Quantum physics problem proved unsolvable: Godel and Turing enter quantum physics

[bananas]

Source: Phys.org

A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid - ICMAT and Technical University of Munich.

It is the first major problem in physics for which such a fundamental limitation could be proven. The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.

A small spectral gap - the energy needed to transfer an electron from a low-energy state to an excited state - is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials. When this energy becomes very small, i.e. the spectral gap closes, it becomes possible for the material to transition to a completely different state. An example of this is when a material becomes superconducting.

Mathematically extrapolating from a microscopic description of a material to the bulk solid is considered one of the key tools in the search for materials exhibiting superconductivity at ambient temperatures or other desirable properties. A study, published today in Nature, however, shows crucial limits to this approach. Using sophisticated mathematics, the authors proved that, even with a complete microscopic description of a quantum material, determining whether it has a spectral gap is, in fact, an undecidable question.

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Read more: http://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html

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This is extremely important, for a number of reasons.

[KamaAina]

1. And those reasons would be?

[El Supremo]

4. ...

[Taitertots]

15. Best quote "stop telling God what to do with his dice"

Last edited Wed Dec 9, 2015, 09:22 PM - Edit history (1)

Niels Bohr in response to Einsteins assertion that God doesn't play dice.

I also like "every sentence I utter must be understood not as an affirmation but has a question"

[Docreed2003]

26. +1000. Lol

[Blue_Tires]

30. God is a degenerate gambler?

We *ARE* truly made in his image, aren't we??

[Bradical79]

33. Suddenly everything makes sense...

You know, if that were the version of God I was presented with when I was growing up I might not have been as quick to question his existence

[Android3.14]

5. Good question

I have training in this area, and I cannot comprehend why the OP would post that final comment without some sort of explanation.

[bananas]

9. I'm busy and wanted to get it in LBN, I'll try to add more later. nt

[bvf]

22. From the link:

"...results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties. New physics like this is often later exploited in technology."

Not a lot of elucidation there, but I take it to hold some promise for materials science.

[Android3.14]

23. That makes sense

Thank you.

[aidbo]

20. Numerous. And important. ;)

[Matthew28]

2. Watch someone in 5 or 500 years solve it.

[truedelphi]

3. People who are well versed in both science and in metaphysical

realities suspect that what is needed is the inclusion of a different dimension.

For instance, when a human being dreams an event will be happening, and knows the location and roughly the date, and then the predicted event occurs, even though said person has never traveled to that place and has no apparent connection to that place, right now, in the way that science is utilized, that prediction cannot be proven or disproven in terms of the laws of physics.

So if we could locate and determine that other reality, which seems to inform everyday normal people of catastrophes predicted before hand, then we might have the way to handle all of this.

But science totally excludes the possibility of this extra dimensional reality.

[rhett o rick]

6. I agree. Scientists don't usually say something can't be solved. They just don't have the tools

yet to solve it. And I think other dimensions may well enter into it. There is probably a whole new mathematics waiting to be discovered.

[bvf]

24. You might like reading up (if you haven't already)

on a mathematician by the name of Shinichi Mochizuki.

There's currently a lot out there on him. He claims to have solved a heretofore intractable question in number theory (the ABC conjecture), but spent over a decade developing his own higher methods to do so.

There's some controversy afoot owing to the very small number of his peers with a sufficiently deep understanding of many of the foundations upon which he based his results. He's no crank, but is highly respected in his field, so academia is paying close attention.

As a fan of the math world (certainly no expert here, but I find it fascinating), I think you might enjoy reading up on it, if the prospect of a "new mathematics" intrigues you.

There's a ton of really arcane material on him, but also a lot of non-technical stuff too, as in Wikipedia and, to a lesser extent, the popular press.

[rhett o rick]

25. I will certainly look into it. Not that I don't already have a full reading list.

Currently interested in artificial intelligence. It appears that there is no way to prevent it from becoming the next evolutionary step.

Well there is one way to prevent the Artificial Super Intelligence from making humans obsolete, that is if we damage our human race so badly that we can no longer work on the development of ASI.

[bvf]

28. Yep.

No way of telling where evolution will take us. The irony would be in it coming to a halt (as far as humanity's concerned, anyway) at the hands of people who don't recognize the fact of evolution.

[rhett o rick]

41. It's possible for the human race to harm itself enough that it become extinct or at least

not able to continue scientific advancements for a long time. Otherwise, the appeal of the power available from artificial intelligence will drive mankind to extinction.

[truedelphi]

45. Thank you for telling us about him. n/t

[bvf]

47. You're very welcome! n/t

[Bradical79]

34. The title is slightly misleading I think

I read the article and they never really said it was "unsolvable".

They've shown it's "undecidable" but were not as insistent that it is an "unsolvable" problem.

Dr Cubitt added, "It's possible for particular cases of a problem to be solvable even when the general problem is undecidable, so someone may yet win the coveted $1m prize. But our results do raise the prospect that some of these big open problems in theoretical physics could be provably unsolvable."

Read more at: http://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html#jCp

And here I think they're talking about a general algorithmic solution for all cases anyway.

[harun]

35. This isn't about solving it. Proving something can't be determined

in a mathematical sense is a solution. (and a very valuable one)

So it is similar to the Heisenberg Uncertainty Principle. Invent all the new math you want, you're never go past these "You shall not pass" points.

[rhett o rick]

40. Maybe not within the framework we now know. nm

[mike_c]

51. to be fair, mathematics isn't science....

As I read the OP, it's the underlying mathematics of the extrapolation problem that are unsolvable. I'm not a mathematician, but I believe they do say some problems are unsolvable. The OP mentions that a small spectral gap is a semiconductor property, so I presume that a spectral gap can be measured. Otherwise how would we know it's small? So the spectral gap of a superconductor should be measurable (by scientists), just not model-able (by mathematicians).

[rhett o rick]

52. I hear you. Just not smart enough to comment further. Thanks for the response. nm

[MGKrebs]

38. "science totally excludes the possibility of this extra dimensional reality."

I don't know why you would say that. Extra dimensions beyond the 3+1 we know are a very active and productive area of physics right now. String theory includes extra dimensions, for example.
There's a new good book called Spooky Action At A Distance by George Musser that explores even the next step- that there are NO dimensions!

[truedelphi]

43. I am quite aware of the string theory.

But the way that string theory has been fleshed out and expressed, and the way that the extra dimensional aspect of it are expressed excludes the whole notion of what I thought it would be. I remember being very excited when the theory first hit the headlines of science mags like "Discovery."

But it doesn't really discuss the universe being one giant loom. Which is how mystics and also people who do various kinds of psychedelics see it.

"You recreate your body in its entirety with each step you take when you walk across the room."

And I don't know that any physics person has expanded on the extra dimensional aspect and said, "This dimension is the dimension where we travel and visit when we dream, and it is from this dimension that predictions arise." If you know of any physics person that has indicated this, I would love to know their name and read their writings. Possibly this physicist, George Musser, would understand. I have to get that book!

[bvf]

48. You might like "The Fabric of Reality"

by David Deutsch.

The New Yorker ran a lengthy profile of him some years ago.

http://www.newyorker.com/magazine/2011/05/02/dream-machine

He's got a few books out there, but I've only read the one I mention. In it, he weaves quantum physics and computing with his theory of the multiverse, thoughts on evolution, epistemology, and probability in a very engaging, accessible way.

Think "everything that can happen does happen," for a taste of his approach.

[truedelphi]

50. Thank you for yr kind reply.

Will check out the book you refer to.

I have had a lot of strange things happen to me. I explain to friends that I do not "always drive my car."

Case in point: about four or five years ago, coming home from a day out with my spouse, we had to leave the Main Street in town for the highway. As we approached the highway, I heard a voice inside my head telling me; "Stop talking with your husband."
"Put both hands on the wheel NOW! Pay attention. In one quarter mile, a pickup truck will come veering off their side of the road into your lane. A roadside shoulder is there - it is perfectly safe - just go on the shoulder and you will be safe."

Now at the point when I was "told" all this, my car came to a stop at the stop light. I cold not see any traffic down where this incident would occur - a big steep hill blocked it from view.

When I pulled on the road, in just about one quarter of a mile, a pickup truck veered right into my lane, and since i knew what to do, I did it: I pulled onto the shoulder without incident.

My husband remarked "How in hell did you do that? It is like you knew ahead of time to maneuver the car like that!"

I tried to tell him, but he didn't get it. We were driving an old van at the time - if that pickup had slammed into us, I would have been paralyzed or lost my legs at the very least, and been outright killed, in the worst case scenario.

Usually this voice in my head gives me directions, and if I don't follow them (For example, I might be told to take the longer route rather than the shorter route home) then I lose time to some accident that has closed down the road. But in this case and several other ones, I have been given life saving information.

Why, I don't know. All I can tell you is that the voice is as real as that of any other voices of real humans then in the car with me - except I know I am the only one hearing it.

####

[bemildred]

7. Thank you, very important indeed.

And likewise one expects that physics is theoretically as well as practially incomplete.

[MisterP]

18. that was John Horgan's question--when can we know that "science is over"?

https://en.wikipedia.org/wiki/John_Horgan_%28journalist%29

[bemildred]

19. Such a gloomy fellow.

I think the message is that it is never over, there is always something new, something undiscovered, something one can only find by experiment. A universe with a closed form solution sounds singularly boring.

[MisterP]

21. infinite experiments are no more supported, however

OTOH we can always just start mixing physics with magic

again ...

[bemildred]

29. It's all magic, Physics is the part we have good models for how the magic works. nt

[MisterP]

37. eh, nobody reads Edward Tylor anymore, and for a good reason

XD

[bemildred]

42. Never heard of him.

I can see why.

I have read a good deal of that sort of twaddle, but not lately.

[MisterP]

44. what he said was that magic was "primitives'" attempts at explaining natural phenomena

and thus an early version of science

to be fair he was pretty evenhanded for a prissy Victorian anthropologist

[bemildred]

46. He has a point there.

But it's not the point I was making.

My point was that in scientific reality too we are reduced to hand waving and speculations for many questions we would like to know the answers to. We have pushed the limits of our knowledge back, greatly, but there are still things "we are not allowed to know". And that will probably always be the case.

And one of the great achievements of the 20th Century was to prove that that was so: relativity, uncertainty, incompleteness, non-computability, Turings halting problem.

To the extent he is criticizing scientism or supporting the natives right to be understood in their own terms, I agree, on the other hand the elaborate theorizing to rationalize it for western audiences I tend to dislike, it smacks of what is called Orientalism in other contexts.

I do think we are much better at inventing explanations than we are at sortiing out which ones "work", and much too fond of the ones we do think up, we get attached to them.

The thinkers of that era had a fondness for vast systems and theories, like Freud for example, or Spengler, which I slogged through at one point and have had a skeptical attitude towards since. Much of my distaste comes from that, I suppose.

[bananas]

8. Science forum thread

http://www.democraticunderground.com/122844106

[Spitfire of ATJ]

10. It will be solvable once mater itself can be designed.

[olddots]

11. my uncle Sidney used to say

"If you can think it you can think it ."

[houston16revival]

12. Someone should ask Donald Trump to solve it

He knows it all

[winstars]

14. Get out of my head!!! LOL Same exact thought, although we aren't exactly pushing the...

envelope for laughs here.....

[houston16revival]

16. LOL

That happens to me frequently ... have a thought, and see that others have
the same idea


Hope we're not becoming a liberal news bubble!

[winstars]

17. No way! And welcome to DU!!!!

[winstars]

13. Why don't they just ask Trump? He is very very very smart.

[Docreed2003]

27. A huuuge huuuge advancement in science....

[Blue_Tires]

31. You're a physicist?

[randome]

36. IOW, sometimes shit happens.

[hr][font color="blue"][center]I'm always right. When I'm wrong I admit it.
So then I'm right about being wrong.[/center][/font][hr]

[Yupster]

49. Whenever I read quantum physics, I

realize we don't know anything yet.