Lifeboat Foundation

Describes and demonstrates the MR technique of Diffusion Tensor Imaging and reviews some of the basic mathematics of Tensors including matrix multiplication, eigenvalues and eigenvectors.

Providing increased resistance to outside interference, topological qubits create a more stable foundation than conventional qubits. This increased stability allows the quantum computer to perform computations that can uncover solutions to some of the world’s toughest problems.

While qubits can be developed in a variety of ways, the topological qubit will be the first of its kind, requiring innovative approaches from design through development. Materials containing the properties needed for this new technology cannot be found in nature—they must be created. Microsoft brought together experts from condensed matter physics, mathematics, and materials science to develop a unique approach producing specialized crystals with the properties needed to make the topological qubit a reality.

Donald Hoffman interview on spacetime, consciousness, and how biological fitness conceals reality. We discuss Nima Arkani-Hamed’s Amplituhedron, decorated permutations, evolution, and the unlimited intelligence.

The Amplituhedron is a static, monolithic, geometric object with many dimensions. Its volume codes for amplitudes of particle interactions & its structure codes for locality and unitarity. Decorated permutations are the deepest core from which the Amplituhedron gets its structure. There are no dynamics, they are monoliths as in 2001: A Space Odyssey.

Continue reading “Exposing the Strange Blueprint Behind ‘Reality’ (Donald Hoffman Interview)” »

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There are loopholes.

Try out my quantum mechanics course (and many others on math and science) on Brilliant using the link https://brilliant.org/sabine. You can get started for free, and the first 200 will get 20% off the annual premium subscription.

Continue reading “I Think Faster Than Light Travel is Possible. Here’s Why” »

face_with_colon_three year 2017.

First observed in liquid helium below the lambda point, superfluidity manifests itself in a number of fascinating ways. In the superfluid phase, helium can creep up along the walls of a container, boil without bubbles, or even flow without friction around obstacles. As early as 1938, Fritz London suggested a link between superfluidity and Bose–Einstein condensation (BEC)³. Indeed, superfluidity is now known to be related to the finite amount of energy needed to create collective excitations in the quantum liquid^4,5,6,7, and the link proposed by London was further evidenced by the observation of superfluidity in ultracold atomic BECs^1,8. A quantitative description is given by the Gross–Pitaevskii (GP) equation^9,10 (see Methods) and the perturbation theory for elementary excitations developed by Bogoliubov¹¹. First derived for atomic condensates, this theory has since been successfully applied to a variety of systems, and the mathematical framework of the GP equation naturally leads to important analogies between BEC and nonlinear optics^12,13,14. Recently, it has been extended to include condensates out of thermal equilibrium, like those composed of interacting photons or bosonic quasiparticles such as microcavity exciton-polaritons and magnons^14,15. In particular, for exciton-polaritons, the observation of many-body effects related to condensation and superfluidity such as the excitation of quantized vortices, the formation of metastable currents and the suppression of scattering from potential barriers^{2,16,17,18,19,20} have shown the rich phenomenology that exists within non-equilibrium condensates. Polaritons are confined to two dimensions and the reduced dimensionality introduces an additional element of interest for the topological ordering mechanism leading to condensation, as recently evidenced in ref. 21. However, until now, such phenomena have mainly been observed in microcavities embedding quantum wells of III–V or II–VI semiconductors. As a result, experiments must be performed at low temperatures (below ∼ 20 K), beyond which excitons autoionize. This is a consequence of the low binding energy typical of Wannier–Mott excitons. Frenkel excitons, which are characteristic of organic semiconductors, possess large binding energies that readily allow for strong light–matter coupling and the formation of polaritons at room temperature. Remarkably, in spite of weaker interactions as compared to inorganic polaritons²², condensation and the spontaneous formation of vortices have also been observed in organic microcavities^23,24,25. However, the small polariton–polariton interaction constants, structural inhomogeneity and short lifetimes in these structures have until now prevented the observation of behaviour directly related to the quantum fluid dynamics (such as superfluidity). In this work, we show that superfluidity can indeed be achieved at room temperature and this is, in part, a result of the much larger polariton densities attainable in organic microcavities, which compensate for their weaker nonlinearities.

Our sample consists of an optical microcavity composed of two dielectric mirrors surrounding a thin film of 2,7-Bis[9,9-di(4-methylphenyl)-fluoren-2-yl]-9,9-di(4-methylphenyl)fluorene (TDAF) organic molecules. Light–matter interaction in this system is so strong that it leads to the formation of hybrid light–matter modes (polaritons), with a Rabi energy 2 Ω_R ∼ 0.6 eV. A similar structure has been used previously to demonstrate polariton condensation under high-energy non-resonant excitation²⁴. Upon resonant excitation, it allows for the injection and flow of polaritons with a well-defined density, polarization and group velocity.

Continue reading “Room-temperature superfluidity in a polariton condensate Physics” »

Machine learning theory is shedding new light on how to think about the mysterious and ineffable nature of art by Peli Grietzer + BIO.

In the math of particle physics, every calculation should result in infinity. Physicists get around this by just ignoring certain parts of the equations — an approach that provides approximate answers. But by using the techniques known as “resurgence,” researchers hope to end the infinities and end up with perfectly precise predictions.

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.