" The simplest form of pseudospin to enable topological sound relies on geometrical asymmetries, for example, an acoustic array of subwave-length resonators with carefully tailored asymmetries act like a spin on sound waves (Ni et al., 2018). The resulting devices are passive and support topological boundary sound waves somewhat robust to disorder.... Topological acoustic quantization, for example, based on two opposite pseudospins, coherence and correlations, can be harnessed to overcome stability and scalability challenges in current approaches to massive-data information processing, within the context of the second quantum revolution (Dowling and Milburn, 2003)."
Topological Acoustics by Pierre Deymer
"Elastic displacement measured with a laser vibrometer over a spatiotemporally modulated array of piezoelectric patches, demonstrating the emergence of a one-way topological boundary propagation of sound (Darabi et al., 2020). b: A topological mechanical metamaterial made of a three-dimensional printed elastic polymer based on asymmetric nonlinearities (Coulais et al., 2017)"
think of gravity as the kinetic mass of light as a supermomentum energy from the future - due to noncommutative time-frequency energy. So gravity is an emergent property that in actually is due to frequency energy as de Broglie discovered momentum is directly proportional to quantum frequency. Noncommutative phase is not limited to the quantum microscale so the noncommutative phase is a nonlocal spin energy that self-amplifies to the macroquantum scale, including humans as a whole.
As Roger Penrose points out the entropy of gravity is the opposite of the entropy of matter. This is why we have the ecological crisis of abrupt global warming due to modern science based on symmetric math of matter as a "religion of technology."
Newton was proven to be inspired for the inverse square law of gravity from the music theory of Archtyas with a string stretched by a weight 4 times greater to double the frequency. So this is only an approximation based on the equal-tempered irrational magnitude logarithms of the Pythagorean Theorem from Archytas. In fact the truth of music theory is noncommutative phase as an asymmetric or "anharmonic" quantum resonance.
You can see Fields Medal Alain Connes lectures on youtube for further details - his Music of the Shapes lectures. Pierre Deymer works at University of Arizona on room temperature quantum computing using noncommutative phase or asymmetric sound phonon energy as a nonlocal room temperature resonance.
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