wp-plugin-hostgator domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home4/scienrds/scienceandnerds/wp-includes/functions.php on line 6114ol-scrapes domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home4/scienrds/scienceandnerds/wp-includes/functions.php on line 6114Source:https:\/\/www.quantamagazine.org\/alien-calculus-could-save-particle-physics-from-infinities-20230406\/#comments<\/a><\/br> But that luck ended when physicists tried to tackle the strong force. The strong force is around 100 times stronger than the electromagnetic force, with an alpha analogue of about 1, and it refuses to be ignored. Squaring or cubing 1 doesn\u2019t create any shrinking effect whatsoever, so the perturbative series heads straight toward infinity from the earliest terms. Physicists have spent decades developing an alternative way to handle the strong force using supercomputers, achieving spectacular results along the way. But the numerical calculations don\u2019t give much insight into how the strong force does what it does.<\/p>\n \u00dcnsal and Dunne recognized that resurgence, with its power to tame divergent series, could take them a step toward the dream of understanding the strong force with pencil and paper. In particular, they set out to solve a mystery that had plagued the theory of the strong force for 40 years.<\/p>\n In 1979, the physicists Gerard \u2019t Hooft<\/a> and Giorgio Parisi<\/a> inferred the existence of tiny, bizarre terms in strong force calculations. They called them renormalons, and no one knew what to make of them. Renormalons didn\u2019t seem to correspond to any specific ripple or other concrete field behavior. But there they were, messing up the calculations nonetheless.<\/p>\n \u00dcnsal and Dunne tackled renormalons with resurgence. Even though they were working in a 2D analogue of the strong force, it took them roughly a year. But in 2012, they showed<\/a> that \u2014 at least in their simplified model \u2014 \u2019t Hooft and Parisi\u2019s renormalons matched behaviors that physicists understood.<\/p>\n They \u201csolved the mystery and could find what it was that the renormalons corresponded to,\u201d said Jordan Cotler<\/a>, a physicist at Harvard University, although he adds that other mysteries still remain. He\u2019s currently mounting a similar attempt to understand some of those mysteries in a more realistic theory of the strong force.<\/p>\n Last year, however, researchers used resurgence to add a further wrinkle. Mari\u00f1o and his collaborators carried out a more rigorous calculation (although also in a simplified theory) and discovered new renormalons<\/a> beyond what the group calls \u201cthe standard lore\u201d of \u2019t Hooft and Parisi. Mari\u00f1o now suspects that renormalons are just the tip of a nonperturbative iceberg. Resurgence and other nonperturbative<\/a> methods<\/a> may reveal that physicists have been spoiled by their historical success in matching individual mathematical terms to specific events. If he\u2019s right, the quantum world may someday become even harder to visualize than it already is.<\/p>\n \u201cI have doubts that this picture \u2014 one exponential [to] one object \u2014 is going to go through in general field theories,\u201d he said. \u201cIt might happen that the world of exponential corrections is really wild.\u201d<\/p>\n Mari\u00f1o has also been a key player in the discovery of a new nonperturbative effect in string theory, the speculative and unproved notion that the universe is not made of pointlike particles but is composed of extended objects such as strings. The wiggling of such strings would determine the properties of the particles we observe.<\/p>\n String theory, like quantum theory, is usually treated as a perturbative series of Feynman-like diagrams representing strings merging and splitting in increasingly complicated ways. But unlike quantum theorists, string theorists lack even the faintest of guides to the theory\u2019s nonperturbative effects. They assume that, just as quantum theory contains tunneling and renormalons, the full nonperturbative formulation of string theory also contains dragons.<\/p>\n One striking example of non-perturbative phenomena in string theory \u2014 sheetlike objects known as D-branes \u2014 was discovered in the 1990s. D-branes would later spur some of string theory\u2019s biggest developments.<\/p>\n Mari\u00f1o wondered what else might be out there.<\/p>\n He was part of a group that in 2010 noticed a series of negative counterparts hiding in the shadow of the D-brane terms. It wasn\u2019t clear what physical phenomenon these partner terms might describe.<\/p>\n A clue came six years later, when Cumrun Vafa<\/a> of Harvard and his collaborators explored a generalized string theory where certain quantities could go negative. They found D-branes with negative tension \u2014 the brane version of having negative mass. These exotic beasts<\/a> warped the structure of reality around them, creating multiple dimensions of time and violating the fundamental principle that probabilities must always add up to 100%. But the group found no indication that these objects should escape from their bizarro world and show up in standard string theory.<\/p>\n Now Ricardo Schiappa<\/a>, a friend of Mari\u00f1o\u2019s and a theoretical physicist at the University of Lisbon, believes he\u2019s found evidence otherwise. In recent months, Schiappa and his collaborators \u00a0used resurgence to scrutinize a handful of simple string theory models. They found that Vafa\u2019s negative-tension D-branes exactly matched the exponentially small terms that Mari\u00f1o had found in 2010. Negative D-branes are unavoidable partners of D-branes, the group argued in a January preprint<\/a>. \u201cWhat we have discovered now is that they are fundamental for perturbation theory,\u201d Schiappa said.<\/p>\n Other theorists aren\u2019t yet sure what to make of the fresh finding. Vafa notes that Schiappa\u2019s crew did their calculations in stripped-down string models, and that the result isn\u2019t guaranteed to hold in more sophisticated formulations. But if it does, and if string theory actually describes our universe, it must contain some other way of stopping negative D-branes from forming.<\/p>\n \u201cThey shouldn\u2019t be there as a regular object in that theory,\u201d Vafa said. Otherwise, \u201cthis opens a whole Pandora\u2019s box of puzzles.\u201d<\/p>\n Despite their progress in spotting renormalons and negative branes, physicists cite two formidable obstacles to crowning resurgence the official successor to perturbation theory.<\/p>\n First, not all theories have been proved to have resurgent structure. The question is particularly acute for quantum field theories, which physicists have been checking on a case-by-case basis. It\u2019s a painstaking process, a bit like studying mammals one species at a time. After observing humans, dolphins and cats, you might start to feel confident that live birth is a universal mammalian feature. But there\u2019s always the chance that around the next corner you\u2019ll find a platypus laying an egg.<\/p>\n That\u2019s why Serone has devoted the last three years to stress-testing resurgence in certain quantum field theories. In 2021, he and his collaborators studied a theory<\/a> that shares key features with the strong force but is still simple enough to allow them to calculate the many a<\/em>\u2019s needed to perform resurgence. They calculated the energy of empty space in such a universe using resurgence and two other methods, showing that all three agreed. There have been qualitative arguments that resurgence should hold in quantum field theory, but this was one of the first concrete calculations, kindling further optimism.<\/p>\n \u201cIn most of the cases it has been tested so far, either resurgence works, or we have good reasons to believe we understand when it doesn\u2019t,\u201d Serone said.<\/p>\n The graver problem is that to spot nonperturbative pieces, you need to know a frightening number of perturbative terms. In his recent research, for instance, Serone picked quantum field theories with mathematical backdoors that let him generate thousands of terms. But for the strong force, calculating just eight or nine is currently out of the question. Even pioneers of the method don\u2019t mince their words about when they expect to see it produce a real number like the mass of the proton (a mathematical feat<\/a> worth a million-dollar prize<\/a>).<\/p>\n \u201cIt\u2019s extremely difficult,\u201d \u00dcnsal said, sighing. \u201cI don\u2019t see an immediate way.\u201d<\/p>\n \u201cWhat \u00c9calle was saying is that the answer is rigorously there in principle. But to actually get the answer is really, really hard,\u201d Bender said. \u201cMy advice would be, don\u2019t stand on one foot while you\u2019re waiting.\u201d<\/p>\n But the daunting difficulty hasn\u2019t killed the dream of trying to get real predictions out of resurgence. For one thing, the technique has already produced otherwise unobtainable results in quantum mechanics. Back in the 1980s, the French mathematical physicists at Saclay used proto-resurgent methods to make an exact prediction for particle tunneling \u2014 a problem that physicists had previously only been able to approximate. Dunne and \u00dcnsal have done similar pen-and-paper calculations using the more refined tools of \u00c9calle. Another group has checked these results using standard methods. They were only able to get as far as six decimal places<\/a> \u2014 a Herculean effort that took months of time and substantial computer power.<\/p>\n Such dramatic examples have motivated Dunne to develop hyper-efficient ways of practicing resurgence, in the hopes of someday porting them to quantum field theories. Over the last five years, together with Ovidiu Costin<\/a>, a mathematician at Ohio State University, he has found techniques that get more bang for the perturbative buck. In some cases (which are still far from the real-world theories), they\u2019ve found that just 10 to 15 terms suffice. \u201cThat number could have come out to be 1,000, and I would have given up and gone somewhere else,\u201d he said. \u201cIt\u2019s kind of tantalizing.\u201d<\/p>\n Dunne and Costin\u2019s work has even managed to catch the eye of \u00c9calle himself. The founder of resurgence hasn\u2019t closely followed the waves his work set off, calling himself \u201can accomplished ignoramus in theoretical physics.\u201d Nevertheless, while worrying that any work on speculative models such as string theory may be \u201cbuilt on quicksand,\u201d he praises the researchers\u2019 efforts to give resurgence a mathematical tune-up.<\/p>\n \u201cEven if the physical ground gives way, the impressive math results of, say, O. Costin and G. Dunne are there to stay,\u201d he said.<\/p>\n For \u00c9calle, resurgence is something of a past chapter. Nearly 40 years have passed since his original trilogy. He continued to develop alien calculus until around 2000, and he has spent the last 20 years exploring a more algebraic offshoot. Should he ever decide to publish a sequel trilogy gathering all his findings in one place, who knows what treasures physicists will find within.<\/p>\n \u201cI think he has discovered many tools that are still to be explored,\u201d Mari\u00f1o said.<\/p>\n
\nHow to Tame the Endless Infinities Hiding in the Heart of Particle Physics<\/br>
\n2023-04-10 21:58:07<\/br><\/p>\nBlack Swans and Other Anomalies<\/strong><\/h2>\n
A New Hope<\/strong><\/h2>\n