Re: Anything goes?

Stephen Jones (
Fri, 12 Jun 1998 05:57:14 +0800


Here is an article from New Scientist about a sort of ultimate Anthropic
Principle. If there is no Intelligent Designer who fine-tuned the universe to
permit life, then there must not only be multiple universes but also multiple
laws of physics!

But as physicist Paul Davies points out, invoking multiple universes to explain
one, is against Occam's razor:

"Another weakness of the anthropic argument is that it seems the very
antithesis of Occam's razor, according to which the most plausible of a
possible set of explanations is that which contains the simplest ideas and
least number of assumptions. To invoke an infinity of other universes just
to explain one is surely carrying excess baggage to cosmic extremes"
(Davies P., "God and the New Physics", 1990, p173)

Anglican priest-physicist Polkinghorne says of such ensemble of universes

"Let us recognize these speculations for what they are. They are not
physics but, in the strictest sense, metaphysics. There is no purely scientific
reason to believe in an ensemble of universes. By construction these other
worlds are unknowable by us. A possible explanation of equal intellectual
respectability - and to my mind greater economy and elegance would
be that this one world is the way it is because it is the creation of the
will of a Creator who purposes that it should be so." (Polkinghorne J.,
"One World: The Interaction of Science and Theology", 1987, p80)




[Archive: 6 June 1998]


Anything goes

Illustration: Frank W. Ockenfels

Why are the laws and constants that govern the Universe so finely
tuned for life to flourish? One physicist thinks he knows and, as
Marcus Chown discovers, the answer is mind-boggling

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.

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

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", New Scientist, 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

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

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 accidentally."

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
01, 02 and so on, then 001, 011, 021 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

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

(c) Copyright New Scientist, RBI Limited 1998

(Chown M., "Anything Goes," New Scientist, 6 June 1998, Vol. 158,
No. 2137, pp26-30)

"Evolution is the greatest engine of atheism ever invented."
--- Dr. William Provine, Professor of History and Biology, Cornell University.

Stephen E (Steve) Jones ,--_|\
3 Hawker Avenue / Oz \
Warwick 6024 ->*_,--\_/ Phone +61 8 9448 7439
Perth, West Australia v "Test everything." (1Thess 5:21)