Hawking radiation temperature equation

$$T=\frac{hc^3}{8\pi, GMk}$$

T=temperature
h=Plank’s constant
c=speed of light
G=Newton’s gravitational constant
M=mass of the black hole
k=Boltzmann’s constant

The equation tells us that as the mass of the black hole gets bigger, its Hawking radiation temperature gets lower.

Kevin Hartnett, Quanta Magazine:

As a result of new work by Amir Ali Ahmadi and Anirudha Majumdar of Princeton University, a classical problem from pure mathematics is poised to provide iron-clad proof that drone aircraft and autonomous cars won’t crash into trees or veer into oncoming traffic.

The guarantee comes from an unlikely place — a mathematical problem known as “sum of squares.” The problem was posed in 1900 by the great mathematician David Hilbert. He asked whether certain types of equations could always be expressed as a sum of two separate terms, each raised to the power of 2.

Mathematicians settled Hilbert’s question within a few decades. Then, almost 90 years later, computer scientists and engineers discovered that this mathematical property — whether an equation can be expressed as a sum of squares — helps answer many real-world problems they’d like to solve.

Yet even as researchers realized that sum of squares could help answer many kinds of questions, they faced challenges to implementing the approach. The new work by Ahmadi and Majumdar clears away one of the biggest of those challenges — bringing an old math question squarely to bear on some of the most important technological questions of the day.

Feynman 100

The first principle is that you must not fool yourself — and you are the easiest person to fool.

You have no responsibility to live up to what other people think you ought to accomplish. I have no responsibility to be like they expect me to be. It’s their mistake, not my failing.

I would rather have questions that can’t be answered than answers that can’t be questioned.

Fall in love with some activity, and do it! Nobody ever figures out what life is all about, and it doesn’t matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough. Work as hard and as much as you want to on the things you like to do the best. Don’t think about what you want to be, but what you want to do. Keep up some kind of a minimum with other things so that society doesn’t stop you from doing anything at all.

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.

― Richard Feynman

From ScienceDaily website, source from Aalto University¹:

Perhaps the strangest prediction of quantum theory is entanglement, a phenomenon whereby two distant objects become intertwined in a manner that defies both classical physics and a “common-sense” understanding of reality. In 1935, Albert Einstein expressed his concern over this concept, referring to it as “spooky action at a distance.” […]

In work recently published in Nature, a team led by Prof. Mika Sillanpää at Aalto University in Finland has shown that entanglement of massive objects can be generated and detected.

The researchers managed to bring the motions of two individual vibrating drumheads – fabricated from metallic aluminium on a silicon chip – into an entangled quantum state. The objects in the experiment are truly massive and macroscopic compared to the atomic scale: the circular drumheads have a diametre similar to the width of a thin human hair. […]

‘The vibrating bodies are made to interact via a superconducting microwave circuit. The electromagnetic fields in the circuit are used to absorb all thermal disturbances and to leave behind only the quantum mechanical vibrations,’ says Mika Sillanpää, describing the experimental setup. […]

The results demonstrate that it is now possible to have control over large mechanical objects in which exotic quantum states can be generated and stabilized. Not only does this achievement open doors for new kinds of quantum technologies and sensors, it can also enable studies of fundamental physics in, for example, the poorly understood interplay of gravity and quantum mechanics.

University of Exeter:

Experts from the University of Exeter have developed a pioneering new technique that uses nanoengineering technology to incorporate graphene into traditional concrete production.

The new composite material, which is more than twice as strong and four times more water resistant than existing concretes, can be used directly by the construction industry on building sites. All of the concrete samples tested are according to British and European standards for construction.

Crucially, the new graphene-reinforced concentre material also drastically reduced the carbon footprint of conventional concrete production methods, making it more sustainable and environmentally friendly.

The research team insist the new technique could pave the way for other nanomaterials to be incorporated into concrete, and so further modernise the construction industry worldwide.

Lisa Zyga, Phys.org:

Cotton thread is made of many tiny fibers, each just 2-3 cm long, yet when spun together the fibers are capable of transmitting tension over indefinitely long distances. From a physics perspective, how threads and yarns transmit tension—making them strong enough to keep clothes from falling apart—is a long-standing puzzle that is not completely understood.

In a new paper published in Physical Review Letters entitled “Why Clothes Don’t Fall Apart: Tension Transmission in Staple Yarns,” physicists Patrick Warren at Unilever R&D Port Sunlight, Robin Ball at the University of Warwick, and Ray Goldstein at the University of Cambridge have investigated yarn tension in the framework of statistical physics. Using techniques from linear programming, they show that the collective friction among fibers creates a locking mechanism, and as long as there is sufficient friction, a random assembly of fibers can in principle transmit an indefinitely large tension.

Matt Waren, Science Mag:

Scientists have gone to great lengths to make the blackest possible surfaces. But it turns out that nature is pretty good at creating light-absorbing structures, too. WIRED reports that certain male birds of paradise have “superblack” feathers that absorb as much as 99.95% of light. The profoundly black appearance is produced by the microscopic structure of the feathers. Whereas other birds’ feathers have lots of tiny filaments that lie flat and are neatly organized, on the birds of paradise these filaments are tightly packed and bend upward, with deep cavities between them. As light enters the feather, it bounces around these cavities and gradually gets absorbed. Writing in Nature Communications, the scientists speculate that superblack feathers make neighboring, colorful patches on the bird appear even brighter to impress females during courtship.

Great Internet Mersenne Prime Search (GIMPS) on phys.org:

The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2^77,232,917-1, having 23,249,425 digits.

[…]

The new prime number, also known as M77232917, is calculated by multiplying together 77,232,917 twos, and then subtracting one. It is nearly one million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 50th known Mersenne prime ever discovered, each increasingly difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 16 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.

The primality proof took six days of non-stop computing on a PC with an Intel i5-6600 CPU. To prove there were no errors in the prime discovery process, the new prime was independently verified using four different programs on four different hardware configurations.

• Aaron Blosser verified it using Prime95 on an Intel Xeon server in 37 hours.

• David Stanfill verified it using gpuOwL on an AMD RX Vega 64 GPU in 34 hours.
• Andreas Höglund verified the prime using CUDALucas running on NVidia Titan Black GPU in 73 hours.
• Ernst Mayer also verified it using his own program Mlucas on 32-core Xeon server in 82 hours. Andreas Höglund also confirmed using Mlucas running on an Amazon AWS instance in 65 hours.