6 ms·

Not down to the planck level. Simulating the universe at the planck level would require at least 10^157 bytes of storage.

ctb9 8y ago
How does one come to that figure?
- fnrslvr 8y ago
  Some combination of the holographic principle and the the information overhead of classically representing a quantum state? (I don't know, I'm not a physicist.) 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.
  - zanmat0 8y ago
    Do you have any sources or further reading for this?
    - stillbourne 8y ago
      https://arxiv.org/pdf/quant-ph/0110141.pdf https://arxiv.org/pdf/quant-ph/0110141.pdf https://web.archive.org/web/20171111160807/http://fab.cba.mit.edu/classes/862.16/notes/computation/Lloyd-2002.pdf https://web.archive.org/web/20171111160807/http://fab.cba.mi... https://www.amazon.com/dp/B000GCFBP6/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1 https://www.amazon.com/dp/B000GCFBP6/ref=dp-kindle-redirect?... Also read the references.
    - fnrslvr 8y ago
      Also, Scott Aaronson gets pulled into speculation on these things a lot, e.g. https://www.scottaaronson.com/blog/?p=3208 https://www.scottaaronson.com/blog/?p=3208
      - stillbourne 8y ago
        I like the idea as a thought experiment in information theory but I am skeptical of the idea in general.
  - stillbourne 8y ago
    That's not even my second objection. My second objection is the rate of Entropy of the computer that would be using to make that computation, the amount of mass of the computer that would be required to use and how long it could continue to make computations before the heat death of computer. Also you would have to consider the fact that as performing multivariate calculus of the expanding universe that is completely gravitationally bound would require that the computer that is performing the calculations that govern the simulation to expand at a rate faster than the simulation that it is computing. Eventually what ever the rate of Entropy is in the Universe of the computer that would be simulating our Universe is would exceed the capability of it to exchange information from one end of the machine to the next as it eventually starts to expand faster than whatever the equivalent of the speed of light would be in the simulating universe.
    - fnrslvr 8y ago
      There's a lot of subjectivity to the "we can simulate the universe" variety of claim stated by the article, but I'd tend to forgive considerations of the scale of the entire universe in that claim. It should be obvious that simulating the trajectory of every last particle is straight up impossible. (Even in principle: you could probably even show outright impossibility on logical grounds with a diagonal argument a la the time hierarchy theorem.) 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.
Simon_says 8y ago
You're probably making some unfounded assumptions about the size of our universe to come up with that number.
- stillbourne 8y ago
  How so? What's the number that you come up with?
  - always_good 8y ago
    It doesn't seem very useful to parcel out the limitations of what can be simulated upstream in terms of the limitations of our own physics.
    - stillbourne 8y ago
      There are some assumptions that we can make about an upstream computers physics, things such as the Fundamental Constants. Not that the constants would be the same in upstream but that those constants need to be defined in order for a fine-tuned universe complex enough to have something like a computer.
  - Simon_says 8y ago
    I ascribe a high likelihood that our universe is infinite in extent, so my answer would be ∞. But for any finite volume, the Bekenstein bound will give you an upper limit. https://en.wikipedia.org/wiki/Bekenstein_bound https://en.wikipedia.org/wiki/Bekenstein_bound
    - stillbourne 8y ago
      I may be incorrect but the radius of the upper bound of the Bekenstein bound would exceed the length of the lower bound of the whole universe. I came up with my number using the observable universe as the radius and the planck length as the volume. Your number would far exceed mine, I think. 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.
gattr 8y ago
Right, but adaptive refinement is bread and butter of today's physics simulations. I imagine that in order to simulate our Universe, you'd go down to elementary particle level only when some of the simulated folks run their accelerators, etc. But for an in-simulation billiard game you'd use a plain impulse-based rigid body dynamics.
- stillbourne 8y ago
  The problem isn't particles, its particle interactions and the orders of magnitude in time these events occur at. There is a reason why planck length is shortest theoretical measurable time interval. I'm sure you are aware of the equation E=mc^2, at the planck length the value of c=1. Therefore a planck length, cubed, of the universe can be considered to be 1 bit, for the purposes of storage for a universe, or at least this one.
  - raattgift 8y ago
    I think you should at least check out the relevant wikipedia page here https://en.wikipedia.org/wiki/Planck_length 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) https://en.wikipedia.org/wiki/Nat_(unit)

ctb9 8y ago

How does one come to that figure?

fnrslvr 8y ago
Some combination of the holographic principle and the the information overhead of classically representing a quantum state? (I don't know, I'm not a physicist.) 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.
- zanmat0 8y ago
  Do you have any sources or further reading for this?
  - stillbourne 8y ago
    https://arxiv.org/pdf/quant-ph/0110141.pdf https://arxiv.org/pdf/quant-ph/0110141.pdf https://web.archive.org/web/20171111160807/http://fab.cba.mit.edu/classes/862.16/notes/computation/Lloyd-2002.pdf https://web.archive.org/web/20171111160807/http://fab.cba.mi... https://www.amazon.com/dp/B000GCFBP6/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1 https://www.amazon.com/dp/B000GCFBP6/ref=dp-kindle-redirect?... Also read the references.
  - fnrslvr 8y ago
    Also, Scott Aaronson gets pulled into speculation on these things a lot, e.g. https://www.scottaaronson.com/blog/?p=3208 https://www.scottaaronson.com/blog/?p=3208
    - stillbourne 8y ago
      I like the idea as a thought experiment in information theory but I am skeptical of the idea in general.
- stillbourne 8y ago
  That's not even my second objection. My second objection is the rate of Entropy of the computer that would be using to make that computation, the amount of mass of the computer that would be required to use and how long it could continue to make computations before the heat death of computer. Also you would have to consider the fact that as performing multivariate calculus of the expanding universe that is completely gravitationally bound would require that the computer that is performing the calculations that govern the simulation to expand at a rate faster than the simulation that it is computing. Eventually what ever the rate of Entropy is in the Universe of the computer that would be simulating our Universe is would exceed the capability of it to exchange information from one end of the machine to the next as it eventually starts to expand faster than whatever the equivalent of the speed of light would be in the simulating universe.
  - fnrslvr 8y ago
    There's a lot of subjectivity to the "we can simulate the universe" variety of claim stated by the article, but I'd tend to forgive considerations of the scale of the entire universe in that claim. It should be obvious that simulating the trajectory of every last particle is straight up impossible. (Even in principle: you could probably even show outright impossibility on logical grounds with a diagonal argument a la the time hierarchy theorem.) 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.

Simon_says 8y ago

You're probably making some unfounded assumptions about the size of our universe to come up with that number.

stillbourne 8y ago
How so? What's the number that you come up with?
- always_good 8y ago
  It doesn't seem very useful to parcel out the limitations of what can be simulated upstream in terms of the limitations of our own physics.
  - stillbourne 8y ago
    There are some assumptions that we can make about an upstream computers physics, things such as the Fundamental Constants. Not that the constants would be the same in upstream but that those constants need to be defined in order for a fine-tuned universe complex enough to have something like a computer.
- Simon_says 8y ago
  I ascribe a high likelihood that our universe is infinite in extent, so my answer would be ∞. But for any finite volume, the Bekenstein bound will give you an upper limit. https://en.wikipedia.org/wiki/Bekenstein_bound https://en.wikipedia.org/wiki/Bekenstein_bound
  - stillbourne 8y ago
    I may be incorrect but the radius of the upper bound of the Bekenstein bound would exceed the length of the lower bound of the whole universe. I came up with my number using the observable universe as the radius and the planck length as the volume. Your number would far exceed mine, I think. 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.

gattr 8y ago

Right, but adaptive refinement is bread and butter of today's physics simulations. I imagine that in order to simulate our Universe, you'd go down to elementary particle level only when some of the simulated folks run their accelerators, etc. But for an in-simulation billiard game you'd use a plain impulse-based rigid body dynamics.

stillbourne 8y ago
The problem isn't particles, its particle interactions and the orders of magnitude in time these events occur at. There is a reason why planck length is shortest theoretical measurable time interval. I'm sure you are aware of the equation E=mc^2, at the planck length the value of c=1. Therefore a planck length, cubed, of the universe can be considered to be 1 bit, for the purposes of storage for a universe, or at least this one.
- raattgift 8y ago
  I think you should at least check out the relevant wikipedia page here https://en.wikipedia.org/wiki/Planck_length 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) https://en.wikipedia.org/wiki/Nat_(unit)