Beyond the God Particle (14 page)

Yet another more confusing aspect of mass, a confusion we hear all the time in the media when things like nuclear power or Higgs bosons and top quarks are discussed, is that “Einstein proved that mass and energy are the same thing.” FALSE! This isn't true and it isn't what Einstein proved. We first need a brief digression on energy. (A more seasoned veteran of this issue can skip to the
next section
.)

Energy is real, yet it is sometimes seemingly intangible. Most physicists can readily define energy of any particular type, but devising a general definition isn't a simple task. In high school physics books, energy is often defined as “the ability to do work.” Great! But this requires a precise definition of “work.” The definition of energy becomes circular very quickly. So, for the moment, trust us that
energy
has a precise definition for all of its various forms, and certain sophisticated mathematical formulations of physics automate the process of determining the energy of something. Let's briefly consider an important specific form of energy known as
kinetic energy
.
³

Kinetic energy
is energy of motion and depends upon the mass and the speed of a moving object. It requires energy to make a massive object move, requiring more energy the more mass that the object has, and the more speed that we desire of the object.

As a simple example of kinetic energy, consider a familiar moving object, such as an automobile. Suppose the automobile has a mass typical of compact automobiles, of about 1,000 kilograms. We'll assume that the automobile is traveling down the highway at a speed of 60 miles per hour, which is approximately 30 meters per second. Physicists then compute
that this automobile has a kinetic energy, or an energy of motion, equal to 450,000 energy units, called “
joules
.” This number is derived by multiplying: (one half) times (the mass of the car in kilograms) times (the speed of the car, in meters per second) times (the speed of the car in meters per second). You have probably seen this formula expressed with the equation E = (½) m v
²
. The energy units are named after James Prescott Joule, a nineteenth-century physicist who spent a great deal of time measuring and studying energy, especially when heat or thermodynamics was involved (Joule also invented electrical arc welding.) The statement that our automobile has a kinetic energy of 450,000 joules is a scientifically precise statement about the motion of the car and its kinetic energy.

For comparison, consider a completely different, and somewhat more bizarre, physical system—the motion of a pulse of protons in the CERN LHC, which is currently the world's highest-energy particle accelerator. One pulse in the LHC may contain about 3 trillion protons, about the number of atoms in a single living cell. The pulse is accelerated until it travels at 99.9999995 percent of the speed of light. We cannot use the simple formula for the automobile to compute the energy of the pulse of protons, because that formula comes from “classical physics” (the physics of Galileo and Newton), and its validity breaks down when things are traveling near the speed of light. Fortunately scientists know what to do in this case—they seize upon Einstein's special theory of relativity, and from this they can correctly compute the energy of the pulse of protons.
⁴
Therefore, even something as far removed from our everyday experience as a pulse of protons traveling near the speed of light in the LHC has a definite value for its energy. The pulse we have described, remarkably, has an energy (using Einstein's theory) of about 3,000,000 joules, about the same kinetic energy as that of a large loaded truck traveling at 60 mph down the highway!

Energy is a well-defined physical quantity that describes everything in the universe, and it always has a precise meaning in physics. Energy
is conserved
in every physical process, i.e., the total initial energy entering a process equals the total energy that comes out. If we had perfect energy conversion efficiency available to us, we could convert the energy in the LHC pulse to make a truck accelerate to 60 mph, or vice versa.

It's easy to get confused by this—if you already have a source of energy, such as a wind farm, or a coal-burning plant, or a nuclear power plant, then
you can readily
convert
that energy to electricity to power your home or a factory. However,
you are always using up the energy you started with
, either from the wind or from coal or from the nuclear fuel in the reactor. You are not creating a net amount of free energy from nowhere. You could use the electricity to break water down into pure hydrogen gas and oxygen gas. You could then use the hydrogen as a fuel in your car, perhaps thinking it was a “clean” and energy-efficient fuel. However, it's just the same energy that you already produced with your windmills or coal-burning or nuclear power plants. It may not be so clean overall, depending upon where you got it. You don't get energy for free.

If energy could be produced from nowhere, or vanish into nothingness, we would say that
energy is not conserved
. However, in every experiment that has ever been conducted to measure such effects, we have always discovered that the total energy we begin with equals the total energy we end up with.
Thus, energy is always conserved in nature.
Of course, many things in our everyday lives are not conserved. The number of living organisms on Planet Earth or the total value of the stock market are two examples. Energy also takes many different forms. Energy is quite apparent in a moving object (kinetic energy) but less so in an object sitting at rest on top of a mountain (potential energy, which can be converted to kinetic energy as it falls). Energy is generally lost in physical processes that convert it into waste forms such as heat and sound. It can be lost in deforming materials, creating dents and crumples, which changes and rearranges the molecules in the material. Energy can be absorbed (or released) in the form of chemical energy, changing the physical state of matter from solid to liquid, or liquid to gas. Energy can stream out of a system carried by light and other forms of radiation. A large star that has run out of fuel, can shrink, converting its gravitational potential energy into light, until the gravitational energy is exhausted and the star becomes finally a
brown dwarf
, or even a
black hole
.

Indeed, it took physicists, chemists, and biologists a long time to understand that the principle of conservation of energy is exact and omnipotent. It governs everything. Even life-forms are governed by energy conservation—there is no special form of energy reserved for living things—all energy can be measured by the same units throughout the entire universe. If you could do all of the detailed bookkeeping and keep track of all forms of energy, you would find that energy is always conserved in any process whatsoever.

What we have learned is that, if the laws of physics were changing in time, then the principle of energy conservation, would cease to be true. If the forces of nature are different at one time than at another, then the amount of energy invested in a physical process will be different than the amount of energy invested in the same process at a later time. However, we've learned from many other diverse observations that
the laws of physics are not changing through time over time scales almost equal to the age of the universe
. Thus, the result of any particular physics experiment that we do tomorrow, or yesterday, or ten seconds ago, or ten billion years ago, or a thousand billion years in the future will produce the same results. The laws of physics, and thus all the correct equations in physics, are the same at any time in the history of the universe. This is an experimental fact. The laws of physics appear to be steadfast and eternal.

We have just glimpsed one of the most important relationships in nature:
Energy conservation is associated with the fact that the laws of physics do not change in time!
This is an example of something of a more general and profound significance known as Noether's theorem. This remarkable mathematical theorem relates conservation laws in physics to underlying and fundamental symmetry principles. It was proved by Emmy Noether, one of the greatest physicists and mathematicians in the early twentieth century.
⁵
The key point is that the non-changing, or
invariance
, of the laws of physics is a
continuous symmetry of the laws of physics
. Noether's theorem says that for every continuous symmetry of the laws of nature, there is a conserved quantity.

RELATIVISTIC ENERGY

As we've noted above, Einstein's theory of relativity gave us a profound insight into the nature of energy and mass. Energy, velocity, and mass are related in Newton's classical physics. But in classical physics you can travel at any speed that you want. There's nothing sacred about the speed of light in Newton's physics—you are free to go faster if you have a really good rocket sled. Einstein overthrew the Newtonian concepts of space and time and discovered that nothing can go faster than the speed of light. Einstein found a new relationship between energy, mass, and velocity that was consistent with his new principle of relativity.

Newton would have concluded that the energy in an object that is sitting still is zero. But Einstein found that for a particle sitting still, with a mass m, there is nonzero energy, and he wrote down what may be the most famous formula ever written:

E = mc
²

The implications of this formula are literally earth-shattering. We emphasize that mass and energy are two different things, but this simple formula informs us that mass can in principle be converted into energy, and vice versa. This equation is so famous that it regularly makes appearances on TV, T-shirts, license plates, cartoons, in Hollywood productions, on subway and restroom walls, in Broadway musicals, on doodles on ink blotters in the Oval Office, and throughout countless other venues. This formula literally unleashes all of the energy in the universe, for better or worse.

For example, suppose we could convert one kilogram (that weighs about 2.2 pounds on Earth) of mass into energy? Einstein's formula says that we'll get about 10,000,000,000,000,000,000 joules of energy. This is an enormous amount of energy, able to make a 10,000-kilogram (about 10 tons) spacecraft travel with a velocity of 99 percent the speed of light.

The conversion of mass into energy happens all the time in nuclear physics. Einstein's energy-mass equivalence tells us that the mass of the nucleus of U
²³⁵
, the stuff used in nuclear reactors, is actually greater than the masses of the daughter nuclei and all the free neutrons that are produced from the disintegration of the U
²³⁵
. The excess energy is what we get out of the nuclear power plant. Any process in which a conversion of mass to energy occurs, that is, in which the total inertial mass is not conserved, is a process that can be described only in Einstein's special theory of relativity. E = mc
²
is the formula that is most identified with the age of nuclear physics. However, it is a formula that holds for all things throughout the entire universe.

BUT WHAT IS MASS?

We've talked about several things mass isn't. It isn't weight and it isn't energy, though it can be converted into energy and vice versa, à la Einstein. And we've talked about how, in its simplest form, mass is just a measure of a quantity of matter. But what is mass? We haven't answered that question, and perhaps we've been lulled into the notion that the question is meaningless.

In fact, mass is a physical phenomenon. Something causes mass. It is “emergent” from something deeper and more fundamental. Now we enter a deeper realm, if not the deepest realm of all, that of elementary particle physics. This is a bit like the trip Alice took down the rabbit hole into Wonderland. In Wonderland the familiar concepts of things are changed. Many times the question we thought we were asking is the wrong question, to be replaced by another that seems to have no relationship to the first, but in the end answers the first question in a profound way while illuminating many more pieces of the grand puzzle. In particle physics we'll find an answer to the question “What causes mass?” We'll also find more questions.

Fasten your seat belt, turn to the
next chapter
, and prepare for a trip down the rabbit hole.

The concept of “mass” as a “quantity of matter” applies to all things that we meet on an everyday scale, upward to the scales of astronomy and downward into the smallest objects in biology and chemistry.

For example, we can with some effort measure the mass of a water molecule, H
₂
O. We get, as expected, a very tiny number, about 0.00000000000000000000000003 kilograms (that is, 3.0 ×10
^–26
; you can see why we prefer to use scientific notation—it uses up less ink). A water molecule therefore has a very tiny mass. The aggregate masses of large things in nature, as Democritus had asserted, is the sum of the masses of all the many constituents. Isn't it remarkable that the concept of mass, invented by the ancients to describe large objects, like urns of olive oil and ingots of gold, applies just as well to tiny viruses, molecules, atoms, the atomic nucleus, and all the way down to the elementary particles, today in the third millennium?
¹