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beautiful
| quote: | Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.
“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.
The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression. |
Source: https://www.simonsfoundation.org/qu...uantum-physics/
[I am quite familiar with the work of Jim Simons, a prominent MIT Mathematician who's worked alongside Edward Witten & Co from Princeton in the field of Superstring Theory -- A field being discarded by the day. Simons also runs one of the most 'successful' hedge-funds in the world -- Renaissance located in the Greenwich, CT -- the financial capital of the world. While quite secretive, it is known as a purely quantitative fund; although, I'm certain this is pure hype -- [[fundamental trading (earnings, earnings yield, E/P ratios and cashflow are long-proven investment strategies that trump any algorithmic daytrading -- you can't beat the market; but that's a story for another thread.] Simons is actively involved in Autism/Asperger research which I am very fond of  ]
| quote: | | The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity. |
| quote: | The amplituhedron looks like an intricate, multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated, “scattering amplitudes,” which represent the likelihood that a certain set of particles will turn into certain other particles upon colliding. These numbers are what particle physicists calculate and test to high precision at particle accelerators like the Large Hadron Collider in Switzerland.
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In the mid-2000s, more patterns emerged in the scattering amplitudes of particle interactions, repeatedly hinting at an underlying, coherent mathematical structure behind quantum field theory. Most important was a set of formulas called the BCFW recursion relations, named for Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten. Instead of describing scattering processes in terms of familiar variables like position and time and depicting them in thousands of Feynman diagrams, the BCFW relations are best couched in terms of strange variables called “twistors,” and particle interactions can be captured in a handful of associated twistor diagrams. The relations gained rapid adoption as tools for computing scattering amplitudes relevant to experiments, such as collisions at the Large Hadron Collider. But their simplicity was mysterious. |
If you are interested in the field of Solitons and Twistors, I recommend this book from Oxford Press.
Arkani-Hamed and Trnka discovered that the scattering amplitude equals the volume of a brand-new mathematical object — the amplituhedron. The details of a particular scattering process dictate the dimensionality and facets of the corresponding amplituhedron. The pieces of the positive Grassmannian that were being calculated with twistor diagrams and then added together by hand were building blocks that fit together inside this jewel, just as triangles fit together to form a polygon.
| quote: | According to modern quantum theory, energy fields permeate the universe, and flurries of energy in these fields, called “particles” when they are pointlike and “waves” when they are diffuse, serve as the building blocks of matter and forces. But new findings suggest this wave-particle picture offers only a superficial view of nature’s constituents.
If each energy field pervading space is thought of as the surface of a pond, and waves and particles are the turbulence on that surface, then the new evidence strengthens the argument that a vibrant, hidden world lies beneath.
For decades, the surface-level description of the subatomic world has been sufficient to make accurate calculations about most physical phenomena. But recently, a strange class of matter that defies description by known quantum mechanical methods has drawn physicists into the depths below.
“I’ve grown up as a physicist just living on that flatland, that 2-D space,” said Subir Sachdev, a physics professor at Harvard University who studies these strange forms of matter. Now, there is a whole new dimension to explore, he said, and “you can think of the particles as just ending on that surface.”
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The holographic duality echoes the wave-particle duality that led to the development of quantum mechanics. In the early 1900s, light, which was previously thought to be a wave, seemed perplexing in some experiments unless it was treated as particles, and electrons, thought to be particles, sometimes didn’t make sense unless they were conceived as waves. “The wave-particle duality was, when first proposed, a big surprise because these were two seemingly different concepts, and we learned that they are the same thing,” Horowitz said. The holographic duality “is more sophisticated, but it has that same feature,” he said. “You have two very different-seeming objects that turn out to be completely equivalent.”
Here's the catch:
| quote: | | String theory, a framework that treats particles as invisibly small, vibrating strings, is one candidate for a theory of quantum gravity that seems to hold up in black hole situations, but its relationship to reality is unproven — or at least confusing. Recently, a strange duality has been found between string theory and quantum field theory, indicating that the former (which includes gravity) is mathematically equivalent to the latter (which does not) when the two theories describe the same event as if it is taking place in different numbers of dimensions. No one knows quite what to make of this discovery. But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway. |
It's not scientifically proven yet. String Theory remains a 'theory', until LHC proves physicists otherwise.
Last edited by Lagrangian on Sep-18-2013 at 07:07
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