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- Hacker News
- It doesn't disprove a theory if it results in the physical universe violating NP!=P. In fact, we already know the universe violates NP!=P via the O(N) sorting algorithm[1]:
[1] which I learned about in "The New Turing Ominbus" by A K Dewdneyfor each element: cut a spaghetti strand to the a the length of the elemnet add strand to bundle of spaghetti hold spaghetti bundle vertical lower spaghetti bundle to a flat surface. loosen grip so that each spaghetti strand comes to rest on flat surface while there is spaghetti in the bundle: lower a second flat surface above the bundle until it touches the topmost spaghetti piece remove the piece, and output it's lengthby advisedwang - i hate every time i hear about spaghettisort.
it is still O(n) weight to transport, so O(n^2) amortised; if you liken having a stronger hand that can carry more spaghetti to parallelisation, it's beaten by O(log^2 n) sorting algorithms on parallelised classical computers.
by DroneBetter - I feel like there's some hidden complexity there. For any finite flat surface there's a point where not all the spaghetti will fit on it simultaneously. So you have to do O(N) compression steps to find the bundle with the long strand. Locating the strand within the bundle also seems non-trivial if it's big enough. Both are easier to see if you start thinking about scaling to sorting like, square miles of spaghetti at a time.
- What does sorting have to do with violating p != np?
The common bound on sorting is you can't do better than O(n lg n) worst-case, but that is strictly only for comparison sorts anyway.
by kadoban - From the abstract:
"Assuming [assumptions] we show that ... can in principle solve..."
Yeah, well, you know... that doesn't sound as promising as the title.
by einpoklum - Shocking..by greenbit
- That's the whole point of the article:
"We show [Assuming {competing physics theory} then {P = NP}]"
(or something along the lines)
"But we actually think P != NP... so [Assuming {P != NP} then {competing physics theory} cant be true]"
by Garlef - Assuming X is true, that implies Y. We don't think Y is true therefore we now doubt that X is true, is a very standard thing to do in math.by bawolff
- But does it solve fluids or n-body gravity?by westurner
- What of the/a dilatant fluid model of gravity which predicts the perihelion of Mercury does not jive with observation?
Doesn't that indicate that CFD is the viable way forward?
The point of the OP is that it's neat or maybe useful that semiclassical gravity solves NP-complete problems; but if the semiclassical model of gravity is insufficient to describe even gravity, why should it be sufficient to solve NPC problems, and what does a sufficient model of n-body fluidic gravity enable low-error predictions of?
by westurner - Scott Aaronson has a really good explainer about complexity theory and physical computing:
https://www.scottaaronson.com/papers/npcomplete.pdf
(Doing my best to ignore his abysmal politics.)
by hiddencost - I was skimming the paper and came to this: > This transformation is like an AND gate - it ignores the index qubit and places the flag qubit in the state |1> if and only if either of the original components had the state |1> for the flag qubit.
Shouldn't that be an OR gate? Not only does the description above say "if and only if either of the original components had the state |1>", which is an OR, but the truth table listed above shows the same thing for the flag qubit.
Of course, one could say it's an AND on the |0> states, which is just De Morgan's law, but that's pretty awkward phrasing.
by SyzygyRhythm - Demorgan's theorem says AND and OR are equivalent, and only depend upon the polarity of the bits. So if "state |1>" is a binary zero, AND is the proper logical operator.by anonymousiam
- Are you sure you're looking at the right paper? I don't find the sentence you mention in the paper.by slwvx
- Anyone care to ELI5 the novelty or significance of this?by aix1
- They essentially are saying semiclassical gravity (a broader theory subsuming classical) is theoretically incorrect. Like doing the konami code IRL and getting infinite money.by casey2
- They use what looks like an impossible computational result to back into the idea that this is indirect evidence that gravity is quantized.
The controversy here is whether gravity is continuous (as classical Einstein models it) all the way down, or if the large scale behavior is built on a quantum foundation like everything else.
As far as I know most physicists believe gravity must be quantized, but we have no theory for it that works and plays nice with the well validated relativistic stuff at scale.
We have some candidates like string theory and loop quantum gravity but testing and refining them requires accelerators the size of the solar system or direct access to a black hole. The latter was the plot of Interstellar.
by api - if the PECTT (Physical Extended Church-Turing Thesis) is true then the current standard way of connecting classical gravity with quantum mechanics is wrong. the authors take it as evidence for full quantum gravity because the alternative is changing the Einstein equations in some arbitrary complex way. im not a physicist so this might be a bad explanation.
the extended thesis it depends on is "No physical procedure can decide an NP-complete problem in polynomially many steps." imo thats a very strong and controversial assumption when we still dont know the limits of what quantum computers can do.
by tancop - Semiclassical gravity is the best we can currently do for a theory of gravity without invoking speculative ideas that are currently untestable. If the paper holds up (I haven't read it), then there are several possibilities:
1. Maybe P = NP, and semiclassical gravity isn't special. 2. Maybe P = NP, and the way we'll prove it is finding an efficient way to simulate semiclassical gravity. 3. P = NP is a hypothesis about traditional theories of computation, but they don't rule out that we can build a special machine that solves them. There's a stronger hypothesis, the extended Church-Turing thesis (ECTT), that says this is impossible. Maybe the extended Church-Turing thesis is wrong, and this is how we'll show it. 4. If ECTT thesis is right, then maybe we can conduct an experiment where semiclassical gravity fails. This gives us a clue to new physics. 5. If we can't eventually conduct an experiment, then at least we learn about a new angle on complexity -- problems that can be efficiently solved this way but not by a deterministic Turing machine.
Both quantum mechanics and general relativity are thought to satisfy the ECTT, so the fact that our most experimentally successful combination of the two doesn't is of some interest. (Semiclassical gravity is thought to fail eventually, but in a way that's out of reach of current experiments.)
by QuesnayJr - I'm not convinced. They aren't actually using the semiclassical Einstein equation, they are using some simplification they call Newton Schrodinger equation. They claim that this equation can lead to distinguish a state that's exponentially close to |0> from |0>. I don't follow their whole argument.
Anyway, I wouldn't be surprised if you could actually do hard computations with semiclassical Einstein equation, because they have strong self consistency - the expectation value of the stress energy tensor curves the metric, which in turn excites the quantum vacuum and causes expectation value of the stress energy tensor. But this isn't what they use in the paper. Nobody knows if this self consistency can be achieved in all configurations, and physicists working with semiclassical gravity usually do only one iteration of the self consistency.
If someone wanted to make semiclassical gravity into quantum gravity, he'll probably assume that gravity causes measurements, which would prevent these kinds of abuses where you have superposition you're probing via gravity while keeping it intact.