Red Rocks and the Two Body Problem

Roxborough State Park, Colorado (Nov 16, 2013)

There are only two problems in physics that we know how to solve: the pendulum and the planetary orbits. Everything else is calculated either by assuming that behaves like one of the two problems above, or by solving in some approximate way more complicated equations using a calculating device.

The difference between the physics of a pendulum and the one of a planet orbiting the Sun is in the relationship between the force and the distance. In the case of the pendulum there is an attractive force that doubles every time the distance double from the center of the oscillation. Galileo figured that out by looking at the chandeliers swinging in the Cathedral of Pisa. In the case of a planet orbiting the Sun the force on the planet decreases as the square of the distance from the Sun. Double the distance and the force will become one fourth. This was understood by Newton, which also had the epiphany that an apple falling towards the center of Earth would feel the same kind of force as a planet continually falling around the Sun. That's why the theory of gravitation is universal: applies to apples as well as planets.

The rest of physics can generally be approximated as one of these two basic problems. The motion of the atoms in a solid crystal? Nothing else than masses connected by springs; and springs also produce a force proportional to the displacement, making the crystal vibrate like a coupled pendulum. This generalized problem is called "harmonic oscillator". Charges into an electric field? The electric force also goes like the inverse square of distance: exactly like gravity (the only complication is that it can be either attractive or repulsive depending on the sign of the charges). The generalized problem of two masses subjected to a reciprocal force going like the inverse square of distance is called "two body problem". If the masses were three it would be a "three body problem". Four masses? You get it... it keeps going until you get the generic "n-body problem".  The kicker is that we only have an exact solution (the one found by Newton) for the two body problem: higher order problems can only be solved numerically, using a computer. Even worse, for a three (or more) body problem the solution is chaotic: this is a mathematical term that means that even an infinitesimal small change in the initial conditions will cause an unpredictable effect to the solution. You don't believe me? Look at this flash applet that simulates the orbit of one planet (the third body) around two stars.

Roxborough State Park

At this point you may ask what the two body problem has to do with red rocks in Colorado. As it turned out, last time we visited Colorado we met with some friends that work in the University there. Both scientists, a physicist and an astronomer, like Mayli and me. Academic couples are quite common, considering that people tend to pair with the people they socialize with. When you are in graduate school with other future scientists... well these are the people you tend to hook-up. This is all good until you graduate and look for a job. That's when your situation becomes a "two body problem".

Two body problems are not unique to academia, but the difficulty to find two academic positions within commuting distance makes them particularly difficult to solve. A recent article on Scientific American reports the results of a survey of two body problems in and out academia. The results? The large majority of the respondent (90%) said that they either had or think they will have to face a two body problem in the future. Of those that have already found the problem, less than half managed to negotiate a double position to solve it. The others? Either one of them had to leave a dream job to accommodate the career of the spouse, or they accepted to live at a non-commuting distance, with divorce or split-up as most common long term outcome.

Depressing? Well, if you have followed what I have written above, the two body problem (the physics version) is in principle solvable without recourse to chaos. There is hope. We got lucky, and after one failed attempt and two years of separation (Mayli in Chicago while I was still in Boston) we managed to get two positions in the same university. It was not easy, and every case is different, but I know many other couples that have found similar arrangements. What typically works best are mid-sized universities: top University can pick whatever faculty they need, and may not care enough to try creating a spousal accommodation. Too small places may not have the resources to find a solution. It also depends on the culture of the university. In our case we could count on funds that were explicitly set aside for this kind of situations: many university have come to the realization that the two body problems is actually a two body opportunity, a way to attract better candidates by offering a very special perk that fancier institutions would not even dream to contemplate.

Roxborough State Park, Colorado (Nov 16, 2013)

The Diaspora of the Italian Astronomers

The Loch, Rocky Mountain National Park, Colorado (May 29, 2003)

It takes about two hours to get from The Denver International Airport to Estes Park, in the heart of the Rocky Mountain National Park. It actually takes less than that, in normal circumstances, if you rent a car and drive up on Interstate 25, and then west on Route 66. That's the smart choice that avoids Boulder, and saves time. But when I went there I was a postdoctoral fellow on a budget, going to a conference on the Astrophysics of Dust. I took the bus.

In case you wonder, yeah there is plenty of dust in space. Mostly, is in the form of fine microscopic particles of sooth or quartz-like material, and fills the interstellar space. Near stars, though, it concentrates in larger particles. The ones that make shooting stars when falling on Earth. Some are even bigger, much bigger. Like asteroids. Some are humongous, like the one you are sitting on at precisely this moment. Planetary size dust grains. This is all stardust: blown out from stars as they die.

The bust was actually chartered by the conference organizers, and as such it was full of astronomers. It was an international conference, so the astronomers were arriving from all over the world. I must really look italian, though, because I didn't even have time to set my bag in the rack that I saw somebody pointing to the seat next to mine, saying: "'che è libero questo posto?". This inevitably proved that my nationality had been discovered, and that of all possible astronomers on the bus, the one that was going to sit next to me for the two hours trip was another italian.

Finding another italian astronomer in the US is not that rare. The diaspora of italian scientists, and astronomers in particular, is a well known fact. Italy has an excellent and free educational system, producing first class scientists at a much higher rate that it can absorb. Well, the production rate is maybe not that high: the problem is on the low employment rate side of the equation. Italy invests in science less than 1.3% of its Gross Domestic Product, which is well below the world average, and less than half than the US (2.8% of GDP). Italian scientists (and a lot of astronomers among them) get their education and leave to sunnier pastures: many try to stay in Europe (France and Germany the preferred destinations) but US is also a favorite place to go. Of all my classmates in graduate schools, none remained in Italy: three of us are in the US, one in Switzerland, the last one went back to his native China. He is the one that had the most successful career.

A not-italian ground squirrel

Of the foreign contingent in my old institution (the Harvard-Smithsonian Center for Astrophysics) the largest community is the italian one. That is particularly true in the high energy division, the realm of X-ray astronomy. The italian dominance is not surprising, because the division was funded by Riccardo Giacconi, the italian X-ray astronomy pioneer that won the Nobel prize in 2002. It was not difficult to find italians at CfA. Among them Cesare, a true "toscanaccio". An excellent guy, always with strong and astute opinions, and colorful ways to express them, as typical in the people from the region of Dante. I remember that he was very unhappy with his run-of-the-mill Windows laptop (he didn't like Bill Gates too much) and wanted to install Linux on it to "stick it to the man". We spent hours to coerce that poor computer to run what at the time was a "rebel" operating system until we managed to have everything working properly, including the internet and Netscape (yes I am that old). Then he returned to Italy. I later learned that when he got home to Florence he sat at the dinner table with a large bowl of soup and the computer in front of him. Ready to finally browse the web without the tyranny of Internet Explorer. It didn't last long: as soon as the first page was slowly loading at dialup speed he got so excited that he bumped into the bowl, all the soup launched at orbital speed to fall back right on the laptop, seeping inside the keyword with fizzling sounds. Despite heroic efforts, the computer was pronounced dead by the time it was brought at the repair store. It is said that Cesare took it quite well, given the circumstances: "it could have been worse" it is believed he said; "instead of soup, it could have been wine".

PS: it turns out that my italian companion on the bus to Estes Park was nobody else than the old thesis advisor of Cesare. We spent the whole trip bitching about how americans do everything wrong (that's another trait of toscanacci, explaining how "everything is wrong and needs to be done over". All in a very strong tuscan accent, totally impenetrable to any english-speaking passenger on the bus (thankfully). The photos were taken after the conference ended: I stayed a few more days to hike in the beautiful rockies and try out my first DSRL. These are the first photos I took with my Nikon D100 camera, that served me well for many years since.

View from Estes Park, Colorado (May 28, 2003)

Cosmological Inflation

From the summit of Mount Hopkins, Arizona (February 5, 2007)

Tomorrow (Monday) a major press conference is scheduled in the main auditorium of my old institution, the Harvard-Smithsonian Center for Astrophysics. It is widely rumored that the event will concern ground-breaking results from the BICEP2 experiment. Ok, so... what will this be all about?

It is a long story, going back all the way to the birth of the Universe, 13.82 billions years ago. That's the time when the Universe was born, starting from a very dense and hot state where radiation and matter were coupled together in a very thick soup. As the universe aged, it expanded. As it stretched, it cooled. Almost 380,000 years later, the Universe became cold enough to form the first atoms in a process that we call recombination. That was a momentous change: at recombination, when most charged particles condensed into forming hydrogen and helium atoms, light was suddenly free to move around without being continuously absorbed. The Universe suddenly became transparent to the electromagnetic radiation.

After recombination, the Universe entered an era dominated by matter, that still lasts today. The newly formed atoms, helped by other mysterious neutral particles that we call dark matter, were pulled together by the force of gravity to form the first galaxies, then the first stars (let there be light), then planets and life as we know it. The primordial light, liberated by the yoke of matter, started to freely move around the Universe, stretched by the expansion of the Cosmos like a long forgotten echo in an enormous cathedral. This faint echo formed billions of years ago was accidentally found by Arno Penzias and Robert Wilson, two physicists working on a prototype microwave antenna built at the Bell Labs in New Jersey. This echo is what we call the Cosmic Microwave Background Radiation (CMBR).

A nice property of the CMBR is that it is exactly the same, anywhere you look in the sky. That should not be a surprise: the background radiation was generated by the cosmic soup at the time of recombination, when the Universe had expanded to a specific density and temperature. If the Universe was homogeneous and isotropic at that time, the CMBR should reflect that. Small anisotropies (less than 1 part in 100,000) are still found in the CMBR, the consequence of small statistical fluctuations in the distribution of the hot gas that emerged from the primordial soup. These fluctuations, that acted as seeds for the gravitational collapse from which galaxies formed, are the holy grail to understand the details of the Universe expansion and to measure its fundamental parameters. The 13.8 billion years age of the Universe I mentioned above, for example, was determined by the European Space Agency and NASA Planck telescope, precisely by measuring the CMBR fluctuations from space.

Tucson, Arizona

The extreme isotropy of the CMBR, however, is also a huge problem. When we measure the background radiation from opposite directions in the sky, we are observing light that traveled, at the speed of light, for almost 14 billions years (from the time of recombination) until it reached us. Since the CMBR looks identical in these two opposite directions, the thermostat of the primordial soup in these two opposite areas of the Universe must have been set at exactly the same temperature. For this to happen, the two regions must have been able to communicate one with the other, in order to agree on their common temperature set point. This is a problem, because any form of physical communication is limited by the speed of light, and these two regions are now almost 2 x 14 = 28 billion light-years apart. Any communication among them would require a time twice the age of the Universe. In other words, the CMBR coming from opposite regions in the sky was produced by parts of the Cosmos that after the Big Bang somehow managed to get separated from any possible causal connection, incapable of communicating the common temperature that is however apparent in the CMBR. How could that be?

The solution to this paradox was proposed in 1980 by Alan Guth, a physicist at Cornell University (and now at MIT). Guth proposed that shortly after the Big Bang (0.0000000000000000000000000000000001 seconds after the Big Bang, to be precise) the Universe underwent a dramatic expansion, at a rate that left even light behind. This expansion "froze" the conditions in the primordial soup as space was stretched almost instantly by many orders of magnitude. Regions of the Universe that at the Big Bang were next to each other, capable to communicate within the limit of the speed of light, suddenly found themselves separated at distances where communication became impossible. Still they retained the common conditions from before this expansion, leading to identical temperatures when the CMBR was finally released. This process, which is analogous to a sudden phase transition like that of suddenly freezing supercooled water, is called inflation.

Inflation is a pillar of modern cosmology, yet it remains a very plausible, but not fully demonstrated, hypothesis. The detailed processes that caused this sudden expansion are largely undetermined, and many different models of inflation have been proposed to date. A direct proof that inflation existed, and a way to discriminate between these different models has so far eluded science. The most promising place to look for guidance, once more, is the CMBR itself.

Any process involving stretching and compressing space (like banging two very heavy masses together) leads to ripples in the space-time known as gravitational waves. Predicted by Einstein's Theory of General Relativity, gravitational waves have never been directly observed. We have however very strong indirect evidences of their existence. Binary pulsars are pairs of very heavy stellar remnants orbiting each other, that dissipate gravitational energy at the rate corresponding to their predicted production of gravitational waves. If gravitational waves do exists, they must have been produced in droves in such a cataclysmic event as the Big Bang, and must have been amplified even more at the time of inflation when space was stretched at an exponential rate. These primordial gravitational waves, propagating all the way to the time of recombination, must have left their own peculiar imprint in the CMBR, a trace that could have survived until today. This is what the BICEP2 experiment is about.

BICEP2 is a small telescope located at the South Pole, designed to measure with great sensitivity the intensity and polarization of the small fluctuations in the CMBR. The polarization of the CMBR is the key to find the footprints of inflation in the background radiation: the so-called polarization B-mode is a unique orientation in the CMBR light that could have only resulted from the perturbation of the primordial gravitational waves as they crossed the cosmological soup emerging from recombination. It is a unique feature that would prove the occurrence of inflation, at the same time restricting the number of possible inflation models. The detection of a signal in the B-mode polarization of the CMBR would be a Nobel-prize discovery, and open the door for studying the unknown physics that happened at the very first instants after the Big Bang.

For more details, tune-in to the Center for Astrophysics press release web site at 12PM EDT Monday, when the press conference will start. A nice article about the discovery with more details about the CMBR B-mode polarization is also available on the Sky and Telescope magazine.

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Today's photos have nothing to do with BICEP2 and the CMBR. The telescope responsible for the discovery is at the South Pole, and unfortunately I have never been there. The main photo above, however, is yet another view from the road to the summit of Mount Hopkins, where the MMT telescope is located. The view is looking south-west towards Mexico. The small image on the left, and the image below are instead taken from a plane flying over southern Arizona. It is indeed time to fly north, leaving the mountains of the US southwest, towards the rockies of Colorado. This will be the destination for the next photoblog post.

Snow-capped mountains in southern Arizona (January 19, 2005)

The Mickey Mouse Telescope

From the summit of Mount Hopkins, Arizona (December 14, 2005)

This is not another post about nocturnal mice visiting graduate student astronomers. This is about the naming of a telescope. The MMT telescope, to be precise, the large 6.5 meter mirror on top of Mount Hopkins, in southern Arizona.

The story of the MMT telescope starts many years ago. Since 1610, when Galileo Galilei first pointed a telescope to the sky, astronomers' needs have fueled an arm's race to build larger and larger telescopes. Big telescopes are doubly advantageous: they collect more light, allowing to see fainter and fainter objects, and have a larger magnification rate, making possible to see smaller details on larger distances. While Galileo's instrument had lenses, Isaac Newton was the first to realize that by using mirrors it was possible to fit the same telescope's power into smaller packages: multiple mirrors can be arranged to fold light more efficiently that a pairs of lenses. Furthermore, mirrors are cheaper to manufacture, and can be shaped and polished in much larger sizes than lenses. The invention of the newtonian telescope made possible the arm's race in modern astronomical instrumentation, culminating in the construction of the gigantic 200-inch (5.1 meter) "Hale" telescope at Mount Palomar. 

The big telescope at Palomar is a monster. Completed in 1948, it was the largest until 1976, when the Russian BTA-6 telescope with its 6.1 meter diameter mirror was completed. The Hale telescope is housed in a huge dome, 42 meters in diameter and 41 meters tall, which is about the same size as the dome of the Pantheon in Rome. The 200-inch mirror, 26 inch thick and weighting over 20 tons, was made in Pyrex (the kind of glass used for heat resistant cooking containers) by Corning, the same company making the iPhone "Gorilla glass". This was the largest mirror that could be effectively built and polished with the technology of the time: its Russian successor, while almost 1 meter larger in diameter, was plagued by imperfections, and never matched the effective performances of the large Hale telescope mirror. The problem with such large mirrors is that they need to be very thick not to break under their own weight, and the thicker they are, the heavier they get. All that weight requires an enormous structure to support it. The whole things needs then to be moved around, as the telescope points to different spots in the sky: as the telescope moves, the weight shifts, deforming the shape of the mirror and producing distorted images as it falls out of alignment.

The MMT dome

This was the state of business in the late 1960's, when astronomers at the Smithsonian Astrophysical Observatory in Cambridge, MA and at the University of Arizona in Tucson started to make plans for a new large telescope to be built at Mount Hopkins. They knew that casting a large mirror was not feasible, so they thought that they could build a larger telescope by assembling 6 smaller (1.8 meter diameter each) mirrors together on the same mount, and then combine their light together as if they were part of a single telescope with an effective area of a 4.5 meter diameter mirror. Thus in 1979 the Multiple Mirror Telescope (MMT) was born, at the time the third larger aperture telescope in the world, a technological testbed for the giant mirror telescopes of the future. Combining multiple mirrors was not the only design innovation attempted for the MMT: while traditional telescopes require huge domes so that the telescope can move to track the stars, the MMT fits snugly into its square dome. The MMT can only move up and down, and it is the entire building that rotates to enable tracking. This allowed to significantly reduce the construction costs of the project, and gave the telescope the same appearance of one of these model boats built inside a bottle.

The new MMT

The MMT was in service for almost 20 years, during which it was at the forefront of technological experimentation. Its success however, was also the cause of its downfall. By the 1990s astronomers became so proficient in phasing together many small mirrors, that it became feasible to build gigantic segmented mirrors made by many smaller hexagonal pieces.  In 1993 the first of the twin Keck telescopes (36 segments to form a 10 meter diameter mirror) started doing science observations from the top of Mauna Kea in Hawaii. It was time for the MMT to be updated, but what to do? The solution came from the master telescope maker at the University of Arizona, Roger Angel. He decided to resurrect the single mirror design but, rather than trying to make the telescope stiffer, he proposed to embrace its floppiness to make a thin and light mirror, that could be easily deformed. A computerized system would then continuously measure the shape of the mirror, calculate in real time the distortions due to its shifting weights, and then restore the ideal optical shape by means of hydraulic actuators pushing the mirror from below. Such intelligent mirrors, called "active optics" are now standard in the construction of modern gigantic telescopes, whose mirror are often cast in the "mirror lab" located below University of Arizona football stadium. The cavernous space hosts the big spinning furnace where the special ultralight glass is fused, and then slowly cooled. Very slowly: it takes one year for each new mirror to cool without cracking. In this lab the new 6.5 meter diameter mirror for the refurbished MMT telescope was born, and the telescope was re-dedicated in the year 2000.

And this is where the famous cartoon mouse enters in this story. As the re-dedication ceremony was approaching, the officials at the Smithsonian and University of Arizona opened a contest to find a new name for the telescope. The rule was that the new name should still initial as M, M and T to preserve the same acronym. The most obvious choice was the "Mono Mirror Telescope", which however was considered silly because most telescopes, at the time, were still made with a single primary mirror. So it was finally decided to call it the "new MMT" telescope, where MMT stands for, recursively, MMT, the name that the pioneering telescope had in its previous incarnation. Among the proposed names that didn't make it, however, there is my favorite: the Mickey Mouse Telescope, an irreverent idea that was rapidly abandoned after somebody started to worry about Disney and its layers.

Ridge Telescopes, FLWO, Arizona (December 14, 2005)

The 4am Mouse

FLWO Observatory, Arizona (December 14, 2005)

The 4am mouse came out every night, reliably on time. Everybody knew about the mouse: it was a celebrity in the close-knit circle of graduate students spending their nights at the FLWO 48-inch telescope. And the mouse knew about the students too: always munching something, while they were desperately trying to stay awake. Where there are students, there are plenty of crumbles to share.

The 4am mouse was one of the features of the smallest among the telescopes at the Fred Lawrence Whipple Observatory. Whippe was the revered scientist that discovered what comets really are: loose mixtures of ice and rocks that hurls through space leaving a trail of shooting stars and glowing ions. Dirty snowballs, he called them, that the sun makes pretty. I remember Fred, still working in his eighties at the central facility in Cambridge, never missing a Colloquium on Thursdays. Always climbing the stairs leaning on the side, to let young people pass in front of him. Because young people have a lot to do and should walk fast, he used to say.

View from Mt. Hopkins

The other feature of the telescope was its own dual-channel infrared camera. Designed to take images simultaneously at two different colors of light, it was equipped with two sensors: a "blue" channel tuned to recording (you guessed) bluer light, and a "red channel" capable to make images in redder light. Except that, since both channels were only sensitive to the invisible infrared (redder than red), these were more like the "black" and "blacker" channel, from the point of view of human sight. The problem with the camera was that it was moody. Every night, at about the same time the mouse got out of its hole, the blue channel stopped working. The first time it happened I panicked. Oh my, what did I do wrong? Did I break it? Should I call the support astronomer in Tucson, wake him up in the middle of the night, and tell him I screwed up? Then I remembered the manual: everything has manuals that nobody reads, and the solution of my problem was there, first line in the FAQ. Apparently it wasn't something I did, or the camera having a sudden attack of musophobia. It was just the "blue" channel being lonely. The solution spelled in the manual was to go to the telescope chamber, hug the big electronic box attached to the cryostat with the detectors, and the blue channel would mysteriously restart to work. Sometimes it just takes a spoonful of sugar.

As a graduate student, I spent many nights at the 48-inch telescope, its mouse and the marvin-esque camera with its blue-channel blues. It is a great telescope, simple enough for a student to use without the assistance of an operator. That's when a student learns more: when the camera gets moody and one has to troubleshoot its depression without the safety net of a "grownup" astronomer. Until recently, access to similar telescopes was offered to the community through the National Optical Astronomy Observatory: these facilities were essential for the training of students from small institutions, that do not have guaranteed access to private telescopes. With the funding cuts in last year's sequestration and the flat research budgets following the great recession, the National Science Fundation has however reviewed the portfolio of facilities that is capable to support. While this was necessary to allocate the funding for the new large telescopes of the future, it had the consequence of dramatically reducing the available "public" time on these same small telescopes which are the bread-and-butter for the training of graduate students. This will not affect large universities and organizations that have their "private" telescope time, but will be felt by the smaller institutions, increasing the gap between the "have" and "have not" in astronomical science.

Souther Arizona, view from Mt. Hopkins, FLWO (December 14, 2005)