Apr 24, 2024 02:48 AM
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AI starts to sift through string theory’s near-endless possibilities
https://www.quantamagazine.org/ai-starts...-20240423/
INTRO: String theory captured the hearts and minds of many physicists decades ago because of a beautiful simplicity. Zoom in far enough on a patch of space, the theory says, and you won’t see a menagerie of particles or jittery quantum fields. There will only be identical strands of energy, vibrating and merging and separating. By the late 1980s, physicists found that these “strings” can cavort in just a handful of ways, raising the tantalizing possibility that physicists could trace the path from dancing strings to the elementary particles of our world. The deepest rumblings of the strings would produce gravitons, hypothetical particles believed to form the gravitational fabric of space-time. Other vibrations would give rise to electrons, quarks and neutrinos. String theory was dubbed a “theory of everything.”
“People thought it was just a matter of time until you could compute everything there was to know,” said Anthony Ashmore, a string theorist at Sorbonne University in Paris.
But as physicists studied string theory, they uncovered a hideous complexity.
When they zoomed out from the austere world of strings, every step toward our rich world of particles and forces introduced an exploding number of possibilities. For mathematical consistency, strings need to wriggle through 10-dimensional space-time. But our world has four dimensions (three of space and one of time), leading string theorists to conclude that the missing six dimensions are tiny — coiled into microscopic shapes resembling loofahs. These imperceptible 6D shapes come in trillions upon trillions of varieties. On those loofahs, strings merge into the familiar ripples of quantum fields, and the formation of these fields could also come about in multitudinous ways. Our universe, then, would consist of the aspects of the fields that spill out from the loofahs into our giant four-dimensional world.
String theorists sought to determine whether the loofahs and fields of string theory can underlie the portfolio of elementary particles found in the real universe. But not only are there an overwhelming number of possibilities to consider — 10500 especially plausible microscopic configurations, according to one tally — no one could figure out how to zoom out from a specific configuration of dimensions and strings to see what macroworld of particles would emerge.
“Does string theory make unique predictions? Is it really physics? The jury is just still out,” said Lara Anderson, a physicist at Virginia Tech who has spent much of her career trying to link strings with particles.
Lara Anderson, a physicist at Virgina Tech, helped develop machine learning algorithms to approximate the shapes of Calabi-Yau manifolds.
Now, a fresh generation of researchers has brought a new tool to bear on the old problem: neural networks, the computer programs powering advances in artificial intelligence. In recent months, two teams of physicists and computer scientists have used neural networks to calculate precisely for the first time what sort of macroscopic world would emerge from a specific microscopic world of strings. This long-sought milestone reinvigorates a quest that largely stalled decades ago: the effort to determine whether string theory can actually describe our world.
“We aren’t at the point of saying these are the rules for our universe,” Anderson said. “But it’s a big step in the right direction.” (MORE - details)
Mathematicians marvel at ‘crazy’ cuts through four dimensions
https://www.quantamagazine.org/mathemati...-20240422/
INTRO: The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists understand such two-dimensional manifolds very well. And they have developed tools that let them make sense of three-dimensional manifolds and those with five or more dimensions.
But in four dimensions, “everything goes a bit crazy,” said Sam Hughes, a postdoctoral researcher at the University of Oxford. Tools stop working; exotic behavior emerges. As Tom Mrowka of the Massachusetts Institute of Technology explained, “There’s just enough room to have interesting phenomena, but not so much room that they fall apart.”
In the early 1990s, Mrowka and Peter Kronheimer of Harvard University were studying how two-dimensional surfaces can be embedded within four-dimensional manifolds. They developed new techniques to characterize these surfaces, allowing them to gain crucial insights into the otherwise inaccessible structure of four-dimensional manifolds. Their findings suggested that the members of a broad class of surfaces all slice through their parent manifold in a relatively simple way, leaving a fundamental property unchanged. But nobody could prove this was always true.
In February, together with Daniel Ruberman of Brandeis University, Hughes constructed a sequence of counterexamples — “crazy” two-dimensional surfaces that dissect their parent manifolds in ways that mathematicians had believed to be impossible. The counterexamples show that four-dimensional manifolds are even more remarkably diverse than mathematicians in earlier decades had realized. “It’s really a beautiful paper,” Mrowka said. “I just keep looking at it. There’s lots of delicious little things there.” (MORE - details)
https://www.quantamagazine.org/ai-starts...-20240423/
INTRO: String theory captured the hearts and minds of many physicists decades ago because of a beautiful simplicity. Zoom in far enough on a patch of space, the theory says, and you won’t see a menagerie of particles or jittery quantum fields. There will only be identical strands of energy, vibrating and merging and separating. By the late 1980s, physicists found that these “strings” can cavort in just a handful of ways, raising the tantalizing possibility that physicists could trace the path from dancing strings to the elementary particles of our world. The deepest rumblings of the strings would produce gravitons, hypothetical particles believed to form the gravitational fabric of space-time. Other vibrations would give rise to electrons, quarks and neutrinos. String theory was dubbed a “theory of everything.”
“People thought it was just a matter of time until you could compute everything there was to know,” said Anthony Ashmore, a string theorist at Sorbonne University in Paris.
But as physicists studied string theory, they uncovered a hideous complexity.
When they zoomed out from the austere world of strings, every step toward our rich world of particles and forces introduced an exploding number of possibilities. For mathematical consistency, strings need to wriggle through 10-dimensional space-time. But our world has four dimensions (three of space and one of time), leading string theorists to conclude that the missing six dimensions are tiny — coiled into microscopic shapes resembling loofahs. These imperceptible 6D shapes come in trillions upon trillions of varieties. On those loofahs, strings merge into the familiar ripples of quantum fields, and the formation of these fields could also come about in multitudinous ways. Our universe, then, would consist of the aspects of the fields that spill out from the loofahs into our giant four-dimensional world.
String theorists sought to determine whether the loofahs and fields of string theory can underlie the portfolio of elementary particles found in the real universe. But not only are there an overwhelming number of possibilities to consider — 10500 especially plausible microscopic configurations, according to one tally — no one could figure out how to zoom out from a specific configuration of dimensions and strings to see what macroworld of particles would emerge.
“Does string theory make unique predictions? Is it really physics? The jury is just still out,” said Lara Anderson, a physicist at Virginia Tech who has spent much of her career trying to link strings with particles.
Lara Anderson, a physicist at Virgina Tech, helped develop machine learning algorithms to approximate the shapes of Calabi-Yau manifolds.
Now, a fresh generation of researchers has brought a new tool to bear on the old problem: neural networks, the computer programs powering advances in artificial intelligence. In recent months, two teams of physicists and computer scientists have used neural networks to calculate precisely for the first time what sort of macroscopic world would emerge from a specific microscopic world of strings. This long-sought milestone reinvigorates a quest that largely stalled decades ago: the effort to determine whether string theory can actually describe our world.
“We aren’t at the point of saying these are the rules for our universe,” Anderson said. “But it’s a big step in the right direction.” (MORE - details)
Mathematicians marvel at ‘crazy’ cuts through four dimensions
https://www.quantamagazine.org/mathemati...-20240422/
INTRO: The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists understand such two-dimensional manifolds very well. And they have developed tools that let them make sense of three-dimensional manifolds and those with five or more dimensions.
But in four dimensions, “everything goes a bit crazy,” said Sam Hughes, a postdoctoral researcher at the University of Oxford. Tools stop working; exotic behavior emerges. As Tom Mrowka of the Massachusetts Institute of Technology explained, “There’s just enough room to have interesting phenomena, but not so much room that they fall apart.”
In the early 1990s, Mrowka and Peter Kronheimer of Harvard University were studying how two-dimensional surfaces can be embedded within four-dimensional manifolds. They developed new techniques to characterize these surfaces, allowing them to gain crucial insights into the otherwise inaccessible structure of four-dimensional manifolds. Their findings suggested that the members of a broad class of surfaces all slice through their parent manifold in a relatively simple way, leaving a fundamental property unchanged. But nobody could prove this was always true.
In February, together with Daniel Ruberman of Brandeis University, Hughes constructed a sequence of counterexamples — “crazy” two-dimensional surfaces that dissect their parent manifolds in ways that mathematicians had believed to be impossible. The counterexamples show that four-dimensional manifolds are even more remarkably diverse than mathematicians in earlier decades had realized. “It’s really a beautiful paper,” Mrowka said. “I just keep looking at it. There’s lots of delicious little things there.” (MORE - details)