Warped Passages - Lisa Randall [71]
Particle physicists often find it convenient to use these units to measure not just energy, but also mass. We can do this because the special relativity relations between mass, momentum, and energy tell us that the three quantities are related through the speed of light, which is the constant c = 299,792,458 meters/second.13 We can therefore use the speed of light to convert a given energy into mass or momentum. For example, Einstein’s famous formula E = mc2 means that there is a definite mass associated with any particular energy. Since everyone knows that the conversion factor is c2, we can incorporate it and express masses in units of eV. The proton mass in these units is 1 billion eV—that is, 1 GeV.
Converting units in this way is analogous to what you do every day when you tell someone, for example, that “The train station is ten minutes away.” You are assuming a particular conversion factor. The distance might be half a mile, corresponding to ten minutes at walking speed, or it might be ten miles, which is ten minutes at highway speeds. There is an agreed-upon conversion factor between you and your conversation partner.
These special relativity relationships, in conjunction with the uncertainty principle, determine the minimum spatial size of the physical processes that a wave or a particle of a particular energy or mass could experience or detect. We will now apply these relations to two very important energies for particle physics that will appear frequently in later chapters (see Figure 46).
The first energy, also known as the weak scale energy, is 250 GeV. Physical processes at this energy determine key properties of the weak force and of elementary particles, most notably how they acquire mass. Physicists (including myself) expect that when we explore this energy, we will see new effects predicted by as yet unknown physical theories and learn a good deal more about the underlying structure of matter. Fortunately, experiments are about to explore the weak scale energy and should soon be able to tell us what we want to know.
Sometimes I will also refer to the weak scale mass, which is related to the weak scale energy through the speed of light. In more conventional mass units, the weak scale mass is 10-21 grams. But as I just explained, particle physicists are content to talk about mass in units of GeV.
The associated weak scale length is 10-16 cm, or one ten thousand trillionth of a centimeter. It is the range of the weak force—the maximum distance over which particles can influence each other through this force.
Because uncertainty tells us that small distances are probed only with high energy, the weak scale length is also the minimum length that something with 250 GeV of energy can be sensitive to—that is, it is the smallest scale on which physical processes can affect it. If any smaller distances could be explored with that energy, the distance uncertainty would have to be less than 10-16 cm, and the distance-momentum uncertainty relation would be violated. The currently operating Fermilab accelerator and the future Large Hadron Collider (LHC), to be built at CERN in Geneva within the decade, will explore physical processes down to that scale, and many of the models I will discuss should have visible consequences at this energy.
The second important energy, known as the Planck scale energy, MPl, is 1019 GeV. This energy is very relevant to any theory of gravity. For example, the gravitational constant, which enters Newton’s gravitational force law, is inversely proportional to the square of the Planck scale energy. Gravitational attraction between two masses is small because the Planck scale energy is large.
Moreover,