Imagine
yourself on a journey backward in time, back not just before our
Earth and solar system, not just before our Milky Ways galaxy began
to form, but much, much further than that, to a time before the first
stars and galaxies began to take form. We are at a point in the
universe’s evolution where it can be modeled fairly accurately as a
gas – a gas composed almost entirely out of hydrogen and some
helium although that is not the critical feature determining its
behavior. Although it is a somewhat rough analogy, it can
essentially be thought of as a gas in a closed flask, characterized
by a specific density, pressure, and temperature. As such, it can be
modeled reasonably well by the gas laws you learned in first year
college chemistry, if you were fortunate enough to have taken them.
What’s that? You never took chemistry in college? No matter; it
is quite straightforward. The basic law governing the behavior of
gasses is the so-called “Ideal Gas” Law, which, placed in
equation form is PV = nRT, where P is the pressure of the gas, V its
volume, and T its temperature. N is the totals number of moles, or
atoms / nolecules of gas in the universe. Never mind the meaning of
R here, the proportionality constant, which remains constant in this
situation anyway; when the equation is re-written as V
T/P ( being the symbol for
proportionality), we see that as V, in this case the volume of the
universe, decreases, either T must increase or P decrease. A
modification to the equation is needed here, however. I am speaking
of ideal gasses, which, in reality, don’t actually exist, but serve
as models for real gasses. In fact, with real gasses, increasing
pressure also raises their temperature. An example of this is the
gasoline vapor / air mixture in the cylinder of a car; as the piston
presses down on the mixture both its pressure and temperature rise –
in a diesel engine, this compression is enough by itself to ignite
the mixture, driving the piston upward and turning the crankshaft.
If
the temperature of a gas rises high enough, the kinetic energy of the
atoms or molecules composing it is sufficient to strip away their
electrons, leading to a state of matter known as a plasma. This
temperature is fairly high, in the thousands or tens of thousands of
degrees. The sun and other stars of equal or greater brightness are
both so hot as to be composed of such gaseous plasmas, whose
temperature rises well up into the millions of degrees in their
centers, enough along with the very high pressures / densities there
to allow the thermonuclear fusion reactions which power their
enormous energy outputs.
If
we continue our backwards time journey, at a point of between three
and four hundred thousand years after the start of the Big Bang, we
reach the point where the temperature of the universe increases to
and above the plasma temperature; after this point, electrons combine
with protons and heavier nuclei to form the first atoms. This is a
critical time in the cosmos’ evolution: prior to it, the
interaction of electromagnetic radiation with the electrically
charged electrons and bare atomic nuclei make it opaque; after it,
when stable atoms form, the electromagnetic radiation can stream
freely through space. This radiation, called the cosmic background
radiation, is a measure of the universe’s temperature. Largely in
the visible range at first, it cools over the billions of years the
universe has been expanding, to the point now where it is almost
entirely in the microwave region, a region of much lower energy than
visible light, indicating a cosmic temperature of only a few degrees
above absolute zero (absolute zero, or 0K on the Kelvin temperature
range, is the complete absence of all heat). By the way, it was the
(accidental) discovery of this microwave radiation in 1964 by Penzias
and Wilson which as much or more than anything else cinched the case
for the Big Bang theory.
Back
to the universe at 3-400,000 years after the Big Bang. Another
important fact of the universe at this time is that, although I have
described it as though it were a gas of uniform, or homogenous,
density throughout, obviously this could not have been the case.
Even then there had to be inhomogenuities present, otherwise there
would have been nothing for stars and galaxies and galactic clusters
and larger scale structures to gravitationally condense around.
These inhomogenuities need only be quite small – you would never
notice their equivalent in a pot of mashed potatoes however hard you
looked – but they had to be there, or else – well, for else one
thing, just as with the discovery of a stable high energy state of
the carbon nucleus, we would not be here to make their prediction.
In fact, they turn out to be so small that it was not until the 1990s
that they were finally unequivocally discovered by a space-based
probe called the Cosmic Background Explorer, or COBE for short. The
discovery was of such significance that some regard it as the most
important scientific discovery of the century, even to the point of
making religious analogies (of the Einsteinian nature) to it.
Three
or four hundred thousand years is not much on our cosmic timeline, if
you recall it from the last chapter, only around four hours.
Actually, this is where the line begins to lose its usefulness,
because the next set of interesting events occur up to only about 20
real minutes after the Big Bang, and reach back to only a
trillionth of a trillionth of a trillionth (10-36) of a
second after the beginning. Indeed, it is difficult to come up with
any type of line that is intuitively useful; if we make 10-36
equal to one second, then events happening at a trillionth of a
second would be 1024 or thirty million billion years
later, over two million times longer than the known age of the
cosmos! So we are going to have to drop our attempts to make such
time intervals intuitively meaningful, and stick with the hard
numbers, as difficult as they are to grasp.
As
it is also impossible to describe the events that happen during this
period of 10-36 second to approximately twenty minutes
without some basic knowledge of nuclear physics, a digression is
necessary before plunging in. Don’t panic, though; it will only be
enough for our purposes here, and besides, I’m not enough of an
expert in the subject to make it too abstruse.
As
you probably already know from your high schooling at least the atom
is composed of a nucleus consisting of at least one (in the case of
the simplest element, hydrogen) or more protons, plus zero or more
neutrons, along with one or more electrons which (though you will
recall from chapter three that this is not really correct) circle it.
Neutral atoms have as many electrons as protons, since the negative
charge on the former exactly equals the positive charge on the
latter. An atom stripped of one or more electrons is called an ion;
high enough temperature or energetic enough radiation has the ability
to do this, and as already mentioned, matter in this state is called
a plasma.
There
is something I must take the time to explain here. You probably
didn’t learn much about the atomic nuclei in your schooling, but a
fairly obvious question should occur to you about it: given that
protons are all positively charged, what holds them together in the
nucleus? Before answering that question, another thing you should
know about both protons and neutrons, which are collectively known as
hadrons, is that they themselves are composed of still smaller
entities bearing the strange name of quarks (a pun I can’t resist
is that there is a type of high-energy quark called the strange
quark). You could say, in fact, that instead of describing nuclei as
being made of two different types of hadrons, we really should say
that they are made of two different kinds, or “flavors”, of
quarks, namely up quarks and down quarks.
Quarks
have “fractional” electric charges, in that they possess ⅓ of
the negative charge of an electron – this is the down quark – or
⅔ of the positive charge of a proton – this is the up quark.
Thus, what we call a proton is really a combination of two up quarks
with a down quark, and a neutron is composed of one up quark with two
down quarks. Add up the charges and you will see they work out,
protons having a +1 charge and neutrons having zero charge.
Quarks
have other interesting properties as well. Individual quarks cannot
be isolated from each other and observed; they always exist in
combinations of two or three (or maybe more). In fact, their
existence was predicted on purely theoretical grounds in the early
1960s by Murray Gell-Mann and George Zweig, and weren’t indirectly
experimentally verified until several years later by particle
scattering experiments.
So
the question isn’t what holds protons and neutrons together in the
nucleus, but what holds the quarks together. Strangely enough, that
question was partially answered several decades earlier (although the
answer had to be modified to account for the quark structure of
hadrons). Again, there is much more to this answer than needs to be
covered here, but yet another brief digression, this time on forces,
is enough to cover the basics. Also, as I have alluded to this
earlier, now is a good time to explain it in more detail.
* * *
There
are four “fundamental” forces in the universe – fundamental in
that any force you encounter consists of one or a combination of
them, working together or against one another. You are actually
already familiar with two of these forces: gravity, which pulls all
mass objects in the universe toward each, including holding you down
on the ground, the moon orbiting Earth, and Earth and the other
planets orbiting the sun; and electromagnetism, which you observe
every time you use a magnet or electrically charged objects – it
is, of course, the force that keeps electrons in their orbits, or
orbitals, around the atomic nucleus. Incidentally, the reason you
are much more aware of gravity than electromagnetism is that the
former is (almost) a universally attractive force, building up as the
mass to generate it accumulates. Electromagnetism, on the other
hand, is both attractive and repulsive, so you only notice it under
the special conditions where an excess of positive or negative
charges occurs, and even then the excess is usually quite small, so
the effect seems relatively weak compared to gravity. In fact,
electromagnetism is some 1039 times more powerful than
gravity! Also, the reason you come into direct contact with both
forces is that they are infinite in range; both fall off only as the
square of the distance between the two attracting (or repelling)
objects.
The
remaining two forces are called nuclear forces because their
intensities fall off so rapidly that they act only on the scale of
atomic nuclei; this is the reason we don’t encounter them directly,
but only indirectly through their effects. One of these forces, the
weak nuclear force, is involved in certain kinds of radioactive
decay. I won’t speak more about it here. The other, the strong
nuclear force, which I have mentioned before, is what answers our
question about what holds the quarks, or the protons and neutrons,
together in the atomic nucleus. This force is approximately a
hundred times stronger than the electromagnetic force at the ranges
typical inside nuclei. Again though, its range is so short that it
takes tremendous kinetic energy to overcome the mutual
electromagnetic repulsion between two nuclei and allow them to come
close enough together to fuse via the strong nuclear force; this is
why it takes the incredibly high temperatures in the core of a star,
or in a thermonuclear weapon, or in the very early universe, to
accomplish this kind of nuclear fusion.
The
reason for the digression to discuss these forces is that, according
to modern theories of nuclear physics, they are all actually
manifestations of a single force, and that at sufficiently high
temperatures and pressures, such as what happens as we get closer and
closer to time zero, they merge together one by one until there is
only a single force. The reason for the digression on quarks is that
prior to a certain time, the temperature of the universe is so high
that they cannot hold together long enough to make stable protons and
neutrons.
* * *
There
is one more digression that needs to be made before we talk about the
earliest moments of cosmic evolution. It is, or so it seems to me, a
non-physicist, to be the Central Problem if we are ever able to fully
understand those moments.
The
problem is that there are two major edifices of physics twentieth
century science has erected to understand matter, energy, space, and
time over the last hundred or so years. The first edifice, which
we’ve already met, is the physics of the ultra-tiny, the world of
the atom and smaller, the physics of quantum mechanics. The other
edifice is the physics that describes the universe on the large
scale, from approximately planet sized objects on up: Einstein’s
General Relativity. And the problem is both simple and deep at the
same time: they simply do not look at and model reality in the same
way.
A
good example of this is how they describe gravity. In quantum
mechanics all forces are carried by a type of particle called a
virtual boson (bosons are particles which carry forces; the particles
which compose mass itself are called fermions). For the
electromagnetic force, this boson is the photon; and for the strong
nuclear force, the gluon. For gravity it is a hypothetical force
dubbed, naturally enough, the graviton. I say hypothetical because
gravity is such a weak force that gravitons have yet to be detected,
although they are well described theoretically; nevertheless,
according to everything we know, they must be there.
According
to general relativity, however, gravity is really not a force at all,
but the result of the Einsteinian curvature of four dimensional
spacetime by massive objects. Another object will fall toward the
object because it is only following the path of least resistance
through this spacetime. Although this curvature is enough to hold us
solidly on Earth, it requires a very massive object to detect it.
One way of doing this is by the way it bends light; historically,
General Relativity was regarded as proven by the slight deflection of
star positions during a solar eclipse in 1919. The bending of light
is used to explain a number of other astronomical phenomena as well,
such as gravitational lensing, and the splitting of the image of a
distance galaxy into two or more images by the presence of an
intervening object of sufficient mass.
Another
difference between the two theories is how they regard spacetime
itself. General relativity requires that spacetime be smooth and
relatively flat on all scales. Quantum mechanics however says that
that is impossible. The uncertainty principle, which we have already
met, means that on small enough scales spacetime must be lumpy and
twisted. An analogy to this might be a woolen blanket which from a
large distance looks smooth but up close is revealed to be composed
of intertwining hair. The uncertainly principle also affects
spacetime on small enough scales in another way, by allowing
“virtual” particles to come into existence over short enough time
periods. This happens because of another way of expressing the
uncertainty principle besides the x
× s
≤ /m
form we encountered in chapter three: t
× E
≤ ,
where t is time and E energy. In this form the equation states that
it is possible for particles of any given mass energy (E)
to exist as long as they disappear within time t.
Despite the term virtual (they are not directly detectable), these
particles are not only quite real in their effects, but they are the
heart of what explains the four fundamental forces in quantum
mechanics.
This
conflict between quantum mechanics and general relativity means that
neither theory encompasses a complete and fully correct vision of
reality. This is not normally a problem for physicists however as
generally, they divide reality into two camps, which deal with it on
such different scales. In dealing with the very early universe
however, they clash like charging elephants at full speed, for we
have now delved into a realm of both the extremely small and
the extremely massive, a place that no one has gone before and where
all our curiosity and imagination and brilliance become less and less
able to predict what we will find there. The only thing that is
certain is that we are not in Kansas anymore.
* * *
It
is time to resume our journey back to the beginning of the universe,
or at least as far as our knowledge of physics permits, back towards
T = 0, if indeed there was such a time. We had stopped at T + 20
minutes, and for good reason. In the universe today, only the
centers of stars are hot enough and dense enough to fuse hydrogen
into helium and heavier elements. But there must have been a time,
if the Big Bang is true, when the universe as a whole existed in
those conditions. There was, and T + 20 minutes marks the end of
that time.
Astronomers
observing our current cosmos discover that it is, by mass,
approximately 75% hydrogen and 24% helium, with only traces of
heavier elements. It is impossible to account for more than a tiny
fraction of that helium by stellar nucleosynthesis, however. One of
the triumphs of Big Bang theory was to account for the remaining
helium; the period between T + 3 and T + 20 minutes in our universe
had just the right conditions in terms of temperature and density,
and lasted just the right amount of time, to create it.
The
earliest periods of the Big Bang are referred to by cosmologists as
epochs. Despite the name, epochs are mostly extremely short periods
of time when the newly born universe was evolving extremely rapidly.
Thus, there is the Planck epoch, the grand unification epoch, the
inflationary epoch, the quark epoch, and so on. These epochs are
defined according to the predominant process(es) or particle(s) which
characterize them. The period of nucleosynthesis we are discussing
is just a part of the photon epoch, the total length of which is from
T + 3 minutes to almost T + three-four hundred thousand years
(although the nucleosynthesis fraction of this time, if you’ll
recall, only lasts up to T + 20 minutes), a time when most of the
energy of the universe is in the form of photons; as mentioned
before, this epoch ends when stable atoms finally form and the
photons are free to stream through space unhindered as the cosmic
background radiation we detect today.
The
epoch preceding the photon epoch is the so-called lepton epoch, which
takes us back to approximately T + 1 second. Leptons are fermions (a
type of mass bearing particle, if you’ll remember) that interact
with all forces except the strong nuclear force; the member of this
family we are most familiar with is the electron, although there are
others, such as the electron neutrino, a very low mass particle
involved in certain types of nuclear reactions. There are also high
energy, short-lived versions of both these particles, such as the
muon and tau high energy analogues of the electron, and their
corresponding neutrinos, the muon neutrino and tau neutrino. In the
lepton epoch leptons dominate the mass of the universe. Excuse me, I
should say leptons and anti-leptons, for we have reached that
period of the universe’s evolution where one of its most
interesting puzzles needs to be addressed: the cosmic asymmetry
between matter and antimatter.
* * *
Antimatter
probably sounds like the stuff of science fiction, especially if you
are a Star Trek fan (this is admittedly where I first heard of
it), but in fact it is very real, and that reality poses a serious
problem. The problem is that every mass carrying particle, or
fermion, has a corresponding antiparticle, which has the same mass
but the opposite electric charge (there are other differences, too).
So every electron, say, has an antielectron – also known as a
positron – every quark has an antiquark, every neutrino an
antineutrino. The real problem is that if a particle and its anti
counterpart should encounter each other, say an electron and a
positron, the result is cataclysmic: both particles mutually
annihilate each other in a burst of high energy photons (photons,
like other force carrying particles, are their own anti-particles;
there are no such things as anti-photons). No, the real
problem is that, in the first few seconds of the cosmos’ existence,
both fermions and their anti counterparts ought to be produced in
equal numbers, only in the next few seconds to completely annihilate
each other, leaving a universe composed of nothing but high energy
radiation; no matter, no stars or galaxies, and no us. As the
universe today, for good theoretical and observational reasons,
appears to be composed almost entirely of matter, with very little if
any antimatter, there must have been a certain asymmetry between the
number of matter and antimatter particles formed in the early
universe. This asymmetry, favoring the creation of matter over
antimatter, need only be quite small; once all of the antimatter had
mutually annihilated by an equal quantity of matter, the excess of
matter would have been left to dominate the cosmos as we see today.
But what could have caused this asymmetry, however small?
This
is no trivial question because symmetry lies at the heart of much of
the laws of physics, especially the laws that govern sub-atomic
particles and their behavior. Violations of certain kinds of
symmetry, however, are known to occur. Symmetry breaking is, indeed,
crucial to the earliest moments of Big Bang cosmology, particularly
in the evolution of the four fundamental forces. Recall that these
forces merge, one by one, into a single force as we close in on T =
0. So it is not unreasonable to hypothesize that some kind of
symmetry breaking is responsible for the matter excess we see in the
universe today. This is an area of active research and intense
debate among cosmologists.
It
is worthwhile to pause here at T + 1 seconds and take stock of where
we are and what is happening in our attempt to unravel the earliest
moments of the cosmos. I mentioned at the beginning of this chapter
that as we went deeper and deeper into the past, we would eventually
reach a point where our understanding of the laws of physics begins
to get increasingly shaky, shaky to the degree that we are no longer
certain of the ground beneath our feet. Like fossil hunters digging
into deeper and deeper strata, what we find is less certain, more
speculative, and harder to lay out with the same confidence that has
carried us this far. My sense and reading and understanding leaves
me to believe that we have arrived at this point, or at least are
very close to it. The one event before T + 1 which does seem well
established, the breaking of electroweak (electromagnetic plus weak
forces) symmetry and the ensuing establishment of the weak nuclear
force and electromagnetism as two separate forces, occurs at
approximately T + 10-12 seconds. At this point all four
fundamental forces have achieved their current form (though not
current strengths), and the quarks in the quark-gluon plasma that
fills the universe acquire their masses via their interaction with a
still hypothetical particle (it is currently being actively searched
for) called the Higgs boson. The subsequent cooling after this point
allows the free quarks to combine into the protons and neutrons and
other hadrons we see today.
* * *
I
think I can say confidently that what happens before T + 10-12
seconds is entirely the subject of theoretical work. The next
symmetry breaking, between the strong nuclear force and the
electroweak force, is the subject of so-called Grand Unification
Theories, or GUTS, of which there are several varieties. By the way,
in a way this name is misleading, as we have still not accounted for
gravity yet. But recalling our earlier discussion of general
relativity and quantum mechanics, we know that a quantum theory of
gravity needs to be formulated and tested before we tread that realm,
and that such a theory is still in such a theoretical stage that one
of its prime candidates, string theory, has yet to be accepted a
real, credible theory by many in the scientific community.
Current
estimates of the break between the strong and electroweak forces
places it at about T + 10-36 seconds, or a trillionth of a
trillionth of a trillionth of a second after the Beginning. And
here, at the risk of understatement, is where things begin to get
interesting, at least if our theoretical models are correct. For
this is where Big Bang cosmology almost fell flat on its face, if I
may be pardoned what is about to be another pun.
Besides
the matter-antimatter asymmetry, two other features of the current
universe need to be explained by events very early in its history:
one is that, on very large scale, its shape is very flat; the second
is that, on more local scales, it is lumpy and inhomogeneous.
The
local inhomogenuity is the easier of the two to understand. We look
around ourselves and we see a universe today in which the matter is
organized into stars / solar systems, galaxies, clusters of galaxies,
clusters of clusters, and so on. This is due to gravity working over
billions of years, of course. But there must have been primordial
inhomogenuities in the early universe for gravity to work on; if the
Big Bang had produced a perfectly homogeneous distribution of
mass-energy, then we would not be here to observe a universe composed
of non-uniformly distributed hydrogen and helium, bathing in an
equally non-uniform sea of background radiation.
Fortunately
for us, the universe is inhomogeneous, and has been since the
de-coupling of matter and energy around T + 3-400,000 years, as
careful studies of the cosmic background radiation (from COBE) have
shown. But where did these inhomogenuities arise from? Classical
Big Bang theory at the time could not answer this question.
The
other problem, that of the flatness of universe on large scales, also
stumped classical theory, although it is a little harder to explain.
This is an issue raised by general relativity; more precisely, by the
so-called “field equations” of general relativity, which have a
number of different solutions, under different conditions. These
solutions, among other things, describe the cosmic curvature of
spacetime due to the presence of mass-energy. There are three
possible curvatures, depending on the mass-energy density, measured
by a value called omega or Ω: if Ω is greater than one, then the
mass-energy density yields a universe characterized by positive
spacetime curvature, causing its expansion to eventually stop, then
reverse into a contraction phase (which would have already happened
by now) which may result in another cosmic singularity and big bang;
if Ω is less than one, however, then spacetime is described as
hyperbolic and the expansion will continue forever; if Ω is exactly
equal to one, than spacetime is flat and the expansion will also
continue forever, albeit slower and slower, gradually grinding to a
stop it will never quite reach.
An
exact measurement of Ω today is difficult, but between the
observational data and theoretical considerations, it should be very
close to if not exactly equal to one. The problem this creates is
that any deviation from Ω = 1 in the early universe would be
exponentially magnified by the cosmos’ expansion until today we
should see a Ω vastly greater or smaller than one. As Ω appears
close to or equal to one today, this must mean that it was even more
exquisitely close to one in the early universe as well. Prior to the
1980s, however, nobody had a convincing reason why that should be the
case. It simply appeared that Ω was another example of the “fine
tuning” problem which we shall return to later.
Human
ingenuity is never to be underestimated, however. In the 1980s the
work of Alan Guth, Andrei Linde, Andreas Albrecht, and Paul
Steinhardt yielded a modified version of Big Bang theory that
included a period of exponential expansion very early in the cosmos’
evolution. They called this extra fast expansion Inflation. The idea
of an ultra-fast, in fact exponential, expansion meant that during
this phase the universe increased in size by many orders of magnitude
(by a factor of at least 1026) in a fantastically short
period of time, from about T + 10-36 to T + 10-32
seconds. The triggering mechanism for this expansion is not known
for sure, but a good candidate appears to be the decoupling of the
strong nuclear force from the electroweak force, especially as they
appear to happen at the same time. It is also a matter of contention
as to what brought inflation to an end, or even whether it ended
everywhere at the same time or broke up into “bubbles” of
ordinary universes formed at different times, of which ours is one.
In fact, inflation could still be going on outside of our own
universe, or perhaps “hyperverse” is the better term, still
creating new universes with perhaps different laws and constants.
Whatever
the physics behind inflation, what initiates it and how it ends, it
neatly solves both the problems of local inhomogenuity and cosmic
flatness (and a number of other problems as well). The flatness
problem is solved because whatever the value of Ω before inflation,
the enormous exponential stretching of spacetime brings it
essentially so close to one that it will not diverge significantly
from this value during the subsequent normal cosmic expansion. The
local inhomegenuity problem is also solved, thanks to quantum
mechanics: in the pre-inflation epoch the cosmos is so small that
random inhomogenuities arise simply due to the uncertainty principle,
which says that spacetime and the distribution of mass-energy can
never be perfectly uniform; the effect of inflation is to “freeze”
and enormously expand these inhomogenuities into the seeds of stars
and galaxies and larger structures we see today.
* * *
So.
We find ourselves at the decoupling of the strong nuclear force from
the electroweak force which, if theory is correct, occurred somewhere
between T + 10-36 and T + 10-32 seconds. The
next step, going back further, T + 10-43 seconds marks the
end of the Planck epoch, named so because according to quantum
mechanics, it is approximately the shortest period of time which can
be even theoretically measured, the shortest period of time one could
say that time can even exist. The Planck epoch is also the time
period in which quantum mechanics and general relativity find
themselves in full collision. Somehow, some way, somewhere, gravity
merges with the strong + electroweak force, although no one knows how
with any certainty. We have entered the realm of pure imagination,
where some scientists play with entities called cosmic strings and
work long hours trying to turn them into the ultimate explanation of
matter, energy, space, and time, while other scientists place their
time and bets on ideas like quantum loop gravity and other exotic
hypotheses. As no one has succeeded to the approval of all, we have
also reached the end of our own, personal journey into the past,
arriving if possible at where we began in Chapter eight, when we
tried to imagine what nothing would really be like and realized that
we couldn’t do it no matter how hard we tried. Of course, perhaps
what preceded the Big Bang wasn’t nothing at all. Quite possibly
our universe is part of a greater reality, in which other universes
are also embedded – the multiverse conjecture. There are also a
number of cyclic universe models, such as the Steinhardt-Turok model
in which the universe oscillates between expansion and contraction,
with each Big Bang triggered by a collisions of two “branes”
(multi-dimensional strings) in a higher dimensional spacetime.
Again, this model could predict many, even an infinite number, of
universes.
Although
any of these models could be true, there is, I think, a philosophical
problem with the whole approach, one ironically not too different
from the concept of a supernatural god(s) being responsible for the
universe. Just as a god needs a greater god to explain it, ad
infinitum, we are potentially postulating an infinite number of
greater or higher dimensional cosmoses to explain our own. To me it
all seems driven by a pathological inability to accept nothing merely
because we are incapable of imagining it. But the limitations of
human imagination prove nothing, except our need to accept them,
however unpleasant. This is a subject we will return to in the last
chapter of the book.
