Quotes from _The Illustrated A Brief History of Time_, by Stephen Hawking

Today scientists describe the universe in terms of two basic partial
theories--the general theory of relativity and quantum mechanics.  They
are the great intellectual achievements of the first half of this century.
The general theory of relativity describes the force of gravity and the
large-scale structure of the universe ...  Quantum mechanics, on the other
hand, deals with phenomena on extremely small scales ... Unfortunately
however, these two theories are known to be inconsistent with each other--
they cannot both be correct.  One of the major endeavors in physics today,
and the major theme of this book, is the search for a new theory that will
incorporate them both--a quantum theory of gravity.  We do not yet have such
a theory, and we may still be a long way from having one, but we do already
know many of the properties it must have.  And we shall see, in later
chapters, that we already know a fair amount about the predictions a quantum
theory of gravity must make.  [p18]

The [Heisenberg] uncertainty principle has profound implications for the
way in which we view the world.  Even after more than fifty years they have
not been fully appreciated by many philosophers, and are still the subject
of much controversy. [p72]

The remarkable fact is that the values of these numbers seem to have been
very finely adjusted to make possible the development of life.  For example,
if the electric charge of the electron had been only slightly different,
stars either would have been unable to burn hydrogen and helium, or else
they would not have exploded.  Of course, there might be other intelligent
forms of life, not dreamed of even by writers of science fiction, that did
not require the light of a star like the sun or the heavier chemical
elements that are made in stars and are flung back into space when the stars
explode.  Nevertheless, it seems clear that there are relatively few ranges
of values that would allow the development of any form of intelligent life.
[p160]

This might suggest that the so-called imaginary time is really the real
time, and what we call real time is just a figment of our imaginations.
... But according to the approach I described in chapter 1, a scientific
theory is just a mathematical model we make to describe our observations:
it exists only in our minds.  So it is meaningless to ask: which is real,
"real" or "imaginary" time?  It is simply a matter of which is the more
useful description. [p179]

The laws of science do not distinguish between the past and the future.
[p182]

The direction of time in which a computer remembers the past is the same
as that in which disorder increases. [p189]

[Summary of the 3 arrows of time p194]

Like the uncertainty principle, Godel's incompleteness theorem may be
a fundamental limitation on our ability to understand and predict the
universe, but so far at least it hasn't seemed to be an obstacle in our
search for a complete unified theory. [p196]

So the question is: if the universe starts out without the kind of curvature
required for time travel, can we subsequently warp local regions of
space-time sufficiently to allow it? [p198]

We thus have experimental evidence both that space-time can be warped
(from the bending of light during eclipses) and that it can be curved in
the way necessary to allow time travel (from the Casimir effect).  One might
hope therefore that as we advance in science and technology, we would
eventually manage to build a time machine.  But if so, why hasn't anyone
come back from the future and told us how to do it?  There might be good
reasons why it would be unwise to give us the secret of time travel at our
present primitive state of development, but unless human nature changes
radically, it is difficult to believe some visitor from the future wouldn't
spill the beans.  ... A possible way to explain the absence of visitors from
the future would be to say that the past is fixed because we have observed
it and seen that it does not have the kind of warping needed to allow travel
back from the future.  On the other hand, the future is unknown and open,
so it might well have the curvature required.  This would mean that any
time travel would be confined to the future.  There would be no chance of
Captain Kirk and the Starship Enterprise turning up at the present time.
[p206]

There seem to be two possible resolutions to the paradoxes posed by time
travel.  One I shall call the consistent histories approach.  It says that
even if space-time is warped so that it would be possible to travel into
the past, what happens in space-time must be a consistent solution of the
laws of physics.  According to this viewpoint, you could not go back in
time unless history showed that you had already arrived in the past and,
while there, had not killed your great great grandfather or committed any
other acts that would conflict with your situation in the present.  Moreover,
when you did go back, you wouldn't be able to change recorded history.  That
means you wouldn't have free will to do what you wanted.  Of course, one
could say that free will is an illusion anyway.  If there really is a
complete, unified theory that governs everything, it presumably also
determines your actions.  But it does so in a way that is impossible to
calculate for an organism that is as complicated as a human being.  The
reason we say human beings have free will is because we can't predict what
they will do.  However, if the human then goes off in a rocket ship and
then comes back before he or she set off, we _will_ be able to predict
what he or she will do because it will be part of recorded history.  Thus,
in that situation, the time traveller would have no free will.
The other possible way to resolve the paradoxes of time travel might be
called the alternative histories hypothesis.  The idea is that when time
travellers go back to the past, they enter alternative histories which
differ from recorded history.  Thus they can act freely, without the
constraint of consistency with their previous history.  Steven Spielberg
had fun with this notion in the _Back to the Future_ films: Marty McFly
was able to go back and change his parent's courtship to a more
satisfactory history.
The alternative histories hypothesis sounds rather like Richard Feynman's
way of expressing quantum theory as a sum over histories, which was
described in Chapters 4 and 8.  This said that the universe didn't just
have a single history: rather it had every possible history, each with its
own probability.  However, there seems to be an important difference
between Feynman's proposal and alternative histories.  In Feynman's sum,
each history comprises a complete space-time and everything in it.  The
space-time may be so warped that it is possible to travel in a rocket
into the past.  But the rocket would remain in the same space-time and
therefore the same history, which would have to be consistent.  Thus
Feynman's sum over histories proposal seems to support the consistent
histories hypothesis rather than the alternative histories. [p207-8]

One would avoid these problems if what I call the chronology protection
conjecture holds.  This says that the laws of physics conspire to prevent
_macroscopic_ bodies from carrying information into the past.  Like the
cosmic censorship conjecture, it has not been proved but there are reasons
to believe it is true.
The reason to believe that chronology protection operates is that when
space-time is warped enough to make travel into the past possible,
virtual particles moving on closed loops in space-time can become real
particles traveling forward in time at or below the speed of light.  As
these particles can go round the loop any number of times, they pass
each point on their route many times.  Thus their energy is counted
over and over again and the energy density will become very large.  This
could give space-time a positive curvature which would not allow travel
into the past.  It is not yet clear whether these particles would cause
positive or negative curvature or whether the curvature produced by
some kinds of virtual particles might cancel that produced by other kinds.
Thus the possibility of time travel remains open.  But I'm not going to
bet on it.  My opponent might have the unfair advantage of knowing the
future. [p210-1]

Why don't we notice all these extra dimensions, if they are really
there?  Why do we see only three space dimensions and one time dimension?
The suggestion is that the other dimensions are curved up into a space
of very small size, something like a million million million million
millionth of an inch.  This is so small that we just don't notice it:
we see only one time dimension and three space dimensions, in which
space-time is fairly flat.  It is like the surface of a straw.  If you
look at it closely, you see it is two-dimensional [...].  But if you look
at it from a distance, you don't see the thickness of the straw, and it
looks one-dimensional. [p220, followed by a discussion of why < 3 or
> 3 space dimensions might be troublesome]

People have searched for this underlying theory, but without any success
so far.  However, I believe that there may not be any single formulation
of the fundamental theory any more than, as Godel showed, one could
formulate arithmetic in terms of a single set of axioms.  Instead it
may be like maps--you can't use a single map to describe the surface
of the earth or an anchor ring: you need at least 2 maps in the case of
the earth and 4 for the anchor ring to cover every point.  Each map is
valid only in a limited region, but different maps will have a region of
overlap.  The collection of maps provides a complete description of the
surface. [...] The whole collection of different [physics] formulations
could be regarded as a complete, unified theory, though one that could
not be expressed in terms of a single set of postulates. [p223]

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. [p225]

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 question 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 philosophers, or anyone else except for 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
through 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--for then we would know the mind
of God.  [end]