluctuated into existence and then evolved into the structures we see now. Here there are human brains attached to sensory apparatus, whose memories correlate fairly well with their history of input (and recordings by ancestors, and fossil records, and so on): a system with much much lower entropy than Boltzmann brains, so what suppresses relatively high-entropy structures (including Boltzmann brains) from dominating (by count) our neighbourhood?
Also, if the universe supports large low-entropy fluctuations, galaxies that briefly (~ hundred thousand years) fluctuated in and out of existence should be much more common than galaxies with a history consistent with billions of years of galactic evolution, and you'd expect random variations in morphology, chemistry, and so forth; that's not what we see.
This is a bit annoying, as it would be handy to point to Boltzmannian fluctuation theory as the source of the tremendously low entropy in the very early universe, i.e., it could have arisen spontaneously in a less precisely ordered space. Oh well.
> why would ... a universe appear to evolve from a low entropy past following a small set of laws
Thermodynamics.
The issue is: where did the low entropy past come from? Once you have that, evolving into a higher entropy structure-filled present is not too hard -- that's essentially what we have with the standard cosmology from about the electroweak epoch onwards.
So in summary:
> sequences of Boltzman brains who all subjectively experience time as sequential
whatever these might be, they aren't Boltzmann brains, since the latter don't subjectively experience anything as objectively they fluctuate out of existence in something like a nanosecond.
Very briefly, the short existence is driven by interacting fields and the need to keep entropy (relatively) high: if your starting point just before the appearance of the brain is a region that is high quality vacuum, you have to come up with protons, calcium nuclei, ... and all that requires very careful aim to have one split-second "movie frame" of brain. You need much better "aim" which really drives down the entropy (which corresponds a much larger fluctuation) to go from vacuum to a Boltzmann brain that doesn't disintegrate starting in the very next frame thanks to overshoots of momentum.
The higher the entropy of the Boltzmann brain, the clearer the stat mech argument. (If one gets stuck thinking about human brains, C. elegans apparently develop memories and store them in their nerve ring. Why isn't the outer space of our solar system full of those Boltzmann-C.-elegans brains fluctuating in and out of existence with each possessing false memories of sensory stimuli? Smaller fluctuations, so there should be many more of those than human Boltzmann brains).
tl;dr: I don't think Boltzmann brains count as "inhabitants" because their worldlines are so short. Considering together a select set of available Boltzmann brains does not really admit something that looks like a long but complicated worldline. By virtue of being a fluctuation in a thermal bath in equilibrium a BB does not affect the wider universe; a Boltzmann flashlight can't blink out a message in Morse code.
The herd of elephants in the room is the exp(- \Delta S) suppression of fluctuations of size \Delta S out of equlibrium.
I think you are saying that we can imagine a set of some billion billion ephemeral Boltzmann brains each having memories associated with a unique fraction of a false life. I agree we can imagine that, but at the cost of having exact duplicates and many many more ephemeral Boltzmann brains with corrupted and even wholly unrelated false memories.
The true causality is the history of the thermal bath and not the memories of the brains.
In principle we can distinguish between a chosen set of same-false-life-at-different-stages Boltzmann brains and a real human with a very complicated FTL-and-time-travel worldline because at each point on the worldline the latter gets stress-energy ("signals", if you like) from the predecessor point, and also from (and to) each point's neighbours not on the same worldline. That is, our real traveller can detect the thermal bath temperature (which matters in an expanding cosmology) and leaks out metabolism photons to infinity. Ephemeral Boltzmann brains do neither.
The "virtual life" Boltzmann brains -- as you note -- do not have to be ordered in any way. I would go further: brains with immediately neighbouring fractions of the virtual life's false memories can be totally causally disconnected, not just causally disordered.
So I don't think the thought experiment says anything other than the Poincaré recurrence theorem admits states that are close (but not arbitrarily close or exact) to the initial state. That is, BB_final will recur, but so will BB_final-minus-one-nanoseconds-of-false-memory, BB_final-minus-two-nanoseconds-of-false-memory, ... but in some arbitrary point in the system's evolution. I don't think that's surprising.
There will also be brief ephemeral fluctuations into (and out of) mouse brains, cockroach brains, microchips, Jeep Wranglers, brains with memories of having lived lives as little green men from Mars, and so on and so forth. If you have BBs full of false human memories, without some unknown suppression mechanism you will also have BBs full of false nonhuman memories, and nonhuman BBs, especially smaller and less complicated ones (\Delta S being much smaller in those cases).
I also don't think it says anything about our universe, since we simply do not know enough about dark energy to make confident guesses about the very far future (i.e., does it really asymptote to de Sitter with the thermal bath from a dS horizon?). We also don't know if protons are stable that far into the future. However, with what we do know (which is not enough), the far future looks pretty empty. If there aren't RQFT interactions at GUT-scale energies that allow for violations of baryon and lepton numbers, maximum entropy in the far future (>> 10^33 years) still fairly low, but also the path to new nuclei from the (photon-dominated) thermal bath probably means no BBs at all (effectively all baryons are behind horizons by ~10^{10^10} years from now, and significant numbers BBs in our future light cone are expected not much earlier than ~10^{10^50}, although of course if BBs can happen at all, the very occasional individual BB may have its ephemeral moment at any time including today.)
So if there are BBs with false memories of human lives, they are so far in the future that an entire 2020s-style solar system fluctuating into existence and persisting (or a time-traveller who reaches that future) could not recover anything like our present cosmology. At best, via a strong Lorentz boost, they might detect relic and horizon photons, and maybe splatter their windscreens with the occasional BB.
The fluctuated-and-persisting-solar-system scientists would quickly realize its false memories of skies full of stars and galaxies were not true memories. A real time-traveller would probably just try to measure what's left of the CMB or find another marker of the cosmological scale factor.
(The time travel can have been to-the-future-only by something as boring as spending a lot of time moving close to the speed of light.)
Not discussed yet: what to do about fluctuations in fields which obey conservation laws that result in antiparticles. My fast answer would be: that's one reason BBs are so short lived; they are ripped apart by matter/antimatter annihilations.
I first encountered this theory and the related "eternalism" philosophy via Alan Moore [1] (Watchmen, V for Vendetta, The Ballad of Halo Jones, Swamp Thing, Batman: The Killing Joke, From Hell, etc.). Watchmen and its non-Moore-affiliated sequel have a lot of riffs on time and determinism.
Q: Jerusalem deals with the idea of eternalism: everything that has happened is happening right now and forever. Could you explain your views on this?
A: My conception of an eternity that was immediate and present in every instant – a view which I have since learned is known as ‘Eternalism’ – was once more derived from many sources, but a working definition of the idea should most probably begin with Albert Einstein. Einstein stated that we exist in a universe that has at least four spatial dimensions, three of which are the height, depth and breadth of things as we ordinarily perceive them, and the fourth of which, while also a spatial dimension, is perceived by a human observer as the passage of time. The fact that this fourth dimension cannot be meaningfully disentangled from the other three is what leads Einstein to refer to our continuum as ‘spacetime’.
This leads logically to the notion of what is called a ‘block universe’, an immense hyper-dimensional solid in which every moment that has ever existed or will ever exist, from the beginning to the end of our universe, is coterminous; a vast snow-globe of being in which nothing moves and nothing changes, forever. Sentient life such as ourselves, embedded in the amber of spacetime, would have to be construed by such a worldview as massively convoluted filaments of perhaps seventy or eighty years in length, winding through this glassy and motionless enormity with a few molecules of slippery and wet genetic material at one end and a handful or so of cremated ashes at the other. It is only the bright bead of our consciousness moving inexorably along the thread of our existence, helplessly from past to future, that provides the mirage of movement and change and transience.
A good analogy would be the strip of film comprising an old fashioned movie-reel: the strip of film itself is an unchanging and motionless medium, with its opening scenes and its finale present in the same physical object. Only when the beam of a projector – or in this analogy the light of human consciousness – is passed across the strip of film do we see Charlie Chaplin do his funny walk, and save the girl, and foil the villain. Only then do we perceive events, and continuity, and narrative, and character, and meaning, and morality. And when the film is concluded, of course, it can be watched again.
Similarly, I suspect that when our individual four-dimensional threads of existence eventually reach their far end with our physical demise, there is nowhere for our travelling bead of consciousness to go save back to the beginning, with the same thoughts, words and deeds recurring and reiterated endlessly, always seeming like the first time this has happened except, possibly, for those brief, haunting spells of déjà vu.
Of course, another good analogy, perhaps more pertinent to Jerusalem itself, would be that of a novel. While it’s being read there is the sense of passing time and characters at many stages of their lives, yet when the book is closed it is a solid block in which events that may be centuries apart in terms of narrative are pressed together with just millimetres separating them, distances no greater than the thickness of a page. As to why I decided to unpack this scientific vision of eternity in a deprived slum neighbourhood, it occurred to me that through this reading of human existence, every place, no matter how mean, is transformed to the eternal, heavenly city. Hence the title.
1: https://alanmooreworld.blogspot.com/2019/11/moore-on-jerusal...