Excerpt from The Universe In A Nutshell by Stephen Hawking, plus links to reviews, author biography & more

Summary |  Excerpt |  Reviews |  Readalikes |  Genres & Themes |  Author Bio

The Universe In A Nutshell

by Stephen Hawking

The Universe In A Nutshell by Stephen Hawking
  • Critics' Opinion:

    Readers' Opinion:

  • Published:
    Nov 2001, 224 pages

  • Rate this book


Buy This Book

About this Book

Print Excerpt


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.

Membership Advantages
  • Reviews
  • "Beyond the Book" backstories
  • Free books to read and review (US only)
  • Find books by time period, setting & theme
  • Read-alike suggestions by book and author
  • Book club discussions
  • and much more!
  • Just $10 for 3 months or $35 for a year
  • More about membership!

Support BookBrowse

Become a Member and discover books that entertain, engage & enlighten!

Join Today!

Editor's Choice

  • Book Jacket: Before We Sleep
    Before We Sleep
    by Jeffrey Lent
    Katey Snow, aged seventeen, leaves home one night. "There was a void within her and one that could ...
  • Book Jacket
    The Hermit
    by Thomas Rydahl
    If you can be comfortable with Scandinavian noir played out against the sun-drenched backdrop of ...
  • Book Jacket: The Radium Girls
    The Radium Girls
    by Kate Moore
    In 1915, Austrian-born Sabin von Sochocky developed a luminescent paint that used radium to create a...

Win this book!
Win News of the World

News of the World

A brilliant work of historical fiction that explores the boundaries of family, responsibility, honor, and trust.

Enter

First Impressions

  • Book Jacket

    The Weight of Ink
    by Rachel Kadish

    An intellectual, suspenseful, and entertaining page-turner.
    Reader Reviews

Word Play

Solve this clue:

T's S I Numbers

and be entered to win..

Book Discussion
Book Jacket
The One-in-a-Million Boy by Monica Wood

A richly layered novel of hearts broken seemingly beyond repair and then bound by a stunning act of human devotion.

About the book
Join the discussion!

Books that     
entertain,
     engage

 & enlighten

Visitors can view some of BookBrowse for free. Full access is for members only.

Join Today!

Your guide toexceptional          books

BookBrowse seeks out and recommends books that we believe to be best in class. Books that will whisk you to faraway places and times, that will expand your mind and challenge you -- the kinds of books you just can't wait to tell your friends about.