Gravitational waves, the man behind them, and two of the deepest puzzles confronting humanity

As we rightly celebrate the amazing discovery of gravitational waves announced yesterday amidst much fanfare, it’s critical to recognize the work of a stunning diversity of scientists, engineers, technicians and yes, even politicians, who poured forth sweat, toil and tears over more than twenty years to bring to fruition a measurement of almost unimaginable precision and sensitivity. Few quantities were ever unearthed from the soul of the universe with more care and patience.

And yet it’s equally paramount to step back for a moment and yet again stand in awe of the man who started it all and appreciate what exactly he did. Almost a hundred years ago Einstein put the finishing touches on his so-called field equations which described gravity in terms of the curvature of spacetime. It's an equation which can easily fit on a handkerchief, and yet one whose scope extends over a range of scales which beggars belief, from right here outside earth to the swirling dance of black holes to the entire large-scale structure of the universe. Even as they sat quietly in our textbooks and on our blackboards, those few symbols were orchestrating the workings of planets, galaxies and nebulae like a conductor wielding a baton whose length stretched across the entire universe.

Millions of man hours since 1915 have been spent in verifying, testing, extending and stretching every single aspect of those few scribbles, in bringing the accumulated wisdom of two thousand years of building machines and manipulating equations to bear on fulfilling one man’s amazing flights of fancy down to sixteen decimal places. Every one of those hours has validated that man and his fellow human beings’ dreams beyond any reasonable doubt. A rider on a light beam, a flash of awesome insight, a stroke of the pen and suddenly, a key that opened the door to an entire hidden reality filled with hitherto unimaginable wonders, some of which even the maker of that key did not believe in – black holes, neutron stars, gamma ray bursts, gravitational waves.

The grand challenge before us now is twofold. The first, longstanding one is to understand how it can possibly be that those few squiggles on a handkerchief describe not only the world that we know but the imagined future that will impinge on our collective consciousness for years to come; it is to figure out what Einstein’s contemporary Eugene Wigner called “the unreasonable effectiveness of mathematics in the physical sciences” (a phrase which must be one of the great understatements of all time). The fact that someone like Einstein can figure out what’s happening around a black hole - an object whose existence he wasn’t even aware of - by writing a few things on a blackboard or a piece of paper should give us all goosebumps.

The second challenge asks us to explain something equally amazing: how it is possible that a three-pound mass of blood, flesh and electrochemical impulses can divine those squiggles by pure thought; it is what Francis Crick called “the astonishing hypothesis”. The fact that a diminutive object composed of nothing more than the exact same atoms that constitute chairs, trees and air can evolve through random changes over billions of years and be housed in an entity which can then sit down and write down equations deciphering the symphony of the stars should also give us goosebumps.

Answering these two challenges will take all the combined wisdom and intuition that we have gained during two thousand years of scientific and technical exploration, along with completely new kinds of thinking that we can’t even imagine yet. For me these twin challenges are what make our continued existence over the next few millennia seem worthwhile. They are what make my spine tingle.

As for Einstein himself, if we had told him that we were still verifying his predictions one hundred years after he made them, I suspect he would have smiled and said exactly what he said then: "If you hadn't found gravitational waves I would have felt sorry for the Lord. The theory is correct."

What does mercury being liquid at room temperature have to do with Einstein's theory of relativity?

Image: Wikipedia Commons

One of the great moments in twentieth century science came when Paul Dirac married quantum mechanics with Einstein's Special Theory of Relativity to produce relativistic quantum mechanics. Dirac's theory did many things - predict electron spin and the positron, analyze atomic collisions, jump-start the revolution in quantum electrodynamics - but it also had very significant repercussions for chemistry. However these repercussions did not become known for another few decades because it turned out that for solving most problems in chemistry you could neglect relativistic effects. Figuring out chemical bonding, predicting the thermodynamic properties of molecules and rates of chemical reactions, understanding the molecular glue that holds proteins together; all these problems succumbed to calculation without chemists worrying about relativity.

All except one problem, that is. And it deals with a question that every child since antiquity has asked: Why is mercury liquid at room temperature? Mercury - the only metal with this property - has beguiled and fascinated men for centuries; a glittering substance that flows with studied gravity, supports the weight of coins, magically seems to dissolve other metals and resists all attempts to scoop it up. A substance that can aid health when calibrated inside a thermometer and can kill when it accumulates in living tissues. But the one quality of mercury that is apparent to everyone who has even the slightest acquaintance with it is its liquid nature.

Why is this so? It turns out that sometimes simple observations in science can have complicated although very interesting explanations, and this is one of those cases. Fortunately the crux of the matter is simple, and it has received its most complete and satisfying treatment in a recent paper published in the journal Angewandte Chemie. But first let's go back to the basics. Mercury is a metal, which means that it occupies the middle of the periodic table along with other metals like gold, zinc and cadmium. In fact it is in the same group as zinc and cadmium, and yet it couldn't be more different from them. Zinc and cadmium are not liquids at room temperature and they crystallize in a different form from mercury. In addition mercury is right next to gold, and yet their properties are utterly dissimilar.

Recall from college chemistry that atomic orbitals come in different flavors; s, p, d and f orbitals are distinguished by different quantum numbers and different "shapes". Metals are characterized by significantly occupied d orbitals. In addition, filled orbitals imply special stability. The singular fact that distinguishes mercury from its neighbors is that it has a filled outermost 6s atomic orbital. This means that the electrons in the orbital are happily paired up with each other and are reluctant to be shared among neighboring mercury atoms. Where the theory of relativity comes in is in accounting for subtle changes in the masses of the electrons in mercury and the atomic radii which nonetheless have profound effects on the physical properties of the metal.

According to special relativity, the apparent mass of an object increases as its velocity approaches the speed of light. From Niels Bohr's theory of atomic structure we know that the velocity of an electron is proportional to the atomic number of an element. For light elements like hydrogen (atomic number 1) the velocity is insignificant compared to the speed of light so relativity can be essentially ignored. But for the 1s electron of mercury (atomic number 80) this effect becomes significant; the electron approaches about 58% of the speed of light, and its mass increases to 1.23 times its rest mass. Relativity has kicked in. Since the radius of an electron orbit in the Bohr theory (orbital to be precise) goes inversely as the mass, this mass increase results in a 23% decrease in the orbital radius. This shrinkage makes a world of difference since it results in stronger attraction between the nucleus and the electrons, and this effect translates to the outermost 6s orbital as well as to other orbitals. The effect is compounded by the more diffuse d and f orbitals insufficiently shielding the s electrons. Combined with the filled nature of the 6s orbital, the relativistic shrinkage makes mercury very reluctant indeed to share its outermost electrons and form strong bonds with other mercury atoms.

The bonding between mercury atoms in small clusters thus mainly results from weak Van der Waals forces which arise from local charge fluctuations in neighboring atoms rather than the sharing of electrons. But all this was conjecture; someone had to do the rigorous calculations, treating every electron in the element relativistically and calculating the relevant properties. In this case the relevant property is the heat capacity of a substance which dramatically changes during a phase transition, say from solid to liquid. The question was simple; using the most state-of-the-art calculations, could you predict the temperature at which mercury melts as indicated by a sudden change in heat capacity? In a paper published in Angewandte Chemie this month, chemists from New Zealand, Germany and France have provided a result which is the most complete one to date. They actually simulated the melting of mercury using quantum molecular dynamics, solving the Schrodinger equation, calculating forces and velocities from quantum mechanics and allowing the atomic clusters to sample different geometric orientations randomly. They carried out the calculations first by excluding relativity and then by including it, and the results were unambiguous; when relativistic effects were taken into account, the melting point of mercury dropped from 355 kelvin to 250 kelvin, in excellent agreement with experiment and accompanied by a sudden change in the heat capacity.

The liquid nature of mercury is not the only thing that the special theory explains. It also explains why gold is yellow while silver is white. In this case, the splitting of orbitals and the lower energy of the 6s orbital results in gold absorbing blue light and emitting yellow and red. Since the 6s level is higher in silver, the energy required to excite an electron corresponds to the UV region instead of the visible region; consequently silver appears devoid of colors from the visible region of the spectrum.

I always feel a twang of pleasure when I come across studies like this. There are few things more satisfying than the successful application of our most cherished and accurate theories to explaining life's most humdrum and yet fascinating phenomena. That's what science is about.

References:

1. Evidence for Low-Temperature Melting of Mercury owing to Relativity; F. Calvo et al. Angew. Chem. Intl. Ed. Engl. 2013, 10.1002/anie.201302742

2. Why is Mercury Liquid? L. Norrby, J. Chem. Ed. 1991, p. 110.

3. Relativistic Effects in Chemistry, D. McKelvey, J. Chem. Ed. 1983, p. 112

This post was first published on the Scientific American Blog Network.

Magic without Magic: John Archibald Wheeler (1911-2008)

Image copyright: NNDB, Soylent communications (2008)

When I heard from a friend about John Wheeler's death this morning, I grimaced and actually loudly let out an exclamation of pain and sadness. That's because not only was Wheeler one of the most distinguished physicists of the century but with his demise, the golden era of physics- that which gave us relativity, quantum theory and the atomic age- finally passes into history. The one consolation is that he lived a long and satisfying life, passing away at the ripe age of 96. It was just a few weeks ago that I asked a cousin of mine who did his PhD. at the University of Texas at Austin whether he ever ran into Wheeler there. My cousin who himself is in his fifties said that Wheeler arrived just as he was finishing- after retirement from Princeton university.

Wheeler was the last survivor of that heroic age that changed the world and he worked with some true prima donnas. He was an unusually imaginative physicist who made excursions into exotic realms; particles traveling backwards in time, black holes, time travel. A list of his collaborators and friends includes the scientific superstars of the century- Niels Bohr, Albert Einstein, Enrico Fermi, Edward Teller and Richard Feynman to name a few. To the interested lay public, he would be best known as Richard Feynman's PhD. advisor at Princeton.

Wheeler is famous for many things- mentor to brilliant students, originator of outrageous ideas, coiner of the phrase "black hole", outstanding teacher and writer. My most enduring memory about him is from John Gribbin's biography of Feynman. Gribbin recounts how Wheeler in his pinstriped suits used to look like a conservative banker, a look that belied one of the most creative scientific minds of his time. The fond incident is about the playful rogue Feynman being summoned into Wheeler's office for the first time. In order to underscore the importance of his time, Wheeler laid out an expensive pocket watch in front of Feynman. Feynman who had a congenital aversion to perceived or real pomposity took note of this and during their next meeting, laid out a dirt-cheap watch on the table. After a moment of stunned silence, both professor and student burst into loud laughter, laughter that almost always accentuated their discussions on physics and life thereafter. Feynman and Wheeler together derived a novel approach to quantum mechanics that involved particles radiating backwards in time. Wheeler also initiated the discussion of the notorious sprinkler problem described by Feynman in Surely you're joking Mr. Feynman

John Wheeler was born in Florida to strong-willed and working class parents. After obtaining his PhD. from Johns Hopkins at the age of 21, he joined Princeton in 1938 where he remained all his working life. Princeton in 1938 was a mecca of physics, largely because of the Institute for Advanced Study nearby which housed luminaries like Einstein, John von Neumann and Kurt Godel. Wheeler knew Einstein well and later sometimes used to hold seminars with his students in Einstein's home. As was customary for many during those times, Wheeler also studied with Niels Bohr at his famous institute in Copenhagen. In 1939 Bohr and Wheeler made a lasting contribution to physics- the liquid drop model of nuclear fission. According to this, the nucleus of especially heavy atoms behaves like a liquid drop, with opposing electrostatic repulsive forces and attractive surface tension and strong forces. Shoot an appropriately energetic neutron into an unstable uranium nucleus and it wobbles sufficiently for the repulsive forces to become dominant, causing it to split. The liquid drop model explained fission discovered earlier. The mathematics was surprisingly simple yet remarkably accurate. Bohr was one of Wheeler's most important mentors; in his biography he describes how he used to have marathon sessions with Bohr, with the great man often insisting on walking around the department, tossing choice tidbits to Wheeler ambling at his side. Caught up in the recent heated debate about the philosophical implications of quantum theory, Wheeler argued the nature of reality with both Einstein and Bohr.

When World War 2 began, Wheeler like many physicists was recruited into the Manhattan Project. Because of his wide-ranging intellect and versatility, he was put in charge as scientific consultant to Du Pont, who was building plutonium producing reactors at Hanford in Washington state. There Wheeler tackled and solved an unexpected and very serious problem. As the reactors were transforming uranium 238 into the precious plutonium, the process suddenly shut down. After some time it started up again. Nobody knew what was happening. Wheeler who was the resident expert worked out the strange phenomenon in an all-night session. What was happening was that some of the fission products produced had a big appetite for neutrons and were therefore "poisoning" the chain reaction. After some time when these products had decayed to sufficiently low levels, they would stop eating up the neutrons and the reactor would start again. This was one of the most valuable pieces of information gained during plutonium production. Ironically, the omission of this information in a second edition of a government history of atomic energy released just after the war alerted the Soviets to its importance. Working on the Manhattan Project was also a poignantly personal experience for Wheeler; the bomb could not save his brother Joe who was killed in action in Italy in 1944. Wheeler later also worked with Edward Teller on the hydrogen bomb, a decision about which he was fairly neutral because he thought it was necessary at the time to stand up to the Soviets.

After the war Wheeler embarked on a lifelong quest in a completely different field and became a pioneer in it- general relativity. He took up where Robert Oppenheimer had left off in 1939. Oppenheimer had made a key contribution to twentieth century physics by first describing what we now know as black holes. Strangely and somewhat characteristically, he lost all interest in the field after the war. But Wheeler took it up and reinitiated a bona fide revolution in the application of general relativity to astrophysics. As his most enduring mark, he coined the word "black hole" in the 1960s. Wheeler became the scientific godfather of a host of other physicists who became pioneers in exploring exotic phenomena- black holes, wormholes, time travel, multiple universes. His most successful student in this regard has been Kip Thorne whose wonderful book expounds on the golden age of relativity. Hugh Everett, the tragic genius who invented multiple universes and the Lagrange multipliers method for optimization problems before plunging into paranoia and depression, left behind choice fodder not just for science but for science fiction; parallel universes have been a staple of our collective imagination ever since then. In retrospect, Wheeler followed his mentor and did for astrophysics what Bohr had done for quantum theory- he served as friend, philosopher and guide for a brilliant new generation of physicists.

Wheeler also was known as an outstanding teacher. His mentoring of Feynman is well-known, and he devoted a lot of time and care to teaching and writing. Along with his students Kip Thorne and Charles Misner, Wheeler produced what is surely the bible of general relativity, Gravitation, a mammoth book running more than a thousand pages whose only discouraging feature may be its length. The book has served as advanced introduction to Einstein and beyond for generations of students. Wheeler also co-authored Spacetime Physics, an introduction to special relativity which even I have timidly managed to savor a little during my college days. His own autobiography, Geons, Black Holes and Quantum Foam: A Life in Physics is worth reading for its evocation of a unique time of the last century, as well as for fond anecdotes about great physicists.

But many people will remember Wheeler as a magician. Sitting in his office in his pinstriped suits, Wheeler's mind roamed across the universe straddling everything from the smallest to the largest, exploring far-flung concepts and realms of the unknown. He grappled with the interpretation of quantum mechanics and was an early proponent of the anthropic principle- in John L Casti's magnificent book Paradigms Lost, Casti quotes Wheeler analogizing observer-created reality with the game in which a group of people asks someone else to guess an object they have in mind by asking questions, except that in the modified version of this game, they let the object be created during the process of questioning. With his mentor Bohr's enduring principle of complementarity as a guide, Wheeler produced esoteric ideas that nonetheless questioned the bedrock of reality. Wheeler was entirely at home with such bizarre yet profound concepts that still tug at the heartstrings of physicist-philosophers. Only Wheeler could have introduced paradoxical and yet meaningful phrases like "mass without mass". In celebration of his sixtieth birthday, physicists produced a volume dedicated to him with a title that appropriately captured the essence of his thinking- "magic without magic".

John Wheeler was indeed a magician. He made great contributions to physics, served as its guide for half a century and motivated and taught new generations to wonder at the universe's complexities as much as he did. He was the last torch-bearer of a remarkable age when mankind transformed the most esoteric and revolutionary investigations into the universe into forces that changed the world. He will be sorely missed.