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Posts Tagged ‘Physics

“To Infinity and Beyond!”*…

The idea of infinity is probably about as old as numbers themselves, going back to whenever people first realized that they could keep counting forever. But even though we have a sign for infinity and can refer to the concept in casual conversation, infinity remains profoundly mysterious, even to mathematicians. Steven Strogatz explores that mystery with Justin Moore

No one really knows where the idea of infinity came from, but it must be very ancient — as old as people’s hopes and fears about things that could conceivably go on forever. Some of them are scary, like bottomless pits, and some of them are uplifting, like endless love. Within mathematics, the idea of infinity is probably about as old as numbers themselves. Once people realized that they could just keep on counting forever — 1, 2, 3 and so on. But even though infinity is a very old idea, it remains profoundly mysterious. People have been scratching their heads about infinity for thousands of years now, at least since Zeno and Aristotle in ancient Greece.

But how do mathematicians make sense of infinity today? Are there different sizes of infinity? Is infinity useful to mathematicians? And if so, how exactly? And what does all this have to do with the foundations of mathematics itself?…

All infinities go on forever, so “How Can Some Infinities Be Bigger Than Others?“, from @stevenstrogatz in @QuantaMagazine.

See also: Alan Lightman‘s “Why the paradoxes of infinity still puzzle us today” (source of the image above).

* Buzz Lightyear


As we envision endlessness, we might send carefully-calculated birthday greetings to Gaspard Monge; he was born on this date in 1746. A mathematician, he is considered the inventor of descriptive geometry, (the mathematical basis of technical drawing), and the father of differential geometry (the study of smooth shapes and spaces, AKA smooth manifolds).

During the French Revolution he was involved in the reform of the French educational system, most notably as the lead founder of the École Polytechnique.


“It is well to remember that the entire universe, with one trifling exception, is composed of others”*…

This artist’s impression shows the temperate planet Ross 128 b, with its red dwarf parent star in the background. Credit: ESO/M. Kornmesser

For centuries, scientific discoveries have suggested humanity occupies no privileged place in the universe. But as Mario Livio argues, studies of worlds beyond our solar system could place meaningful new limits on our existential mediocrity…

When the Polish polymath Nicolaus Copernicus proposed in 1543 that the sun, rather than the Earth, was the center of our solar system, he did more than resurrect the “heliocentric” model that had been devised (and largely forgotten) some 18 centuries earlier by the Greek astronomer Aristarchus of Samos. Copernicus—or, rather, the “Copernican principle” that bears his name—tells us that we humans are nothing special. Or, at least, that the planet on which we live is not central to anything outside of us; instead, it’s just another ordinary world revolving around a star.

Our apparent mediocrity has only ascended in the centuries that have passed since Copernicus’s suggestion. In the middle of the 19th century Charles Darwin realized that rather than being the “crown of creation,” humans are simply a natural product of evolution by means of natural selection. Early in the 20th century, astronomer Harlow Shapley deepened our Copernican cosmic demotion, showing that not only the Earth but the whole solar system lacks centrality, residing in the Milky Way’s sleepy outer suburbs rather than the comparatively bustling galactic center. A few years later, astronomer Edwin Hubble showed that galaxies other than the Milky Way exist, and current estimates put the total number of galaxies in the observable universe at a staggering trillion or more.

Since 1995 we have discovered that even within our own Milky Way roughly one of every five sunlike or smaller stars harbors an Earth-size world orbiting in a “Goldilocks” region (neither too hot nor too cold) where liquid water may persist on a rocky planetary surface. This suggests there are at least a few hundred million planets in the Milky Way alone that may in principle be habitable. In roughly the same span of time, observations of the big bang’s afterglow—the cosmic microwave background—have shown that even the ordinary atomic matter that forms planets and people alike constitutes no more than 5 percent of the cosmic mass and energy budget. With each advance in our knowledge, our entire existence retreats from any possible pinnacle, seemingly reduced to flotsam adrift at the universe’s margins.

Believe it or not, the Copernican principle doesn’t even end there. In recent years increasing numbers of physicists and cosmologists have begun to suspect—often against their most fervent hopes—that our entire universe may be but one member of a mind-numbingly huge ensemble of universes: a multiverse.

Interestingly though, if a multiverse truly exists, it also suggests that Copernican cosmic humility can only be taken so far.

The implications of the Copernican principle may sound depressing to anyone who prefers a view of the world regarding humankind as the central or most important element of existence, but notice that every step along the way in extending the Copernican principle represented a major human discovery. That is, each decrease in the sense of our own physical significance was the result of a huge expansion in our knowledge. The Copernican principle teaches us humility, yes, but it also reminds us to keep our curiosity and passion for exploration alive and vibrant…

Fascinating: “How Far Should We Take Our Cosmic Humility?“, from @Mario_Livio in @sciam.

* John Holmes (the poet)


As we ponder our place, we might send carefully-observed birthday greetings to Arno Penzias; he was born on this date in 1933. A physicist and radio astronomer, he and Robert Wilson, a collegue at Bell Labs, discovered the cosmic microwave background radiation, which helped establish the Big Bang theory of cosmology– work for which they shared the 1978 Nobel Prize in Physics.

MB radiation is something that anyone old enough to have watched broadcast (that’s to say, pre-cable/streaming) television) has seen:

The way a television works is relatively simple. A powerful electromagnetic wave is transmitted by a tower, where it can be received by a properly sized antenna oriented in the correct direction. That wave has additional signals superimposed atop it, corresponding to audio and visual information that had been encoded. By receiving that information and translating it into the proper format (speakers for producing sound and cathode rays for producing light), we were able to receive and enjoy broadcast programming right in the comfort of our own homes for the first time. Different channels broadcasted at different wavelengths, giving viewers multiple options simply by turning a dial.

Unless, that is, you turned the dial to channel 03.

Channel 03 was — and if you can dig up an old television set, still is — simply a signal that appears to us as “static” or “snow.” That “snow” you see on your television comes from a combination of all sorts of sources:

– human-made radio transmissions,

– the Sun,

– black holes,

– and all sorts of other directional astrophysical phenomena like pulsars, cosmic rays and more.

But if you were able to either block all of those other signals out, or simply took them into account and subtracted them out, a signal would still remain. It would only by about 1% of the total “snow” signal that you see, but there would be no way of removing it. When you watch channel 03, 1% of what you’re watching comes from the Big Bang’s leftover glow. You are literally watching the cosmic microwave background…

This Is How Your Old Television Set Can Prove The Big Bang

“Protons give an atom its identity, electrons its personality”*…

If an electron were the size of Earth, the experiment could detect a bump the size of a sugar molecule

If the electron’s charge wasn’t perfectly round, it could reveal the existence of hidden particles– and launch a “new physics.” But, as Zack Savitsky reports, a new measurement approaches perfection…

Imagine an electron as a spherical cloud of negative charge. If that ball were ever so slightly less round, it could help explain fundamental gaps in our understanding of physics, including why the universe contains something rather than nothing.

Given the stakes, a small community of physicists has been doggedly hunting for any asymmetry in the shape of the electron for the past few decades. The experiments are now so sensitive that if an electron were the size of Earth, they could detect a bump on the North Pole the height of a single sugar molecule.

The latest results are in: The electron is rounder than that.

The updated measurement disappoints anyone hoping for signs of new physics. But it still helps theorists to constrain their models for what unknown particles and forces may be missing from the current picture…

More at “The Electron Is So Round That It’s Ruling Out Potential New Particles,” from @savagitsky in @QuantaMagazine.

* Bill Bryson


As we ponder perfection, we might spare a thought for Jean Baptiste Perrin; he died on this date in 1942. A physicist, he studied the Brownian motion of minute particles suspended in liquids (sedimentation equilibrium), and verified Albert Einstein’s explanation of the phenomenon– thereby confirming the atomic nature of matter… for which he was awarded the Nobel Prize for Physics in 1926.


Written by (Roughly) Daily

April 17, 2023 at 1:00 am

“You must not fool yourself, and you are the easiest person to fool”*…

One hallmark of superconductivity is the Meissner effect, which expels all magnetic fields from a material — a property that allows a superconductor to levitate, as seen here.

The quest for room-temperature superconducting seems a bit like the hunt for the Holy Grail. A superconductor is a material that will transmit electricity with no resistance– thus very quickly and with no loss. (Estimates of loss in the U.S. electric grid, most of it due to heat loss from resistance in transmission, range from 5-10%; at the low end, that’s enough to power all seven Central American countries four times over.) Beyond that (already extraordinary) benefit, superconductivity could enable high-efficiency electric motors, maglev trains, low-cost magnets for MRI and nuclear fusion, a promising form of quantum computing (superconducting qubits), and much, much more.

Superconductivity was discovered in 1911, and has been the subject of fervent study ever since; indeed, four Nobel prizes have gone to scientists working on it, most recently in 2003. But while both understanding and application have advanced, it has remained the case that superconductivity can only be achieved at very low temperatures (or very high pressures). Until the mid-80s, it was believed that it could be established only below 30 Kelvin (-405.67 degrees Farenheit); by 2015, scientists had gotten that up to 80 K (-316 degrees Farenheit)… that’s to say, still requiring way too much cooling to be widely practical.

So imagine the excitement earlier this month, when…

In a packed talk on Tuesday afternoon at the American Physical Society’s annual March meeting in Las Vegas, Ranga Dias, a physicist at the University of Rochester, announced that he and his team had achieved a century-old dream of the field: a superconductor that works at room temperature and near-room pressure. Interest was so intense in the presentation that security personnel stopped entry to the overflowing room more than fifteen minutes before the talk. They could be overheard shooing curious onlookers away shortly before Dias began speaking.

The results, published in Nature, appear to show that a conventional conductor — a solid composed of hydrogen, nitrogen and the rare-earth metal lutetium — was transformed into a flawless material capable of conducting electricity with perfect efficiency.

While the announcement has been greeted with enthusiasm by some scientists, others are far more cautious, pointing to the research group’s controversial history of alleged research malfeasance. (Dias strongly denies the accusations.) Reactions by 10 independent experts contacted by Quanta ranged from unbridled excitement to outright dismissal…

Interesting if true– a paper in Nature divides the research community: “Room-Temperature Superconductor Discovery Meets With Resistance,” from @QuantaMagazine.

* Richard Feynman


As we review research, we might pause, on Pi Day, for a piece of pi(e)…


… in celebration of Albert Einstein’s birthday; he was born on this date in 1879.


“Everything should be made as simple as possible, but not simpler.”

Written by (Roughly) Daily

March 14, 2023 at 1:00 am

“To create something from nothing is one of the greatest feelings”*…

Something from nothing? Not exactly. As Charlie Wood explains, it’s even weirder…

For their latest magic trick, physicists have done the quantum equivalent of conjuring energy out of thin air. It’s a feat that seems to fly in the face of physical law and common sense.

“You can’t extract energy directly from the vacuum because there’s nothing there to give,” said William Unruh, a theoretical physicist at the University of British Columbia, describing the standard way of thinking.

But 15 years ago, Masahiro Hotta, a theoretical physicist at Tohoku University in Japan, proposed that perhaps the vacuum could, in fact, be coaxed into giving something up.

At first, many researchers ignored this work, suspicious that pulling energy from the vacuum was implausible, at best. Those who took a closer look, however, realized that Hotta was suggesting a subtly different quantum stunt. The energy wasn’t free; it had to be unlocked using knowledge purchased with energy in a far-off location. From this perspective, Hotta’s procedure looked less like creation and more like teleportation of energy from one place to another — a strange but less offensive idea.

“That was a real surprise,” said Unruh, who has collaborated with Hotta but has not been involved in energy teleportation research. “It’s a really neat result that he discovered.”

Now in the past year, researchers have teleported energy across microscopic distances in two separate quantum devices, vindicating Hotta’s theory. The research leaves little room for doubt that energy teleportation is a genuine quantum phenomenon.

“This really does test it,” said Seth Lloyd, a quantum physicist at the Massachusetts Institute of Technology who was not involved in the research. “You are actually teleporting. You are extracting energy.”…

Physicists Use Quantum Mechanics to Pull Energy out of Nothing,” from @walkingthedot in @QuantaMagazine.

Vaguely related (and fascinating): “The particle physics of you.”

* Prince


As we demolish distance, we might send insightful birthday greetings to Brain Cox; he was born on this date in 1968. A physicist and former musician (he was keyboardist for Dare and D:Ream), he is a professor of particle physics in the School of Physics and Astronomy at the University of Manchester, and a fellow at CERN (where he works on the ATLAS experiment, studying the forward proton detectors for the Large Hadron Collider there).

But Cox is most widely known as the host/presenter of science programs, perhaps especially the BBC’s Wonders of the Universe series, and for popular science books, such as Why Does E=mc²? and The Quantum Universe— which (he avers) were inspired by Carl Sagan and for which Cox has earned recognition as the natural successor to David Attenborough and Patrick Moore.

Science is too important not to be a part of a popular culture.


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