IT’S the ultimate goal in physics—a Theory of Everything that captures
all the fundamental features of reality in a simple set of equations. If
physicists ever get their hands on such a glittering prize, however, they may be
more than a little disappointed. For they will still be faced with an
unanswerable question famously posed by John Wheeler, one of the fathers of 20th
century physics: why does nature obey this set of equations and not another?
Now, a physicist at the Institute for Advanced Study at Princeton, New
Jersey, says that there may be a way to answer Wheeler’s question and explain
why the Universe behaves the way it does. His idea is stretching the minds of
his colleagues to the limit because it involves first accepting that all the
stars and galaxies we can see are simply an infinitesimal subset of reality. If
Max Tegmark is right, all logically possible universes exist.
Tegmark does not just mean universes with different physical
constants—for instance, different values of the strength of gravity or
mass of an electron. Nor does he merely mean universes that began with different
conditions—such as different amounts of clumpiness in the big bang. “What
I have in mind are universes which dance to the tune of entirely different sets
of equations of physics,” says Tegmark. What’s more, he has a way to test his
idea.
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Replacing our Universe with a bewildering profusion of universes may seem
crazy but Tegmark believes it may have a big payoff. The only universes that
will be “perceived” will be the ones containing life. So if he can work out the
conditions necessary for life to evolve, he should be able to explain why we
find ourselves in the Universe that we do. “The conditions for life will specify
the equations governing our Universe and tell us why they and no others apply,”
says Tegmark.
It’s an idea that fellow physicists find intriguing and disturbing in almost
equal measure. “I don’t say I believe it but it’s a very provocative idea,” says
Andreas Albrecht of Imperial College in London. The notion that all possible
universes exist could certainly help circumvent one of the central problems
facing physics. “It’s actually quite difficult to construct a theory where
everything we see is all there is,” says Albrecht.
The idea that there is a vast “ensemble” of universes is by no means new.
“Nature has been telling us for a while and from many different directions that
the ensemble of universes is much bigger than anyone imagined,” adds Tegmark. In
the many worlds interpretation of quantum theory, which is increasingly being
embraced by physicists, the Universe “splits” into parallel realities at every
quantum instant
(see “Dying to know”, 91av,
20/27 December 1997, p 50).
Also, according to a popular theory of the early Universe known as
“inflation”, our Universe is no more than a tiny bubble in a tremendously
bigger universe. Some theorists have even suggested that the laws of physics
“freeze out” differently in different bubbles, which might explain the location
of some of Tegmark’s extra universes.
But the main reason for believing in an ensemble of universes is that it
could explain why the laws governing our Universe appear to be so finely tuned
for our existence. In the 1950s, for instance, Fred Hoyle discovered that the
step-by-step build-up of heavy elements inside stars depends on a series of
spectacular coincidences. Only if the nuclei of beryllium-8, carbon-12 and
oxygen-16 exist in particular energy states can hydrogen be built up into the
elements of life such as calcium, magnesium and iron.
This fine-tuning has two possible explanations. Either the Universe was
designed specifically for us by a creator or there is a multitude of
universes—a “multiverse”. Only in those universes in which the properties
of beryllium-8, carbon-12 and oxygen-16 are right for life would any life arise
to notice any fine-tuning. This is called the anthropic principle.
Many other examples of fine-tuning have been found. For instance, if the
strong nuclear force, which glues nuclei together, were only about 1 per cent
stronger, two protons would stick to make a “di-proton”. In our Universe,
protons are welded in the Sun via the weak nuclear force, which first converts
one of the protons to a neutron, and is extremely slow. It takes about 10
billion years for two protons to combine, ensuring that the Sun burns its fuel
slowly over the billions of years needed for life to evolve. If the di-proton
were stable, the strong force would snap protons together so fast that the Sun
would burn its fuel in less than a second and explode. If the strong force had
always been stronger, all hydrogen nuclei would have been processed into
di-protons in the big bang and there would be no hydrogen for stars to burn.
The weak nuclear force also appears to be finely balanced to permit our
existence. During the catastrophic collapse of a star, the matter in its dense
core is transformed into neutrons and a vast number of neutrinos. The neutrinos
fly outwards and in the process blow away the star’s “envelope”, triggering a
supernova. Yet neutrinos interact with matter in the envelope only via the weak
force. If the weak interaction were slightly stronger, the neutrinos would be
trapped in the heart of the star and the explosion would stall. If it were
slightly weaker, they would escape from the star without interacting with
matter. Either way, the heavy elements forged in massive stars which are
essential for life would not be catapulted into space to be incorporated into
new stars and planets.
Everywhere you look
There are yet more examples. For instance, Tegmark and Martin Rees of the
Institute of Astronomy in Cambridge, have found that stars and galaxies could
not have arisen if the initial clumpiness of the matter emerging from the big
bang had been slightly different
(This Week, 29 November 1997, p 11). And
Tegmark has found that only with three dimensions of space and one of time is
physics both predictable enough and complex enough for the evolution of life,
while yielding stable structures such as atoms and planets (This Week, 13
September 1997, p 11). “Wherever physicists look, they see examples of
fine-tuning,” says Rees.
Many physicists have taken this as evidence for an ensemble of universes,
with each corresponding to differences in the constants of physics or the
initial conditions of the Universe. In proposing that there are universes
corresponding to entirely different equations that are subject to different
starting conditions and with different constants, Tegmark is taking this concept
to its extreme. “I call the ensemble the `ultimate ensemble’ because it embraces
all other ensembles,” he says.
Tegmark came up with the ultimate ensemble idea while he was a graduate
student at the University of California at Berkeley in 1992. “At first, I
suggested it to a friend as a joke,” he says. “But it kept coming back—I
couldn’t stop thinking about it.” He wrote up the idea in a paper in the summer
of 1996. It was never published because Tegmark couldn’t think of a physics
journal where it would fit. Instead, he put it on the Web where it created a big
stir. There is even an Internet newsgroup set up by scientists to discuss the
paper. “It deserves to be published, even though many points are still
unresolved,” says Albrecht.
Physics is maths
What led Tegmark to the ultimate ensemble was thinking about the peculiar
connection between mathematics and physics. It’s long been known that the laws
of physics are expressible mathematically, a fact which in the 1930s led the
Austrian physicist Eugene Wigner to comment on the “unreasonable effectiveness
of mathematics in the physical sciences”.
But this intimate link poses another puzzle, says Tegmark. Over the
centuries, mathematicians have discovered a host of mathematical structures.
Each structure, technically known as a “formal system”, consists of a set of
self-consistent axioms and the theorems that can be derived from those axioms by
applying rules of logic. They range from integers to Boolean algebra—a
simple formal system—and from Euclidean geometry to string theory. Tegmark
likes to think of them as boxes interlinked on a “tree of mathematics”.
The fact that the laws of physics appear to be mathematical leads Tegmark to
infer that that one of the boxes on the tree of mathematics—as yet only
partially glimpsed by physicists—must correspond to our Universe. In other
words, it must contain the equations of the Theory of Everything.
But what about the other boxes? “Why should only one box be privileged above
all others?” asks Tegmark. “Why should only one mathematical structure out of
all the countless mathematical structures be endowed with physical existence?”
Physicists usually try to assume that there is nothing special about our
situation in space or time—an idea called the Copernican principle.
Extending this notion to the mathematical “tree”, Tegmark thinks there is no
reason to believe that the box corresponding to our Universe is special.
Instead, every mathematical box should correspond to its own physical
universe.
This idea is so astonishing it takes a while to sink in. It implies that
there are universes for all conceivable mathematical structures: one that
consists of nothing but Euclidean geometry, another that consists merely of
complex numbers, another of Hilbert spaces, and so on. “The key thing is that
although every mathematical structure exists and has physical existence, only
some are perceived to have physical existence,” says Tegmark. “For instance, a
universe consisting of Euclidean geometry exists but its equations are nowhere
near rich enough in possibilities to evolve observers.”
When Tegmark talks of “observers”, he means any kind of life, not just the
life we have here on Earth. There could be non-organic life based on silicon or
software or some foundation as yet undreamt of. The umbrella term he has coined
to cover them all is “self-aware substructures”, or SASs. Our Universe clearly
contains SASs. So working out the conditions necessary for the evolution of SASs
should help to constrain the theory of everything. “Biology in its widest sense
determines the laws of physics,” says Tegmark.
But although the conditions for life will narrow down the options, they will
not necessarily point to just one universe, he says. “Rather than an island in
parameter space, I think there is an archipelago.”
If that is correct, our Universe is simply one of a subset of universes, all
compatible with life. So how can we explain why our Universe behaves the way it
does? This is the clever part. The laws of physics would be slightly different
for every universe containing life. For instance, the elementary particles might
have slightly different masses. Plotting a graph of the possible values of
electron mass against the number of universes that share each value would then
lead to a “probability distribution” for the electron mass. Conceivably, one
value of the electron mass would be found in a large number of universes while
very different values would be found in only a few universes, producing a graph
like a bell curve.
Grand goal
So to test Tegmark’s idea, all you need to do is assume once again that our
Universe is not particularly special. If so, our laws of physics should always
lie somewhere near the peak of the different distributions. “If we find that,
say, the electron mass in our Universe is not near the peak of the distribution,
then I’m wrong,” says Tegmark. The ultimate ensemble theory is, then, refutable.
Yet if the values do all turn out to be typical, Tegmark will have explained why
our Universe is as it is.
It’s a grand goal, but it will not be easy. “You’re trying to get precision
in physical science by invoking just about the most imprecisely defined
thing—life,” says Albrecht. Tegmark admits that defining the conditions
for SASs will be extremely hard. However, he points out that the great advantage
of the ultimate ensemble theory is that it has no free parameters—for
instance, it does not depend on initial conditions in the big bang—unlike
all other visions of the Theory of Everything.
He will have his work cut out persuading people of his vision. “It’s an
interesting and thought-provoking idea,” says Nick Bostrom, a researcher in
anthropic reasoning at the London School of Economics. “I believe it is false.
However, I don’t rule out the possibility that future discussions may give rise
to a really plausible theory that maybe will use some of Tegmark’s ideas.”
Albrecht is still more cautious. The Theory of Everything may turn out to be
a theory of the remote microscopic world which makes no unique predictions about
our world, he says. “There may be a myriad different ways of breaking the
symmetry of the basic laws of physics and our world might have been reached
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Another difficulty with the ultimate ensemble theory is that it appears very
wasteful. However, Tegmark has an extraordinary argument with which to counter
his critics. He says there is actually less information in the multiverse than
in an individual universe.
To illustrate his argument, Tegmark gives the example of the numbers between
0 and 1. A useful definition of something’s complexity is the length of a
computer program needed to generate it. Imagine trying to generate a single
number between 0 and 1, specified by an infinite number of decimal places.
Expressing it would take an infinitely long computer program. But to generate
all numbers between 0 and 1, all you would have to do is start at 0, step
through 0.1, 0.2 and so on, then 0.01, 0.11, 0.21 and so on—an easy
program to write. In other words, creating all possibilities is much simpler
than creating one very specific one.
“The idea that the ensemble of all worlds is simpler than some of its single
members is an interesting notion,” says Mitchell Porter of the University of
Queensland, in Australia. “But it requires much more thought.”
According to Tegmark, astronomers have no trouble accepting that space might
be boundless, with infinitely many unseen galaxies whose light has not had
enough time to reach us since the big bang. “So the reaction against the
multiverse as somehow wasteful is not rational,” he says. “Why should the
Universe be the way we perceive it?”
- Further reading:
Tegmark’s paper can be found at
http://www.sns.ias.edu/~max/toe.html