Beyond the God Particle

by Leon M. Lederman

  Inside of a superconductor, like a small bar of ultra-cold lead, which can be easily constructed in a laboratory with good cryogenic equipment, the massless photon, the particle of light, becomes heavy—it acquires mass. We can actually, in principle, make photons stand still in a superconductor! It is as though one has created a mini-universe in which the vacuum state has been modified (it is filled with lead, or nickel or niobium, and is cooled to less than 2° above absolute zero temperature, that is, 2° Kelvin) and the quantum dynamics of this material causes a photon, the otherwise massless particle of light, to become a heavy particle. A superconductor allows us to become the architects of a little artificial universe in the lab, and it offers a switch that allows us to turn on or off a mass for an otherwise massless particle.

  The mechanism of a superconductor can be described at different levels of detail, but it provides an insight into how mass, the quantity of matter of a particle, could be created by nature itself through quantum effects. The symmetries that are associated with the massless photon become hidden in a superconductor. The photon blends with the particles in the superconducting state to become something else, a new kind of photon with mass. This tells us that the properties of nature's quantum vacuum itself are inextricably wound up with the properties of particles and their masses.

  Superconductivity is so well understood today that it has become an industrial tool. The enormous magnets of the Large Hadron Collider at CERN, and formerly those at the Fermilab Tevatron, use superconductivity to produce otherworldly strong magnetic fields at minimal cost in electricity. And, as a spin-off of the Fermilab Tevatron magnets, the powerful magnets used in MRI machines were born. Someday you may have a superconducting coffeemaker in your kitchen.

  The underlying theoretical ideas of superconductivity were imported into particle physics by Jeffrey Goldstone, Giovanni Jona-Lasinio, Yoichiro Nambu, and others in the late 1950s to early 1960s.4 The masses of elementary particles, at least the strongly interacting ones, the proton and the neutron, were beginning to look like a dynamical phenomenon, something that had to do with the vacuum of space itself.

  IT'S ALL IN THE VACUUM

  As weird as the quantum world can get, perhaps one of the strangest notions is that the vacuum itself is not empty, but rather, it is a complicated structure. The vacuum is a quantum state. We are pretty sure (not absolutely sure) that it is the state of lowest energy, called the “ground state.” And all quantum states, including the ground state, can have complex features—they are not empty. For example, the ground state of a hydrogen atom has an electron orbiting the proton in a spherical cloud-like wave—it is not empty.

  So, too, we've just seen that the ground state of a superconductor contains a soup of particles that effectively give the photon a mass. Our vacuum's particular structure fundamentally and inextricably influences the properties of particles. Particles are now viewed as “excitations” of the vacuum—the concepts of the vacuum of space and time together with the elementary particles become welded into one. It is as if Shakespeare's Hamlet has as much to do with the other characters onstage as with the stage upon which they perform. (Shakespeare may have been the original quantum theorist.)

  HOW CAN I ESCAPE THE VACUUM?

  So, there's now a new complication we must dissect—the inseparable vacuum and its relationship to matter. These are not disjointed but are united—just as the brain is united with the body. But physicists have to dissect nature, and to do it they need a tool to turn one thing off while another thing is on.

  In the quest of understanding mass, the place to start is to contemplate a particle that doesn't feel the effects of the vacuum structure. This is a particle, like the photon, that can have energy but has no mass at all—a particle that always travels at the speed of light—arriving instantaneously at any destination—and thus has no experience of the vacuum along the way.

  As we noted, the world in which particles are all massless would be a world of profound and elegant simplicity, and simplicity in physics comes from symmetry, while the world in which we, the massive particles, actually live is one of broken-down symmetry. However, as ordinary particles approach the speed of light, they, too, begin to behave much like massless particles. If you hopped on a rocket ship that could travel at nearly the speed of light, you could take the trip from Earth to Andromeda, and the time elapsed on your wristwatch could become as short as you wish, depending upon how close to c, the speed of light, you can get. As you approach the speed of light you become much like a photon, experiencing no lapsing of time as you traverse the entire universe. You become an approximately massless particle yourself, as seen by a stationary observer at rest in the lab! And, by examining the behavior of approximately massless particles in the lab, any heavy particles traveling near the speed of light, we can glimpse the world where the symmetry is restored—the world of masslessness. The effects of the vacuum become decoupled from these near-to-the-speed-of-light particles. We can, therefore, by studying approximately massless particles, i.e., very energetic particles, at least in our mind's eye, restore the vaults and towers and walls of the ancient world of symmetry, much like archaeologists reconstruct a view of an ancient city.

  Let's begin a mental journey into such a perfect world—a world in which there is no mass, a divine world of perfect symmetry, where particles travel always at the speed of light. Our journey toward understanding mass is about to become quite intriguing.

  PARTICLE UTOPIA

  It's essential we now draw some pictures. We begin by drawing a picture of the motion of a massless particle in space and time. That's what physicists did when they started asking these sorts of questions about mass. We're going to draw good old-fashioned pictures on a two-dimensional page of paper. This will be like a map, but it must somehow display the three directions in space and also the one direction in time.

  Figure 5.6, Space-Time. The horizontal axis represents all three directions in space, while the vertical axis represents the flow of time.

  Alas, space is three-dimensional, and we always have a problem in rendering space—it's impossible to exactly draw three dimensions of space on a two-dimensional piece of paper. Furthermore, we will also have to use one of our two dimensions on the piece of paper to draw the fourth dimension—that of time. So, to depict space and time, we can only draw one horizontal axis to represent all of space, and let's say that this represents the east-west direction—like any map, east goes to the right and west to the left. You have to use your imagination to see the two other axes of space, one representing north-south, and the other up-down, coming out of the page and into your living room. The vertical axis in our picture represents time. In figure 5.6 we have drawn the basic map. This is a picture of a new world that we call “space-time.”

  Now, in nature there's something weird about time that distinguishes it from space. In space, we can always decide where we want to be. If we want to be in Antigua, Guatemala, we can hop a plane and enjoy beautiful coastlines and wonderful coffee, the colorful dress and the kite flying of the local Mayan descendants’ culture. But we have no control over where we are in time. We just “are” someplace in time. Of course, when we “are” at some time, we also “are” someplace in space. In our plot, a definite time and a definite location in space is a geometrical point, a “space-time” point. A point in space-time is called an event.

  For example, on the afternoon of July 4, 1927, there was an event at which little Billy Johnson lit off a firecracker in front of his father's hardware store on Main Street in Bedford Falls. The firecracker exploded with a loud bang. That particular instant in time at that particular point in space defined an event in space-time: the “firecracker event.”

  Our world is a fabric of a countless infinity of events. A mosquito stings Mrs. Fenster on her leg at her niece's ballet recital in the gymnasium of her local high school on September 20, 2003, at 2:31 p.m.; an atomic nucleus of Uranium spontaneously decays at exactly 5:23 a.m., GMT, deep in the e
xact center of the earth; a supernova explodes eight billion years ago in the constellation Taurus, at a distance of eight billion light-years from the earth; the light from said supernova will be detected by telescope in Chile at exactly 12:09 a.m. local time on January 12, 2015. These are just a few of the countless infinity of events that define our world. Some are in the deep past, others in the distant future. And some are related to one another, like the observation by very smart aliens many light-years away of the light emitted from the firecracker explosion by Billy Johnson. We might say that physics is the collection of events in space-time and the rules by which they relate to one another.

  Figure 5.7. An Event in Space-Time. This event, consisting of the explosion of a firecracker, is located at some particular value of time (which we have labeled as 1:31 PM, July 4th, 1927) and at some particular location in space (which is directly in front of Mr. Johnson's Hardware store on Main Street in Bedford Falls).

  Let's return to Billy Johnson's firecracker experiment. It's convenient to reset our clocks and call the time of the fire- cracker event “zero,” so our “time coordinate” for the firecracker explosion is defined to be t = 0. And, likewise, we reset our space coordinates so that the location of the exact spot at which the firecracker explodes is also “zero,” or, for our plot x = 0. Our space-time plot for the world then looks like figure 5.8:

  Figure 5.8. Firecracker at Origin. For convenience, we relocate the orign of time and space to coincide with the event of interest. The event, consisting of the explosion of a firecracker, is relocated to a value of time t = 0 by simply resetting our clocks, and a location in space, now denoted x = 0, by resetting our map coordinates.

  Now, when a firecracker explodes, there are physical consequences. If we plot the sequence of events, they look like figure 5.9. Of course, there is an instantaneous heating and compression of the atmosphere at the event of the explosion, and this produces sound waves, actually more of a shock wave in the air, the “bang” that emanates outward triggering an infinity of other events. For example, a brief instant later the shock wave reaches Billy's brother Tommy's ears. Tommy Johnson happened to be standing a mere ten feet from where the firecracker exploded out in the street in front of the hardware store. We label this on our figure 5.9 as event (A). A brief instant later the “bang” shock wave has spread farther and reaches the ears of Mr. Johnson, who is in the backyard of the hardware store unloading boxes, an event we label (B).

  Figure 5.9. Firecracker Sequence of Events. The shock wave of sound emanates outward in space-time from the firecracker event. We see a shock wave that grows larger in radius at later times. This traces out a cone-shaped surface in space-time. Subsequent events (A), (B), and (C) lie on the cone of the shock wave.

  And still another instant later, the shock wave has spread farther and reaches the ears of Ms. McMurrough's two dachshunds that are sleeping in her house down the side street behind the hardware store, at event (C). The sound wave continues outward, fading in strength as the compression wave of air expands out into the atmosphere. It leaves behind a startled Tommy Johnson; a concerned Mr. Johnson, who hurries toward the front of the store; and two frantically barking and jumping dachshunds that start climbing up the drapes of Ms. McMurrough's house.

  Each subsequent event is defined by the time it takes for the the shock wave from the explosion of the firecracker to reach that particular location in space. The firecracker shock wave is expanding spherically out into the atmosphere, growing larger in diameter but weaker in strength as time progresses. On our plot this shows up as a “cone” in space and time. You need to use a little imagination here, since as we've said, we cannot draw all three dimensions of space (we've depicted the top of the cone by a tilted circle to give the impression of more dimensions of space). At any instant in time after the explosion there is a spherical “wave front” of air compression, the shock wave, i.e., the audible “bang,” which we depict by this circle. The distance of the shock-wave-front from the original explosion, x, is just the time from the explosion, t, multiplied by the speed of sound, vsound (that is, distance of “bang” x = vsound times t).

  Of course, there's also a flash of light that is emitted by the firecracker explosion. The light travels at c, the speed of light, which is much, much faster than sound, so we can only draw this in a very exaggerated way on our plot. If we also include the light wave in the same plot as the sound wave, it looks like figure 5.10.

  Note that the light always reaches the distant observers much sooner than the sound wave. That's why these events are so crowded together near the origin, because the light arrives in such a small time interval, but if you look carefully at figure 5.10 you'll see that these events all happen at the same location in space as the sound events. At event An the light flash reaches Tommy Johnson's eyes. The time interval between event (A) and event (A´) is so short that Tommy hardly notices any time difference between hearing the explosion and seeing it. Mr. Johnson is farther away in the backyard of the hardware store when the direct photons from the firecracker reach him at event (B´), with the sound arriving a tiny instant later at (B). Finally, down the street the dachshunds, though sleeping (well, er, um, dachshunds are never 100 percent asleep), see the flash of light at event (C´) and are alerted, and then a noticeable instant later they hear the boom at event (C), which drives them into dachshund high gear whence they go tearing around Ms. McMurrough's house.

  Figure 5.10. Light Sequence of Events. Light also emanates outward in space-time from the firecracker event. This also traces out a cone-shaped surface in space-time. Subsequent events (A´), (B´), and (C´) lie on the light-cone. Note that each of these events occurs at the same space-location, but at much earlier times, than the corresponding events (A), (B), and (C), due to the fact that the speed of light is much greater than the speed of sound.

  The very fast light wave continues to propagate outward through space at 186,000 miles per second. Unlike sound, which can only propagate relatively slowly in the air (about 1,000 feet per second) and cannot go into outer space, the light waves from the firecracker explosion continue far, far out and away from the arth. Within a second and a half the light reaches the moon, and could, in principle, be detected with an extremely powerful telescope there. About 38 hours later the light reaches the orbit of Planet Pluto; about 3.8 years later the light reaches the nearest star, ε-Proxima; about 30,000 years later it has transited the diameter of our Milky Way galaxy; in about 13 billion years it reaches the most distant objects we have ever seen in a telescope, the galaxies whose light is now reaching us as they appeared in their embryonic form, just forming after the big bang.

  Figure 5.11. Cosmic Sequence of Light Events. Light emanates further into the universe from the firecracker event. At any given time, t (we call it a “time slice”), the radius of the sphere of photons is given by (radius) = c t.

  MOTION IN SPACE-TIME

  We can use space-time diagrams to represent things that happen in any physical process. For example, we can use a space-time diagram to represent the motion of particles. Light is made of photons that always move at the speed of light. We can trigger the emission of photons by an event at which a flashbulb goes off. Photons then propagate outward in all directions at the speed of light. In space-time the photons are seen to move forward in time at ever-increasing distances from the flashbulb. This traces out a cone in space-time, what we call the “light-cone,” spreading out in space and time from the point at which the photons were initially produced.

  Figure 5.12. The motion of two photons is indicated by the arrows. These individual photon paths lie on the “light-cone,” emanating into the future from an event that emitted them at the origin. Photons always travel at the speed of light, c.

  By comparison, a single massive particle, like a muon, can in principle travel at any speed, up to nearly the speed of light. A muon, because it has mass, can also sit still. These possibilities are shown in figure 5.13. A muon at rest simply moves, like we
all do, forward in time with no progression in space. On the other hand, a very fast muon is one that moves forward in time but also progresses outward in space in some direction.

  Figure 5.13. Motion of Muons. A muon can have arbitrary velocities less than the speed of light. (a) shows a muon nearly at rest that “moves” forward in time but not in space. (b) shows a faster muon. (c) is an ultra-fast muon traveling at nearly the speed of light.

  We can make a muon move very, very fast, but we can never get any massive particle to travel at exactly the speed of light. At the LHC, protons are made to travel at 99.999999 percent of the speed of light. The muon's little sister, the electrons at CERN's LEP synchrotron, were made to travel 99.9999999925 percent of the speed of light. And we have very sensible ideas about someday building a Muon Collider in which we would get muons to travel at 99.99999999 percent the speed of light. But never will an electron or a proton or a muon get to 100 percent of the speed of light. Nature has an ultimate speed limit that is the speed of light. And the existence of mass implies, according to Einstein, that it would take an infinite amount of energy to make any massive particle travel at the speed we call “c.”

  But suppose, somehow, we could do a master experiment: make a muon have zero mass. We don't know how to do that exactly, but we could get very, very close to this situation experimentally, by making the muon travel as close to the speed of light as possible relative to us. The closer we get the muon to the speed of light, the more and more the muon behaves, as we observe it in our lab, like a massless particle. We can do this with our very powerful future Muon Collider, and as the speed of the muon approaches c, the effects of its mass become undetectable to us. So, what happens to a very, very fast muon as it starts to act like a massless particle?