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Most physicists still instinctively disliked the idea of time having a beginning
or end. They therefore pointed out that the mathematical model might not be
expected to be a good description of spacetime near a singularity. The reason is
that general relativity, which describes the gravitational force, is a classical
theory, as noted in Chapter 1, and does not incorporate the uncertainty of
quantum theory that governs all other forces we know.

This inconsistency does not matter in most of the universe most of the time,
because the scale on which spacetime is curved is very large and the scale on
which quantum effects are important is very small. But near a singularity, the
two scales would be comparable, and quantum gravitational effects would be
important. So what the singularity theorems of Penrose and myself really
established is that our classical region of spacetime is bounded to the past,
and possibly to the future, by regions in which quantum gravity is important. To
understand the origin and fate of the universe, we need a quantum theory of
gravity, and this will be the subject of most of this book.

Quantum theories of systems such as atoms, with a finite number of particles,
were formulated in the 1920s, by Heisenberg, Schrödinger, and Dirac. (Dirac was
another previous holder of my chair in Cambridge, but it still wasn't
motorized.) However, people encountered difficulties when they tried to extend
quantum ideas to the Maxwell field, which describes electricity, magnetism, and
light.

One can think of the Maxwell field as being made up of waves of different
wavelengths (the distance between one wave crest and the next). In a wave, the
field will swing from one value to another like a pendulum.

According to quantum theory, the ground state, or lowest energy state, of a
pendulum is not just sitting at the lowest energy point, pointing straight down.
That would have both a definite position and a definite velocity, zero. This
would be a violation of the uncertainty principle, which forbids the precise
measurement of both position and velocity at the same time. The uncertainty in
the position multiplied by the uncertainty in the momentum must be greater than
a certain quantity, known as Planck's constant—a number that is too long to
keep writing down, so we use a symbol for it:

So the ground state, or lowest energy state, of a pendulum does not have zero
energy, as one might expect. Instead, even in its ground state a pendulum or any
oscillating system must have a certain minimum amount of what are called zero
point fluctuations. These mean that the pendulum won't necessarily be pointing
straight down but will also have a probability of being found at a small angle
to the vertical. Similarly, even in the vacuum or lowest energy state, the waves
in the Maxwell field won't be exactly zero but can have small sizes. The
higher the frequency (the number of swings per minute) of the pendulum or wave,
the higher the energy of the ground state.

Calculations of the ground state fluctuations in the Maxwell and electron fields
made the apparent mass and charge of the electron infinite, which is not what
observations show. However, in the 1940s the physicists Richard Feynman, Julian
Schwinger, and Shin‘ichiro Tomonaga developed a consistent way of removing or "subtracting out" these infinities and dealing only with the finite observed
values of the mass and charge. Nevertheless, the ground state fluctuations still
caused small effects that could be measured and that agreed well with
experiment. Similar subtraction schemes for removing infinities worked for the
Yang-Mills field in the theory put forward by Chen Ning Yang and Robert Mills.
Yang-Mills theory is an extension of Maxwell theory that describes interactions
in two other forces called the weak and strong nuclear forces. However, ground
state fluctuations have a much more serious effect in a quantum theory of
gravity. Again, each wavelength would have a ground state energy. Since there is
no limit to how short the wavelengths of the Maxwell field can be, there are an
infinite number of different wavelengths in any region of spacetime and an
infinite amount of ground state energy.

Excerpted from The Universe in a Nutshell by Stephen Hawking Copyright 2001 by Stephen Hawking. Excerpted by permission of Bantam, a division of Random House, Inc. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.

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