Beyond the God Particle (15 page)

But we have learned new things about mass over the years. For example, as we've seen in the
previous chapter
, things that have mass can be converted to
energy
. This was the great insight that came out of Einstein's theory of relativity and is imbedded in his famous formula, E = mc
²
. This formula tells us the energy for a stationary (nonmoving) object with mass m. A more complicated formula tells us how a particle's energy is determined even when it is moving, involving both its mass and its velocity (or more properly, its “momentum”; see chapter 4,
note 3
.) We can run the formula backward: if we know the energy and we know the velocity (momentum) we can work out the mass. So, even for a mysterious elementary particle, such as the Higgs boson at the CERN LHC, or the top quark at Fermilab's Tevatron, we can figure out its mass by measuring both its energy and its velocity in a large particle detector and by using the fancier formula.

Even in Einstein's theory of relativity, we are still deploying the same old idea: mass is a measure of quantity of matter, the ancient concept that we inherited from the Greeks (or earlier), and it is such a robust concept that it still holds true for the top quark or for a black hole. But, at the level of the truly elementary particles, we need to reexamine the concept of mass in greater detail. And, indeed, there are surprises.

THE MASSES OF ELEMENTARY PARTICLES

In the early twentieth century, with the new laws of quantum physics, the nature of Democritus's atoms was finally revealed and understood. Physics then began an exploratory descent to the shortest distances of nature. This became something of an exercise in opening a sequence of little Russian dolls, the next smaller one nested within the present one, and so on. First Russian doll: What's inside an atom? A: The atomic nucleus sits at the core of the atom and electrons orbit around it in quantum motion, but otherwise like planets in a solar system. Second Russian doll: What's inside the atomic nucleus? A: The nucleus of the atom is composed of protons and neutrons that are tightly bound together by the strong force. Third Russian doll: What causes the strong force? A: It is as described in Yukawa's brilliant theory, the exchange of
π
mesons between protons and neutrons (and here it starts to get complicated because there are many new particles associated with the strong force, and protons, neutrons, and
π
mesons are not truly elementary). Fourth Russian doll: So what's inside of protons and neutrons and
π
mesons? A: Particles called “quarks,” and these are held together by “gluons” (see “Today: The Patterns of Quarks, Leptons, and Bosons” in the Appendix). And so on…

Altogether our list of the tiniest known Russian dolls is somewhat long—it includes the 6 quarks, the 8 gluons, the 6 leptons, and the 4 electroweak gauge bosons (the photon and W
⁺
, W
^–
, and Z
⁰
) and a not-yet-been-seen-but-surely-is-there
graviton
, the quantum of gravity—together with antiparticles, all of these comprise a complete list of all the known elementary particles (see figures
A.35
and
A.36
in the Appendix.) All of these are point-like, i.e., they have no discernible internal structure, so far as we can tell, and are what we mean by the “truly elementary particles.”

You might then ask an obvious question in the spirit of Democritus and based upon the Russian doll experience: “OK, if there are so many of these ‘elementary particles,’ then what are quarks and leptons and all of these bosons, etc., made of?” To this we have no facts to offer—only theoretical speculation. We could quote the current hot theorist rock stars who say, “They're all made of strings.” But in a few decades, with another generation of rock stars, perhaps there will be another speculative theory. It may say that “they're all made of smithereens.” And maybe these ideas are right and maybe they're wrong—maybe we'll never know, no matter how many Discovery Channel documentaries about the Smithereen Theory are produced.

As we've said, today we have an “almost complete list of elementary particles.” And that was the state of affairs on July 3, 2012. Things changed dramatically with the announcement on July 4, 2012, of a new object, which appears to be the Higgs boson. In fact, dozens of alternative theories about the Higgs boson and the Higgs mechanism were destroyed on July 4, as a veritable “mass extinction” of theories occurred. That's not a bad thing—it's progress (there's really no progress when science lapses into pure, almost religious, speculation about untestable things, like smithereens). So we now have the Higgs boson to add to our list. But what is the Higgs boson and why does it exist, and does adding the Higgs boson to our list make it complete? Many questions are raised by the Higgs boson. In short, with respect to the Higgs boson, “Who ordered that?”

When we are at the level of the elementary particles, we are exclusively and deeply within the mysterious realm of quantum mechanics. Here we find that the nature of the phenomenon of mass itself becomes a more enigmatic mystery and a greater puzzle. It becomes more exciting as well—the multi-millennia-old idea of mass merely as a “quantity of matter”—a concept that we've been using since antiquity—starts to break down.

NO MASS

In particle physics, for the first time anywhere in science, we meet something radically new
:
there exist particles that have no mass
. A truly massless particle, but one that has nonzero energy, is unprecedented anywhere else in nature. These particles, by our ancient and traditional concept of mass, would have
absolutely zero “quantity of matter.” Yet massless particles exist—you can count them—they carry energy—so they do have “quantity of matter,” though they have no mass. With particle physics, mass evolves into a new concept that is different than the simple old one of “quantity of matter” that has served us so well since antiquity in describing big aggregate objects. The whole concept of mass starts to become intimately related to the forces, and especially the fundamental symmetries, that govern all of the elementary constituents of all the matter in the universe. In this sense there now emerges an enormous difference between large everyday things and the tiniest denizens of nature.

So, to begin to understand what mass is at a deeper level, as a physical phenomenon of elementary particles, we must first understand what “masslessness” implies. What does it mean for a particle to exist but to have no mass? This is how Hamlet might have attacked the question.

We focus on light, to coin a bad pun. Light is composed of particles called photons. These particles have rather unusual properties compared to things like marbles or billiard balls. Photons are “point-like,” that is, they have absolutely no internal size or structure, as far as we can see. Moreover, as we said, they are always moving, traveling at a well-defined speed called the speed of light, which physicists denote by the letter “c.” The speed of light is very, very large, about 300,000 kilometers per second (186,000 miles per second). In fact, it takes only a little more than a second for a photon to travel from the earth to the moon. Because the speed of light is so great, it took a long time for people to measure it from experimental observations, and they had to resort to a lot of tricks and develop new techniques to do it. Today we know the value of c very precisely.

Photons were the first entities to reveal quantum physics: they also behave like particles and they also behave like waves—that is—they move in a wavelike manner, yet they also at the same time behave like particles—you can “count” them. This is a mind-numbing paradox, but it is true. This “dual” behavior of photons is called a
quantum state
, and all quantum states have it, and all things are quantum states. The wave-particle behavior is shared by all particles, electrons, quarks, muons, etc. This was the conclusion that became the bedrock of “quantum physics,” and if you are a poet (or artist, or musician, or lawyer, or statesman, etc.), we have a book all about this profound yet enigmatic business for you (see
Quantum Physics for Poets
[Amherst, NY: Prometheus Books, 2011], chap. 2,
note 3
).

So, photons can behave like particles, despite their funny quantum waviness and their imperative to always travel at the speed of light. They do have something in common with marbles or billiard balls—each photon carries energy as it moves through the room at the speed of light. Photons can have a lot of energy, and then we call them “X-rays”; still more energy, and we call them “gamma rays,” as when they are the product of such things as radioactive disintegration or supernova explosions. Gamma rays readily will go “tick…tick…tick…tick” as they are counted in a Geiger counter. It's dangerous for living organisms to be exposed to too many X-rays or gamma rays because they tend to destroy biological tissue, such as DNA. But photons can have less energy, becoming the light we see, and with still less energy, will fade off into the far red scale of visibility, becoming warm, gentle infrared light emanating from a soothing fire in the fireplace on a cold winter night, finally becoming at the lowest energy scales microwaves and radio waves.

The intriguing and novel thing about photons is that they each
have absolutely no mass
. As we have said, photons are
massless
particles. In fact, as far as what we have directly observed in the lab, photons are the only truly massless, freely moving particles (we expect there exist other massless particles, such as the hitherto unobserved particles of gravity, called “gravitons,” and the gluons that bind quarks but are trapped forever inside of hadrons, so we never get to see them freely moving as massless particles through space—see
figure A.37
and surrounding text in the Appendix).

“Hold on!” exclaims Katherine, who looks up from studying her law school notes in preparation for the bar exam, “Didn't that grandfatherly old man with long, bushy white hair and a pipe once say that energy is equivalent to mass? So, if a photon has energy, how can it have no mass? If it has no mass, doesn't E = mc
²
tell us it has zero energy? How can a photon therefore exist at all if it always has zero energy?”

Yes, Katherine, indeed the photon has no mass, but it does have energy. The photon defeats this apparent conundrum by never standing still—a photon always moves at the speed of light, and you cannot arrest a photon (in a real sense) and bring it into a stationary state of zero motion. The photon's very existence is a legal loophole in Einstein's relativity that permits massless particles to also have energy (and momentum), provided they always travel at the speed of light (see chapter 4,
note 4
). In fact, this goes
to the core of Einstein's theory of relativity: no matter how fast we chase after a photon, it always moves away from us at exactly the same speed of light. You can never slow a photon down and place it on a balance scale to measure its mass, because its mass is zero and it always moves at c. “I see,” she replies, “photons have no mass, so they always travel at the speed of light. How clever is the fine print on the legal contract of nature! But why?”

Photons are a sort-of exceptional case. Most particles have mass (in fact, all other known elementary particles at this time are massive particles, with the exception of the eternally trapped gluons and unseen gravitons) and thus, at least in principle, any elementary particle can be brought to a state of rest and will then have Einstein's famous amount of “rest energy,” E = mc
²
. But not the photon. The photon is a special particle that
can never be brought to rest
. Now, think about that for a moment. Isn't this interesting? Even if we are talking about a massive particle
at rest
, the formula for its total energy,
at rest
, is E = mc
²
, yet this involves c, the speed of light. The speed of light is intrinsically wrapped up in all of this phenomenon of mass. It is fundamental. We call c a
fundamental constant of nature
. It governs all properties of motion, whether we are at rest or moving near the speed of light.

As we've seen when a massive object moves, relative to us, it acquires additional energy of motion, known in physicists’ jargon as
kinetic energy
. It acquires just a little kinetic energy if it moves slowly. But the kinetic energy becomes greater and greater as the particle moves faster and faster. And, as the massive particle approaches the speed of light, its total energy becomes infinite. So, in fact, no massive particle can ever travel at the speed of light, because it would require an infinite amount of energy to make it do so. The photon does it by being massless, but the photon can therefore never be at rest, and all photons travel at the speed of light.

SYMMETRY IN MASSLESSNESS

The existence of massless particles raises the interesting question: Why must mass exist at all? What kind of world would we have if all other elementary particles were massless?

It certainly wouldn't be a very hospitable place in which to live. One of Einstein's results of special relativity is that time ceases to exist for objects
that travel at the speed of light. That is, if a lowly photon carried a wristwatch and departed Earth from a flashlight heading for a distant galaxy, he would notice that he arrived at his destination instantaneously. The vast distances of intergalactic space present no problem for photons to traverse—from their perspective they do all trips instantaneously. No time would elapse at all on the photon's wristwatch in hopping from Andromeda to the Milky Way, or from Earth to UDFj-39546284, one of the most distant galaxies ever recorded.
²
But, alas, for our little photon there would be no time to read a good book on the trip or to catch up with some zzz's. So, too, if we were all massless particles, we would always take zero time to do everything and anything, and we would always be on the go—at the speed of light. Our world would be completely devoid of experience as we know it. What kind of life would that be? Well, we wouldn't age. But unfortunately, a world without time is non-experiential. We wouldn't age, but we also wouldn't live.