Once found, these enigmatic rules helped particle physicists calculate scattering amplitudes at much higher resolutions than they could achieve using the conventional approach. The restructuring also allowed Dixon and his collaborators to discover the hidden relationship between seemingly unrelated scattering amplitudes.
Antipod Map
At the heart of the duality is the “opposition of the codes” map. In geometry, a cipher map takes a point on a sphere and reflects the coordinates, sending you straight through the center of the sphere to a point on the other side. It is the mathematical equivalent of digging a hole from Chile to China.
In the scattering inflections, the antithesis map that Dixon found is a bit more abstract. It reflects the order of the letters used to calculate the capacity. Apply this antithesis map to all terms in the scattering amplitude of two gluons to become four, and (after a small change in the variables) results in the gluon amplitudes becoming one gluon plus Higgs.
In Dixon’s analogy to DNA, dualism is like reading a genetic sequence backwards and realizing that it encodes an entirely new protein that has nothing to do with the protein encoded by the original sequence.
“We all used to be convinced that the Anticoderm map was useless. It didn’t seem to have any physical significance, or to do anything meaningful,” he said. Matt von Hippel, who is a capacitance specialist at the Niels Bohr Institute in Copenhagen and was not involved in the research. “And now there’s this totally inexplicable duality of using it, and it’s pretty wild.”
Not quite our world
There are now two big questions. First, why does duplication exist? And second, will a similar connection be found in the real world?
The seventeen known elementary particles that make up our universe are bound by a set of equations called Standard Model of Particle Physics. According to the Standard Model, two gluons, the massless particles that stick to some atomic nuclei, easily interact with each other to double their number, becoming four gluons. However, to produce a single gluon and a Higgs particle, the colliding gluons must first transform into a quark and an antiquark. Then it is transformed into a gluon and Higgs by a force different from that which governs the reciprocal interactions of the gluons.
These two scattering processes are so different, that one of them involves a completely different sector of the Standard Model, so that the duality between them is very surprising.
But anti-faceted duality is also unexpected, even in the simplified model of particle physics that Dixon and colleagues have been studying. Their game model controls imaginary gluons with additional symmetries, allowing more accurate calculations of the extent of the scattering. The duality links a scattering process involving these gluons and a process that requires an external interaction with the particles described by a different theory.
Dixon thinks he has a very flimsy idea about the source of the duality.
Remember those inexplicable rules found by Vulovicz and colleagues that define the word combinations allowed in the scattering range. Some rules seem to arbitrarily restrict the characters that can appear next to each other in the amplitude of two-gluon to gluon-plus-higgs. But put these rules on the other side of the duality, and it turns out to be a set of solid rules That ensures causation – ensuring that interactions between incoming particles occur before outgoing particles appear.
For Dixon, this is a slight hint of a deeper physical connection between the two capacitances, and reason to believe that something similar might hold in the Standard Model. “But she is very weak,” he said. “It’s like secondhand information.”
Other dichotomies have already been found among disparate physical phenomena. The AdS-CFT correspondence, for example, in which the theoretical world without gravity is a duality of the gravitational world, has fed thousands of research papers since its discovery in 1997. But this duality also exists only for the gravitational world with a distorted geometry as opposed to the actual universe. However, for many physicists, the fact that there are nearly so many binaries in our universe suggests that they might just scratch the surface of a comprehensive theoretical structure in which these surprising connections manifest. “I think they’re all part of the story,” Dixon said.
original story Reprinted with permission from Quanta MagazineAnd the Independent editorial publication Simmons Foundation Its mission is to advance the general understanding of science by covering research developments and trends in mathematics, the physical sciences, and the life sciences.