The complex problem of physics that has no solution / Weather / Stop thinking. The problem of spectral gap-a central issue in quantum physics and of particulate matter has no solution, at least not in general, according to an international team of researchers whose findings were published Wednesday in the journal Nature.
Scientists at the Complutense University of Madrid (UCM) -Institute of Mathematics (ICMAT), the University College of London (UCL), and the Technical University of Munich (Germany) showed that, even if you have a complete description of the microscopic properties of a material, the macroscopic behavior is not always predictable.
The spectral gap represents the energy required to transfer an electron from a low energy state to an excited state. For example, a small spectral gap is the central property of semiconductors. Similarly, this amount plays a role in many other materials. When the spectral gap is small, it is, it is closed, the material may change to a completely different state (the case, for example, when a material becomes a conductor super).
“The possibility extrapolating the microscopic description of the material properties of the solid is one of the most important tools in the search for superconductors at room temperature or other properties of interest, “says David Perez Garcia, a researcher at the UCM and coauthor of the study.
The study shows a fundamental limitation in this approach. Using sophisticated mathematics, the authors show that, even providing a complete microscopic description of a quantum materials, whether or not spectral gap is unspeakable problem.
“Alan Turing is known for its role in Enigma decoding machine recalls the researcher at University College of London (UCL) and co-author Toby Cubitt- but in mathematics and computer science community is much more famous his work in logic, mathematics showed that some questions are unspeakable. They are neither true nor false. They are simply beyond the scope of mathematics “.
” We have shown that the spectral gap is one of those problems, which means that there can be a general method for determine whether a system described by quantum mechanics, has or does not have spectral gap. This limits the scope that can have our predictions of quantum materials, and even elementary particle physics, “says Cubitt.
The most famous on the spectral gap problem is whether the theory that governs the elementary particles of matter (the so-called standard model of particle physics) has a spectral gap.
The physics experiments particles such as those developed at CERN (European Laboratory for Particle Physics), supercomputers and simulations indicate that there exists in this case, a spectral gap.
However, still no mathematical proof of the matter, known as the hop guess Yang-Mills mass, and that although the Clay Mathematics Institute is offering a reward of one million dollars to whoever finds it.
“There are particular cases of the problem we do have solutions, while the overall formulation is unspeakable, so it is still possible for someone to win a million dollars. But our result opens the possibility that some of the major problems of theoretical physics have no solution, “he added Cubitt.
” From the work of Turing and Gödel in the decade of the 30 are known, in principle, could be untold trouble, “says Michael Wolf, a researcher at the Technical University of Munich.
” But so far this only affected the theory of computation and the more abstract mathematical logic. No one had seriously considered these ideas may affect the heart of theoretical physics, “continues co-author of the study.
” From a philosophical perspective, the result also questions the reductionist view of reality, because the difficulty insurmountable problem lies in moving from the microscopic description of macroscopic properties. “
EFE
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