The Universe Is Not a Simulation, but We Can Now Simulate It
quantamagazine.org
quantamagazine.org
> The Universe Is Not a Simulation
That's based on what? Author of the article opinion? That's cool but then it should be "In my opinion.." and "here's my reasoning".
So title is entirely clickbait, surely? It's not "We're Getting Better at Universe Simulations" that is the content given. I was hoping to find some discussion of the simulation theory and perhaps reasons found that it may not be possible. That's why I clicked and read.
I agree it's kind of weird to raise something in the title and not address it at all in the main article, but that's a minor flaw in what's clearly intended as a joke.
I'm so sick of these bullshit theorists coming up with unverifiable imaginations out of thin air. Produces lots of clicks and laymen books but doesn't do jackshit to help move science forward.
There is no practical way to falsify that so yes, it is just a dreamy theory.
Unlike some other dreamy theories (creationism and astrology come to my mind) nobody has come up with any practical uses for the dreamy theory either, so that would be a second reason why nobody takes this dreamy theory that seriously.
But if this is a simulated game, I would be keen to know how this is scored and how many lifes I have left before game over...
It's much more likely that you are just an NPC waiting to be harvested for some aliens experience points.
The most you can hope for is that you are destroyed in an interesting way, and perhaps your memory lives on in a highlight reel on that aliens stream.
I've often wondered if God existed at one point and we were just his video game. But now God found a more interesting game to play and we are just a forgotten game in chugging along in his steam account. I don't think there is a better explanation for the miracle of the pyramids, or the invention of magnets.
Well, if I think from bayesian point of view, given that only creature here that I personally can be somewhat confident actually having any sentience happens to be me, then it would feel quite likely me being a player. Especially as this can be single player game as well...
But just because something could be cruel doesn't make it less likely. I think we are basically talking about the plot of West World. And pointing out that it doesn't make sense to give an active inner life to characters that exist only to fill out someone else's designed game experience.
But just think about it. If Sims 2099 is capable of giving consciousness to its characters, or at least something so much like it that the characters believe the are conscious, don't you think its very likely players will ask for it? Regardless of the ethical implications.
It can be hard to tell through the popular science stories, where the author is typically unable to relay anything about this research without adding "woo woo" sounds and wiggling their fingers, but it's a real theory.
One thing that may be worth remembering is that in the real theory, the "simulation" is not necessarily running on "a supercomputer just like what we have, only way bigger", which is actually a silly idea for various reasons, and we also do not know that the simulation is literally simulating every particle and every cubic inch of space in the most accurate possible way (i.e., for all we know, far away galaxies could just be a few megabytes in size, rather than fully simulated to the nth degree). The "Great Simulator" is not required to run anything remotely resembling our physics. What seems an absurdly large computation may be smaller than it appears, and may not be an absurdly large amount of a universe running on fundamentally different physics.
(Occasionally when I'm bored, I noodle around with a theory of cellular automata in which the universe has infinite computation power by virtue of being able to split a cell in half or quarters, that then runs at double-speed relative to the outside. If this is done recursively the universe has arbitrary computation abilities relative to the "top level". I've never worked it into anything usable, but I think it can give a flavor of why we should not be sure that our simulation host is necessarily as staggered by the computation as we would be. We are not even capable of saying that they aren't running an exponentially-expensive quantum approximation algorithm with the entire universe actually arbitrary-precision integers under the hood. The staggering amount of computation that represents may not bother them at all.)
It is not a theory that is, strictly speaking, falsifiable thanks to Church-Turing equivalence, but there are ways in which it could potentially (to any arbitrary degree of confidence you may want) be confirmed if it is true. To take one degenerate case, if the Great Simulator broke silence and starting wildly breaking the laws of physics to get our attention, that would certainly put a lot of probability mass on the "we're a simulation" theory. There are less extreme cases we could conceivably pick up on, that just fits into an HN comment nicely.
So in what ways is it a "serious theory"?
Despite what seems to be a popular opinion, we are not actually obligated to curl up into a ball on the floor and cry about our inability to know anything just because science can't be definitive on some point. We just need to be aware of the limits of our knowledge. We have no choice; even in just our day-to-day lives, we are required to make all kinds of decisions for which science is either quiet, insufficiently informative, or (and this one may really hurt to think about too much) simply wrong.
I have no idea what you are referring to here. Can you be bit more specific about what viewpoint or philosophy you are satirizing?
People defend it with a straight face?
The thing is, we don't know where this line of reasoning would even lead. I mean, people used to think that light had to travel in little packets through luminiferous aether [1] and look where that investigation led: Einstein, special relativity, atomic weapons and power, nuclear medicine, etc.
Let's say the universe is fundamentally indistinguishable from a computer simulation. What consequences does that have? What does that say about the types of math that can be used to describe the universe? Or, perhaps better, the types of math that shouldn't be used to describe the universe? What does that say about our ability to model a portion of the universe and therefore predict outcomes? Does it have implications for stochastic processes? Indeed, where is the stochasticism coming from? Is everything predictable or is there some fundamental randomness?
On the other hand, what if we can show that the universe is distinguishable from a computer simulation. What does that mean for our understanding of the universe as it exists? Does it reveal a fundamental aspect of reality that we have missed, or a limitation of our mathematics, or a fault in our computer models or design, etc.? We're dogs learning calculus here, and the universe isn't obligated to make sense.
Even if we can never find a useful test for this hypothesis, the line of thinking itself potentially leads us into new areas of discovery.
[0]: https://gizmodo.com/5950832/how-to-tell-if-the-universe-is-a...
The luminiferous ether was a falsifiable theory - indeed it was a breakthrough for physics because it was falsified (experiments failed to detect it) so new theories had to be developed. So this is completely different from unfalsifiable metaphysics.
The idea that quantum fields exist in multiple states simultaneously until observed become evidence for a simulation, since a simulator could be deferring calculations on things not observed.
Also, the very program this article is referring to could be considered as evidence for it, since if a rough simulation can be made where the observable result is indistinguishable from a result where every atomic element in the entire universe was simulated, then, again, a simulator with limited resources would make do.
The law of conservation of energy is built the same way. There is no way we can test ways that energy is transferred that we don't yet know about, but this law is still considered true, because we have so many examples of it working.
> The idea that quantum fields exist in multiple states simultaneously until observed become evidence for a simulation,
How is that evidence? Current physics can model that without relying on a simulation hypothesis. Adding a simulation hypothesis does not simplify the model, and it is unfalsifiable.
> Adding a simulation hypothesis does not simplify the model, and it is unfalsifiable.
I explain this. It's falsifiable if it can be shown there is some extremely large and complicated process that be observed to be different than any possible rough calculation that could be accomplished by a simulator with very constrained resources (constrained in comparison to all the supposed atomic particles in the universe)
The notion that all forms of energy must be conserved, even undiscovered ones, has been used as the basis for the theory of Hawking radiation, isn't it? Yet claiming that undiscovered forms of energy are conserved, just as known ones, is unfalsifiable, too.
The law of conservation of energy, including undiscovered ones, is in the same boat as the theory that the universe is a simulation.
Until we find a form of energy that isn't conserved, it is simpler to assume all types of energy are conserved.
Similarly, until we find a process that is of large enough scale that it couldn't be simulated on a computer with resources much more limited than the size of the universe, and be observable identical to a process taking much more resources, it is simpler to assume it all is being simulated in such a way.
Sorry I just didn't want to quote the whole comment, didn't mean to imply I was only responding to the first part of the sentence.
I understand you can hypothetically prove that a simulation of the universe would require a simulation engine of at least a certain complexity. But since the simulation engine does not exist in this universe, we have no idea about what limitations or laws of nature (if any) it is subject to. You will never be able to prove or disprove the existence if this hypothetical simulator.
The point is not to prove one way or another whether the universe is a simulation, just like there is no point trying to prove the law of conservation of energy as universal for all forms of phenomena, discovered and undiscovered.
It's just if we can show that all known phenomena can be the result of a very limited simulation, then when analyzing new phenomena, we can also expect it to be runnable on a very limited simulation, too.
It's the same as assuming that the law of conservation of energy would apply to any new phenomena we discover. There is no proof, but it's a good starting point.
The bottom line is that it is possible to devise experiments or observations which would give different outcome if the theory holds and if the theory doesn't hold.
But you cannot devise an experiment which would give different outcomes if the universe is a simulation versus if it isn't. More specifically, you cannot imagine an observation which would prove that the universe isn't a simulation. Therefore it is not a legitimate scientific theory. At best it is a fun thought experiment.
I've already mentioned 5 times in this thread that the theory I'm talking about is of a simulation with very limited resources, but you seem to be ignoring this point.
Show that a particular phenomenon can't be simulated using extremely limited hardware (compared to the size of the universe) and you can falsify this theory.
Does this or does this not apply to a simulation with very limited resources (compared to what it would take to model all the atoms of the universe) or not, then?
But it effectively wasn't for the first 150 years of it's existence. The theory originated in 1720 and it wasn't disproven until 1887. It took that long for someone to come up with a conclusive experiment. Nevertheless, for those 150 years the luminiferous ether theory was widely held, shaped the field of physics, and the research had to go into finding an experiment to test the theory.
Similarly, the idea that atoms might do things when high energy particles hit them was all theory until Wilson's cloud chamber became the first particle detector and suddenly physicists could see what these particles were doing when they hit things.
> The problem is...you can even define what it means for the universe to be a simulation.
You're confusing something that hasn't been done with something that can't be done. Indeed, what they're trying to do is exactly trying to define criteria to test that the universe is a simulation. It's the first day of school and you're complaining that Newton doesn't have his Principia and Gilbert doesn't have his De Magnete.
Theories often predate the knowledge of how to test them. This isn't weird.
It's worth noting that most religions are in exactly the same situation.
Edit, oh, duh.
Yeah, my main take is that there should be evidence for it being a simulation, and in lieu of said evidence it should be assumed untrue
Same problem we have in quantum gravity. We just can't recover known physics from anything at all, any combination of theories at all it seems. That includes all known instances of computation, it just blows up.
Also, Church-Turing has nothing to do with basic problems here, in particular because eventual simulating computation would be unlike computation we know (which again, makes the word lose any meaning here).
None of that matter if there is no theory in the first place. Much was tried. 't Hooft got as far as holographic principle. And there's still no theory at all.
What does such a theory have to do with astronomers or physicists? Its a philosophical issue
It's a theory that predates the internet. In the expanded view, the theory goes back to antiquity.
The modern version is a thought experiment more in line with the drake equation than a dreamy internet theory. It's an idea born of some assumptions and mathematics.
> Like, are astronomers and physicists taking it seriously?
Some are, most aren't. But then again, most astronomers and physicists don't take SETI seriously as they have their own work to focus on. But it certainly isn't anything to be dismissed just like the drake equation or SETI.
One has something to do with the information in black-holes, i can't remember the details but it suggested to me that '3d space' was fundamentally artificial.
Another has to do with quantum entanglement, the explanation for spooky action at a distance could be that the two particles are still in the same 'bit of memory'.
And lastly the Uncertainty principle is thought to act a lot like an on-the-fly loading frame in an RPG.. As silly as that sounds there is not really a satisfying explanation of why things are less certain when we are not interacting with them.
Its worth noting that even if the universe is simulated, it might not be simulated by intelligence, we don't know enough to say its not 'naturally simulated', that might seem paradoxical but 'simulated' and 'artificial' are very loaded words; A reflection of the moon in a pond is in some way an artificial simulation of a moon..
I think the universe as a simulation is less interesting as it's really just taking the notion of materialism to its logical extent. But in fairness to it, it's now part of culture, so if it's causing us to think in ways we wouldn't be aware of, it's harder to see it influencing someone than if he's Feynman getting a sudden phone call from Wheeler.
Many thought experiments can also be useful insights into nature of things. The idea of a Boltzmann brain[2], for instance, challenges your intuitions of infinity and thermodynamics.
[1]: https://en.wikipedia.org/wiki/One-electron_universe [2]: https://en.wikipedia.org/wiki/Boltzmann_brain
If the Universe is a simulation (or might be) what is it simulating and who's simulating it? I'd be more interested to know about -that- than the arbitrary details of some measly little simulation itself. You might say something hand-wavy like, "it's simulating itself"... but OK, when I look at our "simulations" they are always highly referential to the external real... er... possibly real... world. Dwarf Fortress could be called a simulation (perhaps one of the better ones!) ... and while I'd be hard pressed to point to the outside world and say it's simulating any one thing with high fidelity, I can point to trees, mountains, water animals, etc. where the creative element is really just tweaking the attributes of these otherwise externally real things. It's hard to simulate what you're you're completely unaware of, unconscious of ... in fact to be conscious at all is to be conscious "of something" and insofar as simulations are conscious efforts at creation, it's difficult to not have some concrete reference that exists outside of a "simulation".
Of course, perhaps, it's the great mystery of God which I'm always told is beyond mere human understanding. Or maybe its simulations all the way down. Or maybe any explanation talking about simulations requires greater leaps of faith and greater acceptance of more and more unlikely scenarios of reality than just saying the Universe is perhaps a metaphysically real place that doesn't require an appeal to "simulation" for explanation.
I think I'll just stick to the simple minded idea of the Universe is a real place and not a simulation. That part of the title is so likely to be true that the author need not feel bad about the assumption.
The fidelity of the simulation is not an argument for or against: assume we're simulated and it seems likely to me that perceptions by beings within simply wouldn't have the ability to notice a lack of fidelity; or whomever owns this simulation has the computational power to simulate sufficient fidelity to convince inhabitants that their universe is "real."
Because we don't yet have evidence either way, I'd go with 50/50 odds.
I agree that fidelity of a simulation doesn't inform us as to whether or not there is a simulation involved at all. I'm trying to point out that a simulation is a simulation of "something" external to itself at some fidelity. If that's the case, the larger reality would be external to the simulation since 1) the simulation would be a simulation of something, 2) the simulation would simply be a component part of that larger reality. This may all depend on how we define the term: "Universe". If we mean universe to mean the metaphysically complete reality, then a universe by that definition couldn't be a simulation since it would be simulating something outside of itself. If we mean some smaller sense of the word Universe, like the observable universe or the perceivable universe, then perhaps.
I think trying to explain the universe or reality as a simulation or similar is nothing more than humans doing what we have done since long before recorded history: we're projecting existence (and its "causes") onto some explainable, graspable concept with which we are comfortable. This is nothing more than the motivation that created every religion on earth and is at least as likely to be a correct vision as any of those. In the old days we created Gods which resembled us, but had exaggerated qualities and powers to manipulate the universe and act as its cause... today, we feel much more comfortable with modern concepts such as "simulation"... but we have no more justification to make that claim than our ancestors did to mysterious thunderers high up on mountains.
The question of "Is there a God?" or "Is there a simulation?" is not a 50/50 proposition. The default position is the negative: there is no God until proven otherwise, there is no simulation until proven otherwise. We can start to believe and question as evidence mounts, but right now, I don't see much for a simulation (unless perhaps you want to argue that a quantized universe is just a pixelated one as we'd see in our own simulations).
Again, the author is justified in their claim that the Universe Is Not a Simulation until there is sufficient evidence to question it otherwise.
The rest of your comment makes fine arguments.
It's now down to one minor outage every couple years. We are aiming at five nines on the next major release.
I sometimes read hn as the discussions here can add to articles on topics I find interesting but have limited knowledge on, but the 3+ top comment threads (so far) discussing the title and not content of this article is somewhat disappointing.
On a different note, here's a sobering thought for the Universe-as-simulation optimists: while it's possible the simulation's Creators wish us well, e.g. will store your soul/mind and let you live carefree in a Paradise... it might rather work like our current massive simulations (e.g. the Millennium Run [0]). It generates enormous amounts of data, but only some small amount (like a state snapshot every 100M years) is actually captured and analyzed. I.e. the "dumb" computing power at the Creators' disposal is far greater than their mental capacity. The whole existence of humanity might go unnoticed, just a side-effects of the simulation's fidelity.
And if so, I'm wondering if any of that stuff runs on GPUs or if we're still talking about "traditional" supercomputers?
Anyone knowledgeable in the field care to share?
Your ability to detect Fortran is apparently excellent.
Proof left as exercise for the reader?
Surprised that the currently exponential overhead for simulating a quantum system is a distant second in commenter objections here. "Simulating the universe" in the holistic manner that I feel such a phrase entails would require at least clearing that bar (say, with a quantum computer? Or at a longer shot, showing BQP = P?), and that's before thinking about the status of quantum gravity.
Instead I'd take it as meaning something like, "any slice of physical phenomena there is to observe in the universe, we can simulate given reasonable resources to do so." So, put an imaginary box around some reasonably isolated plot of reality, pick your precision and your time scale, and you could replicate what happens in that space with a "reasonable" computational resource overhead. That's what elevates the quantum simulation overhead objection to number 1 in my mind.
Edit: Ah I'm reading this wrong. You are making the argument that an informational density that large would cause a singularity. You are correct, probably.
https://en.wikipedia.org/wiki/Planck_length
to see how strongly it conflicts with what you have written about it.
Among other things catalogued there, the Planck length has dimension of [Length], rather than [Time], and per Bekenstein [1973] (doi:10.1103/PhysRevD.7.2333) "1 bit"[0] relates to the minimal increase in the area of the event horizon of a hairless, monotonically growing, stationary, spherically symmetric (or with some further assumptions, axisymmetric) black hole into which matter is being thrown. This remains contentious because black hole mass is continuous and not discrete (one can throw almost arbitrary wavelength photons in, for instance).
By contrast with what you wrote, if you look at it (e.g. via sci-hub) Bekenstein's PRD paper sure doesn't assert that a horizon area on the order of Planck area would contain "one bit", especially as he was aware of the content of the about-to-be-published Nature paper, Hawking [1974] (doi:10.1038/248030a0), which details the "explosion" of black holes with small horizon areas (and was additionally the first Hawking radiation paper).
Finally, if you don't like wikipedia and sci-hub, your favourite search engine will surely supply numerous discussions among working physicists (including peer-reviewed publications) of the Planck length and whether it is physically significant in any context other than Bekenstein's or close relatives (e.g. Loop Quantum Gravity requires that all surface areas are quantized, although not to integer multiples of the fundamental quantum, which in turn is roughly on the order of the Planck length cubed).
- --
[0] A modern semiclassical statement of this is: to leading order, the entropy of a black hole is proportional to its event horizon area at one nat per four Planck areas. https://en.wikipedia.org/wiki/Nat_(unit)
Let us begin with a maximally dense object, a black hole. It will be assumed that the entropy is found on the horizon and that no more than one bit per Planck area can stored there.
The only thing I stated incorrectly was planck cubed instead of square.
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.74....
The metaphorical name of the principle (’t Hooft, 1993) originates here. In many situations, the covariant entropy bound dictates that all physics in a region of space is described by data that fit on its boundary surface, at one bit per Planck area
https://lib.ugent.be/fulltxt/RUG01/001/787/483/RUG01-0017874...
3.5 Holographic screens
An important implication of the holographic principle is that all the information in a given region can be encoded on a surface B, at a density of one bit per Planck area. We can now ask ourselves if the information contained in an entire spacetime can be encoded on a certain hypersurface, which we will call a screen.
What's that you were saying? I can't hear you over the sound of how right I am.
And why is a planck area one bit?
Because at the planck length, h=G=c=k=1. Where h is the Planck constant, G is Newton's constant, c is the speed of light and k is Boltzmann's constant. Or if you like some Einstein. E=mc^2 reduces to E=m
> "no more than one bit per Planck area can be stored there"
Sure, that's a postulate to help clarify the Susskind's string theory argument about the information content of his 2d holographic screen at infinity from the black hole with all of the above in a 3d spacelike hypersurface at t=const. Being a postulate, the sentence fragment you quote is not proven in the paper, it's just assumed.
Changing the number of states at the horizon in that spacelike hypersurface to an arbitrary finite number does not really frustrate his gravitational argument (but see below about his matter GUT argument), while arguments about the upper and lower limit of states at the horizon are available in Bekenstein [1973] op. cit. and many subsequent papers.
It is perfectly normal for gravitational arguments to set c = G = 1, and possibly normalize some other terms to unity too; the choice of what to set to unity depends on the trade off between ease of writing down formulae and the difficulty of checking their dimensionality. The reason Susskind uses Planck units, and relevantly to our discussion the Planck length, is because it's convenient in analogies as he develops his argument further down the paper using units where the string length is set to unity.
(The majority of the Susskind paper is heavy (pardon the pun relating to scaling of interaction with momentum) with non-gravitational string physics, and I have no expertise on that, but his gravitational arguments are low energy ones, and there I am comfortable).
> The only thing I stated incorrectly was planck cubed instead of square.
You wrote, "shortest theoretical time interval". The word "time" is incorrect since it is a unit of length (this matters in a Lorentzian spacetime), but changing it to "spatial" does not let you claim that the Susskind paper supports your statement at all, for the reasons above.
You can certainly make arguments about states on a stretched horizon (Susskind does in the paper you found) -- complementarity is wildly popular with string theorists. However, their entropy:information argument, as also repeated in the Bousso paper and the master's degree thesis you found, does not set a minimum length scale rather than fixing a limit on the number of microstates you can squash into an area before the macrostate resembles a hairless black hole, the idea being that any sparser region's macrostate grows gently, and moreover that you can with some care use the macrostate to describe all the internal microstates (which is the core content of SUGRA theories, essentially, where the care one takes is in the choice of a conformal field theory to represent the evolution of the macrostate).
> "a planck area [is] one bit [b]ecause at the planck length, h=G=c=k=1"
No. More on that in the paragraph after the following one.
You also wrote "the equation E=mc^2, at the planck length the value of c=1", which is a bit confused. All Planck units set five constants, c = G = hbar = k_e = k_B = 1. Any quantity measured in Planck units will have c = 1 (and also Boltzmann's constant = 1 and the Coulomb constant = 1 etc.). The partial dispersion relation you provide has nothing to do with it, other than that you can solve it for an appropriate system in Planck units just as in S.I. or cms units, and you can simplify by dropping the term normalized to unity, just as your version has already simplified from the fuller special relativistic relation by normalizing momentum to zero.
In the stringy arguments, the reason there is supposedly four nats or one bit or a small finite number of microphysical degrees of freedom or whatever per unit area on the horizon of a black hole is complementarity described in another Susskind paper: https://arxiv.org/abs/hep-th/9306069 (amusingly it should be "coarse graining" in the Abstract, of course, as it is on e.g. p. 3 just above Postulate 3 and several more times throughout the paper; the published PRD version has the same error in the Abstract).
I do not find the BH complementarity model especially convincing as it was contrived to save information from being lost in traditional black holes but does not appear to do the job, appearing to require replacement of black holes with fuzzballs or some other complementarity-preserving resolution of the AMPS problem. Their cosmological model is even shakier, since it is mostly tested on a non-infinite (but large) distance boundary on anti-de Sitter space, with some arguments about how a series of slices of AdS space can resemble a series of slices of a space much more like our expanding universe. The master's thesis you found is interesting in that it tries to tackle the physics in (among others) de Sitter space, which is a fair approximation of our universe at late epochs. YMMV.
Firstly, there is nothing special about natural units compared to any other system of units, except that some popular formulae can take on especially simple forms in that system of units, provided one takes care not to lose dimensionality:
https://en.wikipedia.org/wiki/Dimensional_analysis
You (still) are confusing two different dimensions, length and time. Again, this matters in a spacetime like ours, where the difference in dimensionality gives us a system of causality[1] and a reasonable setting in which to do time-series physics[2]. It also matters when switching from natural units to a different system of units in which c != 1, such that we cannot omit the conversion constant (or change of sign when calculating spacetime intervals [3]).
Changing a physical system like a black hole from one system of units to another does not change the physics of the system, just how we describe them. It is enlightening to do so in general, because it is easy to fall into the trap of treating as physical a condition that vanishes upon switching to a different set of units. A quantity that is a ratio of two dimensionful quantities (area and information) surviving across changes of units on one or both dimensions may be interesting. In the case of black hole complementarity, which earlier you found links for, it's a (near-horizon) density that (according to some string theorists) corresponds directly with a (interior) density (states / volume) taking into account the Ricci tensor's effect on interior volume but removing the physical singularity through string interactions in a "fuzzball" or something similar[4].
Secondly, your second link says of Planck time, "Presumed to be the shortest theoretically measurable time interval (but not necessarily the shortest increment of time - see quantum gravity)", which does not really support your position. Rather than reinvent the wheel for you in qualifying that, which I think would be wasteful given your previous few replies, I'll direct you to physics se and in particular to Lubos Motl's 85 point comment at : https://physics.stackexchange.com/questions/9720/does-the-pl...
Finally, I don't know what you're trying to accomplish although it seems you're set on convincing yourself and perhaps some people who know even less physics than you do that you know what you're talking about. Hopefully it's more optimistic and instead you're trying to learn more than you already do and are just going about it inefficiently.
- --
[1] https://en.wikipedia.org/wiki/Causal_structure
[2] https://arxiv.org/abs/1505.01403 (section 4) - sadly the wikipedia has only scattershot coverage of it in e.g. the short and/or not very accessible pages on the ADM and BSSM formalisms, and on Canonical Quantum Gravity (which is a quantization of the Hamiltonian formulation that is "only" an effective field theory good to one loop, and provokes the question of "the problem of time"). Unfortunately most introductory material about 3+1 formalisms in general is already highly technical (e.g., textbooks aimed at graduate students).
just super cool to think about even if not the case/unrealistic.
Since at least Thomas S. Ray's work on Tierra in the 90s we've been creating universes in which things that could be called "life" have developed.