Not work out the physics of problem: is the result of
core mathematical paradox
Theoretical physicist, according to a new study of godel's incompleteness theorem that is associated with the problem of calculation of quantum mechanics cannot.
Kurt Godel (left) has been proved that there are always some math is undecidable propositions;Alan Turing (right) will be godel's proof that extends to computer science cannot be solved in the algorithm.Image: L: Pictorial Press Ltd/Alamy, R: Photoshot
A mathematics and computer science core logic paradox may also have an effect in the real world, it let us unable to answer some basic questions about the material.
In 1931, was born in Austria mathematician Kurt Godel announced that he proved that there are some mathematical proposition is the undecidable, which we never be able to prove or disprove them, this discovery shocked the academic circle.Today, the three researchers also found that it is the same principle for physicists to calculate an important properties of the material, the ideal model of the atom, the electron lowest energy gap.
One of the authors of the study, the quantum information theory physicist at university college London Toby Cubitt, said the research results show that in particle physics, and a $1 million reward for related issues may be essentially can't solve.
The study was published in the December 9 Nature, the researchers also took a longer paper versions released (140 pages) in the paper on arXiv preprint website.From Barcelona, Spain institute of science in quantum information theory physicist Christian Christian Gogolin said: "a shocking discovery, for all the people who study of condensed matter theory will be a big surprise."
From logic to physics
Godel's findings associated with the physical world for the first time was in 1936, by the British mathematician Alan?Turing complete."In terms of physics and logic relationship, Turing to think more clearly than godel."Godel's biographer, American writer Rebecca Goldstein says.
Turing envisaged an idealized computer, each time can read/write 1 bit of data, and use it in the form of algorithm, the results of godel said to come out.He proved that we can never know whether the computer can in the limited time to complete the calculation, there is no a general test to know whether any given algorithm undecidable.The same restrictions also apply to real computers, because they are in math and Turing machines are equivalent.
Starting in the 1990 s, theoretical physicists have been trying to Turing's work concrete expression for ideal models of physical phenomena, "but they got the undecidable problems haven't been able to contact the physicist concerned with specific problems."Theoretical physicist at the university of western Canada Markus Muller, said he had to goring and another partner in 2012 jointly issued a similar model.
Cupid said: "you can say that, our study is the first time undecidability embodied in a real people will go to try to solve the major physical problems."
Cupid and collaborators is focused on the spectral gap - the material of electrons
occupying the lowest energy level and low level gap between calculation.A physical quantity decided to some basic properties of the material, for example in some materials, reduce the temperature will narrow the gap and make the material into a superconductor.
The team with a kind of ideal material model -- an infinite two-dimensional atomic lattice as the research object.Lattice atom in the quantum state can be regarded as a way of Turing machine, includes the spectrum to find the material gap every step of calculating the required information.
Cupid and his colleagues show that for the infinite lattice, you never know when calculating process, therefore, about the spectral gap exists the problem is not the answer.
But for the limited size of the two-dimensional lattice, calculation steps can end in a limited time, always have a definite answer, therefore, infinite lattice situation seems to be far from the real world: after all, the real material is always limited, they can completely through the experiment measuring the properties of or computer simulations.
But infinite is undecidability, means that even if we knew the spectrum of a certain limited size lattice gap, in material size increases at the same time as it may appear dramatic changes, such as from incompetent gap to have energy gap and so on, even if only adds an atom.In addition, because studies have shown that we are unable to predict whether such circumstance appears, when to appear, we won't be able to a general conclusion from the experiment or the simulation results.
For millions of problems
Cupid said, their ultimate goal is to study a related problem in the field of particle physics, known as Yang - Mills mass - gap problem, the problem is the Clay Mathematics Institute as a the Millennium Prize Problems, one of and a $1 million reward for seeking solutions.
The so-called quality gap problem, with weak interaction and strongly interacting particles associated with the fact that the quality, and which is the weak and the strong interaction effective only within a certain range, and not like gravity and electromagnetism in any distance can be the cause of the work, is also a quark only as a part of the composite particles (such as protons and neutrons), cannot exist alone.Now, however, there is no strict mathematical theory to explain why the carrier of the strong, the weak interaction quality, and the carrier of electromagnetic force, the photons without quality.
Cupid hope their team's thoughts and methods could eventually prove Yang - mills quality gap problem is undecidable, but so far they have not a clear train of thought."We are far from the $1 million prize also."He said