Mathematical laws underpin the fabric of our Universe - not just
atoms, but galaxies, stars and people. The properties of atoms -
their sizes and masses, how many different kinds there are, and
the forces linking them together - determine the chemistry of our
everyday world. The very existence of atoms depends on forces and
particles deep inside them. The objects that astronomers study -
planets, stars and galaxies - are controlled by the force of gravity.
And everything takes place in the arena of an expanding Universe,
whose properties were imprinted into it at the time of the initial
Science advances by discerning patterns and regularities in nature,
so that more and more phenomena can be subsumed into general categories
and laws. Theorists aim to encapsulate the essence of the physical
laws in a unified set of equations and a few numbers. There is still
some way to go, but progress is remarkable.
As the start of the twenty-first century, we have identified six
numbers that seem especially significant. Two of them relate to
the basic forces; two fix the size and overall 'texture' of our
Universe and determine whether it will continue for ever; and two
more fix the properties of space itself:
These six numbers constitute a 'recipe' for a universe.
Moreover, the outcome is sensitive to their values: if any one of
them were to be 'untuned', there would be no stars and no life. Is
this tuning just a brute fact, a coincidence? Or is it the providence
of a benign Creator? I take the view that it is neither. An infinity
of other universes may well exist where the numbers are different.
Most would be stillborn or sterile. We could only have emerged (and
therefore we naturally now find ourselves) in a universe with the
'right' combination. This realisation offers a radically new perspective
on our Universe, on our place in it, and on the nature of physical
The cosmic number omega
measures the amount of material in our Universe - galaxies,
diffuse gas, and 'dark matter'. Omega tells us the relative
importance of gravity and expansion energy in the Universe.
A universe within which omega was too high would have collapsed
long ago; had omega been too low, no galaxies would have formed.
The inflationary theory of the Big Bang says omega should be
one; astronomers have yet to measure its exact value.
It is astonishing that an expanding
universe, whose starting point is so 'simple' that it can be specified
by just a few numbers, can evolve (if these numbers are suitable
tuned) into our intricately structured cosmos.
Another number, epsilon,
defines how firmly atomic nuclei bind together and how all the
atoms on Earth were made. The value of epsilon controls the
power from the Sun and, more sensitively, how stars transmute
hydrogen into all the atoms of the periodic table. Carbon and
oxygen are common, and gold and uranium are rare, because of
what happens in the stars. If epsilon were 0.006 or 0.008, we
could not exist.
Perhaps there are some connections
between these numbers. At the moment, however, we cannot predict
any one of them from the values of the others. Nor do we know whether
some 'theory of everything' will eventually yield a formula that
interrelates them, or that specifies them uniquely. I have highlighted
these six because each plays a crucial and dis-tinctive role in
our Universe, and together they determine how the Universe evolves
and what its internal potentialities are; moreover, three of them
(those that pertain to the large-scale Universe) are only now being
measured with any precision.
Why the Universe is so large
The tremendous timespans involved
in biological evolution offer a new perspective on the question
'why is our Universe so big?' The emergence of human life here on
Earth has taken 4.5 billion years. Even before our Sun and its planets
could form, earlier stars must have transmuted pristine hydrogen
into carbon, oxygen and the other atoms of the periodic table. This
has taken about ten billion years. The size of the observable Universe
is, roughly, the distance travelled by light since the Big Bang,
and so the present visible Universe must be around ten billion light-years
The galaxy pair NGC 6872 and IC 4970 indicate the vastness of
the Universe. Light from the bright foreground star has taken
a few centuries to reach us; the light from the galaxies has
been travelling for 300 million years. The Universe must be
this big - as measured by the cosmic number N - to give
intelligent life time to evolve. In addition, the cosmic numbers
omega and Q must have just the right values for
galaxies to form at all.
||Photo - European
This is a startling conclusion. The
very hugeness of our Universe, which seems at first to signify how
unimportant we are in the cosmic scheme, is actually entailed by
our existence! This is not to say that there couldn't have been
a smaller universe, only that we could not have existed in it. The
expanse of cosmic space is not an extravagant superiority; it's
a consequence of the prolonged chain of events, extending back before
our Solar System formed, that preceded our arrival on the scene.
This may seem a regression to an ancient
'anthropocentric' perspective - something that was shattered by
Copernicus's revelation that the Earth moves around the Sun rather
than vice versa. But we shouldn't take Copernican modesty (some-times
called the 'principle of mediocrity') too far. Creatures like us
require special conditions to have evolved, so our perspective is
bound to be in some sense atypical. The vastness of our universe
shouldn't surprise us, even though we may still seek a deeper explanation
for its distinctive features.
The physicist Max Born once claimed
that theories are never abandoned until their proponents are all
dead - that science advances 'funeral by funeral'. But that's too
cynical. Several long running cosmological debates have now been
settled; some earlier issues are no longer controversial. Many of
us have often changed our minds - I certainly have.
Cosmological ideas are no longer any more
fragile and evanescent than our theories about the history of our
own Earth. Geologists infer that the continents are drifting over
the globe, about as fast as your fingernails grow, and that Europe
and North America were joined together 200 million years ago. We believe
them, even though such vast spans of time are hard to grasp. We also
believe, at least in outline, the story of how our biosphere evolved
and how we humans emerged.
D = 3
The first crucial number is the number of spatial dimensions:
we live in a three-dimensional Universe. Life couldn't exist
if D were two or four. Time is a fourth dimension, but distinctively
different from the others in that it has a built-in arrow: we
'move' only towards the future.
Some key features of out cosmic environment
are now underpinned by equally firm data. The empirical support
for a Big Bang ten to fifteen billion years ago is as compelling
as the evidence that geologists offer on our Earth's history. This
is an astonishing turnaround: our ancestors could weave theories
almost unencumbered by facts, and until quite recently cosmology
seemed little more than speculative mathematics.
A few years ago, I already had 90% confidence
that there was indeed a Big Bang - that everything in our observable
Universe started as a compressed fireball, far hotter than the centre
of the Sun. The case now is far stronger: dramatic advances in observations
and experiments have brought the broad cosmic picture into sharp focus
during the 1990s, and I would now raise my degree of certainty to
N = 1,000,000,000,000,000,000,000,000,000,000,000,000
The cosmos is so vast because there is one crucially important
huge number in nature. N measures the strength of the
electrical forces that hold atoms together, divided by the force
of gravity between them. If it had a few less zeros, only a
short-lived and miniature universe could exist. No creatures
would be larger than insects, and there would be no time for
evolution to lead to intelligent life.
"The most incomprehensible thing
about the Universe is that it is comprehensible" is one of
Albert Einstein's best-known aphorisms. It expresses his amazement
that the laws of physics, which our minds are somehow attuned to
understand, apply not just here on Earth but also in the remotest
galaxy. Newton taught us that the same force that makes apples fall
holds the Moon and planets in their courses. We now know that this
same force binds the galaxies, makes some stars collapse into black
holes, and may eventually cause the Andromeda galaxy to collapse
on top of us. Atoms in the most distant galaxies are identical to
those we can study in our laboratories. All parts of the universe
seem to be evolving in a similar way, as though they shared a common
origin. Without this uniformity, cosmology would have got nowhere.
Recent advances bring into focus new mysteries
about the origin of our Universe, the laws governing it, and even
its eventual fate. These pertain to the first tiny fraction of a second
after the Big Bang, when conditions were so extreme that the relevant
physics isn't understood - where we wonder about the nature of time,
the number of dimensions, and the origin of matter. In this initial
instant, everything was squeezed to such immense densities that the
problems of the cosmos and the micro-world overlap.
Q = 1/100,000
The seeds for all cosmic structures - stars, galaxies and clusters
of galaxies - were all imprinted in the Big Bang. The fabric
- or texture - of our Universe depends on a number that represents
the ratio of two fundamental energies. If Q were even
smaller, the Universe would be inert and structureless; if Q
were much larger, it would be a violent place, dominated by
giant black holes.
Space can't be indefinitely divided.
The details are still mysterious, but most physicists suspect that
there is some kind of granularity on a scale of 10-33
centimetres. This is twenty powers of ten smaller than an atomic
nucleus: as big a decrease as the increase in scale from an atomic
nucleus to a major city. We then encounter a barrier: even if there
were still tinier structures, they would transcend our concepts
of space and time.
What about the largest scales? Are there
domains whose light has not yet had time to reach us in the ten billion
years or so since the Big Bang? We plainly have no direct evidence.
However, there are no theoretical bounds on the extent of our Universe
(in space, and in future time), and on what may come into view in
the remote future - indeed, it may stretch not just millions of times
farther than our currently observable domain, but millions of powers
of ten further.
Measuring the sixth number, lambda,
was the biggest scientific news of 1998, though its precise
value is still uncertain. An unsuspected new force - a cosmic
'antigravity' - controls the expansion of our Universe. Fortunately
for us, lambda is very small. Otherwise its effect would have
stopped galaxies and stars from forming, and cosmic evolution
would have been stifled before it could even begin.
And even that isn't all. Our Universe,
extending immensely far beyond our present horizon, may itself be
just one member of a possibly infinite ensemble. This 'multiverse'
concept, though specula-tive, is a natural extension of current
cosmological theories, which gain credence because they account
for things that we do observe. The physical laws and geometry
could be different in other universes.
What distinguishes our Universe from
all those others may be just six numbers.
Copyright © 1999 Martin Rees. Extracted from JUST SIX NUMBERS published by Weidenfeld & Nicolson at #12.99
Professor Sir Martin Rees is an international
leader in cosmology. He is Royal Society Research Professor at Cambridge
University, and holds the title Astronomer Royal. He is also a member
of the Royal Society, the United States' National Academy of Sciences
and the Russian Academy of Sciences. Together with many international
collaborators, he has contributed many key ideas on black holes, galaxy
formation and high-energy astrophysics. Martin Rees lectures and writes
extensively for general audiences.