A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to an online report on phys.org December 9, 2015. 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 behavior.

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 make a phase 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 (12/9/15) 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.

Godel and Turing are famous for proving that some mathematical questions are `undecidable’ ­ they are neither true nor false, because they are beyond the reach of mathematics. The new research shows that the spectral gap problem in quantum physics is one of these undecidable problems. This means a mathematical method to determine whether matter described by quantum mechanics has a spectral gap or not cannot exist; thus limiting the extent to which we can exactly predict the behavior of quantum materials, and potentially even of fundamental particle physics.

Particle physics experiments at CERN, and numerical calculations on supercomputers suggest that there is a spectral gap. “We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s,” added co-­author Professor Michael Wolf from Technical University of Munich. “So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic”.

   “No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.”

Co­-author, Professor David Pérez­García from Universidad Complutense de Madrid and ICMAT, said: “It’s not all bad news, though. Our results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties.” This statement is the physics equivalent of the ‘butterfly effect’ in chaos theory; and religious beliefs in the rationally unprovable existence of human and Divine free will.

At the most fundamental level: Atheism, Theism, Determinism and Free Will are all scientifically unprovable beliefs. You pay your life; and make your choice how to live it.

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Rabbi Allen S. Maller is the Rabbi Emeritus of Temple Akiba in Culver City, California. His website is: www.rabbimaller.com.  Earlier versions of this article may have appeared elsewhere.

The views expressed by Rabbi Maller are his own and not necessarily those of the Blogmaster. They are published in order to promote this blog’s mission to provide information and foster discussion about matters of faith and science. The Blogmaster thanks Rabbi Maller for his contribution to this forum.

1. JoeBillScott says:

   March 29, 2016 at 1:12 pm

   A bit vague, but cocktail party physics usually is.

   The conclusion is rushed and a bit rough with non-sequiturs replacing reasoned arguments that could have connected the concepts mentioned – e.g., free will and determinism, the only reason I bothered reading the article in the first place.

   Disappointing.

   Reply
2. dave richardson says:

   July 3, 2016 at 3:43 pm

   I have connected the names of the generations of Genesis and their order of birth to the hypothetical events of prehistory.  My elementary math skills put the chance of the correlating permutation at 40,000 to 1.  Perhaps a better mathematician would like to review my proof.  Please email.  Dave

   Reply
3. Wilder Chairs says:

   March 6, 2017 at 4:38 pm

   Of course atheism is "unprovable." No one is expected to prove a negative. The burden of proof is on the person making the positive claim. Bigfoot, UFOs, the Loch Ness Monster, the chupacabra, and gremlins don't need someone to disprove them. That's a ridiculous thing to ask and reflects a severe misunderstanding of how basic logic operates.

   Reply