[HN Gopher] Constraints on physical computers in holographic spa...
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Constraints on physical computers in holographic spacetimes
Author : optimalsolver
Score : 112 points
Date : 2023-11-14 11:24 UTC (11 hours ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| hurryer wrote:
| They seem to be saying that to do a quantum computation there is
| a minimum volume of space required in which to perform it which
| grows in relation to the number of qubits.
| WJW wrote:
| That makes sense. The whole point of the theory about
| holographic spacetime is that the 3d universe is completely
| described by the information densities on its edge. This
| implies that if you need to contain a computation involving a
| certain amount of information, then you need to have at least
| that amount of information on the edge. Since the amount of
| information anywhere is not infinite, this also implies that
| you need a non-zero amount of edge surface for that computation
| and thus a non-zero volume.
|
| TL;DR: If the volume is too small, you just cannot fit enough
| information inside and so you cannot do computations which
| require more information than that.
| PaulHoule wrote:
| But what is the point of computing inside a black hole?
| You're not going to get the answer out.
| hoseja wrote:
| You're currently possibly living inside one. Big Bang? -
| The initial collapse. Universe expansion? - Matter falling
| in. It may be unfalsifiable from inside though.
| WJW wrote:
| From the article:
|
| While we are ultimately interested in the physical limits
| of computers in our universe, working within the context of
| the AdS/CFT correspondence gives us a precise framework for
| quantum gravity. As well, a fundamental observation in
| computer science is that the power of computers is robust
| to "reasonable" changes in the details of the computing
| model: classical computers can be described in terms of
| Turing machines, uniform circuits, etc. and the resources
| needed to solve a given computational problem will change
| only polynomially. Quantum computers are similarly robust.
| This robustness suggests understanding the power of
| computers in AdS is likely to yield insights that apply
| more broadly.
|
| I'm decidedly not an expert in this field but as I
| understand it there are two points to doing the math in
| this way:
|
| - We know how to describe the inside of a black hole
| mathematically from an AdS perspective.
|
| - _IF_ the AdS /CFT correspondence is true (likely but
| unproven), then you can generalize from "works inside black
| hole" to "works inside the normal universe".
|
| It's more an exploratory step towards getting a better
| understanding of complexity theory for quantum computers
| than it is a practical result intended for doing
| computations inside black holes.
| tsimionescu wrote:
| It's important to remember that we know very well that we
| _don 't_ live in an AdS space. It's actually not all that
| likely that many of these theories apply to a de Sitter
| space-time like our universe, though it remains to be
| seen.
|
| That is, even if the AdS/CFT correspondence is true, it
| may still turn out that the dS/CFT correspondence is not,
| and so the results are not applicable to the physical
| universe.
| bee_rider wrote:
| It turns out it is pointless, we just work in a very fad-
| driven industry. Once Google started computing in a black
| hole, it just automatically became popular, and eventually
| it became common knowledge. "Can't get fired for computing
| in a black hole" they'd say.
|
| Then the Hackernews guys put their server in a black hole
| that turned out to be a wormhole, one thing lead to
| another, and posts were getting sprayed across the
| timeline. What a mess.
| Nevermark wrote:
| Greater understanding is never pointless.
|
| Throwing around general accusations of fads doesn't
| reduce a paper to part of a fad. Papers stand on their
| own merits, based on their reasoning, independent if any
| associations with fads.
|
| I expect the properties of a black hole are simply a
| convenient context to talk about the holographic
| principle.
|
| If the holographic principle holds true, it is true
| across any border separating one space from another.
|
| Likewise, mathematicians prove things about infinities,
| which we will never encounter directly, but which have
| useful implications for things in math that can relate to
| things we might create or encounter.
| thomashop wrote:
| I think the comment you are responding to was a joke
| bee_rider wrote:
| The time police insist that I inform everyone that my
| post about accidentally posting across timelines is, in
| fact, just a joke, nothing serious, haha.
| KineticLensman wrote:
| This is how you lose the time war...
| abdullahkhalids wrote:
| People have been working at the intersection of blackhole
| physics and quantum computing/information since the early
| 90s. This is a ripe area to work in, because this is
| where QM+GR are most likely to break.
| labster wrote:
| That's why I stick with Oort cloud computing. It might
| take 22 days to get the request back, but the chance that
| anyone can see that data is astronomical.
| spacecadet wrote:
| Maybe.
| nabla9 wrote:
| They describe computations that are forbidden despite the
| inputs to these computations being small, and the description
| of the computation being easily fit inside the black hole.
| WJW wrote:
| Sure? That doesn't even matter for normal computers though.
| Busy beaver algorithms can be described in very few lines
| of code but can generate incredible complexity. It's not
| super difficult to devise an algorithm that would need many
| more bits of information than just its description+inputs
| to accurately describe all the state required, and that is
| in fact exactly what the authors of this paper did.
| Nevermark wrote:
| Limits on all computational complexity in a given regime
| are a quite different result from noting particular
| algorithms have high computational complexity.
|
| And if these results and the holographic principle holds,
| then these limits would apply to all computers. Even
| "normal" ones.
| goldenkey wrote:
| This makes a lot of sense. Laundauer's principle shows that the
| amount of energy to store a bit is directly proportional to
| temperature, thus, energy loop size/travel time at the speed of
| light. The lower the temperature, the smaller the loop radius,
| the lower the energy requirement. There is no primitive of
| storage in our universe, it's all delay line memory.
|
| https://en.wikipedia.org/wiki/Delay-line_memory
| alecst wrote:
| Landauer's principle is about memory erasure, not storage.
| Charles Bennett talks about this in one of his papers.
| goldenkey wrote:
| From what I understand, the cost of "erasure" is really
| just the cost of replacement. True erasure can't exist in a
| unitary universe. In the same way, the cost of "allocation"
| is effectively the cost of replacement too, since our
| universe is unitary and no information can actually be lost
| at the fundamental level.
|
| Think virtual memory vs actual memory, forks, copy-on-write
| mechanics, etc. Are we juggling/managing memory or actually
| creating any? As far as we know, the universe itself is a
| reversible quantum supercomputer. There are no erasures and
| a reversible computer is 100% efficient.
|
| If the formula is correct at all, it should apply to the
| reverse process of setting bits, not just deletion.
| alecst wrote:
| If you're talking about Landauer's principle, you're
| talking about a universe where entropy increases, which
| means some information is lost.
|
| By the way, here's the paper I was talking about. I feel
| like you might enjoy reading it: https://sites.cc.gatech.
| edu/computing/nano/documents/Bennett...
| ko27 wrote:
| There is one important thing everybody seems to be missing
| here. This applies to the theoretical AdS universe, NOT to our
| universe as far as we know.
| 3cats-in-a-coat wrote:
| But our universe adheres to AdS constraints. As far as we
| know.
|
| When you reach the information density limit in AdS, in our
| universe you get a black hole.
| undersuit wrote:
| A theory used to establish the scene in
| https://en.wikipedia.org/wiki/Vacuum_Diagrams
| snarkconjecture wrote:
| The AdS/CFT correspondence was published slightly after
| that collection. Are you saying Baxter scooped Maldacena?
| queuebert wrote:
| While that correspondence proof is relatively new, AdS as
| a theory is quite old.
| snarkconjecture wrote:
| The great-grandparent comment was talking about an
| "information density limit" and black holes in our
| universe, so I assumed the referenced sci-fi collection
| had something to do with holography. I don't know of any
| particular emphasis on AdS in that context before 1997.
| Elaborate?
|
| Obviously you can stick GR in AdS, but AFAIK nothing
| about that would've seemed interesting with regards to
| holography before Maldacena, let alone plausibly
| providing inspiration to a fiction author.
|
| To be less roundabout than my previous comment: I think
| Baxter may have been inspired by the holographic
| principle in general, but I doubt AdS crossed his mind at
| all when he was writing these stories in the 80s and
| early 90s.
|
| (EDIT: or maybe Baxter was thinking about AdS but not
| about holography. I haven't read his work.)
| undersuit wrote:
| Vacuum Diagrams is a collection of short stories Stephen
| Baxter has written well before 1997, but the published
| collection in 1997 included new intertwining narrative
| stories about an AI named EVE to bind them together. EVE
| is an AI in a black hole? On the edge of one?
|
| Stephen Baxter is known for sch-fi so hard it'll cut you.
| He may have just accidentally come up with similar
| concepts during the same year.
| codethief wrote:
| > But our universe adheres to AdS constraints. As far as we
| know.
|
| No, as far as we know, it doesn't since the cosmological
| constant is slightly positive, so the universe would best
| be described by de Sitter spacetime, not anti-de Sitter.
|
| https://en.m.wikipedia.org/wiki/Anti-de_Sitter_space
| empath-nirvana wrote:
| Our universe is definitely not an ADS.
|
| Think of the spaces in ADS/CFT as mathematical spaces, not
| physical spaces. It lets you take a model constructed in
| one space, translate it into another space, perform some
| calculations there that might be simpler and then translate
| them back.
| nabla9 wrote:
| Our universe can can be thought as effective de Sitter brane
| in an Anti-de Sitter space. Conformal 4-dimensional field
| theory is mapped to AdS_5xS^5
| dustingetz wrote:
| ChatGPT expansion:
|
| de Sitter Space: A model of the universe with a positive
| cosmological constant, leading to a universe that expands
| exponentially. It's a solution to Einstein's equations of
| General Relativity representing a universe dominated by
| dark energy.
|
| Anti-de Sitter (AdS) Space: A spacetime with a constant
| negative curvature. It's the opposite of de Sitter space
| and is a solution to Einstein's equations with a negative
| cosmological constant. AdS spaces are commonly used in
| theoretical physics, especially in string theory.
|
| Brane: Short for "membrane", in string theory and related
| theories, a brane is a physical object that generalizes the
| notion of a point particle to higher dimensions. A universe
| can be conceptualized as a 4-dimensional brane existing in
| a higher-dimensional space.
|
| Conformal Field Theory (CFT): A quantum field theory that
| is invariant under conformal transformations, which are
| transformations that locally preserve angles but not
| necessarily distances. CFTs are important in studying
| phenomena like phase transitions and in string theory.
|
| AdS/CFT Correspondence: A conjecture in theoretical physics
| that proposes a relationship (duality) between a type of
| quantum field theory (Conformal Field Theory) and a theory
| of gravity defined in an Anti-de Sitter space. This duality
| suggests that calculations done in one theory can be
| translated and used in the other.
|
| AdS_5: This denotes a 5-dimensional Anti-de Sitter space,
| often used in the context of the AdS/CFT correspondence.
|
| S^5: Refers to a 5-dimensional sphere, a higher-dimensional
| generalization of a usual sphere. In the context of the
| AdS/CFT correspondence, the theory of gravity is considered
| in a space that is the product of AdS_5 and S^5.
|
| The universe as an "effective de Sitter brane" in an "Anti-
| de Sitter (AdS) space": This suggests that our observable
| universe, which approximates a de Sitter space due to its
| accelerated expansion, can be represented as a brane (a
| boundary or membrane) within a higher-dimensional Anti-de
| Sitter space. AdS spaces are characterized by a constant
| negative curvature, contrasting with the positive curvature
| of de Sitter spaces.
|
| "Conformal 4-dimensional field theory is mapped to
| AdS_5xS^5": This is an instance of the AdS/CFT
| correspondence. It states that a 4-dimensional Conformal
| Field Theory (CFT), which is a quantum field theory
| invariant under conformal transformations, can be
| equivalently described by a 5-dimensional gravity theory in
| an Anti-de Sitter space (AdS_5) times a 5-dimensional
| sphere (S^5). This duality allows for the study of gravity
| in AdS spaces using CFTs and vice versa, providing insights
| into quantum gravity and string theory.
| lanstin wrote:
| Not minimum volume but volume with a minimal boundary area
| proportional to the size of the states your computation
| explores. The weird thing about these holographic mappings is
| that stuff you would expect to be limited by volume is limited
| by surface area of which there is rather a lot less of.
|
| The cool thing is that there are few independent such results,
| starting with the entropy of a black hole, so if you like to
| speculate on possible physics beyond QFT it gives you some
| material.
| konstantinua00 wrote:
| ...so just do a zigzag to fit more in same space?
| cvoss wrote:
| Even if you can imagine a baroque and spacious boundary
| that is to your liking, it remains the case that the
| simpler, economical boundary still exists, and you have to
| reckon with that one.
| narinxas wrote:
| > _They seem to be saying that to do a quantum computation
| there is a minimum volume of space required in which to perform
| it which grows in relation to the number of qubits._
|
| they say information uses up space. got it...
| Woshiwuja wrote:
| ELI5? am dummy
| block_dagger wrote:
| To compute, a minimum physical space is required. Mostly
| impossible inside black holes.
| Woshiwuja wrote:
| Thank you my brother, my physics lingo for this was kinda
| lacking
| Nevermark wrote:
| Correction: a volume with a minimal surface area is required.
|
| Surface area goes up slower than volume, if a volume shape
| simply scales up.
|
| That is the interesting result, if it holds up.
|
| My conjecture: An increasingly fractal surface whose area
| increases as fast or faster than an increasing volume would
| get around this limit.
| narinxas wrote:
| but this could mean that if black holes are spherical, then
| it's also possible to compute in them???
| Suppafly wrote:
| I assumed it was going to be something about how we live in a
| holographic simulation or something.
| bobsmooth wrote:
| This will be useful when humanity needs to retreat into black
| holes to (subjectively) extend the heat death of the universe.
| nielsbot wrote:
| Sounds like a Three Body Problem
| kridsdale3 wrote:
| Maybe that already happened 14 gigayears ago.
| onetimeuse92304 wrote:
| My first glitch happens when trying to parse "computations (...)
| which cannot be implemented inside of black holes".
|
| My assumption is that whatever computer is used it is falling
| between the event horizon and the singularity. The masses
| involved are the mass of black hole before the object falling
| into it and the mass of the object. The amount of computation
| that can be done is dependant on the mass of the object and the
| time available. The time available is some kind of product of the
| mass of the object and the mass of the black hole. As the object
| is reaching the event horizon, the event horizon expands to
| accommodate the object, but this expansion isn't super simple as
| my understanding the expansion itself progresses at a speed of
| light (the other side of the black hole takes time to be affected
| by the object falling).
| user8501 wrote:
| Aw crap! What are we gonna do now?
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