can a universe full of matter and radiation
have zero total energy? While the energy associated with these
quantities, in the absence of considerations of gravity, is indeed
positive, it turns out that the gravitational energy of attraction
between objects is negative. This is another way of saying that it
takes energy to pull objects farther apart, so they have less
energy if they are close together. Hence, all objects of a finite
size have less gravitational energy than they would have if they
were dispersed over infinitely large distances. If we define such a
state in which matter is infinitely diluted as having zero energy,
then all other, smaller, configurations have negative energy. If
this negative energy precisely cancels the positive energy of
matter and radiation in the universe, then general relativity tells
us that the overall curvature of space vanishes.
Moreover, with zero net energy, the possibility
that the universe itself arose spontaneously out of nothing becomes
at least plausible, since one would imagine that “nothing” would
also have zero energy. As Guth put it: “There is such a thing as a
free lunch!” It was theoretical considerations such as these, which
are primarily mathematically aesthetic, that convinced most
theorists and ultimately even many observers, well in advance of
the cosmic microwave background observations, that the universe was
flat. In this case, as sometimes but not always happens in science,
nature cooperated.
However, it was premature to slap ourselves on
our collective backs and congratulate one another. For, what
actually makes the universe flat is something that no one, or at
least almost no one, anticipated. Perhaps the most puzzling
discovery in all of physics during the past century has been the
fact that the dominant form of energy in the universe is not
associated with matter or radiation at all. Rather, it appears that
empty space, devoid of any particles at all, carries energy—enough
energy, in fact, to overwhelm, by a factor of almost three, the
energy of everything else in the universe.
This energy of empty space, sometimes called
“vacuum energy” or “dark energy,” is the most mysterious form of
energy we know of. No one currently has a good explanation of why
empty space should have precisely this amount of energy, and, as we
shall see, trying to understand its nature is currently driving
much of our current scientific thinking about the nature of space
and time itself.
The discovery of a mysterious energy permeating
all of empty space also changed everything in the way we think
about cosmology. Even the original, vital connection between
geometry and destiny is now gone. If empty space can possess
energy, a positively curved universe need not ultimately collapse,
while a negatively curved or flat universe need not expand forever.
Still, as I have suggested, it could be that there might be some
deeper connection between the geometry of space and its energy
content, perhaps something that involves probing yet deeper into
the meaning of space and time. Certainly the puzzle of dark energy
is so revolutionary it motivates even extreme reconsiderations of
the nature of space and time. The resolution of this mystery may
not be as revolutionary as the question itself, but one never knows
until one explores the possibilities. But extraordinary claims
require extraordinary evidence, as Carl Sagan used to say. We shall
return to this mystery later in the book. First, however, we shall
explore how the collective creative imagination of the world
responded to our first revolution in the physics of space and time
inspired by Einstein and later Minkowski: Namely, the existence of
a fourdimensional space-time continuum associated with special
relativity.
C H A P T E R 7
FROM FLATLAND TO
PICASSO
Ever drifting down the
stream—
Lingering in the golden
gleam—
Life, what is it but a
dream?
—Lewis Carroll, Through the
Looking Glass
W hile life may
have zero total energy? While the energy associated with these
quantities, in the absence of considerations of gravity, is indeed
positive, it turns out that the gravitational energy of attraction
between objects is negative. This is another way of saying that it
takes energy to pull objects farther apart, so they have less
energy if they are close together. Hence, all objects of a finite
size have less gravitational energy than they would have if they
were dispersed over infinitely large distances. If we define such a
state in which matter is infinitely diluted as having zero energy,
then all other, smaller, configurations have negative energy. If
this negative energy precisely cancels the positive energy of
matter and radiation in the universe, then general relativity tells
us that the overall curvature of space vanishes.
Moreover, with zero net energy, the possibility
that the universe itself arose spontaneously out of nothing becomes
at least plausible, since one would imagine that “nothing” would
also have zero energy. As Guth put it: “There is such a thing as a
free lunch!” It was theoretical considerations such as these, which
are primarily mathematically aesthetic, that convinced most
theorists and ultimately even many observers, well in advance of
the cosmic microwave background observations, that the universe was
flat. In this case, as sometimes but not always happens in science,
nature cooperated.
However, it was premature to slap ourselves on
our collective backs and congratulate one another. For, what
actually makes the universe flat is something that no one, or at
least almost no one, anticipated. Perhaps the most puzzling
discovery in all of physics during the past century has been the
fact that the dominant form of energy in the universe is not
associated with matter or radiation at all. Rather, it appears that
empty space, devoid of any particles at all, carries energy—enough
energy, in fact, to overwhelm, by a factor of almost three, the
energy of everything else in the universe.
This energy of empty space, sometimes called
“vacuum energy” or “dark energy,” is the most mysterious form of
energy we know of. No one currently has a good explanation of why
empty space should have precisely this amount of energy, and, as we
shall see, trying to understand its nature is currently driving
much of our current scientific thinking about the nature of space
and time itself.
The discovery of a mysterious energy permeating
all of empty space also changed everything in the way we think
about cosmology. Even the original, vital connection between
geometry and destiny is now gone. If empty space can possess
energy, a positively curved universe need not ultimately collapse,
while a negatively curved or flat universe need not expand forever.
Still, as I have suggested, it could be that there might be some
deeper connection between the geometry of space and its energy
content, perhaps something that involves probing yet deeper into
the meaning of space and time. Certainly the puzzle of dark energy
is so revolutionary it motivates even extreme reconsiderations of
the nature of space and time. The resolution of this mystery may
not be as revolutionary as the question itself, but one never knows
until one explores the possibilities. But extraordinary claims
require extraordinary evidence, as Carl Sagan used to say. We shall
return to this mystery later in the book. First, however, we shall
explore how the collective creative imagination of the world
responded to our first revolution in the physics of space and time
inspired by Einstein and later Minkowski: Namely, the existence of
a fourdimensional space-time continuum associated with special
relativity.
C H A P T E R 7
FROM FLATLAND TO
PICASSO
Ever drifting down the
stream—
Lingering in the golden
gleam—
Life, what is it but a
dream?
—Lewis Carroll, Through the
Looking Glass
W hile life may
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