The Strange Second Life of String Theory
String theory has so far failed to live up to its promise as a way to unite gravity and quantum mechanics.
At the same time, it has blossomed into one of the most useful sets of tools in science.
String theory strutted onto the scene some 30 years ago as perfection itself, a promise of elegant simplicity that would solve knotty problems in fundamental physics — including the notoriously intractable mismatch between Einstein’s smoothly warped space-time and the inherently jittery, quantized bits of stuff that made up everything in it.
It seemed, to paraphrase Michael Faraday, much too wonderful not to be true: Simply replace infinitely small particles with tiny (but finite) vibrating loops of string. The vibrations would sing out quarks, electrons, gluons and photons, as well as their extended families, producing in harmony every ingredient needed to cook up the knowable world. Avoiding the infinitely small meant avoiding a variety of catastrophes. For one, quantum uncertainty couldn’t rip space-time to shreds. At last, it seemed, here was a workable theory of quantum gravity.
The amplituhedron is a multi-dimensional object that can be used to calculate particle interactions.
Physicists such as Chris Beem are applying techniques from string theory in special geometries where “the amplituhedron is its best self,” he says.
Even more beautiful than the story told in words was the elegance of the math behind it, which had the power to make some physicists ecstatic.
To be sure, the theory came with unsettling implications. The strings were too small to be probed by experiment and lived in as many as 11 dimensions of space. These dimensions were folded in on themselves — or “compactified” — into complex origami shapes. No one knew just how the dimensions were compactified — the possibilities for doing so appeared to be endless — but surely some configuration would turn out to be just what was needed to produce familiar forces and particles.
For a time, many physicists believed that string theory would yield a unique way to combine quantum mechanics and gravity. “There was a hope. A moment,” said David Gross, an original player in the so-called Princeton String Quartet, a Nobel Prize winner and permanent member of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. “We even thought for a while in the mid-’80s that it was a unique theory.”
A
Calabi–Yau manifold, also known as a Calabi–Yau space, is a special
type of manifold that is described in certain branches of mathematics
such as algebraic geometry. The Calabi–Yau manifold’s properties, such
as Ricci flatness, also yield applications in theoretical physics.
Particularly in superstring theory, the extra dimensions of spacetime
are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau
manifold, which led to the idea of mirror symmetry.
Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions are sometimes used. They were named “Calabi–Yau spaces” by Candelas et al. (1985) after Eugenio Calabi (1954, 1957) who first conjectured that such surfaces might exist, and Shing-Tung Yau (1978) who proved the Calabi conjecture.
And then physicists began to realize that the dream of one singular theory was an illusion. The complexities of string theory, all the possible permutations, refused to reduce to a single one that described our world. “After a certain point in the early ’90s, people gave up on trying to connect to the real world,” Gross said. “The last 20 years have really been a great extension of theoretical tools, but very little progress on understanding what’s actually out there.”
Many, in retrospect, realized they had raised the bar too high.
Coming off the momentum of completing the solid and powerful “standard model” of particle physics in the 1970s, they hoped the story would repeat — only this time on a mammoth, all-embracing scale. “We’ve been trying to aim for the successes of the past where we had a very simple equation that captured everything,” said Robbert Dijkgraaf, the director of the Institute for Advanced Study in Princeton, New Jersey. “But now we have this big mess.”
Like many a maturing beauty, string theory has gotten rich in relationships, complicated, hard to handle and widely influential. Its tentacles have reached so deeply into so many areas in theoretical physics, it’s become almost unrecognizable, even to string theorists.
“Things have gotten almost postmodern,” said Dijkgraaf, who is a painter as well as mathematical physicist.
At the same time, it has blossomed into one of the most useful sets of tools in science.
String theory strutted onto the scene some 30 years ago as perfection itself, a promise of elegant simplicity that would solve knotty problems in fundamental physics — including the notoriously intractable mismatch between Einstein’s smoothly warped space-time and the inherently jittery, quantized bits of stuff that made up everything in it.
It seemed, to paraphrase Michael Faraday, much too wonderful not to be true: Simply replace infinitely small particles with tiny (but finite) vibrating loops of string. The vibrations would sing out quarks, electrons, gluons and photons, as well as their extended families, producing in harmony every ingredient needed to cook up the knowable world. Avoiding the infinitely small meant avoiding a variety of catastrophes. For one, quantum uncertainty couldn’t rip space-time to shreds. At last, it seemed, here was a workable theory of quantum gravity.
The amplituhedron is a multi-dimensional object that can be used to calculate particle interactions.
Physicists such as Chris Beem are applying techniques from string theory in special geometries where “the amplituhedron is its best self,” he says.
Even more beautiful than the story told in words was the elegance of the math behind it, which had the power to make some physicists ecstatic.
To be sure, the theory came with unsettling implications. The strings were too small to be probed by experiment and lived in as many as 11 dimensions of space. These dimensions were folded in on themselves — or “compactified” — into complex origami shapes. No one knew just how the dimensions were compactified — the possibilities for doing so appeared to be endless — but surely some configuration would turn out to be just what was needed to produce familiar forces and particles.
For a time, many physicists believed that string theory would yield a unique way to combine quantum mechanics and gravity. “There was a hope. A moment,” said David Gross, an original player in the so-called Princeton String Quartet, a Nobel Prize winner and permanent member of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. “We even thought for a while in the mid-’80s that it was a unique theory.”
A
Calabi–Yau manifold, also known as a Calabi–Yau space, is a special
type of manifold that is described in certain branches of mathematics
such as algebraic geometry. The Calabi–Yau manifold’s properties, such
as Ricci flatness, also yield applications in theoretical physics.
Particularly in superstring theory, the extra dimensions of spacetime
are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau
manifold, which led to the idea of mirror symmetry.Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions are sometimes used. They were named “Calabi–Yau spaces” by Candelas et al. (1985) after Eugenio Calabi (1954, 1957) who first conjectured that such surfaces might exist, and Shing-Tung Yau (1978) who proved the Calabi conjecture.
And then physicists began to realize that the dream of one singular theory was an illusion. The complexities of string theory, all the possible permutations, refused to reduce to a single one that described our world. “After a certain point in the early ’90s, people gave up on trying to connect to the real world,” Gross said. “The last 20 years have really been a great extension of theoretical tools, but very little progress on understanding what’s actually out there.”
Many, in retrospect, realized they had raised the bar too high.
Coming off the momentum of completing the solid and powerful “standard model” of particle physics in the 1970s, they hoped the story would repeat — only this time on a mammoth, all-embracing scale. “We’ve been trying to aim for the successes of the past where we had a very simple equation that captured everything,” said Robbert Dijkgraaf, the director of the Institute for Advanced Study in Princeton, New Jersey. “But now we have this big mess.”
Like many a maturing beauty, string theory has gotten rich in relationships, complicated, hard to handle and widely influential. Its tentacles have reached so deeply into so many areas in theoretical physics, it’s become almost unrecognizable, even to string theorists.
“Things have gotten almost postmodern,” said Dijkgraaf, who is a painter as well as mathematical physicist.
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