Page 31 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 4
CHAPTER 4

THE UNCERTAINTY PRINCIPLE

The success of scientific theories, particularly Newton’s theory of gravity, led the French scientist the Marquis de Laplace
at the beginning of the nineteenth century to argue that the universe was completely deterministic. Laplace suggested
that there should be a set of scientific laws that would allow us to predict everything that would happen in the universe, if
only we knew the complete state of the universe at one time. For example, if we knew the positions and speeds of the
sun and the planets at one time, then we could use Newton’s laws to calculate the state of the Solar System at any other
time. Determinism seems fairly obvious in this case, but Laplace went further to assume that there were similar laws
governing everything else, including human behavior.

The doctrine of scientific determinism was strongly resisted by many people, who felt that it infringed God’s freedom to
intervene in the world, but it remained the standard assumption of science until the early years of this century. One of the
first indications that this belief would have to be abandoned came when calculations by the British scientists Lord
Rayleigh and Sir James Jeans suggested that a hot object, or body, such as a star, must radiate energy at an infinite
rate. According to the laws we believed at the time, a hot body ought to give off electromagnetic waves (such as radio
waves, visible light, or X rays) equally at all frequencies. For example, a hot body should radiate the same amount of
energy in waves with frequencies between one and two million million waves a second as in waves with frequencies
between two and three million million waves a second. Now since the number of waves a second is unlimited, this would
mean that the total energy radiated would be infinite.
In order to avoid this obviously ridiculous result, the German scientist Max Planck suggested in 1900 that light, X rays,
and other waves could not be emitted at an arbitrary rate, but only in certain packets that he called quanta. Moreover,
each quantum had a certain amount of energy that was greater the higher the frequency of the waves, so at a high
enough frequency the emission of a single quantum would require more energy than was available. Thus the radiation at
high frequencies would be reduced, and so the rate at which the body lost energy would be finite.

The quantum hypothesis explained the observed rate of emission of radiation from hot bodies very well, but its
implications for determinism were not realized until 1926, when another German scientist, Werner Heisenberg,
formulated his famous uncertainty principle. In order to predict the future position and velocity of a particle, one has to be
able to measure its present position and velocity accurately. The obvious way to do this is to shine light on the particle.
Some of the waves of light will be scattered by the particle and this will indicate its position. However, one will not be able
to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs
to use light of a short wavelength in order to measure the position of the particle precisely. Now, by Planck’s quantum
hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum. This quantum will
disturb the particle and change its velocity in a way that cannot be predicted. moreover, the more accurately one
measures the position, the shorter the wavelength of the light that one needs and hence the higher the energy of a single
quantum. So the velocity of the particle will be disturbed by a larger amount. In other words, the more accurately you try
to measure the position of the particle, the less accurately you can measure its speed, and vice versa. Heisenberg
showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the
particle can never be smaller than a certain quantity, which is known as Planck’s constant. Moreover, this limit does not
depend on the way in which one tries to measure the position or velocity of the particle, or on the type of particle:
Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world.

The uncertainty principle had profound implications for the way in which we view the world. Even after more than seventy
years they have not been fully appreciated by many philosophers, and are still the subject of much controversy. The
uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be
completely deterministic: one certainly cannot predict future events exactly if one cannot even measure the present state
of the universe precisely! We could still imagine that there is a set of laws that determine events completely for some
supernatural being, who could observe the present state of the universe without disturbing it. However, such models of
the universe are not of much interest to us ordinary mortals. It seems better to employ the principle of economy known as
Occam’s razor and cut out all the features of the theory that cannot be observed. This approach led Heisenberg, Erwin
Schrodinger, and Paul Dirac in the 1920s to reformulate mechanics into a new theory called quantum mechanics, based
on the uncertainty principle. In this theory particles no longer had separate, well-defined positions and velocities that
could not be observed, Instead, they had a quantum state, which was a combination of position and velocity.

In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number
of different possible outcomes and tells us how likely each of these is. That is to say, if one made the same measurement
on a large number of similar systems, each of which started off in the same way, one would find that the result of the

file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/c.html (1 of 5) [2/20/2001 3:14:40 AM]