RELATIVISTIC ALCHEMY

Back to Contents

    In the Fifth Century B.C. the Greek philosophers faced a dilemma of their own making and, being Greek, were having way too much fun arguing about it. It all started when, after some spectacular successes with the deductive nature of plane geometry, certain Greek philosophers got into their minds the notion that they could figure out the way the world works, that they could reason out an explanation for everything they saw. On one side of the dilemma stood Parmenides and his followers, who believed that existence was entirely static and that all change was an illusion. On the other side stood those philosophers, like Heraclitus, who believed that all was change and that those things that seem static are merely changing too slowly for us to notice. Taking the middle road was a fellow named Leucippus and his pupil Democritus, who said that Reality is both stasis and change in that the things that we see are ever-changing arrangements of unchanging elements, which they called "atomos" (the uncuttable). That idea then languished in obscurity for nearly twenty-four centuries, largely (in Europe certainly) because it was interpreted as an heretical denial of the Doctrine of Transubstantiation (the foundation of the Sacrament of the Eucharist).

    In 1807 John Dalton reintroduced the atomic theory into natural philosophy, in particular into chemistry. He used atoms as a useful fiction to explain the observations made over the preceding decades that substances combine chemically in rational proportions. Those observations imply rather strongly that all substances comprise assemblies of discrete units of matter that come in a variety of distinct species. By 1869 chemists knew of 63 such species and in that year Dmitri Mendeleyev organized them into the array whose expanded version, the Periodic Table of the Chemical Elements, hangs on a wall in every chemistry laboratory and classroom in the world. According to the latest version of that table, all matter in the Universe is made up of 92 naturally occurring elements, to which physicists have added 20 artificial ones since the 1940's.

    Initially all that chemists knew about the chemical elements in the way of fundamental properties were relative mass and chemical valence (the number that tells how an element will combine with other elements to form compounds). They knew, for example, that an atom of carbon is about twelve times as massive as is one of hydrogen and has a valence of plus four and that one atom of oxygen is about sixteen times as massive as is one of hydrogen and has a valence of minus two. In Mendeleyev's original table the elements were organized in order of increasing relative mass, which, fortuitously enough, is the same as the order of increasing atomic number, which is the modern index of organization of the table. Nineteenth Century chemists did not have atomic number as an organizing concept because they had no knowledge of how atoms are structured and so long as they conceived atoms as amorphous, uncuttable blobs they could not even guess at what form atomic structure might take.

    Happily for chemists and physicists, atoms do not live up to their Greek name. In 1897 physicists discovered that they could cut out of atoms things that came to be called electrons, lightweight particles that each carry a standard unit of negative electric charge. Chemists gained two new ideas from that discovery. First, they discerned that the atoms of each chemical element have a specific number of electrons associated with them: hydrogen has one, helium has two, lithium has three, and so on. That number of electrons, the atomic number of the element, is now considered the characteristic property of the element, equal to the element's rank in the Periodic Table of the Chemical Elements. Second, the chemists discerned that it is the sharing of electrons that binds atoms together into molecules and that the specific propensity of each element's atoms to share electrons accounts for the columns in the Periodic Table: thus, species whose atoms donate one electron, such as hydrogen, lithium, and sodium, fall into one column and species whose atoms tend to absorb two extra electrons, such as oxygen and sulfur, fall into another column. With that concept in mind, chemists could account for two hydrogen atoms (giving up two electrons) combining with one oxygen atom (absorbing the two donated electrons) to form a molecule of water.

    But the physicists were only getting started on a process of onion peeling that continues to this day. Every time they stripped another layer of mystery off the atom they found another awaiting their attentions. Here's the second layer. If I can pull negatively charged parts off an atom, which normally has no net electric charge, then the atom must necessarily have a positively charged part. Further, an atom must have an integer number of standard positive charges, one for each of the atom's electrons. But, physicists quickly discovered, though it's easy to pull electrons off atoms one by one, by the beginning of the Twentieth Century no one had succeeded in doing the same with the positively charged part of an atom. Why not? Is there something special about the way in which the positively charged part is put together?

    Ernest Rutherford provided an affirmative answer to that latter question in 1911. He had conceived and conducted the archetype of the subatomic exploration experiment and had obtained results that astounded him. What he wanted to do was to gain some information about how the positive charge is distributed within an atom. To understand the method that he devised imagine that you want to measure the area of a small lake that lies within a certain square mile of land and that you are obliged to do so from the top of a mountain overlooking that square mile. One way, assuming that there are no people in the way, is to set up a battery of cannons on your mountaintop and to fire them randomly in directions more or less oriented toward your lake, ensuring that the shells drop uniformly onto your square mile and the land surrounding it. You can then calculate the area of the lake by dividing the number of shells that hit the lake by the total number of shells that hit the square mile the lake occupies and then multiplying the resulting fraction by one square mile (or 640 acres, or 27,878,400 square feet, or...).

    Rutherford designed the apparatus of his experiment to direct alpha rays from a sample of radium at a leaf of gold foil, beyond which he erected a small phosphorescent screen. The alpha rays, which were known at the time to comprise positively charged particles (and are now known to be the nuclei of helium atoms), would pass through the gold and strike sparkles of light off the screen when and where they hit it. Rutherford figured that if the positive charge were distributed uniformly, the alpha rays would not be deflected from their original paths and would strike the screen at one point. To the extent that the distribution is not uniform some of the alpha rays would be deflected away from that one point. By measuring the number of deflected rays and the angles through which they were deflected, Rutherford could then calculate the degree to which the positively charged part of the atom is concentrated. Instead of a moderate number of rays being deflected by small angles, as he had expected, Rutherford found that most of the rays were undeflected and a small number of rays were deflected by large angles, some rays even coming back toward their source. Rutherford commented that the discovery was as astonishing as if a shell fired from a naval gun at a tissue had bounced off the tissue and returned to the gun. The conclusion that the evidence compelled Rutherford to reach is that the positive charge in an atom is tightly condensed into a small volume, and that, therefore, the atom comprises a tiny, massive, positively charged nucleus and light, negatively charged electrons revolving in wide orbits about that nucleus to give the atom its size and its spectrographic and chemical properties.

    The next level of mystery on the atomic onion was revealed by experiments that confirmed that all electrons are identical to each other. That fact necessitates an understanding that the nucleus of the atom is built up from identical particles, each carrying one positive unit of the standard electric charge. That's an easy idea to test, as science requires. Divide the atomic mass of each element on the Periodic Table by its atomic number (which is equal to the number of standard positive charges in the nucleus of one of its atoms). For all of the elements except hydrogen you will calculate a number slightly larger than two and you will see that from element to element the fractional part of that number will not follow any pattern. That's not what we expect of objects built up from standardized parts.

    Our expectation turned out to be correct, though. In 1913 Ernest Rutherford and Frederick Soddy discovered that the chemical elements can be further subdivided. They discovered that not all of the atoms of a given chemical element have the same mass. Thus, while it's true that most atoms of carbon are about twelve times as massive as is an atom of hydrogen, there are also carbon atoms that are about thirteen and fourteen times as massive as is an atom of hydrogen. And in any sample of chlorine about three quarters of the atoms are each about thirty-five times as heavy as is an atom of hydrogen and the remaining atoms are each about thirty-seven times as massive as is an atom of hydrogen. And so it goes throughout the Periodic Table, each atom being one of several isotopes of its species (the word isotope coming from the Greek for "same place" because the isotopes of an element occupy the same place on the Periodic Table). It's as if we could transmute an atom of one isotope into an atom of the next heavier isotope by shoving a nucleus of hydrogen (a proton) and an electron into the atom's nucleus together. Indeed, it turned out that there is a particle, called a neutron, that is essentially an electron and a proton stuck together and that atomic nuclei are thus clusters of protons and neutrons.

    Thus we obtained the model of the atom that we use today, which model comes before our mind's eye as a cluster of weird little grapes with a swarm of gnats flittering about it. That model is what lets us bring Relativity into play in the game of science.

    In 1920 Arthur Eddington carried out a remarkable calculation. Considering the idea that an atom of helium might be made by sticking the nuclei and two of the electrons of four hydrogen atoms together into a new nucleus (leaving the other two electrons free to revolve about that new nucleus), he multiplied the mass of the hydrogen atom by four and obtained a result that was a little over 7/10 of a percent greater than the mass of one helium atom; that is, if one kilogram of hydrogen were converted into helium, the resulting helium would ponder a mass a little over 7 grams shy of a full kilogram. That seven-plus grams cannot simply disappear, as we deduced in the essay on E=mc2: it must be transformed into something else that also possesses or confers inertia. Eddington figured that something to be energy, in accordance with Einstein's equation, in the form of kinetic energy in the helium (heat) or electromagnetic radiation or some combination of the two in the amount of one hundred and seventy-nine million kilowatt-hours. That is a whale of a lot of energy to come out of the hydrogen that you could get out of less than two gallons of water, so it's quite natural to ask what it would take to make that process of nuclear fusion work.

    First, Eddington understood, the nuclei of the hydrogen atoms, the protons, must have enough linear momentum that they can overcome their mutual electric repulsion just enough to come close enough together that the nuclear binding force can take over and pull them into a mutual embrace. A large amount of linear momentum corresponds to a large amount of kinetic energy, so the gas comprising the hydrogen atoms must be very hot. Second, the gas must be dense, keeping the nuclei so close together that they will collide often, each collision being another chance at fusion. Those conditions of heat and density must be imposed upon the gas and maintained by some kind of container, one that contributes the pressure needed to oppose the gas's natural tendency to expand and provides thermal insulation to oppose the tendency of heat to flow too quickly out of the gas. The most natural container Eddington could imagine was simply a thick atmosphere of hydrogen held together by its own gravitation and when he calculated the mass that such an atmosphere would require to maintain a continuous, steady rate of fusion, Eddington found that he had sketched the mathematical description of a familiar object - a star. He had figured out what makes the sun shine. More, he calculated that, although the light that the sun shines into space reduces the sun's mass by four million tonnes every second, the sun will shine, much as it does now, for a full ten billion years.

    That latter calculation solved a long-standing puzzle. Since the Eighteenth Century geologists had been claiming, based on their studies of the Earth, that Earth is vastly older than the six thousand years calculated from the data in the Bible, but no one had been able to explain how the sun could shine as it does today for much more than those few millenia. In the middle of the Nineteenth Century Charles Darwin and Alfred Wallace produced a theory that all of the life on Earth evolved from simple beginnings via the interplay between mutation and natural selection, a process that requires millions upon millions of years to reach the stage that we see today. The hypothesis that thermonuclear fusion lights the sun and the stars gave geologists and biologists a depth of time sufficient to allow the slow drift of continents, the waxing and waning of seas, the advance and retreat of glaciers to shape the world we inhabit and the creatures that inhabit it.

    Take Eddington's calculation to its logical conclusion. Take the most common isotope of each element and look at the number of protons and neutrons that a nucleus of each of its atoms contains (that number, called the atomic mass number, is often displayed as a suffix to the chemical symbol of the element as a means of identifying the isotope: thus, for example, U-235 represents one atom of uranium with two hundred and thirty-five protons and neutrons in its nucleus). Multiply that number by the mass of an atom of hydrogen and subtract from the result the mass of the isotope in question (to do this you need the Table of the Isotopes from the Handbook of Chemistry and Physics, a good calculator, and a lot of patience). The result is the mass defect of the isotope, the amount of mass that would go missing if you could take that many hydrogen atoms and convert them into one atom of your chosen isotope. Now divide that mass defect by the atomic mass number: the result is roughly the number of kilograms of mass that would go missing if you could convert one kilogram of hydrogen into your chosen isotope. Thus, for three examples, you would calculate for helium 7.16 grams, for iron 8.964 grams, and for iodine 8.665 grams going missing from your kilogram of hydrogen. If you had calculated the equivalent numbers for all the other naturally occurring elements and had then plotted their values on a graph that shows atomic number increasing horizontally to the right, you would have obtained a picture made up of dots that suggest a curved line, one that begins low at helium, rises to a maximum height at iron, and then bends gently downward. That line is called the Curve of Binding Energy and it shows us a problem and an opportunity, though that opportunity brings with it a few problems of its own.

    What the Curve of Binding Energy tells us immediately is that, of all the chemical elements, iron has the most stable nucleus. What that means is that, if you build up nuclei by adding hydrogen nuclei to them, you will get back more energy than you put into the reaction if the nuclei that you create are those of the first twenty-six elements. Thus, you can stick a proton and a neutron onto a nucleus of carbon to create one of nitrogen, then stick a proton and a neutron onto that to create one of oxygen, and then stick a proton and a neutron onto that to create one of fluorine, and so on and all of those reactions will give back more energy than you put into them until you have created a nucleus of iron. If you continue the process to create nuclei of atoms heavier than iron, you will be obliged to put more energy into your reactions than you get out of them. You will have gone from transforming mass into energy to transforming energy into mass and that prospect poses a problem. We can see how the stars can create all of the elements up through iron: the reactions release heat to keep the reactions going. But the reactions to create elements heavier than iron absorb heat and would thus cool the fuel and shut down the reactions. So whence come silver and gold, copper and tin for a Bronze Age, superconducting niobium and photoelectric selenium?

    According to the astrophysicists, it's all stardust. Current theory tells us that the stars do, indeed, create the elements up through iron. For most of its life a star converts hydrogen into helium and a few other light elements, but when the star begins to die its core shrinks, the pressure and temperature there rise, and the star begins to create heavier elements in layers, drawing its last flickers of light from the less energetic reactions that lead from helium to iron. For most stars the final fading of those reactions leaves them as white dwarves, once glorious orbs shrunk to the size of Earth and slowly dimming out over the coming eons. But for stars that ponder more than 144 percent of our sun's mass the going out is a bit more spectacular. The white dwarf shrinks further as it cools, each layer of its body growing heavier as it is drawn closer to the center (in accordance with the law of gravity). Eventually the quantum-mechanical forces that support the star's weight are overwhelmed and the core implodes. Electrons are driven into nuclei and the nuclei are driven together to form an object made of nothing but neutrons. The gravitational potential energy being converted into kinetic energy and pounded into that growing neutronium ball raises the neutronium's temperature into the quadrillions of degrees, giving a large fraction of the neutrons energies that correspond to motion at speeds near the speed of light. Those relativistic neutrons blow out of the core and slam into the star's dallying outer layers, stopping them dead, lifting them against the star's intense gravity, and driving them outward at eight to ten percent of lightspeed, pouring so much heat into them that the resulting expanding spherical shell will shine brighter than a trillion suns. This event is called a supernova and astrophysicists believe it to be the source of the elements heavier than iron. Certainly the heat and pressure imposed upon the star's outer layers by the relativistic neutron wind are sufficient to drive a few energy-absorbing fusions. In this manner the elements are created and then blown into space to be gathered up in the creation of new stars and new planets.

    But if the elements heavier than iron absorb energy when they are made, then we can assume reasonably that we could gain energy from them by taking them apart; that is, that their nuclei would release extra energy if we could make them split apart. That is so much easier said than done that Ernest Rutherford declared that the very idea of actually converting mass into energy was mere moonshine (which may lead us to think that it must have been one helluva moon that rose over the New Mexico desert in July 1945). The atomic nucleus is so small that no conceivable instrument can grip it and pry it apart. To split a nucleus, we must strike it with a projectile that will either break the bonds among the protons and neutrons or will put the nucleus into a naturally unstable state that will fission spontaneously. In 1938 Lise Meitner and her nephew, Otto Hahn, discovered that the isotope uranium-235 is so ticklish that striking it with a slowly moving neutron makes it fission. Better, each fissioning nucleus releases, on average, two-and-a-half more neutrons, so fission in uranium-235 (and in plutonium-239, which can be made from the more common uranium-238) can be made to cascade catastrophically, releasing energy in heat and radiation with a bang that can flatten a city. If some of the neutrons generated in the chain reaction are absorbed, then the fission process can be made to proceed more gently and the heat used to boil water into steam that is then used to drive turbogenerators into pumping electricity through our power lines.

    No sooner had the physicists begun exploring the realm of nuclear reactions than they began also to probe at the next layer of mystery in the atom. If atoms are not as uncuttable as the Greeks believed them to be, they asked, then might the constituents of atoms also be divisible into yet smaller parts? Up until 1947 physicists didn't think so. Yes, they knew that the neutron left to itself decays into a proton, an electron, and an antineutrino, but they regarded the neutron as a composite particle. The proton and the electron were regarded as fundamental and, therefore, uncuttable. And, yes, they had inferred the existence of other particles from the tracks that cosmic rays leave in a Wilson cloud chamber (the tracks being threadlike lines of fog created by electrically charged particles as they pass through a supercooled vapor): those particles were labeled pi mesons (or pions) and mu mesons (or muons) and they and their decays were regarded as aspects of the decay of the neutron or of the force particle believed to hold the nucleus together. But in December 1947 a photograph of cloud chamber tracks revealed something completely new - the track that could only have been made by a new kind of subatomic particle, which came to be called the K meson (or kaon).

    Intrigued, the physicists began to augment their nucleus-pounding cyclotrons with nucleon-shattering synchrotrons. Where they had been able to give protons millions of electron-volts of kinetic energy (one electron-volt being the energy that a proton or an electron gains when it falls through an electric potential of one volt) in order to study the transmutation of isotopes, they were soon able to give protons billions of electron-volts with the intent of shattering protons and neutrons to see what they might yield. The experiment is still Rutherford's, but the higher energies given to the projectiles make them smaller, so they can measure smaller features in their scattering patterns. The cannon on the mountain has become a machine gun that can now measure puddles as well as lakes, even though it destroys them in the process. Because the mass of a single proton is equivalent to an energy of 938.28 million electron-volts, the protons in the new synchrotrons were carrying enough energy to create new protons ex nihilo and in 1955 physicists discovered that they had done even better than that when the analysis of debris tracks from UC Berkeley's Bevatron revealed the creation of antiprotons, the antimatter counterparts to the nucleus of hydrogen.

    Antimatter!? To borrow I. I. Rabi's remark concerning the muon, Who ordered that? Actually it was Paul Dirac. In 1927 he applied Relativity to the fundamental equation of the quantum theory and used the result to describe the electron, obtaining two solutions to his relativistic equation. The first solution was the description that he had sought, even including as a necessary feature the fact that the electron spins. The second solution made no sense, though: it seemed to describe an electron, but one with a positive electric charge and a rest-mass energy that was negative. Dirac couldn't dismiss that second solution, so he interpreted it: he hypothesized that it represents a kind of electron-shaped hole in space and that the hole (called a positron) would behave just like an electron except that it would react to electric and magnetic fields as if it were carrying a positive electric charge instead of the electron's usual negative charge. Further, if a positron encountered an electron, the particles would attract each other and the electron would fill the hole so perfectly that both particles would then cease to exist. The rest-mass energy of the particles (511 thousand electron-volts per electron or positron) would then be manifested in a pair of gamma rays (high-energy photons). Because it annihilates ordinary matter in that way, Dirac's negative-energy solution was called antimatter. It seemed a silly idea at the time, but at the end of 1931 Carl Anderson, working at Cal Tech examining pictures of cosmic ray tracks, found a track that could only have been made by a particle with the mass of an electron and with a positive electric charge. Antimatter, while very rare, is also very real.

    So now the physicists had a new complication in a picture that was to become downright bewildering. Throughout the 1950's physicists, using their new synchrotrons to shatter nuclei, discovered dozens of new mesons and baryons (particles with a family resemblance to protons and neutrons) and their antimatter counterparts in the sprays of particles that emanated from the collisions among high-energy protons and stationary targets. By 1960 the physics of elementary particles was in complete chaos, so much so that one Nobel Laureate facetiously suggested that the discoverers of any new subatomic particles be assessed a $10,000 fine. Then the fog was lifted.

    In 1961 Murray Gell-Mann organized the particles then known into a set of diagrams expressing what Gell-Mann called The Eightfold Way (because the first diagrams displayed octets of particles), thereby doing for elementary particle physics what Dmitri Mendeleyev had done for chemistry nearly a century earlier. And, just as Mendeleyev used gaps in his Periodic Table to predict the existence and basic properties of three new chemical elements (gallium, scandium, and germanium), so Gell-Mann used a gap in his chart to predict the existence and properties of a particle called an omega-minus (which was discovered experimentally in 1964). In 1964 Gell-Mann took the next step beyond classification and presented a theoretical explanation for The Eightfold Way, one in which the particles are represented as being composed of more fundamental particles that Gell-Mann called quarks. Just as the rules for combining protons, neutrons, and electrons explain the Periodic Table of the Elements, so the rules for combining quarks explain Gell-Mann's charts.

    At first Gell-Mann's quark model seemed silly (as new ideas often do) but over the next two decades, as physicists discovered new particles and fitted them into Gell-Mann's scheme, that model evolved into what physicists now call the Standard Model. According to the Standard Model, all matter in the Universe is made up of some combination selected from six kinds of quark (up, down, strange, charm, top, and bottom), six kinds of lepton (the electron, the muon, the tauon, and their respective neutrinos), and four kinds of mediator particle that represent three kinds of forcefield (the photon, representing the electromagnetic force; the gluon, representing the strong nuclear force, which holds the protons and neutrons together in an atomic nucleus; and two kinds of vector boson, representing the weak nuclear force, which prevents electrons from being pulled into the nucleus and thereby collapsing the atom and which also causes radioactive decay of certain isotopes).

    Though there's still a great amount of research and experimentation to be done with the Standard Model, we are ready to begin exploring the next layer of mystery in the composition of matter. But there doesn't seem to be another layer. There doesn't seem to be any possibility of identifying parts of a quark, for example. The reason behind that statement is that the work that would have to be done to pull a lone quark out of a particle of which it is a part is greater that the amount of energy required to create the mass of a quark-antiquark pair. Consider what might happen if we were to try to pull one of the up quarks out of a proton (which comprises one down quark and two up quarks). The energy that we put into the struggle might materialize a down quark and an anti-down quark. We would thus end up with one particle comprising two down quarks and one up quark (a neutron) and one particle comprising one up quark and one anti-down quark (a positively charged pi meson). We are never going to create a free quark, much less break one apart into smaller pieces, a task that would require even greater amounts of energy. If quarks have any structure to them at all, then we will be obliged to infer it from a more subtle version of Rutherford's experiment.

    At this point, then, we can claim that, for all practical purposes, we understand the fundamental structure of matter and that we have some hope of discovering how it came to be.

efefefaaabbbefefef

Back to Contents