Monthly Archives: March 2022

Paul M. Sutteris an astrophysicist at SUNY Stony Brook and the Flatiron Institute, host of "Ask a Spaceman" and "Space Radio," and author of "How to Die in Space."

A seemingly harmless, random number with no units or dimensions has cropped up in so many places in physics and seems to control one of the most fundamental interactions in the universe.

Its name is the fine-structure constant, and it's a measure of the strength of the interaction between charged particles and the electromagnetic force. The current estimate of the fine-structure constant is 0.007 297 352 5693, with an uncertainty of 11 on the last two digits. The number is easier to remember by its inverse, approximately 1/137.

If it had any other value, life as we know it would be impossible. And yet we have no idea where it comes from.

Watch: The Most Important Number in the Universe

Atoms have a curious property: They can emit or absorb radiation of very specific wavelengths, called spectral lines. Those wavelengths are so specific because of quantum mechanics. An electron orbiting around a nucleus in an atom can't have just any energy; it's restricted to specific energy levels.

When electrons change levels, they can emit or absorb radiation, but that radiation will have exactly the energy difference between those two levels, and nothing else hence the specific wavelengths and the spectral lines.

But in the early 20th century, physicists began to notice that some spectral lines were split, or had a "fine structure" (and now you can see where I'm going with this). Instead of just a single line, there were sometimes two very narrowly separated lines.

The full explanation for the "fine structure" of the spectral line rests in quantum field theory, a marriage of quantum mechanics and special relativity. And one of the first people to take a crack at understanding this was physicist Arnold Sommerfeld. He found that to develop the physics to explain the splitting of spectral lines, he had to introduce a new constant into his equations a fine-structure constant.

Related: 10 mind-boggling things you should know about quantum physics

The introduction of a constant wasn't all that new or exciting at the time. After all, physics equations throughout history have involved random constants that express the strengths of various relationships. Isaac Newton's formula for universal gravitation had a constant, called G, that represents the fundamental strength of the gravitational interaction. The speed of light, c, tells us about the relationship between electric and magnetic fields. The spring constant, k, tells us how stiff a particular spring is. And so on.

But there was something different in Sommerfeld's little constant: It didn't have units. There are no dimensions or unit system that the value of the number depends on. The other constants in physics aren't like this. The actual value of the speed of light, for example, doesn't really matter, because that number depends on other numbers. Your choice of units (meters per second, miles per hour or leagues per fortnight?) and the definitions of those units (exactly how long is a "meter" going to be?) matter; if you change any of those, the value of the constant changes along with it.

But that's not true for the fine-structure constant. You can have whatever unit system you want and whatever method of organizing the universe as you wish, and that number will be precisely the same.

If you were to meet an alien from a distant star system, you'd have a pretty hard time communicating the value of the speed of light. Once you nailed down how we express our numbers, you would then have to define things like meters and seconds.

But the fine structure constant? You could just spit it out, and they would understand it (as long as they count numbers the same way as we do).

Sommerfeld originally didn't put much thought into the constant, but as our understanding of the quantum world grew, the fine-structure constant started appearing in more and more places. It seemed to crop up anytime charged particles interacted with light. In time, we came to recognize it as the fundamental measure for the strength of how charged particles interact with electromagnetic radiation.

Change that number, change the universe. If the fine-structure constant had a different value, then atoms would have different sizes, chemistry would completely change and nuclear reactions would be altered. Life as we know it would be outright impossible if the fine-structure constant had even a slightly different value.

So why does it have the value it does? Remember, that value itself is important and might even have meaning, because it exists outside any unit system we have. It simply is.

In the early 20th century, it was thought that the constant had a value of precisely 1/137. What was so important about 137? Why that number? Why not literally any other number? Some physicists even went so far as to attempt numerology to explain the constant's origins; for example, famed astronomer Sir Arthur Eddington "calculated" that the universe had 137 * 2^256 protons in it, so "of course" 1/137 was also special.

Today, we have no explanation for the origins of this constant. Indeed, we have no theoretical explanation for its existence at all. We simply measure it in experiments and then plug the measured value into our equations to make other predictions.

Someday, a theory of everything a complete and unified theory of physics might explain the existence of the fine-structure constant and other constants like it. Unfortunately, we don't have a theory of everything, so we're stuck shrugging our shoulders.

But at least we know what to write on our greeting cards to the aliens.

Learn more by listening to the "Ask a Spaceman" podcast, available oniTunesand askaspaceman.com. Ask your own question on Twitter using #AskASpaceman or by following Paul @PaulMattSutter and facebook.com/PaulMattSutter.

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Life as we know it would not exist without this highly unusual number - Space.com

The Bohr model, introduced by Danish physicist Niels Bohr in 1913, was a key step on the journey to understand atoms.

Ancient Greek thinkers already believed that matter was composed of tiny basic particles that couldn't be divided further. It took more than 2,000 years for science to advance enough to prove this theory right. The journey to understanding atoms and their inner workings was long and complicated.

It was British chemist John Dalton who in the early 19th century revived the ideas of ancient Greeks that matter was composed of tiny indivisible particles called atoms. Dalton believed that every chemical element consisted of atoms of distinct properties that could be combined into various compounds, according to Britannica.

Dalton's theories were correct in many aspects, apart from that basic premise that atoms were the smallest component of matter that couldn't be broken down into anything smaller. About a hundred years after Dalton, physicists started discovering that the atom was, in fact, really quite complex inside.

Related: There's a giant mystery hiding inside every atom in the universe

British physicist Joseph John Thomson made the first major breakthrough in the understanding of atoms in 1897 when he discovered that atoms contained tiny negatively charged particles that he called electrons. Thomson thought that electrons floated in a positively charged "soup" inside the atomic sphere, according to Khan Academy.

14 years later, New Zealand-born Ernest Rutherford, Thomson's former student, challenged this depiction of the atom when he found in experiments that the atom must have a small positively charged nucleus sitting at its center.

Based on this finding, Rutherford then developed a new atom model, the Rutherford model. According to this model, the atom no longer consisted of just electrons floating in a soup but had a tiny central nucleus, which contained most of the atom's mass. Around this nucleus, the electrons revolved similarly to planets orbiting the sun in our solar system, according to Britannica.

Some questions, however, remained unanswered. For example, how was it possible that the electrons didn't collapse onto the nucleus, since their opposite charge would mean they should be attracted to it? Several physicists tried to answer this question including Rutherford's student Niels Bohr.

Bohr was the first physicist to look to the then-emerging quantum theory to try to explain the behavior of the particles inside the simplest of all atoms; the atom of hydrogen. Hydrogen atoms consist of a heavy nucleus with one positively-charged proton around which a single, much smaller and lighter, negatively charged electron orbits. The whole system looks a little bit like the sun with only one planet orbiting it.

Bohr tried to explain the connection between the distance of the electron from the nucleus, the electron's energy and the light absorbed by the hydrogen atom, using one great novelty of physics of that era: the Planck constant.

The Planck constant was a result of the investigation of German physicist Max Planck into the properties of electromagnetic radiation of a hypothetical perfect object called the black body.

Strangely, Planck discovered that this radiation, including light, is emitted not in a continuum but rather in discrete packets of energy that can only be multiples of a certain fixed value, according to Physics World.That fixed value became the Planck constant. Max Planck called these packets of energy quanta, providing a name to the completely new type of physics that was set to turn the scientists' understanding of our world upside down.

What role does the Planck constant play in the hydrogen atom? Despite the nice comparison, the hydrogen atom is not exactly like the solar system. The electron doesn't orbit its sun the nucleus at a fixed distance, but can skip between different orbits based on how much energy it carries, Bohr postulated. It may orbit at the distance of Mercury, then jump to Earth, then to Mars.

The electron doesn't slide between the orbits gradually, but makes discrete jumps when it reaches the correct energy level, quite in line with Planck's theory, physicist Ali Hayek explains on his YouTube channel.

Bohr believed that there was a fixed number of orbits that the electron could travel in. When the electron absorbs energy, it jumps to a higher orbital shell. When it loses energy by radiating it out, it drops to a lower orbit. If the electron reaches the highest orbital shell and continues absorbing energy, it will fly out of the atom altogether.

The ratio between the energy of the electron and the frequency of the radiation it emits is equal to the Planck constant. The energy of the light emitted or absorbed is exactly equal to the difference between the energies of the orbits and is inversely proportional to the wavelength of the light absorbed by the electron, according to Ali Hayek.

Using his model, Bohr was able to calculate the spectral lines the lines in the continuous spectrum of light that the hydrogen atoms would absorb.

The Bohr model seemed to work pretty well for atoms with only one electron. But apart from hydrogen, all other atoms in the periodic table have more, some many more, electrons orbiting their nuclei. For example, the oxygen atom has eight electrons, the atom of iron has 26 electrons.

Once Bohr tried to use his model to predict the spectral lines of more complex atoms, the results became progressively skewed.

There are two reasons why Bohr's model doesn't work for atoms with more than one electron, according to the Chemistry Channel. First, the interaction of multiple atoms makes their energy structure more difficult to predict.

Bohr's model also didn't take into account some of the key quantum physics principles, most importantly the odd and mind-boggling fact that particles are also waves, according to the educational website Khan Academy.

As a result of quantum mechanics, the motion of the electrons around the nucleus cannot be exactly predicted. It is impossible to pinpoint the velocity and position of an electron at any point in time. The shells in which these electrons orbit are therefore not simple lines but rather diffuse, less defined clouds.

Only a few years after the model's publication, physicists started improving Bohr's work based on the newly discovered principles of particle behavior. Eventually, the much more complicated quantum mechanical model emerged, superseding the Bohr model. But because things get far less neat when all the quantum principles are in place, the Bohr model is probably still the first thing most physics students discover in their quest to understand what governs matter in the microworld.

Read more about the Bohr atom model on the website of the National Science Teaching Association or watch this video.

Heilbron, J.L., RutherfordBohr atom, American Journal of Physics 49, 1981 https://aapt.scitation.org/doi/abs/10.1119/1.12521

Olszewski, Stanisaw, The Bohr Model of the Hydrogen Atom Revisited, Reviews in Theoretical Science, Volume 4, Number 4, December 2016 https://www.ingentaconnect.com/contentone/asp/rits/2016/00000004/00000004/art00003

Kraghm Helge, Niels Bohr between physics and chemistry, Physics Today, 2013 http://materias.df.uba.ar/f4Aa2013c2/files/2012/08/bohr2.pdf

Follow Tereza Putarova on Twitter at @TerezaPultarova. Follow us on Twitter @Spacedotcom and on Facebook.

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The Bohr model: The famous but flawed depiction of an atom - Space.com

We don't know who came up with common core math. We hate it so much, as a matter of fact, that we're not even going to bother looking up where it came from. It sucks, it's hard, and everybody hates it.

Luckily, politicians in Idaho are thinking about replacing it. This is lovely, because over 300,000 Idaho students are being taught common core, and we're not here for it.

We're here to help. We've come up with a list of studies that aremucheasier to understand than common core. Let's dive in:

Why study numbers when you can study the behavior of matter and energy on a subatomic level? Quantum physics (or quantum mechanics, if you're nasty) is one of the most difficult areas of study in all of math and science. And yes, it's way easier to comprehend than common core.

Numbers are boring, right? It definitely sounds way easier to learn a 2,000-year-old dead language that is no longer in use. Think of how fun it'd be to converse with your friends out in public in Sanskrit so no one can understand you! Still easier than common core.

Seriously, how do they work?

Sure, relationships are hard, until you compare them to common core. Then it's easy!

See? Who needs common core when we have been provided all these other amazing options? Here's to hoping Idaho comes to its senses and replaces this devil math with something more palatable.

Like, literally anything.

Idaho's top twenty-five high schools ranked from 25-1.

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Idaho Wants To Replace Common Core. We Have Some Ideas. - KIDO Talk Radio

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that some mathematicians say itor some aspect of itbelongs in the esteemed ranks of the Millennium Prize Problems, a list of the top open questions in math. Edward Frenkel, a mathematician at the University of California, Berkeley, has even dubbed the Langlands program a Grand Unified Theory of Mathematics.

The program is named after Robert Langlands, a mathematician at the Institute for Advanced Study in Princeton, N.J. Four years ago, he was awarded the Abel Prize, one of the most prestigious awards in mathematics, for his program, which was described as visionary.

Langlands is retired, but in recent years the project has sprouted into almost its own mathematical field, with many disparate parts, which are united by a common wellspring of inspiration, says Steven Rayan, a mathematician and mathematical physicist at the University of Saskatchewan. It has many avatars, some of which are still open, some of which have been resolved in beautiful ways.

Increasingly mathematicians are finding links between the original programand its offshoot, geometric Langlandsand other fields of science. Researchers have already discovered strong links to physics, and Rayan and other scientists continue to explore new ones. He has a hunch that, with time, links will be found between these programs and other areas as well. I think were only at the tip of the iceberg there, he says. I think that some of the most fascinating work that will come out of the next few decades is seeing consequences and manifestations of Langlands within parts of science where the interaction with this kind of pure mathematics may have been marginal up until now. Overall Langlands remains mysterious, Rayan adds, and to know where it is headed, he wants to see an understanding emerge of where these programs really come from.

The Langlands program has always been a tantalizing dance with the unexpected, according to James Arthur, a mathematician at the University of Toronto. Langlands was Arthurs adviser at Yale University, where Arthur earned his Ph.D. in 1970. (Langlands declined to be interviewed for this story.)

I was essentially his first student, and I was very fortunate to have encountered him at that time, Arthur says. He was unlike any mathematician I had ever met. Any question I had, especially about the broader side of mathematics, he would answer clearly, often in a way that was more inspiring than anything I could have imagined.

During that time, Langlands laid the foundation for what eventually became his namesake program. In 1969Langlands famously handwrote a 17-page letter to French mathematician Andr Weil. In that letter, Langlands shared new ideas that later became known as the Langlands conjectures.

In 1969 Langlands delivered conference lectures in which he shared the seven conjectures that ultimately grew into the Langlands program, Arthur notes. One day Arthur asked his adviser for a copy of a preprint paper based on those lectures.

He willingly gave me one, no doubt knowing that it was beyond me, Arthur says. But it was also beyond everybody else for many years. I could, however, tell that it was based on some truly extraordinary ideas, even if just about everything in it was unfamiliar to me.

Two conjectures are central to the Langlands program. Just about everything in the Langlands program comes in one way or another from those, Arthur says.

The reciprocity conjecture connects to the work of Alexander Grothendieck, famous for his research in algebraic geometry, including his prediction of motives. I think Grothendieck chose the word [motive] because he saw it as a mathematical analogue of motifs that you have in art, music or literature: hidden ideas that are not explicitly made clear in the art, but things that are behind it that somehow govern how it all fits together, Arthur says.

The reciprocity conjecture supposes these motives come from a different type of analytical mathematical object discovered by Langlands called automorphic representations, Arthur notes. Automorphic representation is just a buzzword for the objects that satisfy analogues of the Schrdinger equation from quantum physics, he adds. The Schrdinger equation predicts the likelihood of finding a particle in a certain state.

The second important conjecture is the functoriality conjecture, also simply called functoriality. It involves classifying number fields. Imagine starting with an equation of one variable whose coefficients are integerssuch as x2 + 2x + 3 = 0and looking for the roots of that equation. The conjecture predicts that the corresponding field will be the smallest field that you get by taking sums, products and rational number multiples of these roots, Arthur says.

With the original program, Langlands discovered a whole new world, Arthur says.

The offshoot, geometric Langlands, expanded the territory this mathematics covers. Rayan explains the different perspectives the original and geometric programs provide. Ordinary Langlands is a package of ideas, correspondences, dualities and observations about the world at a point, he says. Your world is going to be described by some sequence of relevant numbers. You can measure the temperature where you are; you could measure the strength of gravity at that point, he adds.

With the geometric program, however, your environment becomes more complex, with its own geometry. You are free to move about, collecting data at each point you visit. You might not be so concerned with the individual numbers but more how they are varying as you move around in your world, Rayan says. The data you gather are going to be influenced by the geometry, he says. Therefore, the geometric program is essentially replacing numbers with functions.

Number theory and representation theory are connected by the geometric Langlands program. Broadly speaking, representation theory is the study of symmetries in mathematics, says Chris Elliott, a mathematician at the University of Massachusetts Amherst.

Using geometric tools and ideas, geometric representation theory expands mathematicians understanding of abstract notions connected to symmetry, Elliot notes. That area of representation theory is where the geometric Langlands program lives, he says.

The geometric program has already been linked to physics, foreshadowing possible connections to other scientific fields.

In 2018 Kazuki Ikeda, a postdoctoral researcher in Rayans group, published a Journal of Mathematical Physics study that he says is connected to an electromagnetic duality that is a long-known concept in physics and that is seen in error-correcting codes in quantum computers, for instance. Ikeda says his results were the first in the world to suggest that the Langlands program is an extremely important and powerful concept that can be applied not only to mathematics but also to condensed-matter physicsthe study of substances in their solid stateand quantum computation.

Connections between condensed-matter physics and the geometric program have recently strengthened, according to Rayan. In the last year the stage has been set with various kinds of investigations, he says, including his own work involving the use of algebraic geometry and number theory in the context of quantum matter.

Other work established links between the geometric program and high-energy physics. In 2007 Anton Kapustin, a theoretical physicist at the California Institute of Technology, and Edward Witten, a mathematical and theoretical physicist at the Institute for Advanced Study, published what Rayan calls a beautiful landmark paper that paved the way for an active life for geometric Langlands in theoretical high-energy physics. In the paper, Kapustin and Witten wrote that they aimed to show how this program can be understood as a chapter in quantum field theory.

Elliott notes that viewing quantum field theory from a mathematical perspective can help glean new information about the structures that are foundational to it. For instance, Langlands may help physicists devise theories for worlds with different numbers of dimensions than our own.

Besides the geometric program, the original Langlands program is also thought to be fundamental to physics, Arthur says. But exploring that connection may require first finding an overarching theory that links the original and geometric programs, he says.

The reaches of these programs may not stop at math and physics. I believe, without a doubt, that [they] have interpretations across science, Rayan says. The condensed-matter part of the story will lead naturally to forays into chemistry. Furthermore, he adds, pure mathematics always makes its way into every other area of science. Its only a matter of time.

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The Evolving Quest for a Grand Unified Theory of Mathematics - Scientific American

Fidel Moreno thought he was teaching his students until one of them gave him a lesson about the world of coffee roasting.

SAN ANTONIO About eight years ago, Fidel Moreno took an unexpected deep dive into the world of coffee. It all started with a student, Mohammed "Mo" Alawalla, who noticed his daily coffee habit and led Moreno to creating a small business called Quantum Coffee Roasters on the northwest side.

"(He) noticed that I would drink coffee every morning. And little did I know that he was already roasting his own coffee," Moreno said. "And he gave me about a pound of the coffee that he had roasted. And I will admit that I tasted it at first. And I really didn't care for it because it wasn't my typical commercial brand."

But the Clark High School physics teacher didn't want to waste it, so he powered through finishing the bag. He couldn't believe what would happen next.

"I went back to my original choice and really noticed the difference between coffees. There's an entire world of flavors and notes that you can pick up with really good quality coffee," he said.

Moreno started experimenting roasting out of his kitchen and then sharing his concoctions with friends. The idea of starting up a small family business kept percolating and finally evolved into a brick-and-mortar location at "Just the Drip" (located at the Point Park and Eats on Boerne Stage Road west of I-10). Moreno's daughter and son, both college students, keep the business going along with along wife, who is also a teacher.

A few months ago, Moreno's coffee caught the attention of Food Network star and chef Alton Brown, who posted a picture of him trying out Moreno's coffee when he visited San Antonio.

The name of Moreno's family business connects his passion for physics and love for quality coffee.

"The name Quantum (represents) that next level, kind of like what quantum physics is, is that next level of physics that is, you know, just being discovered that next level of coffee that we provide to people that you really can't get anywhere else," Moreno said. "We have some single-origin coffees that nobody else in the country has. So that's pretty much what we have in hopes for quantum coffee."

Quantum Coffee Roasters recently started experimenting with a popular option for coffee drinkers on the go. It was a decision Moreno weighed heavily.

Moreno was worried about the environmental impact of selling K-cup pods since the foil lids are not recyclable. So being a science teacher, he hypothesized he knew there had to be a more eco-friendly solution.

After lots of research, he found ones that can be 100% recycled by rinsing the grounds out and tossing the entire pod into the recycle bin.

"We've got coffees from everywhere anywhere from South America, Central America to African coffees... We get things from Kenya. We get things from Ethiopia, Colombia, Nicaragua, but pretty much anywhere that produces coffee," Moreno added.

The business is doing so well, that Moreno just ordered his third roaster machine, which is much larger than his current one, and is about to move to a location next door.

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Meet the science teacher behind Quantum Coffee Roasters - KENS5.com