Slashdot Mirror
We're Not Living in a Computer Simulation, New Research Shows (cosmosmagazine.com)
A reader shares a report: A team of theoretical physicists from Oxford University in the UK has shown that life and reality cannot be merely simulations generated by a massive extraterrestrial computer. The finding -- an unexpectedly definite one -- arose from the discovery of a novel link between gravitational anomalies and computational complexity. In a paper published in the journal Science Advances, Zohar Ringel and Dmitry Kovrizhi show that constructing a computer simulation of a particular quantum phenomenon that occurs in metals is impossible -- not just practically, but in principle. The pair initially set out to see whether it was possible to use a technique known as quantum Monte Carlo to study the quantum Hall effect -- a phenomenon in physical systems that exhibit strong magnetic fields and very low temperatures, and manifests as an energy current that runs across the temperature gradient. The phenomenon indicates an anomaly in the underlying space-time geometry. [...] They discovered that the complexity of the simulation increased exponentially with the number of particles being simulated. If the complexity grew linearly with the number of particles being simulated, then doubling the number of partices would mean doubling the computing power required. If, however, the complexity grows on an exponential scale -- where the amount of computing power has to double every time a single particle is added -- then the task quickly becomes impossible.
There is no viability to Pro or Con studies for this. We simply would not be capable of knowing if we're simulated as our own thought processes would in fact be governed by the same rules of the system we're attempting to prove or disprove. You're trying prove a proof by using the proof as proof. It's just an exercise in futility as any civilization or system capable of creating such a complete simulation will undoubtedly have put in to place provisions for "what if the simulation starts questioning reality".
Even if it's imperfect, if the Hall effect is anomalous behavior, how do we know it's not already caused by the simulation "skipping frames" and/or cheating on calculations?
There's a fundamental problem with this conclusion. It shows that we are incapable, in this universe, of simulating this phenomenon due to its complexity. However, if this universe is a simulation, the laws of this universe do not necessarily apply to the universe in which this simulation resides. We can say nothing as to the characteristics of such a universe, and therefore cannot conclude at all whether we are in a simulation or not. This merely shows that it isn't feasible for us to simulate such an effect should we choose to create our own simulated universes.
What they do suggests (but does not prove) that a purely classical simulation would require exponential size. So, nothing here rules out using a quantum computer to efficiently simulate a quantum system. Moreover, they don't give any proof of the claim, just a strong plausibility argument with an identified potential obstruction; rigorously proving what they want would be a stronger claim than P != PSPACE. Here P is the set of problems which can be solved on a classical computer in time polynomial of the input, and PSPACE is the same thing but for space, https://en.wikipedia.org/wiki/PSPACE . This is about one step away from the very famous P ?= NP problem. In fact, their claim if they had a proof would be even stronger than P !=PSPACE because it essentially comes down to making what amounts to an argument that P != BQP (where BQP is what a quantum computer can do in polynomial time https://en.wikipedia.org/wiki/BQP). We already have very good evidence that quantum systems cannot be easily classically simulated even without gravitational effects like they are talking about here; In particular, Aaronson and Arkhipov's work on Boson Samplying https://en.wikipedia.org/wiki/Boson_sampling strongly suggests that even a system just trying to accurately simulate the behavior of photons cannot be simulated classically without superpolynomial sized resources. Frankly, I'm a bit surprised that they don't cite or mention boson sampling at all. It is possible that I'm misinterpreting this new result, but if I'm correct this really isn't a big deal at all.
True believers of the simulation hypothesis, that there exists some otherworldy all-powerful other responsible for the whole of creation, should sound familiar. They're basically those drawn towards spiritual or other woo-woo thinking, but have been raised in a technological society.
There is no viability to Pro or Con studies for this. We simply would not be capable of knowing if we're simulated as our own thought processes would in fact be governed by the same rules of the system we're attempting to prove or disprove.
What you're proposing is a philosophical proof, and it's not rigorous.
It turns out that we *can* prove or disprove certain statements about our universe. The fundamental fact (to prove, or disprove) is whether the universe is computable.
Computability has a couple of slightly different meanings in the literature depending on certain assumptions, but in general terms it means that the results of a computation can be done with a) a computer, b) using finite memory, and c) in a finite amount of time(*).
The Church-Turing thesis implies that all computers are equivalent, so the type of computer doesn't matter.
What *does* matter is the finite limits on time and memory. You can't use real (in the mathematical sense) numbers, because they take an infinite amount of memory to store, and would take an infinite amount of processing just to load one into a register. This implies that position, if your universe has this as a feature, must be quantized in some way. The amount of information in a particle's position must be finite. Time also has to be quantized.
If time and position are quantized, you might need some sort of "fuzzing" algorithm to avoid jaggies and other artifacts in your universe. Something like Bresenham's algorithm, or some other anti-aliasing method. Maybe use sines and cosines to represent the probability of a position between two quantized locations or something similar.
If we can identify an effect that the universe has that is non-computable, then we could (at that time) definitely state that the universe is not some sort of simulation.
That being said, I don't think this paper rules out computability per-se. The fact that complexity is exponential does not specifically rule out being computable, the thing about exponentiality comes from the post and not the abstract of the paper, the paper abstract itself states that the question is still open, and the paper is speculative and might be subject to re-interpretation or dispute by subsequent papers.
It's also really, really dense.
Whether the universe is computable is a really interesting question. Consider the resolution of the probability values of QM experiments; ie - is there a limit to the resolution one can have on a probability measurement? If it's a finite amount of information, it's kept in a finite number of bits, which means that it has a fundamental fractional resolution.
Is there an experiment that would show this fundamental resolution limit? (Do photons from distant galaxies arrive in tiny quantized angles, for instance?)
(*) With one possible exception, which is the overall program of the universe. The universe itself can run for infinite time, so long as each interaction can be computed in a finite amount of time. Basically, you can have exactly one while(1) in the main() of your universe, and all subroutines must return in a finite amount of time.
Not to mention why limit yourself to a standard CPU architecture where one CPU is simulating frames for many objects? Instead you could do a massively parallel system where a single processor could simulate a single atom or even subatomic particle. Then with a flexible network it would communicate only with the other particles it directly communicates with (even have "particles" representing parts of space for EM radiation).
You could possibly do this with something like a 3 dimensional FPGA where x number of gates are used to simulate the particle and are connected through gates to other "particles" in the simulation. Reprogramming those gates on the fly based on state changes could let the simulation effectively move through the FPGA. This is something we could almost do on a small 2d scale now.
Sure a lot of this is prevented on a large scale by physics but if we are in a simulation, that doesn't necessarily tell us anything about the real universe we are living in. The parent universe could have more than 3 dimensions, possibly a lot more. Now it could be almost trivial to simulate a 3d universe of very large scale. It doesn't even have to be able to simulate it quickly, who says we would notice that a second of our time takes a century in the "real" universe, or whatever time they might have?