Knocking on Heaven's Door (40 page)

[
FIGURE 44
]
The
W
boson can decay into a charged lepton and its associated neutrino, or into an up and down quark, or a charm and strange quark. In reality, the physical particles are superpositions of different types of quarks or neutrinos. This allows the
W
to some-times decay into particles from different generations simultaneously.

Particle masses are also critical in determining allowed decays. A particle can decay only into other particles whose masses add up to a smaller mass than the initial particle. Although the
W
also interacts with the top and bottom quarks, the top quark is heavier than the
W
, so this decay isn’t allowed.
⁵⁶

Let’s consider the
W
decaying into two quarks, since in that case the experimenters measure both decay products (not true for lepton and neutrino since the neutrino is “missing”). Because energy and momentum are conserved, measuring the total energy and momentum of both
final state
quarks tells us the energy and momentum of the particle that decayed into them, namely, the
W
.

At this point both Einstein’s special theory of relativity combined with quantum mechanics make the story a bit more interesting. Einstein’s special theory of relativity tells us how mass is related to energy and momentum. Most people know the shorthand
E
=
mc
²
. This formula holds for particles at rest if m is interpreted as m0, the intrinsic mass of a particle when it’s stationary. Once particles move, they have momentum and the more complete formula
E
²
-
p
²
c
²
=
m
₀
²
c
⁴
comes into play.
⁵⁷
With this formula, the energy and momentum let experimenters deduce the particle’s mass, even when the initial particle has long since disappeared via its decay. Experimenters add up all the momentum and energy and apply this equation. The initial mass is then determined.

The reason quantum mechanics comes into play is more subtle. A particle won’t always seem to have exactly its real and true mass. Because the particle can decay, the quantum mechanical uncertainty relation, which says that it takes infinitely long to precisely measure energy, tells us that the energy for any particle that doesn’t live forever can’t be precisely known. The energy can be off by an amount that will be bigger when the decay is faster and the lifetime shorter. This means that in any given measurement, the mass can be close to—but not precisely—the true average value. Only with many measurements can experimenters deduce both the mass—the value that is most probable and to which the average will converge—and the lifetime, since it is the length of time a particle exists before decaying that determines the spread in measured masses. (See Figure 45.) This is true for the
W
boson, and also for any other decaying particle.

[
FIGURE 45
]
Measurements of decaying particles center around their true masses, but allow for a spread of mass values according to their lifetime. The figure shows this for the
W
gauge boson.

When experimenters piece together what they measure, using the methods this chapter has described, they might find a Standard Model particle. (See Figure 46 for a summary of Standard Model particles and their properties.)
⁵⁸
But they might also end up identifying something entirely new. The hope is that the LHC will create new exotic particles that will yield insights into the underlying nature of matter—or even space itself. The next part of the book explores some of the more interesting possibilities.

[
FIGURE 46
]
A summary of Standard Model particles, organized according to type and mass. The gray circles (sometimes inside the squares) give particle masses. We see the mysterious variety of the elements of the Standard Model.

MODELING, PREDICTING, AND ANTICIPATING RESULTS

TRUTH, BEAUTY, AND OTHER SCIENTIFIC MISCONCEPTIONS

In February 2007, the Nobel Prize—winning theoretical physicist Murray Gell-Mann spoke at the elite TED conference in California, where innovators working in science, technology, literature, entertainment, and other forefront arenas gather once a year to present new developments and insights about a wide variety of subjects. Murray’s crowd-pleasing talk, which was rewarded with a standing ovation, was on the topic of truth and beauty in science. The basic premise of the talk can best be summarized with his words, which echo those of John Keats: “Truth is beauty and beauty is truth.”

Gell-Mann had good reasons to believe his grand statement. He had made some of his most significant Nobel Prize—winning discoveries about quarks by searching for an underlying principle that could elegantly organize the seemingly random set of data that experiments had discovered in the 1960s. In Murray’s experience, the search for beauty—or at least simplicity—had also led to truth.

No one in the audience disputed his claim. After all, most people love the idea that beauty and truth go together and that the search for one will more often than not reveal the other. But I confess that I have always found this assumption a little slippery. Although everyone would love to believe that beauty is at the heart of great scientific theories, and that the truth will always be aesthetically satisfying, beauty is at least in part a subjective criterion that will never be a reliable arbiter of truth.

The basic problem with the identification of truth and beauty is that it does not always hold—it holds only when it does. If truth and beauty were equivalent, the words “ugly truth” would never have entered our vocabulary. Even though those words weren’t specifically directed toward science, observations about the world are not always beautiful. Darwin’s colleague Thomas Huxley nicely summarized the sentiment when he said “science is organized common sense where many a beautiful theory was killed by an ugly fact.”
⁵⁹

To make matters more difficult, physicists have to allow for the disconcerting observation that the universe and its elements are not entirely beautiful. We observe a plethora of messy phenomena and a zoo of particles that we’d like to understand. Ideally, physicists would love to find a simple theory capable of explaining all such observations that uses only a spare set of rules and the fewest possible fundamental ingredients. But even when searching for a simple, elegant, unifying theory—one that can be used to predict the result of any particle physics experiment—we know that even if we find it, we would need many further steps to connect it to our world.

The universe is complex. New ingredients and principles are generally needed before we can connect a simple, spare formulation to the more complicated surrounding world. Those additional ingredients might destroy the beauty present in the initial proposed formulation, much as earmarks all too often interfere with a congressional bill’s initial idealistic legislation.

Given the potential pitfalls, how do we go about trying to go beyond what we know? How do we try to interpret as-yet-unexplained phenomena? This chapter is about the idea of beauty and the role of aesthetic criteria in science, and the advantages and disadvantages of beauty as a guide. It also introduces
model building
, which uses a bottom-up approach to science, while paying attention to aesthetic criteria in attempts to guess what comes next.

BEAUTY

I recently spoke with an artist who humorously remarked how one of the great ironies of modern science is that today’s researchers seem more likely than contemporary artists to present beauty as their goal. Of course, artists haven’t abandoned aesthetic criteria, but they are at least as likely to talk about discovery and invention when discussing their work. Scientists cherish those other attributes too, but they simultaneously strive to find the elegant theories they often find most compelling.

Yet despite the value many scientists place on elegance, they can have divergent notions about what is simple and beautiful. Just as you and your neighbor might violently disagree over the artistic merits of a contemporary artist such as Damien Hirst, different scientists find distinct aspects of science satisfying.

Together with like-minded researchers, I prefer to search for underlying principles that illuminate connections among superficially disparate observed phenomena. Most of my string theory colleagues study specific solvable theories in which they use difficult mathematical formulations to tackle toy problems (problems not necessarily relevant to any real physical setup) that might only later find applications to observable physical phenomena. Other physicists prefer to focus only on theories with a concise elegant formalism that generate many experimental predictions which they can systematically calculate. And others simply like computing.

Interesting principles, advanced mathematics, and complicated numerical simulations are all part of physics. Most scientists value all of them, but we choose our priorities according to what we find most pleasing or most likely to lead to scientific advances. In reality, we often also choose our approach according to which method best suits our unique inclinations and talents.

Not only do current views of beauty vary. As is also true with art, attitudes evolve over time. Murray Gell-Mann’s own specialty, quantum chromodynamics, presents an excellent case in point.

Gell-Mann’s conjecture about the strong nuclear force was based on a brilliant insight about how the many particles that were constantly being discovered in the 1960s could be organized into sensible patterns that would explain their abundance and types. He hypothesized the existence of more basic elementary particles known as quarks, which he suggested carry a new type of charge. The strong nuclear force would then influence any object that carried the conjectured charge, and cause quarks to bind together to form neutral objects—much as the electric force binds electrons with charged nuclei to form neutral atoms. If true, all the particles being discovered could be interpreted as bound states of these quarks—aggregate objects that have no net charge.

Gell-Mann realized that if there were three different types of quarks, each of which carried a distinct color charge, many such combinations of neutral bound states would form. And these many combinations could (and did) correspond to the plethora of particles that were being found. Gell-Mann thereby had found a beautiful explanation for what seemed like an inexplicable mess of particles.

However, when Murray—as well as the physicist (and later neurobiologist) George Zweig—first proposed this idea, people didn’t even believe it was a proper scientific theory. The reason is somewhat technical but interesting. Particle physics calculations rely on particles not interacting when they are far apart, so that we can compute the finite effects of the interactions that occur when they are close together. With this assumption, any interaction can be entirely captured by the local forces that apply when the interacting particles are in close proximity.

The force that Gell-Mann had conjectured, on the other hand, was stronger when particles were farther apart. That meant that quarks would always interact, even when very distant. According to the then-reigning criteria, Gell-Mann’s guess didn’t even correspond to a true theory that could be used for reliable calculations. Because quarks always interact, even their so-called
asymptotic states
—the states involving quarks that are far away from everything else—are very complicated. In an apparent concession to ugliness, the asymptotic states they postulated weren’t the simple particles you’d like to see in a calculable theory.