Macroscopic quantum objects cannot exist if P ≠ NP? • Hacker News Board

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#31

Post by scott_s » Thu, Jul 24, 2014, 8:06 PM UTC

kang wrote: post #26

raverbashing wrote: post #6

I'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 prop…

Your 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.

For the record: I consider raverbashing's comments constructive. He/she is honestly engaging with the material and other people. The second point is similar to one several people have already made on the thread.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#32

Post by ColinDabritz » Thu, Jul 24, 2014, 8:08 PM UTC

Dunnorandom wrote: post #15

For anyone interested, here's Scott Aaronson's response to the paper: http://www.scottaaronson.com/blog/?p=1767#comment-103591

It 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.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#33

Post by JulianMorrison » Thu, Jul 24, 2014, 8:12 PM UTC

wcoenen wrote: post #30

We 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…

Box closed: two cats, one scientist. Box opened: two cats, two scientists, each sees one cat. Entangling yourself with the superposition pulls you into it.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#34

Post by kang » Thu, Jul 24, 2014, 8:13 PM UTC

raverbashing wrote: post #29

kang wrote: post #26

Earlier quoted context omitted.

Your 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.

"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.

yes. now i realize.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#35

Post by ctdonath » Thu, Jul 24, 2014, 8:18 PM UTC

This 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.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#36

Post by trhway » Thu, Jul 24, 2014, 8:24 PM UTC

JulianMorrison wrote: post #33

wcoenen wrote: post #30

We 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…

Box closed: two cats, one scientist. Box opened: two cats, two scientists, each sees one cat. Entangling yourself with the superposition pulls you into it.

>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.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#37

Post by mdxn » Thu, Jul 24, 2014, 8:35 PM UTC

raverbashing wrote: post #29

kang wrote: post #26

Earlier quoted context omitted.

Your 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.

"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.

This 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.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#38

Post by nemo1618 » Thu, Jul 24, 2014, 8:36 PM UTC

swombat wrote: post #13

raverbashing wrote: post #6

I'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 prop…

Unless, of course, our entire reality is running on a very powerful, but not infinitely powerful computer, and the Great Programmers in the Sky decided to cheat by putting in a hack that cuts off quantum behaviour at a larger scale... Unlikely, but cute...

http://www.simulation-argument.com/

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#39

Post by IanCal » Thu, Jul 24, 2014, 8:36 PM UTC

raverbashing wrote: post #6

I'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 prop…

With 2, are you saying there are situations in nature that can solve NP-hard problems in polynomial time? Because if so, we could just use those to solve our hard problems and therefore P=NP.

P=NP is not just statement about difficult problems or big equations, it's a very particular class of problems.

Re: Macroscopic quantum objects cannot exist if P ≠ NP?

#40

Post by baddox » Thu, Jul 24, 2014, 8:38 PM UTC

> 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.