Warped Passages - Lisa Randall [72]
Quantum mechanics and the uncertainty principle tell us that when particles achieve this energy, they are sensitive to physical processes at distances as short as the Planck scale length,* which is 10-33 cm. This is an extremely small distance—far less than anything measurable. But to describe physical processes that occur over distances this small a theory of quantum gravity is required, and that theory might be string theory. For this reason, the Planck scale length, along with the Planck scale energy, are important scales that will reappear in later chapters.
Bosons and Fermions
Quantum mechanics makes an important distinction among particles, dividing the world of particles into bosons and fermions. Those particles could be fundamental particles such as the electron and quarks, or composite entities such as a proton or the atomic nucleus. Any object is either a boson or a fermion.
Whether such an object is a boson or a fermion depends on a property called intrinsic spin. The name is very suggestive, but the “spin” of particles does not correspond to any actual motion in space. But if a particle has intrinsic spin, it interacts as if it were rotating, even though in reality it is not.
For example, the interaction between an electron and a magnetic field depends on the electron’s classical rotation—its actual rotation in space. But the electron’s interaction with the magnetic field also depends on the electron’s intrinsic spin. Unlike the classical spin that arises from actual motion in physical space,* intrinsic spin is a property of a particle. It is fixed and has a specific value now and for ever. For example, the photon is a boson and has spin-1. That is a property of the photon; it is as fundamental as the fact that the photon travels at the speed of light.
In quantum mechanics, spin is quantized. Quantum spin can take the value 0 (i.e., no spin at all), or 1, or 2, or any integer number units of spin. I’ll call this spin-0 (pronounced “spin-zero”), spin-1, spin-2, and so on. Objects called bosons, named after the Indian physicist Satyendra Nath Bose, have intrinsic spin—the quantum mechanical spin that is independent of rotation—and that is also an integer: bosons can have intrinsic spin equal to 0, 1, 2, and so on.
Fermion spin is quantized in units that no one would have thought possible before the advent of quantum mechanics. Fermions, named after the Italian physicist Enrico Fermi, have half-integer values such as ½ or 3/2. Whereas a spin-1 object returns to its initial configuration after it is rotated a single time, a spin -½ particle would do so only after it were rotated twice. Despite the apparent weirdness of the half-integer values of fermions’ spins, protons, neutrons, and electrons are all fermions with spin -½. Essentially all familiar matter is composed of spin -½ particles.
The fermionic nature of most fundamental particles determines many properties of the matter around us. The Pauli exclusion principle, in particular, states that two fermions of the same type will never be found in the same place. The exclusion principle is what gives the atom the structure upon which chemistry is based. Because electrons with the same spin can’t be in the same place, they have to be in different orbits.
That is why I could make the analogy with different floors of a tall building earlier on. The different floors represented the different possible quantized electron orbits that the Pauli exclusion principle tells us get occupied when a nucleus is surrounded by many electrons. The exclusion principle is also the reason you can’t poke your hand through a table or fall into the center of the Earth. Tables