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P vs. NP Problem Linked To the Quantum Nature of the Universe
KentuckyFC writes: "One of the greatest mysteries in science is why we don't see quantum effects on the macroscopic scale; why Schrodinger's famous cat cannot be both alive and dead at the same time. Now one theorist says the answer is because P is NOT equal to NP. Here's the thinking: The equation that describes the state of any quantum object is called Schrodinger's equation. Physicists have always thought it can be used to describe everything in the universe, even large objects, and perhaps the universe itself. But the new idea is that this requires an additional assumption — that an efficient algorithm exists to solve the equation for complex macroscopic systems. But is this true? The new approach involves showing that the problem of solving Schrodinger's equation is NP-hard. So if macroscopic superpositions exist, there must be an algorithm that can solve this NP-hard problem quickly and efficiently. And because all NP-hard problems are mathematically equivalent, this algorithm must also be capable of solving all other NP-hard problems too, such as the traveling salesman problem. In other words, NP-hard problems are equivalent to the class of much easier problems called P. Or P=NP. But here's the thing: computational complexity theorists have good reason to think that P is not equal to NP (although they haven't yet proven it). If they're right, then macroscopic superpositions cannot exist, which explains why we do not (and cannot) observe them in the real world. Voila!"
I have not had time to read the article, but the summary is either incoherent or wrong.
Here is an analog to illustrate why :
The basic equations for fluid dynamics are the Navier-Stokes equation. But the new idea is that this requires an additional assumption — that an efficient algorithm exists to solve the equation for complex macroscopic systems. But is this true?
In the case of the Navier-Stokes equation, almost certainly not. In fact, it is generally not even clear if solutions even exist, or if they are non-singular.
If this is right, then complex fluid motions cannot exist, which explains why we do not (and cannot) observe them in the real world. Voila!"
So, I guess we can cancel this years hurricane season.
In other words, there are many things in nature that are computationally hard, and yet happen any way. Using computational hardness as a reason why a physical theory cannot be right does not, to put it mildly, agree with past experience.
BOOM.
My God can beat up your God. Just kidding...don't take offense. I know there's no God.
I'm trying to work this into an everyday analogy of a traveling half-dead-cat salesman, but am getting stuck.
Table-ized A.I.
My impression is that it's saying that quantum effects perhaps can in theory be used to explain macro-physics, but it's too difficult for humanity to run the models to compute the macro affects using quantum models such that we are stuck with separate models (approximations) for the macro side versus the micro-side.
In other words, a near-perfect simulation of quantum affects may properly mirror macro-effects in an emergent-behavior kind of way, but doing such is not practical using existing computer technology.
It's roughly comparable to the human brain: we have plenty of nice little models of neurons and small neural nets, but we don't have the computational power to see if it matches human behavior on a bigger scale. (It's probably more than just horse-power; many of the organizational details are still murky, but just go with me on this as a rough example.) Thus, we are stuck with "psychology" for the large scale instead of modelling human behavior at the neuron level.
I don't think they are saying that the universe itself can't "run" the "computations", but that part is not clear. We don't know that the universe's OS is time-dependent or even what the universe's OS is (although its predicted birth and death pattern resembles Windows: designed to run so many years until enough cruft builds up over time that it slows to a crawl such that it becomes indistinguishable from no OS, and then you have trash the whole thing, keep a few pet files, buy version Windows N+1 and install from scratch. Elvis and Michael Jackson are two of the "pet files" kept from Universe N-1, I bet, and they'll be put back into N+1.)
Table-ized A.I.
The summary is actually accurate! This was quite a surprise to me, since as many other posters have correctly commented here, these claims are absurd. The Universe is not inconvenienced by the difficulty of computing something about its properties.
Perhaps this paper should have been released two days ago.
Hmm... the Incomputatibility of the Universe, maybe this is an avenue for proving the the Universe is not a simulation?
Starships were meant to fly, Hands up and touch the sky - Nicky Minaj
Yes, the paper is meaningless. A very well-argued brand of meaningless-- but still. "Efficiency" of computation doesn't matter. It's also a slick glide from saying that a problem is soluble in polynomial time to saying it's easy. No. That's computer speak. Polynomial time is not defined as "easy;" it's not even necessarily fast. (It deals more with the scale-up than with the actual difficulty).
The Schrödinger equation is a differential equation-- that means, the solution at any given point in time and space depends on the fields and wave function, and the derivatives of the fields and wave function at that point-- it's local. So, the universe doesn't have to "solve" the Schrödinger equation; it only has to solve the equation for time t + epsilon, given the initial condition of the solution at time t. This is NOT a polynomial-time problem. If the universe is twice as big, it has twice as many calculations to do... and twice as much "stuff" to do it with. It's local.
The difficulty is that wave-function collapse is not local. This is inherent in the mathematical logic of quantum mechanics. It's not a matter of how hard it is to compute.
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