The Cosmic Landscape by Leonard Susskind Read Free Book Online

less certain we can be of the momentum. Thus, if we were to measure the velocity of the ball confined to the table, it would be somewhat random and fluctuating. Even if we removed as much kinetic energy as possible, this residual fluctuation motion could not be eliminated. Brian Greene has used the term
quantum jitters
to describe this motion, and I will follow his lead. 9 The kinetic energy associated with the quantum jitters is called
zero-point energy,
and it cannot be eliminated.
    The quantum jitters implied by the Uncertainty Principle have an interesting consequence for ordinary matter as we try to cool it to zero temperature. Heat is, of course, the energy of random molecular motion. In classical physics, as a system is cooled, the molecules eventually come to rest at absolute zero temperature. The result: at absolute zero all the kinetic energy of the molecules is eliminated.
    But each molecule in a solid has a fairly well-defined location. It is held in place, not by billiard table cushions, but by the other molecules. The result is that the molecules necessarily have a fluctuating velocity. In a real material subject to the laws of quantum mechanics, the molecular kinetic energy can never be totally removed, even at absolute zero!
    Position and velocity are by no means unique in having an Uncertainty Principle. There are many pairs of so-called conjugate quantities that cannot be determined simultaneously: the better one is fixed, the more the other fluctuates. A very important example is
energy-time uncertainty principle:
it is impossible to determine both the exact time that an event takes place and the exact energy of the objects that are involved. Suppose an experimental physicist wished to collide two particles at a particular instant of time. The energy-time uncertainty principle limits the precision with which she can control the energy of the particles and also the time at which they hit each other. Controlling the energy with increasing precision inevitably leads to increasing randomness in the time of collision—and vice versa.
    Another important example that will come up in chapter 2 involves the electric and magnetic fields at a point of space. These fields, which will play a key role in subsequent chapters, are invisible influences that fill space and control the forces on electrically charged particles. Electric and magnetic fields, like position and velocity, cannot be simultaneously determined. If one is known, the other is necessarily uncertain. For this reason the fields are in a constant state of jittering fluctuation that cannot be eliminated. And, as you might expect, this leads to a certain amount of energy, even in absolutely empty space. This
vacuum energy
has led to one of the greatest paradoxes of modern physics and cosmology. We will come back to it many times, beginning with the next chapter.
    Uncertainty and jitters are not the whole story. Quantum mechanics has another side to it: the quantum side. The word
quantum
implies a certain degree of discreteness or graininess in nature. Photons, the units of energy that comprise light waves, are only one example of quanta. Electromagnetic radiation is an oscillatory phenomenon; in other words, it is a vibration. A child on a swing, a vibrating spring, a plucked violin string, a sound wave: all are also oscillatory phenomena, and they all share the property of discreteness. In each case the energy comes in discrete quantum units that can’t be subdivided. In the macroscopic world of springs and swings, the quantum unit of energy is so small that it seems to us that the energy can be anything. But, in fact, the energy of an oscillation comes in indivisible units equal to the frequency of the oscillation (number of oscillations per second) times Planck’s very small constant.
    The electrons in an atom, as they sweep around the nucleus, also oscillate. In this case the quantization of energy is described by imagining discrete orbits. Niels Bohr,