The fact that solitons may have a role in quantum gravity is intriguing.
In a paper in ArXiv, by Leone Di Mauro Villari, Giulia Marcucci, Maria Chiara Braidotti (all of them top complexlight students), and CC, a toy model concerning Hawking radiation by moving black holes is proposed.
Within a simple one-dimensional theory, based on solitons of the Sine-Gordon equation, the authors claim that Hawking emission may be extracted by the concomitant observation of gravitational and electromagnetic waves emitted by colliding black holes. The effect is due to the black-hole-velocity dependent emission spectrum (figure above), which results into an electromagnetic frequency chirp detected by the observer.
The fact that black holes are solitons is not very well known. Abdus Salam and others outlined this issue several years ago. Stephen Hawking predicted that Black Holes evaporate, and this is a quantum effect on classical gravity governed by the highly nonlinear Einstein-Hilbert equations.
Leone Villari, Ewan Wright, Fabio Biancalana and Claudio Conti report on the possibility that all types of classical solitons may evaporate in the quantum regime. A paper in the arXiv contains the theory on the exact quantization of the nonlinear Schroedinger equation: solitons emit a blackbody radiation spectrum at a temperature given by the same formula of Hawking!
This result is intriguing. On one hand, because it represents the first theoretical prediction of the Hawking radiation in a fully nonlinear quantum field theory. The standard Hawking theory relies on the quantization of a linear field in a curved background. The theory may hence provide insights for a true quantum gravity based on the complete quantization of the Einstein-Hilbert equations.
On the other hand, the result is also important because the Hawking radiation from a quantum soliton may furnish a novel highly tunable quantum source with many possible applications.
In recent years, researchers question about the limits of the uncertainty relation.
Hints from quantum gravity theories suggest that the Heisenberg principle should be generalized.
Some considered implications in high energy physics, others have considered the mechanical motion of massive objects to look for possible tests of these supposed limits to the most important paradigm of quantum mechanics.
In a project funded by the John Templeton Foundation (grant number 58277), we consider the case of the photon, and study the possible way a generalized uncertainty principle may play a role in modern photonics, nonlinear and quantum optics.
The project started in 2015 and will finish in 2018, stay tuned.
The Quest for Quantum Gravity in Optics
The Math of Irreversibility
Black holes evaporate, black holes are solitons, solitons evaporate !
Time Travel is NOT Possible (press release)
In a paper in arXiv Giulia Marcucci and Claudio Conti report on the mathematical structures of the so-called Time Asymmetric Quantum Mechanics. This theory predicts that time-travel is not possible and explain evidences as the Big Bang or the decay of unstable particles. The authors argue that possible shaping of the initial state of a system may furnish a road to validate these fascinating developments in quantum mechanics. The work also follows the experimental evidence of the quantization of the decays rates.
The picture above shows a pictorial representation of the Gelfand triplet, the phase space of the Time Asymmetric Quantum Mechanics