The God Particle

by Leon Lederman

  Before we leave "Eff equals emm ay," lets dwell a bit on its power. It is the basis of our mechanical, civil, hydraulic, acoustic, and other types of engineering; it is used to understand surface tension, the flow of fluids in pipes, capillary action, the drift of continents, the propagation of sound in air and in steel, the stability of structures like the Sears Tower or one of the most wonderful of all bridges, the Bronx-Whitestone Bridge, arching gracefully over the waters of Pelham Bay. As a boy, I would ride my bike from my home on Manor Avenue to the shores of Pelham Bay, where I watched the construction of this lovely structure. The engineers who designed that bridge had an intimate understanding of Newton's equation; now, as our computers become faster and faster, our ability to solve problems using F = ma ever increases. Ya did good, Isaac Newton!

  I promised three laws and have delivered only two. The third law is stated as "action equals reaction." More precisely it asserts that whenever an object A exerts a force on an object B, B exerts an equal and opposite force on A. The power of this law is that it is a requirement for all forces, no matter how generated—gravitational, electrical, magnetic, and so on.

  ISAAC'S FAVORITE F

  The next most profound discovery of Isaac N. had to do with the one specific force he found in nature, the Pof gravity. Remember that the F in Newton's second law merely means force, any force. When one chooses a force to plug into the equation, one must first define, quantify that force so the equation will work. That means, God help us, another equation.

  Newton wrote down an expression for F (gravity)—that is, for when the relevant force is gravity—called the universal law of gravitation. The idea is that all objects exert gravitational forces on one another. These forces depend on how far apart the objects are and how much stuff each object has. Stuff? Wait a minute. Here Newton's partiality for the atomic nature of matter came in. He reasoned that the force of gravity acts on all atoms of the object, not only, for example, those on the surface. The force is exerted by the earth on the apple as a whole. Every atom of the earth pulls on every atom of the apple. And also, we must add, the force is exerted by the apple on the earth; there is a fearful symmetry here, as the earth must move up an infinitesimal amount to meet the falling apple. The "universal" attribute of the law is that this force is everywhere. It's also the force of the earth on the moon, of the sun on Mars, of the sun on Proxima Centauri, its nearest star neighbor at a distance of 25,000,000,000,000 miles. In short, Newton's law of gravity applies to all objects anywhere. The force reaches out, diminishing with the amount of separation between the objects. Students learn that it is an "inverse-square law," which means that the force weakens as the square of the distance. If the separation of two objects doubles, the force weakens to one fourth of what it was; if the distance triples, the force diminishes to one ninth, and so on.

  WHAT'S PUSHING UP?

  As I've mentioned, force also points—down for gravity on the surface of the earth, for example. What is the nature of the counterforce, the "up" force, the action of the chair on the backside of the sitter, the impact of wooden bat on baseball, or hammer on the nail, the push of helium gas that expands the balloon, the "pressure" of water that propels a piece of wood up if it is forced beneath the surface, the "boing" that holds you up when you lie on bedsprings, the depressing inability of most of us to walk through a wall? The surprising, almost shocking, answer is that all of these "up" forces are different manifestations of the electrical force.

  This idea may seem alien at first. After all, we don't feel electric charges pushing us upward when we stand on the scale or sit on the sofa. The force is indirect. As we have learned from Democritus (and experiments in the twentieth century), most of matter is empty space and everything is made of atoms. What keeps the atoms together, and accounts for the rigidity of matter; is the electric force. (The resistance of solids to penetration has to do with the quantum theory, too.) This force is very powerful. There is enough of it in a small metal bathroom scale to offset the pull of the entire earth's gravity. On the other hand, you wouldn't want to stand in the middle of a lake or step off your tenth-floor balcony. In water and especially in air, the atoms are too far apart to offer the kind of rigidity that will offset your weight.

  Compared to the electrical force that holds matter together and gives it its rigidity, the gravitational force is extremely weak. How weak? I do the following experiment in a physics class I teach. I take a length of wood, say a one-foot-long piece of two-by-four, and draw a line around it at the six-inch mark. I hold up the two-by-four vertically and label the top half "top" and the bottom half "bot." Holding top, I ask, "Why does bot stay up when the entire earth is pulling down on it?" Answer: "It is firmly attached to top by the cohesive electrical forces of the atoms in the wood. Lederman is holding top." Right.

  To estimate how much stronger the electrical force of top pulling up on bot is than the gravitational force (earth pulling down on bot), I use a saw to cut the wood in half along the dividing line. (I've always wanted to be a shop teacher.) At this point I've reduced the electrical forces of top on bot to essentially zero with my saw. Now, about to fall to the floor, two-by-four bot is conflicted. Two-by-four top, its electrical power thwarted by the saw, is still pulling up on bot with its gravity force. The earth is pulling down on bot with gravity. Guess which wins. The bottom half of the two-by-four drops to the floor.

  Using the equation for the law of gravity, we can calculate the difference between the two gravitational forces. It turns out that the earth's gravity on bot wins out by being more than one billion times stronger than top's gravity on bot. (Trust me on this one.) Conclusion: The electrical force of top on bot before the saw cut was at least one billion times stronger than the gravitational force of top on bot. That's the best we can do in a lecture hall. The actual number is 1041, or a one followed by forty-one zeroes!! Let's write that out:

  100,000,000,000,000,000,000,000,000,000,000,000,000,000

  The number 1041 can't be appreciated, no way, but perhaps this will help. Consider an electron and a positron one hundredth of an inch apart. Calculate their gravitational attraction. Now calculate how far apart they would have to be to reduce their electrical force to the value of their gravitational attraction. The answer is some thousand trillion miles (fifty light-years). This assumes that the electric force decreases as the square of the distance—just like the gravitational force. Does that help? Gravity dominates the many motions Galileo first studied because every bit of the planet earth pulls on the things near its surface. In the study of atoms and smaller objects, the gravitational effect is too small to be noticed. In many other phenomena, gravity becomes irrelevant. For example, in the collision of two billiard balls (physicists love collisions as a tool for understanding), the influence of the earth is removed by doing the experiment on a table. The vertical downward pull of gravity is countered by the upward push of the table. What then remains are the horizontal forces that come into play when ball strikes ball.

  THE MYSTERY OF THE TWO MASSES

  Newton's law of universal gravitation provided the F in all cases in which gravitation is relevant. I mentioned that he wrote his F so that the force of any object, say the earth, on any other object, say the moon, would depend on the "gravitational stuff" contained in the earth times the gravitational stuff contained in the moon. To quantify this profound truth, Newton came up with another formula, around which we have been dancing. In words, the force of gravity between any two objects, call them A and B, is equal to some numerical constant (usually denoted by the symbol G) times the stuff in A (let's denote it by MA) times the stuff in B (MB) all divided by the square of the distance between object A and object B. In symbols:

  We'll call this Formula II. Even diehard innumerates will recognize the economy of our formula. For concreteness you can think of A as the earth and B as the moon, although in Newton's powerful synthesis the formula applies to all bodies. A specific equation for that two-body system would look like this
:

  The earth-moon distance, R, is about 250,000 miles. The constant G, if you want to know, is 6.67 × 10−11 in units that measure the M's in kilograms and R in meters. This precisely known constant measures the strength of the gravitational force. You don't need to memorize this number or even care about it. Just note that the 10−11 means that it is very small. F becomes really significant only when at least one of the M's is huge, like all the "stuff" in the earth. If a vengeful Creator could make G equal to zero, life would end pretty quickly. The earth would head off on a tangent to its elliptical orbit around the sun and global warming would be dramatically reversed.

  The exciting thing is M, which we call gravitational mass. I said it measures the amount of stuff in the earth and the moon, the stuff that, by our formula, creates the gravity force. "Wait a second," I hear somebody in the back row groaning. "You've got two masses now. The mass (m) in F = ma (formula I) and the mass (M) in our new formula II. What gives?" Very perceptive. Rather than being a disaster this is a challenge.

  Let's call these two different kinds of masses big M and little m. Big M is the gravitational stuff in an object that pulls on another object. Little m is inertial mass, the stuff in an object that resists a force and determines the resulting motion. These are two quite different attributes of matter. It was Newton's insight to understand that the experiments carried out by Galileo (remember Pisa!) and many others strongly suggested that M = m. The gravitational stuff is precisely equal to the inertial mass that appears in Newton's second law.

  THE MAN WITH TWO UMLAUTS

  Newton did not understand why the two quantities are equal; he just accepted it. He even did some clever experiments to study their equality. His experiments showed equality to about 1 percent. That is, M/m = 1.00; M divided by m results in a 1 to two decimal places. More than two hundred years later, this number was dramatically improved. Between 1888 and 1922, a Hungarian nobleman, Baron Roland Eötvös, in an incredibly clever series of experiments using pendulum bobs of aluminum, copper, wood, and various other materials, proved that the equality of these two very different properties of matter was accurate to better than five parts in a billion. In math this says: M(gravity)/m(inertia) = 1.000 000 000 plus or minus .000 000 005. That is, it lies between 1.000 000 005 and .999 999 995.

  Today we have confirmed this ratio to more than twelve zeroes past the decimal point. Galileo proved in Pisa that two unequal spheres fall at the same rate. Newton showed why. Since big M equals little m, the force of gravity is proportional to the mass of the object. The gravitational mass (M) of a cannonball might be a thousand times greater than that of a ball bearing. That means the gravitational force on it will be a thousand times greater. But that also means that its inertial mass (m) will muster a thousand times more resistance to the force than the inertial mass of the ball bearing. If the two objects are dropped from the tower, the two effects cancel. The cannonball and the ball bearing hit the ground at the same time.

  The equality of M and m was an incredible coincidence, and it tormented scientists for centuries. It was the classical equivalent of 137. And in 1915 Einstein incorporated this "coincidence" into a profound theory known as the general theory of relativity.

  Baron Eötvös's research on M and m was his most noteworthy scientific work but by no means his major contribution to science. Among other things, he was a pioneer in punctuation. Two umlauts! More important, Eötvös became interested in science education and in the training of high school teachers, a subject near and dear to me. Historians have noted how Baron Eötvös's educational efforts led to an explosion of genius—such luminaries as the physicists Edward Teller; Eugene Wigner, Leo Szilard, and the mathematician John von Neumann all came out of Budapest during the Eötvös era. The production of Hungarian scientists and mathematicians in the early twentieth century was so prolific that many otherwise calm observers believe Budapest was settled by Martians in a plan to infiltrate and take over the planet.

  The work of Newton and Eötvös is dramatically illustrated by space flight. We have all seen the space capsule video: the astronaut releases his pen, which hovers near him in a delightful demonstration of "weightlessness." Of course, the man and his pen aren't really weightless. The force of gravity is still at work. The earth tugs on the gravitational mass of capsule, astronaut, and pen. Meanwhile, the motion in orbit is determined by the inertial masses, given by formula I. Since the two masses are equal, the motion is the same for all objects. Astronauts, pen, and capsule move together in a dance of weightlessness.

  Another approach is to think of the astronaut and pen in free fall. As the capsule orbits the earth, it is actually falling toward the earth. That's what orbiting is. The moon, in a sense, is falling toward the earth; it just never gets there because the surface of the spherical earth falls away at the same rate. So if our astronaut is free falling and his pen is free falling, they're in the same position as the two weights dropped from the Leaning Tower. In the capsule or in free fall, if the astronaut could manage to stand on a scale, it would read zero. Hence the term "weightlessness." In fact, NASA uses the free-fall technique for training astronauts. In simulations of weightlessness, astronauts are taken to high altitude in a jet, which flies a series of forty or so parabolas (there's that form again). On the dive side of the parabola, the astronauts experience free fall ... weightlessness. (Not without some discomfort, however. The plane is unofficially known as the "vomit comet.")

  Space-age stuff. But Newton knew all about the astronaut and his pen. Back in the seventeenth century, he could have told you what would happen on the space shuttle.

  THE GREAT SYNTHESIZER

  Newton led a semireclusive life in Cambridge, with frequent visits to his family estate in Lincolnshire, at a time when most of the other great scientific minds of England were hanging out in London. From 1684 to 1687 he toiled over what was to be his major work, the Philosophiae Naturalis Principia Mathematica. This work synthesized all of Newton's previous studies in mathematics and mechanics, much of which had been incomplete, tentative, ambivalent. The Principia was a complete symphony, encompassing all of his past twenty years of effort.

  To write the Principia, Newton had to recalculate, rethink, review, and collect new data—on the passage of comets, on the moons of Jupiter and Saturn, on the tides in the estuary of the Thames River, and more and more. It is here that he began to insist on absolute space and time and it is here that he expressed with rigor his three laws of motion. Here he developed the concept of mass as the quantity of stuff in a body: "The quantity of matter is that which rises conjointly from its density and its magnitude."

  This frenzy of creative production had its side effects. According to the testimony of an assistant who lived with him:

  So intent, so serious upon his studies that he eats very sparingly, nay, oft times he forgets to eat at all....At rare times when he decided to dine in the Hall, he would ... go out into the street, stop, realize his mistake, would hastily turn back and, instead of going into the Hall, return to his Chambers....He would occasionally begin to write at his desk standing, without giving himself the leisure to draw a chair.

  Such is the obsession of the creative scientist.

  The Principia hit England, indeed Europe, like a bombshell. Rumors of the publication spread rapidly, even before it emerged from the printers. Among physicists and mathematicians, Newton's reputation was already large. The Principia catapulted him to legend status and brought him to the attention of philosophers such as John Locke and Voltaire. It was a smash. Disciples, acolytes, and even such eminent critics as Christiaan Huygens and Gottfried Leibniz joined in praise of the awesome reach and depth of the work. His archrival, Robert "Shorty" Hooke, paid Newton's Principia the ultimate compliment, asserting that it was plagiarized from him.

  When I last visited Cambridge University, I asked to see a copy of the Principia, expecting to find it in a glass case in a helium atmosphere. No, there it was, first edition, on the bookshelf in the p
hysics library! This is a book that changed science.

  Where did Newton get his inspiration? Again, there was a substantial literature on planetary motion, including some very suggestive work by Hooke. These sources probably had as much influence as the intuitive power suggested by the timeworn tale of the apple. As the story goes, Newton saw an apple fall one late afternoon with an early moon in the sky. That was his link. The earth exerts its gravitational pull on the apple, a terrestrial object, but the force continues and can reach the moon, a celestial object. The force causes the apple to drop to the ground. It causes the moon to circle the earth. Newton plugged in his equations, and it all made sense. By the mid-1680s Newton had combined celestial mechanics with terrestrial mechanics. The universal law of gravitation accounted for the intricate dance of the solar system, the tides, the gathering of stars in galaxies, the gathering of galaxies in clusters, the infrequent but predictable visits of Halley's comet, and more. In 1969, NASA sent three men to the moon m a rocket. They needed space-age technology for the equipment, but the key equations programmed into NASA's computers to chart the trajectory to the moon and back were three centuries old. All Newton's.

  THE TROUBLE WITH GRAVITY

  We've seen that on the atomic scale, say the force of an electron on a proton, the gravitational force is so small that we'd need a one followed by forty-one zeros to express its weakness. That's like... weak! On the macroscopic scale the inverse-square law is verified by the dynamics of our solar system. It can be checked in the laboratory only with great difficulty, using a sensitive torsion balance. But the trouble with gravity in the 1990s is that it is the only one of the four known forces that does not conform to the quantum theory. As mentioned earlier, we have identified force-carrying particles associated with the weak, strong, and electromagnetic forces. But a gravity-related particle still eludes us. We have given a name to the hypothetical carrier of the gravity force—it's called the graviton—but we haven't detected it yet. Large, sensitive devices have been built to detect gravity waves, which would emerge from some cataclysmic astronomical event out there—for example, a supernova, or a black hole that eats an unfortunate star, or the unlikely collision of two neutron stars. No such event has yet been detected. However, the search goes on.