by Mark Buchanan
30 March 2009
Magazine issue 2701
Mark Buchanan is a writer based in Cambridge, UK
QUANTUM theory just seems too weird to
be in more than one place at a time. They
don't exist until you measure them. Spookier still, they can even
stay in touch when they are separated by great distances.
Einstein thought this was all a bit much, believing it to be
evidence of major problems with the theory, as many critics still
suspect today. Quantum enthusiasts point to the theory's
extraordinary success in explaining the behavior of atoms,
electrons and other quantum systems. They insist we have to accept
the theory as it is, however strange it may seem.
But what if there were a way to reconcile these two opposing views,
by showing how quantum theory might emerge from a deeper level of
If you listen to physicist Tim Palmer, it begins to sound
What has been missing, he argues, are some key ideas from
an area of science that most quantum physicists have ignored:
science of fractals, those intricate patterns found in everything
from fractured surfaces to oceanic flows.
Take the mathematics of fractals into account, says Palmer, and the
long-standing puzzles of quantum theory may be much easier to
understand. They might even dissolve away.
It is an argument that is drawing attention from physicists around
"His approach is very interesting and refreshingly
different," says physicist Robert Spekkens of the
Institute for Theoretical Physics in Waterloo, Canada.
just trying to reinterpret the usual quantum formalism, but actually
to derive it from something deeper."
That Palmer is making this argument may seem a little odd, given
that he is a climate scientist working at the
European Centre for
Medium-Range Weather Forecasting in Reading, UK.
It makes more sense
when you learn that Palmer studied general relativity at the
University of Oxford, working under the same PhD adviser as Stephen
So while Palmer has spent the last 20 years establishing a
reputation as a leading mathematical climatologist, he has also
continued to explore the mysteries of his first interest, quantum
"It has taken 20 years of thinking," says Palmer, "but I do think
that most of the paradoxes of quantum theory may well have a simple
and comprehensible resolution."
Arguments over quantum theory have raged since the 1920s, starting
with a series of famous exchanges between Einstein and the Danish
Bohr and his supporters believed that the theory's successful
description of atoms and radiation meant you should abandon old
philosophical concepts, such as the idea that objects have definite
properties even when no one is there to measure them.
Einstein and his followers countered that such radicalism was wildly
premature. They argued that much of the quantum weirdness was
nothing more than a lack of adequate knowledge.
Find a quantum
system's "hidden variables", Einstein suspected, and quantum theory
might make common sense, a view that quantum enthusiasts thought was
ultra conservative and out of touch.
The argument rages to this day.
Palmer believes his work shows it is possible that Einstein and Bohr
may have been emphasizing different aspects of the same subtle
"My hypothesis is motivated by two concepts that wouldn't
have been known to the founding fathers of quantum theory," he says:
black holes and fractals.
Palmer's ideas begin with gravity. The force that makes apples fall
and holds planets in their orbit is also the only fundamental
physical process capable of destroying information.
It works like
this: the hot gas and plasma making up a star contain an enormous
amount of information locked in the atomic states of a huge number
of particles. If the star collapses under its own gravity to form a
black hole, most of the atoms are sucked in, resulting in almost all
of that detailed information vanishing. Instead, the black hole can
be described completely using just three quantities - its mass,
angular momentum and electric charge.
Many physicists accept this view, but Palmer thinks they haven't
pursued its implications far enough. As a system loses information,
the number of states you need to describe it diminishes. Wait long
enough and you will find that the system reaches a point where no
more states can be lost. In mathematical terms, this special subset
of states is known as an invariant set. Once a state lies in this
subset, it stays in it forever.
A simple way of thinking about it is to imagine a swinging pendulum
that slows down due to friction before eventually coming to a
complete standstill. Here the invariant set is the one that
describes the pendulum at rest.
black holes destroy information, Palmer suggests that the
universe has an invariant set too, though it is far more complicated
than the pendulum.
Complex systems are affected by chaos, which means that their
behavior can be influenced greatly by tiny changes. According to
mathematics, the invariant set of a chaotic system is a fractal.
Fractal invariant sets have unusual geometric properties. If you
plotted one on a map it would trace out the same intricate structure
as a coastline. Zoom in on it and you would find more and more
detail, with the patterns looking similar to the original unzoomed
Gravity and mathematics alone, Palmer suggests, imply that the
invariant set of the universe should have a similarly intricate
structure, and that the universe is trapped forever in this subset
of all possible states. This might help to explain why the universe
at the quantum level seems so bizarre.
For example, it may point to a natural explanation for one of the
biggest puzzles of quantum physics, what physicists refer to as its
"contextuality". Quantum theory seems to insist that particles do
not have any properties before they are measured. Instead, the very
act of measurement brings their properties into being. Or, put
another way, quantum systems have meaning only in the context of the
particular experiments performed on them.
Ever since Einstein, many physicists have hoped that a new approach
might go beyond quantum theory and find a way to restore belief in
objective and independent properties. But in 1967, mathematicians
Simon Kochen and Ernst Specker published a
theorem showing that this
dream, if possible, cannot be done in quite the way physicists would
Central to Kochen and Specker's theorem is a thought experiment.
you choose to measure different properties of a quantum system, such
as the position or velocity of a quantum particle. Each time you do
so, you will find that your measurements agree with the predictions
of quantum theory. Kochen and Specker showed that it is impossible
to conceive a hypothesis that can make the same successful
predictions as quantum theory if the particles have pre-existing
properties, as would be the case in classical physics.
This result has driven many physicists to reach a startling
conclusion about how to interpret quantum theory.
Either you have to
abandon the existence of any kind of objective reality, instead
believing that objects have no properties until they are measured,
or you have to accept that distant parts of the universe share a
spooky connection that allows them to share information even when
the distance and timing means that no signal could have passed
between them without travelling faster than light.
Palmer's idea suggests a third possibility - that the kinds of
experiments considered by Kochen and Specker are simply impossible
to get answers from and hence irrelevant.
The key is the invariant set. According to Palmer's hypothesis, the
invariant set contains all the physically realistic states of the
universe. So any state that isn't part of the invariant set cannot
Suppose you perform the Kochen-Specker thought experiment and
measure the position of an electron. Then you ask what you would
have found if you repeated the experiment, only this time measuring
the electron's velocity instead.
According to Palmer, when you repeat the experiment you are testing
a hypothetical universe that is identical to the real one except
that the position-measuring equipment is replaced with
This is where the fractal nature of the invariant set matters.
Consider a place of interest you want to visit along a coastline. If
you get the coordinates even slightly wrong you could end up in the
sea rather than where you want to be. In the same way, if the
hypothetical universe does not lie on the fractal, then that
universe is not in the invariant set and so it cannot physically
Due to the spare and wispy nature of fractals, even subtle changes
in the hypothetical universes could cause them to fall outside the
invariant set. In this way, Spekkens says, Palmer's hypothesis may
help to make some sense of quantum contextuality.
"I think his approach is really interesting and novel," says
Spekkens. "Other physicists have shown how you can find a way out of
the Kochen-Specker problem, but this work actually provides a
mechanism to explain the theorem."
Following on from this, Palmer believes that many other features of
quantum theory also fall into place. For example, quantum theory is
famous for making only statistical predictions - it can only tell
you the probability of finding an electron with its
quantum-mechanical spin pointing up.
This arises naturally, suggests Palmer, because quantum theory is
blind to the intricate fractal structure of the invariant set. Just
as our eyes cannot discern the smallest details in fractal patterns,
quantum theory only sees "coarse grain approximations", as if it is
looking through fuzzy spectacles.
Other physicists seem inspired by the novelty of Palmer's approach.
"What makes this really interesting is that it gets away from the
usual debates over multiple universes and hidden variables and so
on," says Bob Coecke, a physicist at the University of Oxford.
suggests there might be an underlying physical geometry that physics
has just missed, which is radical and very positive."
Coecke points out that very few scientists working on fundamental
physics have explored how fractals might be incorporated into the
theory, even though they are commonplace in other parts of physics.
Palmer is hoping that will change. In a paper submitted to the
journal Proceedings of the Royal Society A, he shows how the basic
idea can account for quantum uncertainty, contextuality and other
quantum puzzles (The
Invariant Set Postulate - A New Geometric Framework for the
Foundations of Quantum Theory and the Role Played by Gravity).
Many details still need to be fleshed out, says Coecke.
manages to explain some quantum phenomena," he says, "but he hasn't
yet derived the whole rigid structure of the theory. This is really
Palmer accepts the criticism and is hopeful that he will be able to
improve his theory over time. In the best of worlds, he thinks his
framework may provide a way to finally reunite the warring parties
of Einstein's and Bohr's followers.
After all, the theory backs Einstein's view that quantum theory
really is incomplete. It is, Palmer says, blind to the fractal
structure of the invariant set. If it wasn't, it would see that the
world is not only deterministic, but it never exhibits any spooky
On the other hand, it also agrees with the view of Bohr and his
the properties of individual quantum systems are not
independent of the entire world, especially the experiments we
humans use to explore them. We are stuck with the disturbing fact
that how we measure always influences what we find.
For now, quantum theory remains mysterious but its air of mystique
may not last forever.
When Tim Palmer finished his PhD in physics at the University of
Oxford 30 years ago, he had the opportunity to work as a postdoc
with Stephen Hawking at the University of Cambridge. The hot topic
in theoretical physics back then was supergravity, a theory that
aimed to include gravity in a universe with 11 dimensions.
Despite Hawking's enthusiasm for the idea, Palmer remained lukewarm.
Supergravity takes quantum theory as an unquestioned starting point
and then tries to bring gravity within its fold, an approach Palmer
"I felt that quantum theory was at best a provisional theory,"
Instead, he switched to climate science where he rapidly established
an international reputation. Today Palmer is known for pioneering a
method called ensemble forecasting, which incorporates the role of
chaos to create climate forecasts that include specific estimates of
their own accuracy.
But even as Palmer's work became widely
influential - so much so that he has taken a key role on the
Intergovernmental Panel on Climate Change - he could never forget
the quantum puzzles that so occupied him before.
What is a fractal?
Fractals are geometrical shapes that aren't smooth like circles or
They are irregular structures with the same structure
repeating on ever finer scales. No matter how much you blow up a
picture of a fractal, it will always look the same.
The natural world contains many examples of fractals, including
ferns, broccoli, river networks, blood vessels and coastlines.