《时间简史―从大爆炸到黑洞》 ――史蒂芬?霍金

A Brief History of Time - Stephen Hawking... Chapter 11
basic than the quarks and electrons that we now regard as “elementary” particles.
However, it seems that gravity may provide a limit to this sequence of “boxes within boxes.” If one had a
particle with an energy above what is called the Planck energy, ten million million million GeV (1 followed by
nineteen zeros), its mass would be so concentrated that it would cut itself off from the rest of the universe and
form a little black hole. Thus it does seem that the sequence of more and more refined theories should have
some limit as we go to higher and higher energies, so that there should be some ultimate theory of the
universe. Of course, the Planck energy is a very long way from the energies of around a hundred GeV, which
are the most that we can produce in the laboratory at the present time. We shall not bridge that gap with
particle accelerators in the foreseeable future! The very early stages of the universe, however, are an arena
where such energies must have occurred. I think that there is a good chance that the study of the early
universe and the requirements of mathematical consistency will lead us to a complete unified theory within the
lifetime of some of us who are around today, always presuming we don’t blow ourselves up first.
What would it mean if we actually did discover the ultimate theory of the universe? As was explained in Chapter
1, we could never be quite sure that we had indeed found the correct theory, since theories can’t be proved.
But if the theory was mathematically consistent and always gave predictions that agreed with observations, we
could be reasonably confident that it was the right one. It would bring to an end a long and glorious chapter in
the history of humanity’s intellectual struggle to understand the universe. But it would also revolutionize the
ordinary person’s understanding of the laws that govern the universe. In Newton’s time it was possible for an
educated person to have a grasp of the whole of human knowledge, at least in outline. But since then, the pace
of the development of science has made this impossible. Because theories are always being changed to
account for new observations, they are never properly digested or simplified so that ordinary people can
understand them. You have to be a specialist, and even then you can only hope to have a proper grasp of a
small proportion of the scientific theories. Further, the rate of progress is so rapid that what one learns at school
or university is always a bit out of date. Only a few people can keep up with the rapidly advancing frontier of
knowledge, and they have to devote their whole time to it and specialize in a small area. The rest of the
population has little idea of the advances that are being made or the excitement they are generating. Seventy
years ago, if Eddington is to be believed, only two people understood the general theory of relativity. Nowadays
tens of thousands of university graduates do, and many millions of people are at least familiar with the idea. If a
complete unified theory was discovered, it would only be a matter of time before it was digested and simplified
in the same way and taught in schools, at least in outline. We would then all be able to have some
understanding of the laws that govern the universe and are responsible for our existence.
Even if we do discover a complete unified theory, it would not mean that we would be able to predict events in
general, for two reasons. The first is the limitation that the uncertainty principle of quantum mechanics sets on
our powers of prediction. There is nothing we can do to get around that. In practice, however, this first limitation
is less restrictive than the second one. It arises from the fact that we could not solve the equations of the theory
exactly, except in very simple situations. (We cannot even solve exactly for the motion of three bodies in
Newton’s theory of gravity, and the difficulty increases with the number of bodies and the complexity of the
theory.) We already know the laws that govern the behavior of matter under all but the most extreme
conditions. In particular, we know the basic laws that underlie all of chemistry and biology. Yet we have
certainly not reduced these subjects to the status of solved problems: we have, as yet, had little success in
predicting human behavior from mathematical equations! So even if we do find a complete set of basic laws,
there will still be in the years ahead the intellectually challenging task of developing better approximation
methods, so that we can make useful predictions of the probable outcomes in complicated and realistic
situations. A complete, consistent, unified theory is only the first step: our goal is a complete understanding of
the events around us, and of our own existence.

A Brief History of Time - Stephen Hawking... Chapter 12
CHAPTER 12
CONCLUSION
We find ourselves in a bewildering world. We want to make sense of what we see around us and to ask: What
is the nature of the universe? What is our place in it and where did it and we come from? Why is it the way it is?
To try to answer these questions we adopt some “world picture.” Just as an infinite tower of tortoises supporting
the fiat earth is such a picture, so is the theory of superstrings. Both are theories of the universe, though the
latter is much more mathematical and precise than the former. Both theories lack observational evidence: no
one has ever seen a giant tortoise with the earth on its back, but then, no one has seen a superstring either.
However, the tortoise theory fails to be a good scientific theory because it predicts that people should be able to
fall off the edge of the world. This has not been found to agree with experience, unless that turns out to be the
explanation for the people who are supposed to have disappeared in the Bermuda Triangle!
The earliest theoretical attempts to describe and explain the universe involved the idea that events and natural
phenomena were controlled by spirits with human emotions who acted in a very humanlike and unpredictable
manner. These spirits inhabited natural objects, like rivers and mountains, including celestial bodies, like the
sun and moon. They had to be placated and their favor sought in order to ensure the fertility of the soil and the
rotation of the seasons. Gradually, however, it must have been noticed that there were certain regularities: the
sun always rose in the east and set in the west, whether or not a sacrifice had been made to the sun god.
Further, the sun, the moon, and the planets followed precise paths across the sky that could be predicted in
advance with considerable accuracy. The sun and the moon might still be gods, but they were gods who
obeyed strict laws, apparently without any exceptions, if one discounts stories like that of the sun stopping for
Joshua.
At first, these regularities and laws were obvious only in astronomy and a few other situations. However, as
civilization developed, and particularly in the last 300 years, more and more regularities and laws were
discovered. The success of these laws led Laplace at the beginning of the nineteenth century to postulate
scientific determinism; that is, he suggested that there would be a set of laws that would determine the
evolution of the universe precisely, given its configuration at one time.
Laplace’s determinism was incomplete in two ways. It did not say how the laws should be chosen and it did not
specify the initial configuration of the universe. These were left to God. God would choose how the universe
began and what laws it obeyed, but he would not intervene in the universe once it had started. In effect, God
was confined to the areas that nineteenth-century science did not understand.
We now know that Laplace’s hopes of determinism cannot be realized, at least in the terms he had in mind.
The uncertainty principle of quantum mechanics implies that certain pairs of quantities, such as the position and
velocity of a particle, cannot both be predicted with complete accuracy. Quantum mechanics deals with this
situation via a class of quantum theories in which particles don’t have well-defined positions and velocities but
are represented by a wave. These quantum theories are deterministic in the sense that they give laws for the
evolution of the wave with time. Thus if one knows the wave at one time, one can calculate it at any other time.
The unpredictable, random element comes in only when we try to interpret the wave in terms of the positions
and velocities of particles. But maybe that is our mistake: maybe there are no particle positions and velocities,
but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. The
resulting mismatch is the cause of the apparent unpredictability.
In effect, we have redefined the task of science to be the discovery of laws that will enable us to predict events
up to the limits set by the uncertainty principle. The question remains, however: how or why were the laws and
the initial state of the universe chosen?
In this book I have given special prominence to the laws that govern gravity, because it is gravity that shapes
the large-scale structure of the universe, even though it is the weakest of the four categories of forces. The
laws of gravity were incompatible with the view held until quite recently that the universe is unchanging in time:

A Brief History of Time - Stephen Hawking... Chapter 12
the fact that gravity is always attractive implies that the universe must be either expanding or contracting.
According to the general theory of relativity, there must have been a state of infinite density in the past, the big
bang, which would have been an effective beginning of time. Similarly, if the whole universe recollapsed, there
must be another state of infinite density in the future, the big crunch, which would be an end of time. Even if the
whole universe did not recollapse, there would be singularities in any localized regions that collapsed to form
black holes. These singularities would be an end of time for anyone who fell into the black hole. At the big bang
and other singularities, all the laws would have broken down, so God would still have had complete freedom to
choose what happened and how the universe began.
When we combine quantum mechanics with general relativity, there seems to be a new possibility that did not
arise before: that space and time together might form a finite, four-dimensional space without singularities or
boundaries, like the surface of the earth but with more dimensions. It seems that this idea could explain many
of the observed features of the universe, such as its large-scale uniformity and also the smaller-scale
departures from homogeneity, like galaxies, stars, and even human beings. It could even account for the arrow
of time that we observe. But if the universe is completely self-contained, with no singularities or boundaries,
and completely described by a unified theory, that has profound implications for the role of God as Creator.
Einstein once asked the question: “How much choice did God have in constructing the universe?” If the no
boundary proposal is correct, he had no freedom at all to choose initial conditions. He would, of course, still
have had the freedom to choose the laws that the universe obeyed. This, however, may not really have been all
that much of a choice; there may well be only one, or a small number, of complete unified theories, such as the
heterotic string theory, that are self-consistent and allow the existence of structures as complicated as human
beings who can investigate the laws of the universe and ask about the nature of God.
Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes
fire into the equations and makes a universe for them to describe? The usual approach of science of
constructing a mathematical model cannot answer the questions of why there should be a universe for the
model to describe. Why does the universe go to all the bother of existing? Is the unified theory so compelling
that it brings about its own existence? Or does it need a creator, and, if so, does he have any other effect on
the universe? And who created him?
Up to now, most scientists have been too occupied with the development of new theories that describe what
the universe is to ask the question why. On the other hand, the people whose business it is to ask why, the
philosophers, have not been able to keep up with the advance of scientific theories. In the eighteenth century,
philosophers considered the whole of human knowledge, including science, to be their field and discussed
questions such as: did the universe have a beginning? However, in the nineteenth and twentieth centuries,
science became too technical and mathematical for the philosophers, or anyone else except a few specialists.
Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of
this century, said, “The sole remaining task for philosophy is the analysis of language.” What a comedown from
the great tradition of philosophy from Aristotle to Kant!
However, if we do discover a complete theory, it should in time be understandable in broad principle by
everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able
to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to
that, it would be the ultimate triumph of human reason

ALBERT EINSTEIN
Einstein’s connection with the politics of the nuclear bomb is well known: he signed the famous letter to
President Franklin Roosevelt that persuaded the United States to take the idea seriously, and he engaged in
postwar efforts to prevent nuclear war. But these were not just the isolated actions of a scientist dragged into
the world of politics. Einstein’s life was, in fact, to use his own words, “divided between politics and equations.”
Einstein’s earliest political activity came during the First World War, when he was a professor in Berlin.
Sickened by what he saw as the waste of human lives, he became involved in antiwar demonstrations. His
A Brief History of Time - Stephen Hawking... Chapter 12
advocacy of civil disobedience and public encouragement of people to refuse conscription did little to endear
him to his colleagues. Then, following the war, he directed his efforts toward reconciliation and improving
international relations. This too did not make him popular, and soon his politics were making it difficult for him to
visit the United States, even to give lectures.
Einstein’s second great cause was Zionism. Although he was Jewish by descent, Einstein rejected the biblical
idea of God. However, a growing awareness of anti-Semitism, both before and during the First World War, led
him gradually to identify with the Jewish community, and later to become an outspoken supporter of Zionism.
Once more unpopularity did not stop him from speaking his mind. His theories came under attack; an
anti-Einstein organization was even set up. One man was convicted of inciting others to murder Einstein (and
fined a mere six dollars). But Einstein was phlegmatic. When a book was published entitled 100 Authors
Against Einstein, he retorted, “If I were wrong, then one would have been enough!”
In 1933, Hitler came to power. Einstein was in America, and declared he would not return to Germany. Then,
while Nazi militia raided his house and confiscated his bank account, a Berlin newspaper displayed the
headline “Good News from Einstein

A Brief History of Time - Stephen Hawking... Chapter 12
Copernicanism, regretted having allowed its publication. The Pope argued that although the book had the
official blessing of the censors, Galileo had nevertheless contravened the 1616 decree. He brought Galileo
before the Inquisition, who sentenced him to house arrest for life and commanded him to publicly renounce
Copernicanism. For a second time, Galileo acquiesced.
Galileo remained a faithful Catholic, but his belief in the independence of science had not been crushed. Four
years before his death in 1642, while he was still under house arrest, the manuscript of his second major book
was smuggled to a publisher in Holland. It was this work, referred to as Two New Sciences, even more than his
support for Copernicus, that was to be the genesis of modern physics.
ISAAC NEWTON
Isaac Newton was not a pleasant man. His relations with other academics were notorious, with most of his later
life spent embroiled in heated disputes. Following publication of Principia Mathematica

A Brief History of Time - Stephen Hawking... Glossary
GLOSSARY
Absolute zero: The lowest possible temperature, at which substances contain no heat energy.
Acceleration: The rate at which the speed of an object is changing.
Anthropic principle: We see the universe the way it is because if it were different we would not be here to
observe it.
Antiparticle: Each type of matter particle has a corresponding antiparticle. When a particle collides with its
antiparticle, they annihilate, leaving only energy.
Atom: The basic unit of ordinary matter, made up of a tiny nucleus (consisting of protons and neutrons)
surrounded by orbiting electrons.
Big bang: The singularity at the beginning of the universe.
Big crunch: The singularity at the end of the universe.
Black hole: A region of space-time from which nothing, not even light, can escape, because gravity is so
strong.
Casimir effect: The attractive pressure between two flat, parallel metal plates placed very near to each other in
a vacuum. The pressure is due to a reduction in the usual number of virtual particles in the space between the
plates.
Chandrasekhar limit: The maximum possible mass of a stable cold star, above which it must collapse into a
black hole.
Conservation of energy: The law of science that states that energy (or its equivalent in mass) can neither be
created nor destroyed.
Coordinates: Numbers that specify the position of a point in space and time.
Cosmological constant: A mathematical device used by Einstein to give space-time an inbuilt tendency to
expand.
Cosmology: The study of the universe as a whole.
Dark matter: Matter in galaxies, clusters, and possibly between clusters, that can not be observed directly but
can be detected by its gravitational effect. As much as 90 percent of the mass of the universe may be in the
form of dark matter.
Duality: A correspondence between apparently different theories that lead to the same physical results.
Einstein-Rosen bridge: A thin tube of space-time linking two black holes. Also see Wormhole.
Electric charge: A property of a particle by which it may repel (or attract) other particles that have a charge of
similar (or opposite) sign.
Electromagnetic force: The force that arises between particles with electric charge; the second strongest of
the four fundamental forces.
Electron: A particle with negative electric charge that orbits the nucleus of an atom.
Electroweak unification energy: The energy (around 100 GeV) above which the distinction between the
electromagnetic force and the weak force disappears.

A Brief History of Time - Stephen Hawking... Glossary
Elementary particle: A particle that, it is believed, cannot be subdivided.
Event: A point in space-time, specified by its time and place.
Event horizon: The boundary of a black hole.
Exclusion principle: The idea that two identical spin-1/2 particles cannot have (within the limits set by the
uncertainty principle) both the same position and the same velocity.
Field: Something that exists throughout space and time, as opposed to a particle that exists at only one point at
a time.
Frequency: For a wave, the number of complete cycles per second.
Gamma rays: Electromagnetic rays of very short wavelength, produced in radio-active decay or by collisions of
elementary particles.
General relativity: Einstein’s theory based on the idea that the laws of science should be the same for all
observers, no matter how they are moving. It explains the force of gravity in terms of the curvature of a
four-dimensional space-time.
Geodesic: The shortest (or longest) path between two points.
Grand unification energy: The energy above which, it is believed, the electro-magnetic force, weak force, and
strong force become indistinguishable from each other.
Grand unified theory (GUT): A theory which unifies the electromagnetic, strong, and weak forces.
Imaginary time: Time measured using imaginary numbers.
Light cone: A surface in space-time that marks out the possible directions for light rays passing through a
given event.
Light-second (light-year): The distance traveled by light in one second (year).
Magnetic field: The field responsible for magnetic forces, now incorporated along with the electric field, into the
electromagnetic field.
Mass: The quantity of matter in a body; its inertia, or resistance to acceleration.
Microwave background radiation: The radiation from the glowing of the hot early universe, now so greatly
red-shifted that it appears not as light but as microwaves (radio waves with a wavelength of a few centimeters).
Also see COBE, on page 145.
Naked singularity: A space-time singularity not surrounded by a black hole.
Neutrino: An extremely light (possibly massless) particle that is affected only by the weak force and gravity.
Neutron: An uncharged particle, very similar to the proton, which accounts for roughly half the particles in an
atomic nucleus.
Neutron star: A cold star, supported by the exclusion principle repulsion between neutrons.
No boundary condition: The idea that the universe is finite but has no boundary (in imaginary time).
Nuclear fusion: The process by which two nuclei collide and coalesce to form a single, heavier nucleus.
Nucleus: The central part of an atom, consisting only of protons and neutrons, held together by the strong

A Brief History of Time - Stephen Hawking... Glossary
force.
Particle accelerator: A machine that, using electromagnets, can accelerate moving charged particles, giving
them more energy.
Phase: For a wave, the position in its cycle at a specified time: a measure of whether it is at a crest, a trough,
or somewhere in between.
Photon: A quantum of light.
Planck’s quantum principle: The idea that light (or any other classical waves) can be emitted or absorbed
only in discrete quanta, whose energy is proportional to their wavelength.
Positron: The (positively charged) antiparticle of the electron.
Primordial black hole: A black hole created in the very early universe.
Proportional: ‘X is proportional to Y’ means that when Y is multiplied by any number, so is X. ‘X is inversely
proportional to Y’ means that when Y is multiplied by any number, X is divided by that number.
Proton: A positively charged particle, very similar to the neutron, that accounts for roughly half the particles in
the nucleus of most atoms.
Pulsar: A rotating neutron star that emits regular pulses of radio waves.
Quantum: The indivisible unit in which waves may be emitted or absorbed.
Quantum chromodynamics (QCD): The theory that describes the interactions of quarks and gluons.
Quantum mechanics: The theory developed from Planck’s quantum principle and Heisenberg’s uncertainty
principle.
Quark: A (charged) elementary particle that feels the strong force. Protons and neutrons are each composed of
three quarks.
Radar: A system using pulsed radio waves to detect the position of objects by measuring the time it takes a
single pulse to reach the object and be reflected back.
Radioactivity: The spontaneous breakdown of one type of atomic nucleus into another.
Red shift: The reddening of light from a star that is moving away from us, due to the Doppler effect.
Singularity: A point in space-time at which the space-time curvature becomes infinite.
Singularity theorem: A theorem that shows that a singularity must exist under certain circumstances

Uncertainty principle: The principle, formulated by Heisenberg, that one can never be exactly sure of both the
position and the velocity of a particle; the more accurately one knows the one, the less accurately one can
know the other.
Virtual particle: In quantum mechanics, a particle that can never be directly detected, but whose existence
does have measurable effects.
Wave/particle duality: The concept in quantum mechanics that there is no distinction between waves and
particles; particles may sometimes behave like waves, and waves like particles.
Wavelength: For a wave, the distance between two adjacent troughs or two adjacent crests.
Weak force: The second weakest of the four fundamental forces, with a very short range. It affects all matter
particles, but not force-carrying particles.
Weight: The force exerted on a body by a gravitational field. It is proportional to, but not the same as, its mass.
White dwarf: A stable cold star, supported by the exclusion principle repulsion between electrons.
Wormhole: A thin tube of space-time connecting distant regions of the universe. Wormholes might also link to
parallel or baby universes and could provide the possibility of time travel.

A Brief History of Time - Stephen Hawking... Acknowledgments
ACKNOWLEDGMENTS
Many people have helped me in writing this book. My scientific colleagues have without exception been
inspiring. Over the years my principal associates and collaborators were Roger Penrose, Robert Geroch,
Brandon Carter, George Ellis, Gary Gibbons, Don Page, and Jim Hartle. I owe a lot to them, and to my
research students, who have always given me help when needed.
One of my students, Brian Whitt, gave me a lot of help writing the first edition of this book. My editor at Bantam
Books, Peter Guzzardi, made innumerable comments which improved the book considerably. In addition, for
this edition, I would like to thank Andrew Dunn, who helped me revise the text.
I could not have written this book without my communication system. The software, called Equalizer, was
donated by Walt Waltosz of Words Plus Inc., in Lancaster, California. My speech synthesizer was donated by
Speech Plus, of Sunnyvale, California. The synthesizer and laptop computer were mounted on my wheelchair
by David Mason, of Cambridge Adaptive Communication Ltd. With this system I can communicate better now
than before I lost my voice.
I have had a number of secretaries and assistants over the years in which I wrote and revised this book. On the
secretarial side, I’m very grateful to Judy Fella, Ann Ralph, Laura Gentry, Cheryl Billington, and Sue Masey. My
assistants have been Colin Williams, David Thomas, and Raymond Laflamme, Nick Phillips, Andrew Dunn,
Stuart Jamieson, Jonathan Brenchley, Tim Hunt, Simon Gill, Jon Rogers, and Tom Kendall. They, my nurses,
colleagues, friends, and family have enabled me to live a very full life and to pursue my research despite my
disability.
Stephen Hawking
ABOUT THE AUTHOR
Stephen Hawking, who was born in 1942 on the anniversary of Galileo’s death, holds Isaac Newton’s chair as
Lucasian Professor of Mathematics at the University of Cambridge. Widely regarded as the most brilliant
theoretical physicist since Einstein, he is also the author of Black Holes and Baby Universes, published in 1993,
as well as numerous scientific papers and books.