Sep 30, 2024 03:35 AM
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The Two Faces of Space-Time
https://www.quantamagazine.org/the-two-f...-20240925/
INTRO: Anyone who has seen the classic rabbit-duck optical illusion knows the magic and confusion of duality. One might see a duck facing to the left with its bill hanging slightly open or a rabbit with its nose pointing to the right and its ears extending behind it. Both perspectives are valid.
In physics, duality is when a single physical system can be described with two completely different sets of equations. Invariably, when physicists encounter such a situation, having multiple, distinct approaches leads to a new understanding of the Janus-like system.
“[You realize] ‘Oh, now I can solve the problem, or now I have a better picture,’” said Daniel Ranard, a physicist at the California Institute of Technology.
Many of today’s physicists are grappling with a duality so surprising that it has called into question basic features of reality. It is called the AdS/CFT correspondence, and it ups the ante on the rabbit-duck illusion by equating two radically different views of an entire cosmos (albeit a toy cosmos with an exotic shape unlike that of the real universe).
In one perspective, physicists see a two-dimensional universe that is flat. In an equivalent, “dual” view, they see what they call a “bulk” universe that pops out to fill a volume, a bit like a hologram. Two sets of equations with wildly different conceptual messages end up describing exactly the same physical events.
“That is some crazy stuff,” said Adam Brown (opens a new tab), a physicist at Stanford University. “You have a whole spatial dimension that just wasn’t there at the start.”
spacetime promo card
The AdS/CFT duality has had an enormous influence on fundamental physics this century, as physicists grapple with the nature of the space-time fabric that fills our real cosmos. They’re led to wonder: Does our universe, too, have a dual description? When do dualities arise? And how common are they?
“With AdS/CFT, there are already two helpful ways of looking at it,” said Ranard. “Could there have been more helpful ways? How do we find those different ways?” (MORE - details, no ads)
If the Universe Is a Hologram, This Long-Forgotten Math Could Decode It
https://www.quantamagazine.org/if-the-un...-20240925/
EXCERPTS: John von Neumann came about as close as humanly possible to embodying the Platonic ideal of a genius. Conversant in ancient Greek by age 6, the Hungarian made significant mathematical advances in his teens. Then, as an adult, he invented game theory and helped design the atomic bomb and the modern computer.
Along the way, as a young man in 1932, von Neumann rewrote the rules of quantum mechanics, formulating the strange new theory of particles and their fluctuating, probabilistic behavior in the mathematical language used today. Then he went further. He developed a framework known as “operator algebras” to describe quantum systems in a more powerful but more abstract way. Unlike his earlier work on quantum theory, this framework was hard to understand and did not catch on widely in theoretical physics. It was literally a century ahead of its time.
Over the past few years, however, more physicists have been dusting off von Neumann’s ideas. His operator algebras are now helping them see their way around the most mysterious quantum system yet: the substructure of space and time.
Even before von Neumann did his work, Albert Einstein’s theories of relativity merged space and time into a four-dimensional fabric known as “space-time.” Einstein showed that the force of gravity is generated by curves in this fabric. But physicists know that the fabric can’t be the whole story. Dying stars puncture it, creating intensely warped regions called black holes where the equations of general relativity break down. And even in calmer parts of space-time, when you zoom in to the smallest scales, quantum fluctuations seem to shred it apart.
Many theoretical physicists therefore believe that space-time will go the way of water, metals, and so many other substances before it; what seems like a smooth and simple medium will turn out to be made of a complicated collection of primitive quantum entities. For decades, theorists have wondered about those entities and how the space-time fabric emerges from them.
These physicists are now gaining a deeper understanding of space-time’s quantum weave. They’re developing new ways of predicting what happens in extreme regions where space-time as we know it unravels, as well as identifying the conditions that normally allow it to hang together. At the heart of the progress has been von Neumann’s abstruse research.
“People have been kind of scared of it,” said Antony Speranza, a physicist at the University of Amsterdam. But “it does seem to give you these algebraic tools for seeing that a space-time is emerging.”
[...] No one knows if the space-time fabric of our real universe is holographic. One convenient feature of negative-energy AdS space is that it has a spatial boundary for those quantum ripples to live on; our universe does not. But the AdS/CFT correspondence provides a toy model for exploring this kind of space-time emergence...
[...] Von Neumann and a collaborator, Francis Murray, eventually identified (opens a new tab) three types of operator algebras. Each one applies to a different kind of physical system. The systems are classified by two physical quantities: entanglement and a property called entropy.
[...] Type I algebras are the simplest. They describe systems with a finite number of parts, which can be completely disentangled from the rest of the universe....
[...] Type II algebras are trickier. They describe systems that have an infinite number of parts, all inextricably entangled with the outside...
[...] The final type, type III, is the worst: It describes a system with infinite parts, infinite entanglement with the outside, and no uniform pattern in the entanglement to help you get oriented...
[...] When von Neumann and Murray first encountered type III algebras, they found them too alien to understand. The nature of these algebras would remain mysterious for more than three decades until Alain Connes, a French mathematician, managed to define them in 1973. he feat won Connes the Fields Medal, math’s highest honor. He determined that what set type III algebras apart was related to a fearsomely technical property called modular flow.
Very roughly speaking, modular flow resembles the flow of time — but it’s more abstract. It’s a physical process that takes a system at a particular temperature and keeps it at that temperature. A room-temperature cup of tea naturally experiences modular flow (and normal physical time) because it stays at room temperature. But for a steaming-hot cup of tea, modular flow is the sequence of operations needed to keep it eternally hot. That’s not something that would ever happen naturally, since it requires constantly fiddling with all the tea’s atoms, but it’s a process that can be specified mathematically. Connes realized that a type III algebra describes a system so entangled with its surroundings that the system’s modular flow also becomes inseparable from what’s going on outside.
Mathematicians — and a few intrepid physicists — would continue to study von Neumann algebras and their modular flows. But only in the last few years have quantum gravity researchers come to appreciate their power...
[...] The traditional approach to understanding space-time and gravity has been to posit the nature of reality at tiny scales — particles? quantum waves? strings of energy? — and zoom out to see if it matches our world. Holographers attempt to invert this approach: They start with the space-time fabric they know exists and try to zoom in as far as they can.
Von Neumann’s work, which mapped out what Sorce calls the “universe of allowed mathematics” for quantum theories, is guiding researchers as they tease apart Einstein’s fabric and see what sorts of quantum threads it could be consistent with. The findings continue a long-running trend that the threads look holographic; they can be described in 2D or in 3D. Now researchers are eager to learn more.
“I feel like the door is wide open for us to explore,” Liu said. “I find these algebraic ways to be very powerful...” (MORE - missing details, no ads)
https://www.quantamagazine.org/the-two-f...-20240925/
INTRO: Anyone who has seen the classic rabbit-duck optical illusion knows the magic and confusion of duality. One might see a duck facing to the left with its bill hanging slightly open or a rabbit with its nose pointing to the right and its ears extending behind it. Both perspectives are valid.
In physics, duality is when a single physical system can be described with two completely different sets of equations. Invariably, when physicists encounter such a situation, having multiple, distinct approaches leads to a new understanding of the Janus-like system.
“[You realize] ‘Oh, now I can solve the problem, or now I have a better picture,’” said Daniel Ranard, a physicist at the California Institute of Technology.
Many of today’s physicists are grappling with a duality so surprising that it has called into question basic features of reality. It is called the AdS/CFT correspondence, and it ups the ante on the rabbit-duck illusion by equating two radically different views of an entire cosmos (albeit a toy cosmos with an exotic shape unlike that of the real universe).
In one perspective, physicists see a two-dimensional universe that is flat. In an equivalent, “dual” view, they see what they call a “bulk” universe that pops out to fill a volume, a bit like a hologram. Two sets of equations with wildly different conceptual messages end up describing exactly the same physical events.
“That is some crazy stuff,” said Adam Brown (opens a new tab), a physicist at Stanford University. “You have a whole spatial dimension that just wasn’t there at the start.”
spacetime promo card
The AdS/CFT duality has had an enormous influence on fundamental physics this century, as physicists grapple with the nature of the space-time fabric that fills our real cosmos. They’re led to wonder: Does our universe, too, have a dual description? When do dualities arise? And how common are they?
“With AdS/CFT, there are already two helpful ways of looking at it,” said Ranard. “Could there have been more helpful ways? How do we find those different ways?” (MORE - details, no ads)
If the Universe Is a Hologram, This Long-Forgotten Math Could Decode It
https://www.quantamagazine.org/if-the-un...-20240925/
EXCERPTS: John von Neumann came about as close as humanly possible to embodying the Platonic ideal of a genius. Conversant in ancient Greek by age 6, the Hungarian made significant mathematical advances in his teens. Then, as an adult, he invented game theory and helped design the atomic bomb and the modern computer.
Along the way, as a young man in 1932, von Neumann rewrote the rules of quantum mechanics, formulating the strange new theory of particles and their fluctuating, probabilistic behavior in the mathematical language used today. Then he went further. He developed a framework known as “operator algebras” to describe quantum systems in a more powerful but more abstract way. Unlike his earlier work on quantum theory, this framework was hard to understand and did not catch on widely in theoretical physics. It was literally a century ahead of its time.
Over the past few years, however, more physicists have been dusting off von Neumann’s ideas. His operator algebras are now helping them see their way around the most mysterious quantum system yet: the substructure of space and time.
Even before von Neumann did his work, Albert Einstein’s theories of relativity merged space and time into a four-dimensional fabric known as “space-time.” Einstein showed that the force of gravity is generated by curves in this fabric. But physicists know that the fabric can’t be the whole story. Dying stars puncture it, creating intensely warped regions called black holes where the equations of general relativity break down. And even in calmer parts of space-time, when you zoom in to the smallest scales, quantum fluctuations seem to shred it apart.
Many theoretical physicists therefore believe that space-time will go the way of water, metals, and so many other substances before it; what seems like a smooth and simple medium will turn out to be made of a complicated collection of primitive quantum entities. For decades, theorists have wondered about those entities and how the space-time fabric emerges from them.
These physicists are now gaining a deeper understanding of space-time’s quantum weave. They’re developing new ways of predicting what happens in extreme regions where space-time as we know it unravels, as well as identifying the conditions that normally allow it to hang together. At the heart of the progress has been von Neumann’s abstruse research.
“People have been kind of scared of it,” said Antony Speranza, a physicist at the University of Amsterdam. But “it does seem to give you these algebraic tools for seeing that a space-time is emerging.”
[...] No one knows if the space-time fabric of our real universe is holographic. One convenient feature of negative-energy AdS space is that it has a spatial boundary for those quantum ripples to live on; our universe does not. But the AdS/CFT correspondence provides a toy model for exploring this kind of space-time emergence...
[...] Von Neumann and a collaborator, Francis Murray, eventually identified (opens a new tab) three types of operator algebras. Each one applies to a different kind of physical system. The systems are classified by two physical quantities: entanglement and a property called entropy.
[...] Type I algebras are the simplest. They describe systems with a finite number of parts, which can be completely disentangled from the rest of the universe....
[...] Type II algebras are trickier. They describe systems that have an infinite number of parts, all inextricably entangled with the outside...
[...] The final type, type III, is the worst: It describes a system with infinite parts, infinite entanglement with the outside, and no uniform pattern in the entanglement to help you get oriented...
[...] When von Neumann and Murray first encountered type III algebras, they found them too alien to understand. The nature of these algebras would remain mysterious for more than three decades until Alain Connes, a French mathematician, managed to define them in 1973. he feat won Connes the Fields Medal, math’s highest honor. He determined that what set type III algebras apart was related to a fearsomely technical property called modular flow.
Very roughly speaking, modular flow resembles the flow of time — but it’s more abstract. It’s a physical process that takes a system at a particular temperature and keeps it at that temperature. A room-temperature cup of tea naturally experiences modular flow (and normal physical time) because it stays at room temperature. But for a steaming-hot cup of tea, modular flow is the sequence of operations needed to keep it eternally hot. That’s not something that would ever happen naturally, since it requires constantly fiddling with all the tea’s atoms, but it’s a process that can be specified mathematically. Connes realized that a type III algebra describes a system so entangled with its surroundings that the system’s modular flow also becomes inseparable from what’s going on outside.
Mathematicians — and a few intrepid physicists — would continue to study von Neumann algebras and their modular flows. But only in the last few years have quantum gravity researchers come to appreciate their power...
[...] The traditional approach to understanding space-time and gravity has been to posit the nature of reality at tiny scales — particles? quantum waves? strings of energy? — and zoom out to see if it matches our world. Holographers attempt to invert this approach: They start with the space-time fabric they know exists and try to zoom in as far as they can.
Von Neumann’s work, which mapped out what Sorce calls the “universe of allowed mathematics” for quantum theories, is guiding researchers as they tease apart Einstein’s fabric and see what sorts of quantum threads it could be consistent with. The findings continue a long-running trend that the threads look holographic; they can be described in 2D or in 3D. Now researchers are eager to learn more.
“I feel like the door is wide open for us to explore,” Liu said. “I find these algebraic ways to be very powerful...” (MORE - missing details, no ads)
