Beyond the God Particle (13 page)

As the talks begin, you can hear a pin drop. The speakers nervously yet painstakingly review, in glorious detail, the data collected by the two large detectors and the complex statistical analysis required to extract a signal of any new particles from the data. They conclude at about 4:30 a.m., Fermilab time, to a standing ovation. The two CERN experimental collaborations at the LHC have just presented the official scientific discovery of the Higgs boson to the world. It is the biggest scientific discovery in the third millennium so far. We all then partied, watched the sun come up, and the next day began poring over the data in still greater detail.

For a moment the whole world stopped and gave heed to something abstract, something mind-bending, something ephemeral. From the
Hong Kong Economic Times
to the
Jerusalem Post
, from the
Fiji Sun
to the
Herald Tribune
from the
Kane County Chronicle
, to the
New York Times
, the story was carried on all the front pages of all the world's newspapers. But gradually, over the subsequent weeks, the daily news returned to the slowly recovering housing market, to a horrific mass murder, to the lingering unemployment rate, to an upcoming election, and to the usual rancid political squabbling in the US House of Representatives.

But now a much larger issue looms in the distance for human knowledge: What is the Higgs boson? Why does this thing exist? Is the Higgs a loner, or is there more to come? Are the next lessons far, far out of reach, or are we about to enter an era of rich new discoveries? What are the organizing
principles? What new and mysterious reality lies beyond the Higgs boson? It all revolves around one big question.

WHAT IS MASS?

There were lots of bad jokes out there about the Higgs boson and how it gives mass to particles. For example: “A God Particle walks into a church and the priest says, ‘What are you doing here?’ and the Higgs boson replies, ‘You can't have a mass without me.’” There was a Twitter quip by Neil deGrasse Tyson, “The Higgs discovery makes me feel heavier already. What we need instead is the anti-Higgs…a particle that takes mass away.”
¹
And, from our most reliable news source of all, the
Onion
, a more egalitarian comment: “Yeah, the Higgs boson is getting a lot of attention, but there are a lot of lower-profile bosons that are worth checking out if you get the chance.”
²

Of course, what we mean by “mass” in physics is not what is meant in other contexts, such as religion or as the term is used with “hysteria.” But after some perusing of Internet sites that try to explain what physical mass is, we concluded that you'll only get confused if you start there. In part, this reflects the general confusion throughout the history of physics at arriving at a valid definition of mass. There are in fact many definitions. So let's take a fresh look at this and adopt a simple definition of mass, one that works fairly generally, and one that can efficiently launch us into the depths of elementary particles. Following Mies van der Rohe, “Less is more.”

MASS IS A MEASURE OF QUANTITY OF MATTER

Yes, it's that simple. At least for the everyday objects, those that we encounter throughout our lives, mass is just a “measure of a quantity of matter.” A feather or an ant has a small mass, while an automobile or an elephant has a large mass. Perhaps it is remarkable that such a simple concept is meaningful in nature, if you pause to think about it. All forms of matter, from water to steel, from putty to peanut butter and jelly, from magma to Kool-Aid
^®
and vodka, to the interior of the sun and the cosmic
rays in the depths of space—all share a common property—we can talk about how much matter they “are” in terms of something we call
mass
. We needn't specify “jelly mass” to distinguish it from “Kool-Aid mass”—it's all the same—it's just mass, which is just so-and-so much matter.

Now that's seemingly simple. But there are challenges in implementing this concept. For example, how does one measure the mass of something like a quark, which is forever trapped inside of a larger particle, together with other quarks and things called “gluons,” etc., which can push and pull and actually change the mass of a quark? Just in case you've already considered some of the litany of subtleties surrounding the concept of mass in a high school physics course, then you've probably already encountered something called “inertial mass.” Inertial mass has to do with the
resistance of motion
of an object
to an applied force
. This was defined by an equation written several centuries ago by Isaac Newton, “
Force equals mass times acceleration
.” This means that, for a given applied force, an object with a larger inertial mass will accelerate more slowly than an object with a smaller inertial mass.

We would like to think the issue ends there and that “inertial mass” is all we ever have to worry about, but alas, it isn't so simple. For example, in dealing with gravitating systems, like galaxies and black holes, there are at least three types of mass, “inertial mass,” “gravitational mass,” and “passive gravitational mass.” For quarks there's “constituent mass,” “current mass,” and, more generally, “off mass-shell mass.” Then in discussions of relativity there's “transverse mass,” “longitudinal mass,” and “rest mass,” etc. These definitions are all very technical and refer to specific instances in which even the best-trained physicists can become confused about energy content, motion, interactions with other stuff, and the simple idea of plain old inertial mass just doesn't cut it.

For now, let's be naive and simple-minded and forget these nasty complications and stick with plain and simple “mass is a measure of quantity of matter.” The jolting revelations will come later.

MASS IS NOT WEIGHT

One reason that mass is generally a confusing concept for many people begins immediately with a trip to the moon. Most people think that the simplest measure of the quantity of matter (usually that which is their own quantity of matter, including their left foot, their head, that slight circumferential inner tube of abdominal fat, and perhaps the Big Mac
^®
still in their stomach that was consumed at lunch, i.e., all that faces them every morning on the bathroom scale) is actually their
weight
. But, no doubt, if you took Mr. Naylor's physics class in high school, you remember some admonishment such as: “Do not confuse weight with mass!
Weight is not mass and mass is not weight
.”

In 1969, on the Apollo 11 lunar mission, humans first reached the nearest orb to their own world: the moon. When Neil and Buzz first jumped off that ladder on July 21, from their spaceship to the moon's surface, they were featherweights. Their bathroom scale weight on the moon would have been a mere 30 pounds if they'd weighed 180 pounds on Earth. They had experienced the multi-billion-dollar diet of departing from Planet Earth onboard a
Saturn V
rocket and successfully navigated to the lunar surface where the force of gravity is one-sixth of that on Earth. But—hold on—while their weight loss was a spectacular 83 percent, apart from a lean diet of mulched meat, veggies, and Tang orange liquid, their body's inertial mass was no different on the moon than on Earth. The quantity of matter that is Neil or Buzz had not changed in traversing the 200,000 miles to the moon.

The catch, of course, is that weight is a
force
, and force is not mass. While the net force of gravity that an object experiences depends upon its mass, it also depends upon the strength of the gravitational field (this is Newton's way of thinking about gravity). The gravitational field at the surface of the moon is one-sixth of that on the earth, and hence the force experienced by Neil and Buzz is one-sixth of what they experience on the earth. If NASA had shipped a bathroom scale to the moon they would have read weights that were only one-sixth of what they would read on the earth. Bathroom scales measure the
force
of gravity acting on you, and not your mass. But the quantity of matter, and hence inertial mass, that Buzz and Neil are made of is not changed by an expensive trip to the moon.

Incidentally, the extra cost of shipping the bathroom scale to the moon would have been about four million dollars (in 1969!).

MEASURING MASS CAN BE TRICKY

The best way to measure mass, in anyone's gravitational field, such as here at home on Earth, is one you have surely witnessed and that dates to the ancients. It is to use a “balance scale.” A balance scale simply compares the mass of some object, let us a say a nugget of gold, to a standard predetermined quantity of matter. To establish standards, we could select our delegates and send them to a stuffy scientific conference somewhere in Eastern Europe, and there they agree upon a “standard of mass.” For example, we legislate that, worldwide and henceforth, a cube of water that measures 10 centimeters on each side, at standard temperature (20° C) and pressure (1 atmosphere at sea level), has a mass of matter we call “one kilogram.” We can compare any other amount of matter to our newly defined kilogram measure with our balance scale. If we place a gold nugget on one side of the balance and a 10 cm × 10 cm × 10 cm cube of water on the other side of the scale, we can immediately determine which is the greater mass: if the balance scale tips toward the gold, the nugget has more than a kilogram of mass; if the balance scale tips toward the cube of water, then the water has more mass. Voilà! We've thus made a very crude determination of the mass, or quantity of matter, that is the gold nugget.

And we can refine this in many ways. First, it's really inconvenient to use a cube full of water in our measuring apparatus as a counterweight standard of mass, because we'll surely spill it all sooner or later, and we have to correct our measurement for the mass of the container vessel of the water. So, we make counterweights: cleverly balance little pieces of lead against a carefully measured standard kilogram of water. We add or subtract shavings of lead from the lead side of the scale until it exactly balances. We then have our local blacksmith melt the lead and pour it into a mold to make a conveniently shaped cylindrical weight, much like the weight used in a grandfather clock. We then double- (and triple-) check that the resulting weight exactly balances the one-kilogram mass of water. This might take several tries, but eventually we'll have a conveniently shaped cylindrical lead weight to use on our scale instead of the cube of water that is exactly one kilogram of mass. We ask our blacksmith to make a dozen of these. We can then ask our blacksmith to forge, with extreme care, ten smaller weights that each contain exactly one-tenth the amount of lead. We can
use the balance to check that each smaller weight is the same as the others, and then use the balance to check that ten such smaller weights exactly balance the one kilogram weight we started with. In this way we develop a “one-tenth kilogram” weight, also known as a “100-gram” weight. And we can go further, down to a “one gram” and beyond to a “decigram” (tenth of a gram), a “centigram” (hundredth of a gram) until it simply becomes too difficult to make a smaller weight. We now have a wide range of weights at our disposal to use with the balance.

So we can now do a refined measure of the weight of the gold nugget. Simply add or subtract lead counterweights until the lead weights balance the gold nugget. Then count how many weights are needed to achieve the exact balance. For example, we may find that we need a
one
-kilogram weight,
three
one-hundred-gram weights,
five
ten-gram weights, and
two
one-gram weights to exactly balance the nugget. Ergo, the nugget of gold weighs exactly 1.352 kilograms! And, if we ask our blacksmith and our local clockworker to make a much better scale, we might find that we also need
seven
one-tenth-gram weights and
four
one-hundredth-gram weights to get a precise balance. Hence the nugget, more precisely, weighs 1.35274 kilograms.

At this point we may find the air motion fluctuating about in the room, the atmospheric pressure of today's weather and moisture condensed on the scale, etc.; each causes some tiny amount of “noise” in the measurement of the mass of the nugget. So, our final precise measurement of the mass of the nugget of gold is 1.35274 ± 0.00003 kilograms, where the number after the “±” is the “error” in our measurement. It's important to understand that no experiment can measure anything to infinitely good precision, that is, there is never zero error in any scientific measurement. This, perhaps more than anything, distinguishes science from crackpot beliefs and superstitions about the world that are always supposed to be exactly true.

The main point here is that the balance scale makes a comparison measurement and not an “absolute measurement.” The balance scale would work just as well on the moon, that is, we would find that we required exactly the same amount of lead to exactly balance the gold nugget on the moon, even though the moon's gravity is one-sixth of the earth's, and even though the nugget (and the lead weights) had a weight that was one-sixth as much as on the earth.

So, ultimately, we have made a comparison of the mass of a gold nugget
to a certain amount of water that defines a kilogram that is needed to represent the same mass. A kilogram of gold and kilogram of lead and a kilogram of water all have the same mass—they are all the same quantity of matter. Note that instead of using our balance scale we might have used a “fish scale” that measures the displacement of a spring when loaded with a mass. The spring balances against the mass by exerting a
force
associated with compressing the spring, and thus the spring scale is measuring
weight
, not mass. So a spring scale would measure one-sixth the force on the moon.

MASS IS NOT ENERGY