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Category: mathematics – Page 94

The received view in physics is that the direction of time is provided by the second law of thermodynamics, according to which the passage of time is measured by ever-increasing disorder in the universe. This view, Julian Barbour argues, is wrong. If we reject Newton’s faulty assumptions about the existence of absolute space and time, Newtonian dynamics can be shown to provide a very different arrow of time. Its direction, according to this theory, is given by the increase in the complexity and order of a system of particles, exactly the opposite of what the received view about time suggests.

Two of the most established beliefs of contemporary cosmology are that the universe is expanding and that the direction of the arrow of time in the universe is defined by ever-increasing disorder (entropy), as described by the second law of thermodynamics. But both of these beliefs rest on shaky ground. In saying that the universe is expanding, physicists implicitly assume its size is measured by a rod that exists outside the universe, providing an absolute scale. It’s the last vestige of Newton’s absolute space and should have no place in modern cosmology. And in claiming that entropy is what gives time its arrow, physicists uncritically apply the laws of thermodynamics, originally discovered through the study of steam engines, to the universe as a whole. That too needs to be questioned.

Time min

Einstein and why the block universe is a mistake Read more In the absence of an absolute space and external measuring rods, size is always relative — relative to a measure of distance internal to the system. Starting from the simplest case, a triangle, what we find is that the internal measure of size produces a ratio which also happens to be related to a mathematical measure of complexity that intriguingly plays the central role in Newtonian universal gravitation. Applying these findings to the universe as a whole, we find that Newton’s theory of gravity, contrary to what physicists believe, contains within it an intrinsic arrow of time. This provides a strong hint that the direction of time is not defined by an increase in entropy, but by an increase in structure and complexity.

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This research paper presents the design of a wireless power transfer (WPT) circuit integrated with magnetic resonance coupling (MRC) and harvested radio frequency (RF) energy to wirelessly charge the battery of a mobile device. A capacitor (100 µF, 16 V) in the RF energy harvesting circuit stored the converted power, and the accumulated voltage stored in the capacitor was 9.46 V. The foundation of the proposed WPT prototype circuit included two coils (28 AWG)—a transmitter coil, and a receiver coil. The transmitter coil was energized by the alternating current (AC), which produced a magnetic field, which in turn induced a current in the receiver coil. The harvested RF energy (9.46 V) was converted into AC, which energized the transmitter coil and generated a magnetic field. The electronics in the receiver coil then converted the AC into direct current (DC), which became usable power to charge the battery of a mobile device. The experimental setup based on mathematical modeling and simulation displayed successful charging capabilities of MRC, with the alternate power source being the harvested RF energy. Mathematical formulae were applied to calculate the amount of power generated from the prototype circuit. LTSpice simulation software was applied to demonstrate the behavior of the different components in the circuit layout for effective WPT transfer.

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For now, the acrylic table is under construction and open only to the stuffed mouse, originally a cat toy, used to help set up the cameras. The toy squeaks when Kennedy presses it. “Usually, you do a surgery to remove the squeaker” before using them to set up experiments, says Kennedy, assistant professor of neuroscience at Northwestern University in Chicago, Illinois.

The playful squeak is a startling sound in a lab that is otherwise defined by the quiet of computational modeling. Among her projects, Kennedy is expanding her work with an artificial-intelligence-driven tool called the Mouse Action Recognition System (MARS) that can automatically classify mouse social behaviors. She also uses her modeling work to study how different brain areas and cell types interact with one another, and to connect neural activity with behaviors to learn how the brain integrates sensory information. In her office on the fifth floor of Northwestern’s Ward Building in downtown Chicago, most of this work happens on computers with data, code and graphs. Quiet also prevails in a room down the hall, where Kennedy’s small group of postdoctoral researchers and technicians sit at workstations in a lab that she launched less than a year and a half ago.

Kennedy’s ability to talk about abstract concepts, with a little stuffed animal as a prop, sets her apart, her colleagues say. She is a rare theoretical neuroscientist who can translate her mathematical work into real-world experiments. “That is her gift,” says Larry Abbott, a theoretical neuroscientist at Columbia University who was Kennedy’s graduate school advisor. “She’s good at the technical stuff, but if you can’t make that reach across to the data and the experiments, a person is not going to be that effective. She’s really just great at that — finding the right mathematics to apply to the particular problem that she’s looking at.”

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Check out the math & physics courses that I mentioned (many of which are free!) and support this channel by going to https://brilliant.org/Sabine/ where you can create your Brilliant account. The first 200 will get 20% off the annual premium subscription.

This is a video I have promised you almost two years ago: How does superdeterminism make sense of quantum mechanics? It’s taken me a long time to finish this because I have tried to understand why people dislike the idea that everything is predetermined so much. I hope that in this video I have addressed the biggest misconceptions. I genuinely think that discarding superdeterminism unthinkingly is the major reason that research in the foundations of physics is stuck.

If you want to know more about superdeterminism, these two papers (and references therein) may give you a good starting point:

https://arxiv.org/abs/1912.06462

Continue reading “Does Superdeterminism save Quantum Mechanics? Or does it kill free will and destroy science?” | >

“The final theory of nature must be octonionic,” observed Michael Atiyah, a British mathematician who united mathematics and physics during the 1960s in a way not seen since the days of Isaac Newton.

“Octonions are to physics what the Sirens were to Ulysses,” Pierre Ramond, a particle physicist and string theorist at the University of Florida, said to Natalie Walchover for Quanta.

Many physicists and mathematicians over the decades suspected that the peculiar panoply of forces and particles that comprise reality spring logically from the properties of eight-dimensional numbers called “octonions.” Proof surfaced in 1,898, writes Walchover in Quanta, that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided.

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“It is very exciting to see this unusual phase of matter realized in an actual experiment, especially because the mathematical description is based on a theoretical ‘extra’ time dimension,” Philipp Dumitrescu, study co-author and research fellow at the Flatiron Institute’s Center for Computational Quantum Physics, told the magazine.

In order to successfully create the topological phase, and thus the “extra” dimension, the scientists targeted a quantum computer’s quantum bits — or qubits — with a quasi-periodic laser pulse based on the Fibonacci sequence. Think quasicrystal.

“The Fibonacci sequence is a non-repeating but also not totally random sequence,” study co-author Andrew Potter, a quantum physicist at the University of British Columbia, told Vice. “Which effectively lets us realize two independent time-dimensions in the system.”

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Researchers at the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory (PPPL) have found that updating a mathematical model to include a physical property known as resistivity could lead to the improved design of doughnut-shaped fusion facilities known as tokamaks.

“Resistivity is the property of any substance that inhibits the flow of electricity,” said PPPL physicist Nathaniel Ferraro, one of the collaborating researchers. “It’s kind of like the viscosity of a fluid, which inhibits things moving through it. For example, a stone will move more slowly through molasses than water, and more slowly through water than through air.”

Scientists have discovered a new way that can cause instabilities in the edge, where temperatures and pressures rise sharply. By incorporating resistivity into models that predict the behavior of plasma, a soup of electrons and that makes up 99% of the visible universe, scientists can design systems for future that make the plasma more stable.

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The bottomless bucket is Karl Marx’s utopian creed: “From each according to his ability, to each according to his needs.” In this idyllic world, everyone works for the good of society, with the fruits of their labor distributed freely — everyone taking what they need, and only what they need. We know how that worked out. When rewards are unrelated to effort, being a slacker is more appealing than being a worker. With more slackers than workers, not nearly enough is produced to satisfy everyone’s needs. A common joke in the Soviet Union was, “They pretend to pay us, and we pretend to work.”

In addition to helping those who in the great lottery of life have drawn blanks, governments should adopt myriad policies that expand the economic pie, including education, infrastructure, and the enforcement of laws and contracts. Public safety, national defense, dealing with externalities are also important. There are many legitimate government activities and there are inevitably tradeoffs. Governing a country is completely different from playing a simple, rigged distribution game.

I love computers. I use them every day — not just for word processing but for mathematical calculations, statistical analyses, and Monte Carlo simulations that would literally take me several lifetimes to do by hand. Computers have benefited and entertained all of us. However, AI is nowhere near ready to rule the world because computer algorithms do not have the intelligence, wisdom, or commonsense required to make rational decisions.

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Research in the field of machine learning and AI, now a key technology in practically every industry and company, is far too voluminous for anyone to read it all. This column, Perceptron, aims to collect some of the most relevant recent discoveries and papers — particularly in, but not limited to, artificial intelligence — and explain why they matter.

In this batch of recent research, Meta open-sourced a language system that it claims is the first capable of translating 200 different languages with “state-of-the-art” results. Not to be outdone, Google detailed a machine learning model, Minerva, that can solve quantitative reasoning problems including mathematical and scientific questions. And Microsoft released a language model, Godel, for generating “realistic” conversations that’s along the lines of Google’s widely publicized Lamda. And then we have some new text-to-image generators with a twist.

Meta’s new model, NLLB-200, is a part of the company’s No Language Left Behind initiative to develop machine-powered translation capabilities for most of the world’s languages. Trained to understand languages such as Kamba (spoken by the Bantu ethnic group) and Lao (the official language of Laos), as well as over 540 African languages not supported well or at all by previous translation systems, NLLB-200 will be used to translate languages on the Facebook News Feed and Instagram in addition to the Wikimedia Foundation’s Content Translation Tool, Meta recently announced.

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