Jun 13, 2023 03:22 PM
Has a mathematician solved the ‘invariant subspace problem’? And what does that even mean?
https://theconversation.com/has-a-mathem...ean-206859
INTRO: Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title “On the invariant subspace problem in Hilbert spaces”. The paper is just 13 pages long and its list of references contains only a single entry.
The paper purports to contain the final piece of a jigsaw puzzle that mathematicians have been picking away at for more than half a century: the invariant subspace problem. Famous open problems often attract ambitious attempts at solutions by interesting characters out to make their name. But such efforts are usually quickly shot down by experts.
However, the author of this short note, Swedish mathematician Per Enflo, is no ambitious up-and-comer. He is almost 80, has made a name for himself solving open problems, and has quite a history with the problem at hand... (MORE - details )
A New Experiment Casts Doubt on the Leading Theory of the Nucleus
https://www.quantamagazine.org/a-new-exp...-20230612/
INTRO: A new measurement of the strong nuclear force, which binds protons and neutrons together, confirms previous hints of an uncomfortable truth: We still don’t have a solid theoretical grasp of even the simplest nuclear systems.
To test the strong nuclear force, physicists turned to the helium-4 nucleus, which has two protons and two neutrons. When helium nuclei are excited, they grow like an inflating balloon until one of the protons pops off. Surprisingly, in a recent experiment, helium nuclei didn’t swell according to plan: They ballooned more than expected before they burst. A measurement describing that expansion, called the form factor, is twice as large as theoretical predictions.
“The theory should work,” said Sonia Bacca, a theoretical physicist at the Johannes Gutenberg University of Mainz and an author of the paper describing the discrepancy, which was published in Physical Review Letters. “We’re puzzled.”
The swelling helium nucleus, researchers say, is a sort of mini-laboratory for testing nuclear theory because it’s like a microscope — it can magnify deficiencies in theoretical calculations. Physicists think certain peculiarities in that swelling make it supremely sensitive to even the faintest components of the nuclear force — factors so small that they’re usually ignored. How much the nucleus swells also corresponds to the squishiness of nuclear matter, a property that offers insights into the mysterious hearts of neutron stars. But before explaining the crush of matter in neutron stars, physicists must first figure out why their predictions are so far off.
Bira van Kolck, a nuclear theorist at the French National Center for Scientific Research, said Bacca and her colleagues have exposed a significant problem in nuclear physics. They’ve found, he said, an instance where our best understanding of nuclear interactions — a framework known as chiral effective field theory — has fallen short.
“This transition amplifies the problems [with the theory] that in other situations are not so relevant,” van Kolck said... (MORE - details)
https://theconversation.com/has-a-mathem...ean-206859
INTRO: Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title “On the invariant subspace problem in Hilbert spaces”. The paper is just 13 pages long and its list of references contains only a single entry.
The paper purports to contain the final piece of a jigsaw puzzle that mathematicians have been picking away at for more than half a century: the invariant subspace problem. Famous open problems often attract ambitious attempts at solutions by interesting characters out to make their name. But such efforts are usually quickly shot down by experts.
However, the author of this short note, Swedish mathematician Per Enflo, is no ambitious up-and-comer. He is almost 80, has made a name for himself solving open problems, and has quite a history with the problem at hand... (MORE - details )
A New Experiment Casts Doubt on the Leading Theory of the Nucleus
https://www.quantamagazine.org/a-new-exp...-20230612/
INTRO: A new measurement of the strong nuclear force, which binds protons and neutrons together, confirms previous hints of an uncomfortable truth: We still don’t have a solid theoretical grasp of even the simplest nuclear systems.
To test the strong nuclear force, physicists turned to the helium-4 nucleus, which has two protons and two neutrons. When helium nuclei are excited, they grow like an inflating balloon until one of the protons pops off. Surprisingly, in a recent experiment, helium nuclei didn’t swell according to plan: They ballooned more than expected before they burst. A measurement describing that expansion, called the form factor, is twice as large as theoretical predictions.
“The theory should work,” said Sonia Bacca, a theoretical physicist at the Johannes Gutenberg University of Mainz and an author of the paper describing the discrepancy, which was published in Physical Review Letters. “We’re puzzled.”
The swelling helium nucleus, researchers say, is a sort of mini-laboratory for testing nuclear theory because it’s like a microscope — it can magnify deficiencies in theoretical calculations. Physicists think certain peculiarities in that swelling make it supremely sensitive to even the faintest components of the nuclear force — factors so small that they’re usually ignored. How much the nucleus swells also corresponds to the squishiness of nuclear matter, a property that offers insights into the mysterious hearts of neutron stars. But before explaining the crush of matter in neutron stars, physicists must first figure out why their predictions are so far off.
Bira van Kolck, a nuclear theorist at the French National Center for Scientific Research, said Bacca and her colleagues have exposed a significant problem in nuclear physics. They’ve found, he said, an instance where our best understanding of nuclear interactions — a framework known as chiral effective field theory — has fallen short.
“This transition amplifies the problems [with the theory] that in other situations are not so relevant,” van Kolck said... (MORE - details)