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Macroscopic quantum objects cannot exist if P ≠ NP?
- jjgreen 12y agoThe Navier-Stokes equations are also hard to solve, that does not stop fluids from obeying them.
- sleepysort 12y agoI'm not totally familiar with the Navier-Stokes equations, but from what I've just read (please correct me if I'm wrong!), I think the difficulty of the Navier-Stokes equation is reasoning about the solution set, while with quantum constructions the issue is whether or not a solution exists for some specific macroscopic system.
- kazinator 12y agoAlso, how can N bodies orbit each other? Don't they know there is no analytic solution to their problem? Sheesh! (Maybe they are using floating-point?)
- raverbashing 12y agoI agree For those who never saw the Navier-Stokes equation: http://en.wikipedia.org/wiki/Navier_Stokes#Derivation_and_description http://en.wikipedia.org/wiki/Navier_Stokes#Derivation_and_de... That's it. It looks simple but it involves Tensor math.
- kazinator 12y agoThis hypothesis seems to rest in the flawed idea that quantum processes must unfold as if by a step by step calculation which consumes time, in the ordinary temporal dimension. And so certain complex state changes are impossible simply because they don't have enough time to execute within some predetermined slot, or something like that. Time in the simulation is not the same as time in the simulator. Come on, this is not even basic science as much as basic sci-fi! :)
- sambeau 12y agoSurely Schrodinger’s Paradox implies cause and effect?
- raverbashing 12y agoI'm not buying it 1 - P=NP is a mathematical problem. It has nothing to do with Physics. Physics has to do with Mathematics but one should be very careful when extrapolating (range, constraints, etc). 2 - Nature has no problem whatsoever solving complicated equations. Our mathematical models are the ones who suffer to model simple everyday stuff in Physics. Turbulence and Navier-Stokes equations, electromagnetic propagation, the way lightning goes through the air, etc.
- kang 12y agoYour comments are non-constructive. This second point was almost religious. To say that a mathematical problem has nothing to do with physics would not be right, since physics' major theories of today are essentially maths.
- raverbashing 12y ago"To say that a mathematical problem has nothing to do with physics would not be right, since physics' major theories of today are essentially maths." No Physics depends on mathematics, not the opposite. Math exists regardless of physics.
- kang 12y agoyes. now i realize.
- mdxn 12y agoThis is overly general. And we need to make a distinction between actual physics (laws of Nature) and our theoretical models of such. Yes. Our theoretical models of the laws of physics are usually formal and axiomatic systems of logic (basically mathematics). Yes. We understand and describe it using mathematical constructions we know of. However, the laws of Nature do govern what kinds of models of computation are realizable (theoretically and physically). Limits on computability influence the design and sophistication of logic and mathematics. A good model of computation that we choose for this is some variant of a Turing machine. If this is true for our brains as well, then there is a limit on how sophisticated and powerful mathematics can be from our perspectives. In other words, the laws of Nature are dictating how good of a system of mathematics we come up with can be from a logical standpoint.
- dllthomas 12y ago"Nobody knows why we don’t observe these kinds of strange superpositions in the macroscopic world." Yeah, why can't we observe processes that rely on lack of observation?
- bcbrown 12y agoWe can observe processes that rely on lack of observation in the microscopic world. Look up the one-slit and two-slit experiments[0]. In the two-slit experiment, we don't observe which slit the photon takes, but we can observe the interference pattern on the screen. The two-slit experiment works with photons, but not with bullets, or cars, or baseballs. [0]: http://en.wikipedia.org/wiki/Two_slit_experiment http://en.wikipedia.org/wiki/Two_slit_experiment
- dllthomas 12y agoHmm, probably fair.
- Iftheshoefits 12y agoI think the explanation for why we don't observe macroscopic quantum phenomena is rather more simple than that, and likely has more to do with the results of a superposition of a large ensemble of possible states than some fairly strained analogy with computation (think of it as something like fourier decomposition of a function).
- kipple 12y agoOne part I didn't like is towards the beginning the author says: "Nobody knows why we don’t observe these kinds of strange superpositions in the macroscopic world. For some reason, quantum mechanics just doesn’t work on that scale. And therein lies the mystery, one of the greatest in science." But I thought the reason we dont see macroscopic events exhibiting quantum superposition behavior was because of quanutm decoherence? It's just so hard to get a macroscopic situation that hasnt already been observed and collapsed. But then the author kinda hints at this point later when he mentions: "Physicists have become increasingly skilled at creating conditions in which ever larger objects demonstrate quantum behaviour." Am I missing something, or is he blowing the problem (and the impact of Bolotin's computational limit theory) way out of proportion?
- bcbrown 12y agoAn interesting assertion. I don't think it's valid to object that this is just about hard-to-solve equations. As I understand the article, this is the argument: 1) It's not possible to directly observe a macroscopic quantum object. This is because the act of observation collapses the wave function. 2) It's possible in theory to describe macroscopic quantum objects in the solutions to Schrodinger's equation 3) That solution for macroscopic systems is NP-hard 4) A physical theory that can neither be observed nor modeled is "nothing more than [a] nontestable empty [abstraction]"
- pndmnm 12y agoInteresting and semi-related: http://www.opticsinfobase.org/oe/abstract.cfm?id=140598 http://www.opticsinfobase.org/oe/abstract.cfm?id=140598 Essentially, solving the traveling salesman problem in quadratic time using photon interference -- however, since the photons scale up as N^N, the Schwarzschild radius of the effect means it's not observable in less than exponential time.
- Dunnorandom 12y agoFor anyone interested, here's Scott Aaronson's response to the paper: http://www.scottaaronson.com/blog/?p=1767#comment-103591 http://www.scottaaronson.com/blog/?p=1767#comment-103591
- ColinDabritz 12y agoIt sounds like the paper is pretty much gibberish from a scientific perspective, which makes sense. It was, however, an interesting thought for me, and brought up a lot of classic philosophy questions about the nature of our universe, e.g. why would it matter if anyone could calculate it or not? If it was true would it lend evidence to a 'universe is computer-like' model? Still neat to consider.
- awhitty 12y agoI understand that people get a little passionate about their fields of study, but the tone of Aaronson's response is wildly inappropriate. Phrases like "a common novice mistake" and "as if he just emerged from a cave" are unnecessary and entirely condescending. This style of discourse fosters a really awful and exclusive atmosphere, and I wish it wasn't the norm. I don't know this guy at all, and I'm guessing he's pretty respected in his field, but at the end of the day, he doesn't have to be a jerk to get his point across.
- mdxn 12y agoI can see how it can be read that way, though you should also to look at this from his perspective (or at least my guess as to a possible perspective). The internet (and the field) is flooded with nonsense papers that don't respect the hard work of others. A lot of them really do come from these "common novice mistakes". The authors are taking very superficial views of complexity theory and physics against the advice of researchers in those fields. This particular one hasn't, but a lot of them have incredibly bad and egotistical attitudes. I think researchers see this as incredibly insulting, ignorant, and a severe lack of humility. People aren't showing enough respect and care to this field. This wouldn't be such a problem if it didn't happen more often than not. On top of that, these poor findings end up swarming around the media and dilute the field. Look, Aaronson is a well known guy who has spent a lot of time trying to point out and explain these mistakes. Though people, including pseudo-scientists, completely ignore him. They even start fights with him. He and others get spammed with this stuff weekly if not daily. For him, I bet it's simply too much to ignore.
- tomp 12y agoWait what? What this article is arguing is totally absurd - just because we can't model certain physical objects, they cannot exist?! That's like saying that since we can't model three gravitational objects interacting (i.e. the numerical solutions diverge, therefore to properly model the system, we would require increasing amounts of memory and time), therefore they cannot exist. I'm not saying that the physical claim is wrong - I'm just saying that the explanation in the article is severely lacking/logically inconsistent.
- bcbrown 12y agoIf something can neither be modeled nor observed, in what sense does it exist?
- yid 12y agoWhat does modeling have to do with observability?
- jerf 12y agoWe observe n-body systems continuously. We are all participants in n-body systems continuously.
- scott_s 12y agoThat's not the question. Macroscopic behavior as described by Schrodinger's equation has never been observed. Because of having no observations, we assume it does not exist. The linked paper is arguing, "Because solving Schrodinger's equation is non-polynomial, and such solutions are infeasible when N is large, then they can't exist." The linked paper is stating that the phenomenon has not been observed, assuming it does not exist, and then trying to explain why. tomp's point is that we observe systems in our Universe that we can't model efficiently all the time. Hence, the line of argument in the paper doesn't hold up.
- SnacksOnAPlane 12y agoI'm a simulationist. I believe that the universe we're experiencing is a simulation made by a far-advanced civilization. So in my reality, if something can't be modeled, it can't exist. Not saying that this is the truth, just the way I choose to understand things.
- typon 12y agoThis is such a poorly written article. I can't even begin to point out the mistakes. I'm sure Scott Aaronson will write a response and strike this down.
- Strilanc 12y agoI hope Scott Aaronson blogs about this article, because it espouses several of the wrong-facts he complains about and then cites him. - Limitations on computers within physics are not limitations on physics itself. Analogously, you can simulate system so simple that a computer can't be made in them without your computer unmaking itself. Relevant: xkcd.com/505 - We do understand why we don't observe superpositions. It all comes down to this thing we call "quantum mechanics", which precisely describes those sorts of situations. - The article consistently mixes up NP-Hard and NP-Complete. > "And how does the universe decide whether a system is going to be quantum or not?" Seriously, is this article a satire?
- PeterisP 12y agoAn interesting point is that limitations on math (i.e., things that would be true regardless of the details of the physical world) would put limitations on any physics simulations - including hypothetical physics simulations done by someone outside of our universe with potentially different physical limitations. So the point of the article is something like - if phenomenon-X can't be simulated by anyone, no matter how good their computers become; and if our universe is a simulation (which is a possibility), then our universe won't contain phenomenon-X.
- TheLoneWolfling 12y agoThe problem is that there is no proof that there is any such thing as something that would be true regardless of the details of the physical world.
- wcoenen 12y agoWe can't directly observe superpositions (macroscopic or otherwise) because when doing so, we become entangled with the state of the observed object. The only thing special about macroscopic objects is that it is difficult to prevent or postpone their entanglement with the environment. Think about Schrödingers' gedankenexperiment from the cat's point of view. It finds itself to be either comfortable or dying by toxic fumes; it can't see the superposition because it is inside of that superposition. The same thing happens to any observer trying to look at a quantum superposition.
- JulianMorrison 12y agoBox closed: two cats, one scientist. Box opened: two cats, two scientists, each sees one cat. Entangling yourself with the superposition pulls you into it.
- trhway 12y ago>Entangling yourself with the superposition pulls you into it. following that logic and taking cat as the observer, Mr.Cat PhD, the superposition is that doubles the number of cats (and PhD's :). Yet it works in the other direction - entangling a cat (a macro-object with macro-state) with superposition had already destroyed the superposition well before box is opened. >> it can't see the superposition because it is inside of that superposition. it can't see the superposition because the superposition is gone because he got entangled with it.
- JulianMorrison 12y agoThe cat is pulled into the superposition by interacting with the results of the detector and the poison vial. There are two cats from the "outside", but from each cat's perspective it sees only a single "random" outcome. Superpositions aren't destroyed - you are subsumed within them.
- trhway 12y ago>There are two cats from the "outside", but from each cat's perspective it sees only a single "random" outcome. in a given Universe there is only one cat. A human observer just doesn't know what the state of the cat in his Universe. The cat knows.
- ctdonath 12y agoThis is radiantly insightful. It makes perfect sense to me. The effect of reading it is like drinking a Pan Galactic Gargle Blaster: feeling like my brains were smashed out by a slice of lemon wrapped round a large gold brick. Yes, in real physics solves vastly complex equations fast. That's not enough to discount the point here. There are limits on physics itself: the particles in a cat (presumably one owned by Schrodenger) are so numerous that for all of them to express, within a reasonable time, superpositioning the effects of a single radioactive atom's unobserved state would require particle interactions occur way faster than Planck time. Nothing moves faster than light. There are a finite, albeit large, number of particles in the universe. Nothing can be smaller than Planck length, and no particle interaction can occur faster than the time light takes to move one such unit. Upshot: macroscopic superpositionining effects cannot occur because it takes too long for full propagation among particles numbering on the magnitude of Avagadro's number. There's an upper limit to what can happen, because there's only so much stuff and "happen" can only be so fast.
- baddox 12y ago> What’s interesting about NP-hard problems is that they are mathematically equivalent. So a solution for one automatically implies a solution for them all. That's a mistake. The author is describing NP-complete problems, which are all roughly equivalent (reducible in polynomial time). NP-hard includes all NP-complete problems, but also includes problems much harder than those in NP-complete, including undecidable problems like the halting problem which aren't even in NP.
- pcvarmint 12y ago> That's a mistake. The author is describing NP-complete problems... Correct. I think that quote basically killed the whole article for me.
- baddox 12y agoIt didn't kill the whole article for me, although it seems to be a consistent misconception rather than an isolated typo. To be fair, the naming convention is pretty tricky, considering NP-hard contains things outside NP.
- icodestuff 12y agoAnd the diagram did get the terminology right. The author may need a (better) proofreader, but it wasn't impossible to see what the author meant. They only conflated the names, not the concepts.
- lfuller 12y agoBy this logic, shouldn't the existence of the universe be impossible since simulating it mathematically in its entirety is infeasible?
- snake_plissken 12y agoI thought you could observe quantum effects but only when it was the superposition of all the eigenfunctions? You never observe the ones with a low probability density because they are dominated by the others. And also does it matter if you could solve numerically all of the functions for a macroscopic group of particles if in the end all you would care about is the average value (due to Planck's constant and the uncertainty principle)?
- agorism 12y agoThis is almost the same as the free-will vs determinism problem. Our universe is deterministic, but computing into the future is NP-complete.
- TheLoneWolfling 12y agoAn interesting tidbit: If the smallest proof for something takes up more than ~10^123 bits, or the fastest proof requires more than ~10^120 operations, it cannot be proven in our universe.