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#54946 12/11/15 07:15 PM
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http://www.nature.com/news/paradox-at-th...=ODIxNTQyNjU3S0
Quote:
Cubitt and his collaborators focused on calculating the ‘spectral gap’: the gap between the lowest energy level that electrons can occupy in a material, and the next one up. This determines some of a material’s basic properties. In some materials, for example, lowering the temperature causes the gap to close, which leads the material to become a superconductor.
The team started with a theoretical model of a material: an infinite 2D crystal lattice of atoms. The quantum states of the atoms in the lattice embody a Turing machine, containing the information for each step of a computation to find the material's spectral gap.
Cubitt and his colleagues showed that for an infinite lattice, it is impossible to know whether the computation ends, so that the question of whether the gap exists remains undecidable.
For a finite chunk of 2D lattice, however, the computation always ends in a finite time, leading to a definite answer. At first sight, therefore, the result would seem to have little relation to the real world. Real materials are always finite, and their properties can be measured experimentally or simulated by computer.
But the undecidability ‘at infinity’ means that even if the spectral gap is known for a certain finite-size lattice, it could change abruptly — from gapless to gapped or vice versa — when the size increases, even by just a single extra atom. And because it is “provably impossible” to predict when — or if — it will do so, Cubitt says, it will be difficult to draw general conclusions from experiments or simulations.


Would this not be a problem only if change could occur twice (once in each direction) between two measurements. If this were possible, how would solving the problem for an infinite lattice help? Couldn’t it change an infinite number of times between minimal and infinite lattice sizes?


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Sigh .. you have to love our science media who like to beat up myths and legends rather than study things.

Let me first start with an aside that it is worth looking at Alan Turing and whether he was playing a private joke on dumb people when he published his halting theorem (https://en.wikipedia.org/wiki/Halting_problem). I think he may well have been poking fun at the other papers in the area. The irony would be that it is the paper most associate him with, yet I think he was well aware of the liar paradox his paper enshrines.

Okay so lets cut to the chase and you sort of got to the problem that no theory can describe something that doesn't or can't be described smile

That is the basis of the liar paradox where a "liar declares he is lying". The whole paradox roles around a falsehood because if we impose that the liar must always lie then the liar can't make that statement. Analysis post that point is stupid and yet people over the years have attempted it and come to an understanding that it says "something profound".

Read carefully the authors description of what he has found smile

What I have found is how profoundly stupid intelligent people can sometimes be.

Again it's sort of like the girl appearing on the barstool joke which rolls on the fact that everything in the universe is in a state of flux. However no-one really believes it is possible because now you are demanding trillions of specific atoms pop into a precise location at the same moment, something that is forbidden. The joke works because layman think they are saying something about how crazy scientists are and the scientists take the deeper meaning of just how little layman really understand anything and the jokes on them.

This paper is a version of that, and goes into a pile of analysis on a question that can't happen. It was a second rate paper and why it got this much attention was beyond me but I guess in the mathematics world there isn't much news around at the moment.

Last edited by Orac; 12/13/15 05:03 AM.

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Originally Posted By: Orac
Let me first start with an aside that it is worth looking at Alan Turing and whether he was playing a private joke on dumb people when he published his halting theorem.


I think you may be right about Turing having a joke; but then, I think Hilbert was doing that with his "Hotel".


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Originally Posted By: Orac
you are demanding trillions of specific atoms pop into a precise location at the same moment, something that is forbidden


Not arguing with that, but what forbids it?


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Remember particles when they "pop into existence" are virtual pairs (energy conservation).

https://en.wikipedia.org/wiki/Pair_production => However, all other conserved quantum numbers (angular momentum, electric charge, lepton number) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other.

In your speak something from zero I avoided using nothing smile

So problem (A) our girl went from "virtual to real" and (B) where are her virtual pair particles?

At the very least I demand two girls one matter one antimatter to come into existence and don't hang around the antimatter girl smile

Last edited by Orac; 12/15/15 04:07 AM.

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Quote:
you are demanding trillions of specific atoms pop into a precise location at the same moment, something that is forbidden


Is popping into a precise location the same as popping into existence? Isn’t the argument that if we wait long enough, any configuration of atoms, including low entropy versions, can occur?


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Originally Posted By: Bill S.
Is popping into a precise location the same as popping into existence? Isn’t the argument that if we wait long enough, any configuration of atoms, including low entropy versions, can occur?

That statement is sort of a mixture of two different concepts of virtual pair production and entropy.

These particle events are virtual and the pairs are fleeting unless some weird exotic physics is at play like say near a black hole event horizon (Hawkings argument).

So I guess you could argue wait long enough the girl could appear for a fleeting fraction of a second but the joke makes the girl more permanent than that you are going to buy her a drink. So under no circumstance could that ever happen.

Technical background is matter creation (https://en.wikipedia.org/wiki/Matter_creation) and the only way we know to make it on a permanent basis is using "real" photon pairs. So real photons become real matter hence my objection from making a virtual girl into a real girl above.

If a normal section of spacetime could make matter by just the virtual process the whole of spacetime would be pretty much all matter. I am sure you are familiar with the experiments where we create exotic conditions that the virtual particles can become real and we can measure them directly. However we are providing relatively huge amount of energy and creating exotic conditions to make the few virtual particles persist which we then measure.

Perhaps there is somewhere in the universe these sorts of exotic conditions and energy do exist, all we can say with certainty is not in the normal areas of space we can see, the virtual process is exactly that virtual.

The entropy stuff doesn't real come into play because the particles aren't real and are not subject to it's laws. In some ways the very existence of the virtual pairs defies the laws of entropy because you are getting something from zero.

Last edited by Orac; 12/16/15 12:01 AM.

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Orac, I think we are still talking about different things.

You are talking about virtual particles; I was thinking more along the lines of the real particles of which the Universe is made, re-arranging themselves over time.

Think the divided box of gas which starts with all the molecules in one side (lowest entropy), but gradually the molecules make their way through a small hole so that they are evenly distributed between the two sides.

Once equilibrium is reached, any further movement through the hole will lead to lower entropy. There are those who maintain that, given enough time, a closed system could/would return to lowest entropy; even if only for a brief moment.


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Originally Posted By: Bill S.
Orac, I think we are still talking about different things.

I said that => That statement is sort of a mixture of two different concepts of virtual pair production and entropy.

In your post directly above we are talking about real particles and you have a box an entropy etc. Got that.

Here is your first statement
Originally Posted By: Bill S
Is popping into a precise location the same as popping into existence? Isn’t the argument that if we wait long enough, any configuration of atoms, including low entropy versions, can occur?

So my question is why in this quote is the popping into existence even in this same discussion.

You just mixed apples with oranges. On one hand we are talking about virtual particles which are NOT subject to the laws on entropy mixed with real particles in a box which are ... I don't get why you mixed the two in the same quote ???????????

I am trying to work out is the problem that you don't understand that virtual particles don't have to obey the laws of entropy ... hell they can move backward in time if they want as you or I could never prove it either way smile

[Edit expanding that]

You need to remember our physics only describes things we can measure we can't be imposing those rules on something we can't measure like virtual particles. I am not sure anyone has a theory of what laws virtual particles obey mainly because we only ever see them in very controlled specific ways when they enter our universe.

Originally Posted By: https://en.wikipedia.org/wiki/Virtual_particle
Virtual particle terms represent "particles" that are said to be "off mass shell". For example, they can progress backwards in time, or travel faster than light.

.....

A virtual particle does not necessarily appear to carry the same mass as the corresponding real particle. This is because it appears as "short-lived" and "transient", so that the uncertainty principle allows it to appear not to conserve energy and momentum.

Virtual particles seem to break any and all rules so I am stuck how I relate entropy laws to them and hence I am totally confused by your post.

Last comment is "Virtual Particles" may not even be one grouping, it be different forms of waveform with that name just a place holder for things that are not what we call real particles.

Last edited by Orac; 12/17/15 03:49 AM.

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Originally Posted By: Orac
So my question is why in this quote is the popping into existence even in this same discussion.


I think it was the use of "popping into" that caused the problem.

You said:

Quote:
you are demanding trillions of specific atoms pop into a precise location at the same moment, something that is forbidden


I was thinking more of things that already exist arranging themselves in lower entropy configurations, if we wait long enough.


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Originally Posted By: Bill S.
I was thinking more of things that already exist arranging themselves in lower entropy configurations, if we wait long enough.

Gotcha that just isn't in context with the joke however.


I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.

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