Archive for the ‘mathematics’ category

Jul 16, 2021

We Now Have Precise Math to Describe How Black Holes Reflect The Universe

Posted by in categories: cosmology, information science, mathematics, physics

A new set of equations can precisely describe the reflections of the Universe that appear in the warped light around a black hole.

The proximity of each reflection is dependent on the angle of observation with respect to the black hole, and the rate of the black hole’s spin, according to a mathematical solution worked out by physics student Albert Sneppen of the Niels Bohr Institute in Denmark.

This is really cool, absolutely, but it’s not just really cool. It also potentially gives us a new tool for probing the gravitational environment around these extreme objects.

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Jul 12, 2021

Backflipping MIT Mini Cheetah

Posted by in categories: bioengineering, mathematics, physics, robotics/AI

Circa 2019

MIT’S new mini cheetah robot is the first four-legged robot to do a backflip. At only 20 pounds the limber quadruped can bend and swing its legs wide, enabling it to walk either right side up or upside down. The robot can also trot over uneven terrain about twice as fast as an average person’s walking speed. (Learn more: http://news.mit.edu/2019/mit-mini-cheetah-first-four-legged-…kflip-0304)

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Jul 12, 2021

Chinese achieve new milestone with 56 qubit computer

Posted by in categories: computing, mathematics, quantum physics

A team of researchers affiliated with multiple institutions in China, working at the University of Science and Technology of China, has achieved another milestone in the development of a usable quantum computer. The group has written a paper describing its latest efforts and have uploaded it to the arXiv preprint server.

Back in 2019, a team at Google announced that they had achieved “quantum supremacy” with their Sycamore machine—a 54 processor that carried out a calculation that would have taken a traditional approximately 10000 years to complete. But that was soon surpassed by other teams from Honeywell and a team in China. The team in China used a different technique, one that involved the use of photonic qubits—but it was also a one-trick pony. In this new effort, the new team in China, which has been led by Jian-Wei Pan, who also led the prior team at the University of Science and Technology has achieved another milestone.

The new effort was conducted with a 2D programable computer called Zuchongzhi—one equipped to run with 66 qubits. In their demonstration, the researchers used only 56 of those qubits to tackle a well-known computer problem—sampling the output distribution of random quantum circuits. The task requires a variety of computer abilities that involve mathematical analysis, matrix theory, the complexity of certain computations and probability theory—a task approximately 100 times more challenging than the one carried out by Sycamore just two years ago. Prior research has suggested the task set before the Chinese machine would take a conventional computer approximately eight years to complete. Zuchongzhi completed the task in less than an hour and a half. The achievement by the team showed that the Zuchongzhi machine is capable of tackling more than just one kind of task.

Jul 12, 2021

Classical approach extends the range of noisy quantum computers

Posted by in categories: computing, information science, mathematics, quantum physics

Quantum computing algorithms can simulate infinitely-large quantum systems thanks to mathematical tools known as tensor networks.

Jul 11, 2021

Islands behind the horizon

Posted by in categories: cosmology, mathematics, neuroscience

Math about black holes:

If you’ve been following the arXiv, or keeping abreast of developments in high-energy theory more broadly, you may have noticed that the longstanding black hole information paradox seems to have entered a new phase, instigated by a pair of papers [1, 2] that appeared simultaneously in the summer of 2019. Over 200 subsequent papers have since appeared on the subject of “islands”—subleading saddles in the gravitational path integral that enable one to compute the Page curve, the signature of unitary black hole evaporation. Due to my skepticism towards certain aspects of these constructions (which I’ll come to below), my brain has largely rebelled against boarding this particular hype train. However, I was recently asked to explain them at the HET group seminar here at Nordita, which provided the opportunity (read: forced me) to prepare a general overview of what it’s all about. Given the wide interest and positive response to the talk, I’ve converted it into the present post to make it publicly available.

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Jul 9, 2021

Mathematicians Prove Symmetry of Phase Transitions

Posted by in category: mathematics

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

Jul 9, 2021

Einstein’s “Time Dilation” Prediction Verified

Posted by in categories: mathematics, particle physics, quantum physics

Circa 2014

Physicists have verified a key prediction of Albert Einstein’s special theory of relativity with unprecedented accuracy. Experiments at a particle accelerator in Germany confirm that time moves slower for a moving clock than for a stationary one.

The work is the most stringent test yet of this ‘time-dilation’ effect, which Einstein predicted. One of the consequences of this effect is that a person travelling in a high-speed rocket would age more slowly than people back on Earth.

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Jul 3, 2021

Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory

Posted by in categories: habitats, mathematics, quantum physics

Nathan Seiberg, 64, still does a lot of the electrical work and even some of the plumbing around his house in Princeton, New Jersey. It’s an interest he developed as a kid growing up in Israel, where he tinkered with his car and built a radio.

“I was always fascinated by solving problems and understanding how things work,” he said.

Seiberg’s professional career has been about problem solving, too, though nothing as straightforward as fixing radios. He’s a physicist at the Institute for Advanced Study, and over the course of a long and decorated career he has made many contributions to the development of quantum field theory, or QFT.

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Jul 1, 2021

Math Has a Fatal Flaw

Posted by in categories: computing, mathematics, quantum physics

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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Jun 26, 2021

The Early Universe Explained by Neil deGrasse Tyson

Posted by in categories: cosmology, information science, mathematics, neuroscience, nuclear energy, particle physics, singularity

Neil deGrasse Tyson explains the early state of our Universe. At the beginning of the universe, ordinary space and time developed out of a primeval state, where all matter and energy of the entire visible universe was contained in a hot, dense point called a gravitational singularity. A billionth the size of a nuclear particle.

While we can not imagine the entirety of the visible universe being a billion times smaller than a nuclear particle, that shouldn’t deter us from wondering about the early state of our universe. However, dealing with such extreme scales is immensely counter-intuitive and our evolved brains and senses have no capacity to grasp the depths of reality in the beginning of cosmic time. Therefore, scientists develop mathematical frameworks to describe the early universe.

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