Random thoughts about random subjects… From science to literature and between manga and watercolours, passing by data science and rugby; including film, physics and fiction, programming, pictures and puns.
In a new paper in the Journal of Mathematical Physics, Tim Netzer and Tom Drescher from the Department of Mathematics and Gemma De las Cuevas from the Department of Theoretical Physics have introduced the notion of the quantum magic square, which is a magic square but instead of numbers one puts in matrices.
This is a non-commutative, and thus quantum, generalization of a magic square. The authors show that quantum magic squares cannot be as easily characterized as their “classical” cousins. More precisely, quantum magic squares are not convex combinations of quantum permutation matrices. “They are richer and more complicated to understand,” explains Tom Drescher. “This is the general theme when generalizations to the non-commutative case are studied. Check out the paper!
I had intended to post this much ealier on, and certainly closer to the actual announcement of the Nobel Prizes in early October. It has however been a very busy period. Better late than never, right?
I was very pleased to see that the winners of the 2020 Nobel Prize in Physics were a group that combined the observational with the theoretical. Sir Roger Penrose, Reinhard Genzel, and Andrea Ghez are the recipients of the 2020 Nobel Prize in Physics. Penrose receives half the 10 million Swedish krona while Ghez and Genzel will share the other half.
Penrose’s work has taken the concept of black holes from the realm of speculation to a sound theoretical idea underpinning modern astrophysics. With the use of topology and general relativity, Penrose has provided us with an explanation to the collapse of matter due to gravity leading to the singularity at the centre of a black hole.
A few decades after the 1960’s work from Penrose we have Genzel and Ghez whose independent work using adaptive optics and speckle imaging enabled them to analyse the motion of stars tightly orbiting Sagittarius A*. Their work led to the conclusion that the only explanation for the radio source at the centre of the Milky Way’s was a black hole.
In 1916 Karl Schwarzwild described a solution to Einstein’s field equation for the curved spacetime around a mass of radius . Some terms in the solution either diverged or vanished for or . A couple of decades later, Oppenheimer and his student Hartland Snyder realised that the former value corresponded to the radius within which light, under the influence of gravity, would no longer be able to reach outside observers – the so called event horizon. Their work would need more than mathematical assumptions to be accepted.
By 1964 Penrose came up with topological picture of the gravitational collapse described and crucially doing so without the assumptions made by Oppenheimer and Snyder. His work required instead the idea of a trapped surface. In other words a 2D surface in which all light orthogonal to it converges. Penrose’s work showed that inside the event horizon, the radial direction becomes time-like. It is impossible to reverse out of the black hole and the implication is that all matter ends up at the singularity. Penrose’s research established black holes as plausible explanation for objets such s quasars and other active galactic nuclei.
Closer to Home
Although our own galaxy is by no means spewing energy like your average quasar, it still emits X-rays and other radio signals. Could it be that there is a black hole-like object at the heart of the Milky Way? This was a question that Genzel and Ghez would come to answer in time.
With the use of infrared (IR) spectroscopy, studies of gas clouds near the galactic centre showed rising velocities with decreasing distances to the centre, suggesting the presence of a massive, compact source of gravitation. These studies in the 1980s were not definitive but provided a tantalising possibility.
In the mid 1990s, both Genzel and Ghez set out to obtain better evidence with the help of large telescopes operating in the near-IR to detect photons escaping the galactic center. Genzel and colleagues began observing from Chile, whereas Ghez and her team from Hawaii.
Their independent development of speckle imaging, a technique that corrects for the distortions caused by Earth’s atmosphere enabled them to make the crucial observations. The technique improves the images by stacking a series of exposures, bringing the smeared light of individual stars into alignment. In 1997, both groups published their measurements stars movements strongly favouring the black hole explanation.
Further to that work, the use of adaptive optics by both laureates not only improved the resolutions obtained, but also provided the possibility of carrying out spectroscopic analyses which enabled them to get velocities in 3D and therefore obtain precise orbits.
The “star” object in this saga is the so-called S0-2 (Ghez’s group) or S2 (Genzel’s group) star. It approaches within about 17 light-hours of Sagittarius A* every 16 years in a highly elliptical orbit.
This is a reblog go the post in Physics Today, written by Andrew Grant.
The researchers are recognized for their contributions to theoretical cosmology and the study of extrasolar planets.
James Peebles, Michel Mayor, and Didier Queloz will receive the 2019 Nobel Prize in Physics for helping to understand our place in the universe through advances in theoretical cosmology and the detection of extrasolar planets, the Royal Swedish Academy of Sciences announced on Tuesday. Peebles is a theoretical cosmologist at Princeton University who helped predict and then interpret the cosmic microwave background (CMB) and later worked to integrate dark matter and dark energy into the cosmological framework. Mayor and Queloz are observational astronomers at the University of Geneva who in 1995 discovered 51 Pegasi b, the first known exoplanet to orbit a Sunlike star. Peebles will receive half of the 9 million Swedish krona (roughly $900 000) prize; Mayor and Queloz (who also has an appointment at the University of Cambridge) will share the other half.
The contributions of Peebles and of Mayor and Queloz helped jumpstart their respective fields. Over the past few decades, researchers have developed the successful standard model of cosmology, Lambda CDM, though the nature of both dark energy and dark matter remains an open question. Meanwhile, astronomers have used the radial velocity technique employed by Mayor and Queloz, along with the transit method and even direct imaging, to discover and characterize a diverse population of thousands of exoplanets. Data from NASA’s Kepler telescope suggest that the Milky Way harbors more planets than stars.
Connecting past with present
“More than any other person,” writes Caltech theoretical physicist Sean Carroll on Twitter, Peebles “made physical cosmology into a quantitative science.” His contributions began even before Arno Penzias and Robert Wilson’s 20-foot antenna at Bell Labs picked up the unexpected hum of 7.35 cm microwave noise that would come to be known as the CMB. Working as a postdoc with Robert Dicke at Princeton, Peebles predicted in a 1965 paper that the remnant radiation from a hot Big Bang, after eons of propagating through an expanding universe, would have a temperature of about 10 K. In a subsequent paper Peebles connected the temperature of the CMB, measured by Penzias and Wilson at 3.5 K (now known to be 2.7 K), to the density of matter in the early universe and the formation of light elements such as helium.
In 1970 Peebles and graduate student Jer Yu predicted a set of temperature fluctuations imprinted in the CMB due to the propagation of acoustic waves in the hot plasma of the infant universe. Decades later, the Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and, most recently, the Planck satellite would measure a similar power spectrum in the CMB. “The theoretical framework that he helped create made testable predictions,” says Priyamvada Natarajan, a Yale theoretical astrophysicist. “They still inform a lot of the observational tests of cosmology.”
Peebles also considered the connection between those fluctuations and the large-scale structure of the universe we observe today, as measured through galaxy clusters in sky surveys. “His idea that you can see the initial conditions and dynamics of the universe in the clustering of galaxies transformed what we could do as a community,” says New York University astrophysicist David W. Hogg.
Peebles’s view of the CMB and what it embodies proved especially important in the early 1980s, when cosmologists struggled to reconcile the deduced densities of matter in the infant universe with the large-scale structure that ultimately emerged. In a 1982 paper, Peebles proposed a solution in the form of nonrelativistic dark matter. Long after escaping the dense confines of the infant cosmos, that cold dark matter (CDM) would form the cocoons in which ordinary matter clumped into galaxies and then galaxy clusters. His paper built on the work of Vera Rubin, whose measurements with Kent Ford of the rotation curves of the Andromeda galaxy were critical toward demonstrating that dark matter must be the dominant component of galactic halos, to keep disks of stars and gas from flying apart. Subsequent satellite measurements have revealed that collectively dark matter has about five times the mass of ordinary matter.
By the 1990s it was becoming clear that a model containing just CDM, ordinary matter, and photons couldn’t account for all the observed properties of the universe, notably the value of the Hubble constant. The result is Lambda CDM, the cosmological model that describes the universe with six precisely measured parameters and accounts for the 1998 discovery that the universe’s expansion is accelerating. Peebles was one of the theorists to propose resurrecting Albert Einstein’s once-discarded cosmological constant to describe the newly discovered dark energy, which makes up more than two-thirds of the mass–energy content of the universe.
Ushering in the exoplanet era
To appreciate the contribution of Mayor and Queloz, consider that in 1995 the least massive known object outside the solar system was a star of 0.08 solar masses; Jupiter, for comparison, is about 0.001 M☉. Mayor was part of a team that in 1989 reported the probable detection of an object 11 times as massive as Jupiter that could be classified as either a very large planet or a brown dwarf. Pennsylvania State University astronomer Jason Wright says that other teams amassed preliminary evidence of extrasolar planets, but it was unconvincing and led planetary scientist William Cochran to declare, “Thou shalt not embarrass thyself and thy colleagues by claiming false planets.”
In 1992 Alexander Wolszczan and his colleagues discovered two planets orbiting the pulsar PSR B1257+12 via timing variations in the dead star’s radio beacon. (A third later found around the same pulsar remains the lowest-mass exoplanet yet discovered.) The discovery showed that exoplanets are out there, but the question remained of how common they are around stars like the Sun, where well-placed ones would presumably have the potential to support life.
At the Haute-Provence Observatory in southeastern France, Mayor and his graduate student Queloz conducted a survey of 142 stars using a spectrograph called ELODIE, which they designed to enable the observation of fainter stars than had previously been surveyed. The researchers’ approach, first proposed in 1952 by Otto Struve, was to detect the Doppler shift in the stellar spectrum due to the star’s motion as it is pushed and pulled by an orbiting planet. The expected stellar wobble due to a planet’s tug was on the order of 10 m/s; even now, the best spectrometers have a resolution of about 1000 m/s, Hogg says. Mayor and Queloz needed to be able to pinpoint a shift that accounted for a hundredth, or even a thousandth, of a pixel.
That’s exactly what they did through analysis of the signal from 51 Pegasi, a star located about 50 light-years away in the constellation Pegasus. The Doppler shift was consistent with the motion of a Jupiter-mass planet in a four-day orbit at 0.05 astronomical units, far shorter than the distance between Mercury and the Sun. The discovery of a “hot Jupiter” was surprising but also helpful, as the short period enabled Mayor and Queloz, and competing groups, to easily conduct follow-up observations. The astronomers announced their discovery at a conference in Italy almost exactly 24 years ago, on 6 October 1995, and soon published their result in Nature. Another group promptly confirmed the finding.
“It’s a discovery that has completely changed our view of who we are,” says Yale University astronomer Debra Fischer. “And it came at a time when we thought that maybe there weren’t many planets around other stars.”
However, the astronomy community wasn’t yet convinced by Mayor and Queloz’s claim. Many researchers didn’t think it was possible for such a massive planet to either form so close to the star or migrate inward without getting incinerated. Theorists proposed that the observed stellar wobbles might not be caused by an exoplanet at all, but rather by phenomena such as stellar brightness oscillations. But even the most skeptical came around in 1999, with discoveries of the first multi-exoplanet system by Fischer and colleagues, and of HD 209548 b. That planet was detected via the drop in brightness it caused when it passed in front of its star.
The early planet confirmations convinced observatory directors to build and install spectrographs. They also ultimately helped coax NASA to greenlight the development of a space telescope proposal that had been languishing for decades, a mission called Kepler. That satellite, which was launched in 2009, and instruments such as the Transiting Exoplanet Survey Satellite have detected thousands of planets and planet candidates.
Nearly a quarter century after Mayor and Queloz’s discovery, exoplanet science is a powerhouse endeavor that engages a significant percentage of the astrophysics community. Researchers join the field to study not only the planets but also the stars they orbit, which in turn has led to new insights in stellar astrophysics. By pairing transit measurements, which determine planets’ radii, with radial velocity, which provides masses, researchers have determined that many of the galaxy’s planets don’t resemble those in our solar system. The lack of resemblance challenges theories of planet formation and extends the range of planetary types that theories have to accommodate.
The most tantalizing goal of the field set in motion by Mayor and Queloz is to find planets that resemble Earth and to detect biosignatures. Researchers are already probing the atmospheres of individual worlds using the Hubble Space Telescope and other tools. Next-generation instruments, particularly the James Webb Space Telescope and the Wide Field Infrared Survey Telescope, will aid in that effort.
It was great to have been able to attend a lecture at the new home of the Institute of Physics. I have been a member for almost two decades and I have even served as an officer for one of the interest groups, the Computational Physics Group is you must know.
The event was a talk by Stephen Hilton from the School of Pharmacy, UCL 3D Printing and its Application in Chemistry and Pharmacy. It was a very useful talk covering applications ranging from teaching, cost saving in chemistry labs, personalised medicine and chemistry itself.
As for the building, it was nice to finally see the end result, with a hint of brutalist architecture and some nice details such as the electromagnetic wave diagram in some of the windows, and Orion in the cealing!
Although Bose-Einstein condensation has been observed in several systems, the limits of the phenomenon need to be pushed further: to faster timescales, higher temperatures, and smaller sizes. The easier creating these condensates gets, the more exciting routes open for new technological applications. New light sources, for example, could be extremely small in size and allow fast information processing.
In experiments by Aalto researchers, the condensed particles were mixtures of light and electrons in motion in gold nanorods arranged into a periodic array. Unlike most previous Bose-Einstein condensates created experimentally, the new condensate does not need to be cooled down to temperatures near absolute zero. Because the particles are mostly light, the condensation could be induced in room temperature.
‘The gold nanoparticle array is easy to create with modern nanofabrication methods. Near the nanorods, light can be focused into tiny volumes, even below the wavelength of light in vacuum. These features offer interesting prospects for fundamental studies and applications of the new condensate,’ says Academy Professor Päivi Törmä.
The main hurdle in acquiring proof of the new kind of condensate is that it comes into being extremely quickly.’According to our theoretical calculations, the condensate forms in only a picosecond,’ says doctoral student Antti Moilanen. ‘How could we ever verify the existence of something that only lasts one trillionth of a second?’
Turning distance into time
A key idea was to initiate the condensation process with a kick so that the particles forming the condensate would start to move.
‘As the condensate takes form, it will emit light throughout the gold nanorod array. By observing the light, we can monitor how the condensation proceeds in time. This is how we can turn distance into time,’ explains staff scientist Tommi Hakala.
The light that the condensate emits is similar to laser light. ‘We can alter the distance between each nanorod to control whether Bose-Einstein condensation or the formation of ordinary laser light occurs. The two are closely related phenomena, and being able to distinguish between them is crucial for fundamental research. They also promise different kinds of technological applications,’ explains Professor Törmä.
Both lasing and Bose-Einstein condensation provide bright beams, but the coherences of the light they offer have different properties. These, in turn, affect the ways the light can be tuned to meet the requirements of a specific application. The new condensate can produce light pulses that are extremely short and may offer faster speeds for information processing and imaging applications. Academy Professor Törmä has already obtained a Proof of Concept grant from the European Research Council to explore such prospects.
1 Tommi K. Hakala, Antti J. Moilanen, Aaro I. Väkeväinen, Rui Guo, Jani-Petri Martikainen, Konstantinos S. Daskalakis, Heikki T. Rekola, Aleksi Julku, Päivi Törmä. Bose–Einstein condensation in a plasmonic lattice. Nature Physics, 2018; DOI: 10.1038/s41567-018-0109-9
New quantum method generates really random numbers
Researchers at the National Institute of Standards and Technology (NIST) have developed a method for generating numbers guaranteed to be random by quantum mechanics. Described in the April 12 issue of Nature, the experimental technique surpasses all previous methods for ensuring the unpredictability of its random numbers and may enhance security and trust in cryptographic systems.
The new NIST method generates digital bits (1s and 0s) with photons, or particles of light, using data generated in an improved version of a landmark 2015 NIST physics experiment. That experiment showed conclusively that what Einstein derided as “spooky action at a distance” is real. In the new work, researchers process the spooky output to certify and quantify the randomness available in the data and generate a string of much more random bits.
Random numbers are used hundreds of billions of times a day to encrypt data in electronic networks. But these numbers are not certifiably random in an absolute sense. That’s because they are generated by software formulas or physical devices whose supposedly random output could be undermined by factors such as predictable sources of noise. Running statistical tests can help, but no statistical test on the output alone can absolutely guarantee that the output was unpredictable, especially if an adversary has tampered with the device.
“It’s hard to guarantee that a given classical source is really unpredictable,” NIST mathematician Peter Bierhorst said. “Our quantum source and protocol is like a fail-safe. We’re sure that no one can predict our numbers.”
“Something like a coin flip may seem random, but its outcome could be predicted if one could see the exact path of the coin as it tumbles. Quantum randomness, on the other hand, is real randomness. We’re very sure we’re seeing quantum randomness because only a quantum system could produce these statistical correlations between our measurement choices and outcomes.”
The new quantum-based method is part of an ongoing effort to enhance NIST’s public randomness beacon, which broadcasts random bits for applications such as secure multiparty computation. The NIST beacon currently relies on commercial sources.
Quantum mechanics provides a superior source of randomness because measurements of some quantum particles (those in a “superposition” of both 0 and 1 at the same time) have fundamentally unpredictable results. Researchers can easily measure a quantum system. But it’s hard to prove that measurements are being made of a quantum system and not a classical system in disguise.
In NIST’s experiment, that proof comes from observing the spooky quantum correlations between pairs of distant photons while closing the “loopholes” that might otherwise allow non-random bits to appear to be random. For example, the two measurement stations are positioned too far apart to allow hidden communications between them; by the laws of physics any such exchanges would be limited to the speed of light.
Random numbers are generated in two steps. First, the spooky action experiment generates a long string of bits through a “Bell test,” in which researchers measure correlations between the properties of the pairs of photons. The timing of the measurements ensures that the correlations cannot be explained by classical processes such as pre-existing conditions or exchanges of information at, or slower than, the speed of light. Statistical tests of the correlations demonstrate that quantum mechanics is at work, and these data allow the researchers to quantify the amount of randomness present in the long string of bits.
That randomness may be spread very thin throughout the long string of bits. For example, nearly every bit might be 0 with only a few being 1. To obtain a short, uniform string with concentrated randomness such that each bit has a 50/50 chance of being 0 or 1, a second step called “extraction” is performed. NIST researchers developed software to process the Bell test data into a shorter string of bits that are nearly uniform; that is, with 0s and 1s equally likely. The full process requires the input of two independent strings of random bits to select measurement settings for the Bell tests and to “seed” the software to help extract the randomness from the original data. NIST researchers used a conventional random number generator to generate these input strings.
From 55,110,210 trials of the Bell test, each of which produces two bits, researchers extracted 1,024 bits certified to be uniform to within one trillionth of 1 percent.
“A perfect coin toss would be uniform, and we made 1,024 bits almost perfectly uniform, each extremely close to equally likely to be 0 or 1,” Bierhorst said.
Other researchers have previously used Bell tests to generate random numbers, but the NIST method is the first to use a loophole-free Bell test and to process the resulting data through extraction. Extractors and seeds are already used in classical random number generators; in fact, random seeds are essential in computer security and can be used as encryption keys.
In the new NIST method, the final numbers are certified to be random even if the measurement settings and seed are publicly known; the only requirement is that the Bell test experiment be physically isolated from customers and hackers. “The idea is you get something better out (private randomness) than what you put in (public randomness),” Bierhorst said.
Peter Bierhorst, Emanuel Knill, Scott Glancy, Yanbao Zhang, Alan Mink, Stephen Jordan, Andrea Rommal, Yi-Kai Liu, Bradley Christensen, Sae Woo Nam, Martin J. Stevens, Lynden K. Shalm. Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals. Nature, 2018 DOI: 10.1038/s41586-018-0019-0