"NOBODY understands quantum mechanics," lamented Richard Feynman. But Anton Zeilinger at the University of Vienna aims to prove him wrong. His research group has demonstrated the futuristic phenomena of quantum teleportation and quantum encryption, and these successes have encouraged Zeilinger to search for the essence of quantum mechanics--the irreducible kernel from which everything else flows. He believes that he has found it. If he is right, all the mysteries of the quantum world will turn out to be inescapable consequences of a single, simple idea.
Quantum theory describes the world with
astonishing precision, whether applied to elementary particles a
hundred thousand times smaller than atoms or to currents in
superconducting rings a billion times larger. And yet it seems to
present a catalogue of intertwined conundrums. The most
fundamental is quantisation, the notion that energy, spin and
other quantities only come in discrete steps. Another enigma is
the probabilistic nature of the quantum world, at odds with the
classical world of definite physical properties. Then there is
entanglement, the profound connectedness of objects and processes
across large distances, and superposition, the astonishing
proposition that an electron can be both here and there, a current
can flow simultaneously clockwise and anticlockwise, and a cat can
be both dead and alive, until you look to see which.
Physicists have anxiously devised one
philosophical interpretation of quantum mechanics after another.
In the Copenhagen interpretation, the outcome of an experiment is
only revealed when the quantum system interacts with a macroscopic
apparatus in the laboratory, which eliminates all possibilities
but one. The many-worlds interpretation insists that all possible
outcomes of an experiment actually occur in as many parallel
universes, but as we only occupy a single branch of the
hydra-headed multiverse, we experience only one outcome. Or, if
you prefer, there's the guiding wave interpretation, which assigns
an undetectable "pilot wave" to each particle to steer it along a
perfectly determined path. Altogether there are at least eight
serious and reputable interpretations of the theory, which implies
that no single one is convincing.
Zeilinger thinks that before we can truly
understand quantum theory, it must be connected in some way to
what we know and feel. The problem, he says, is the lack of a
simple underlying principle, an Urprinzip. All the other
major theories of physics are based on such principles--pithy,
comprehensible maxims that anchor the formulae in the everyday
Take the science of heat. Though highly
mathematical and abstract, thermodynamics is based on two basic
principles that can be described in colloquial terms. The first
law of thermodynamics is just the conservation of energy: it means
that there are no perpetual motion machines. The second law of
thermodynamics is simply the statement that heat tends to flow
from warm objects to cooler ones. When the stuff called energy was
invented to quantify these laws, it was strange and undefinable,
and even today we don't know what energy is. Yet energy quickly
became a robust term in daily conversation and government policy.
The special theory of relativity is also based
on two principles, namely, "Inside a speeding transatlantic jet,
you have no way of knowing how fast you are going," and "The speed
of light shone from this jet is the same as the speed of light
from a stationary source." That second statement is
counterintuitive, but it is simple to understand and turns out to
be a stubborn experimental fact. And general relativity,
Einstein's theory of gravity, is based on the thought that a
freely falling person feels no weight. None of these theories
suffer from the confusions of quantum mechanics.
Now Zeilinger proposes to rebuild quantum
mechanics on a similar basis, to put it in terms that need no
Perhaps it is no surprise that the terms he
uses are those of information. We live in the age of information.
We depend increasingly on information technology, our schools
teach information processing and information science, and our
industry and commerce are information based. But until now, the
concept of information has only hovered on the edge of physics.
About a decade ago, John Archibald Wheeler
urged that information should take centre stage. What we call
reality, he thinks, arises from the questions we ask about it and
the responses we receive. "Tomorrow, we will have learned to
understand and express all of physics in the language of
information," he said.
The atom of information is the
bit--the quantity contained in the answer to a yes or no question.
If experiments are questions we ask of nature, then the simplest
of them have yes or no answers: "Did the photon arrive here, or
not?", "Did the counter click, or not?" We can also ask more
complex questions, but they can always be built up from simpler
yes or no questions like these.
Zeilinger's conceptual leap is to associate
bits with the building blocks of the material world. In quantum
mechanics, these building blocks are called elementary systems,
and the archetypal elementary system is the spin of an electron.
The only possible outcomes of measuring an electron's spin are
"up" and "down". You can choose any axis to measure the spin
along--vertical, horizontal or tilted--but once that axis is
chosen, only the two results are possible, as if the electron were
a spinning top that can be one way up or the other, but can't
point to any intermediate direction. These outcomes could just as
well be labelled "yes" and "no", or, in the fashion of digital
computers, "1" and "0".
This system is far more general than it seems.
The formulae that describe it apply, unchanged, to every
conceivable quantum-mechanical system characterised by just two
states--from polarised light and molecules with just two energy
levels to counterrotating currents in a superconducting ring. Not
forgetting that touchstone of quantum mechanics, the two-slit
experiment (see "Two becomes one").
Zeilinger avoids the question "What is an
elementary system?" and asks instead, "What can be said about an
elementary system?" His conclusion is simply stated: an
elementary system carries one bit of information.
It sounds innocuous. But the consequences of
Zeilinger's principle promise to be breathtaking. In the first
place, it contains the fact that the world is quantised--the very
starting point of quantum mechanics. Because we can only
interrogate nature the way a lawyer interrogates a witness, by
means of simple yes-or-no questions, we should not be surprised
that the answers come in discrete chunks. Because there is a
finest grain to information there has to be a finest grain to our
experience of nature. This is why electrons are restricted to
fixed energy levels in atoms, why light comes in pieces we call
photons, and perhaps, ultimately, why the Universe seems to be
made out of discrete particles. To the question, "Why does the
world appear to be quantised?" Zeilinger replies, "Because
information about the world is quantised."
Less obviously, Zeilinger's principle leads to
the intrinsic randomness found in the quantum world. Consider the
spin of an electron. Say it is measured along a vertical axis
(call it the z axis) and found to be pointing up. Because
one bit of information has been used to make that statement, no
more information can be carried by the electron's spin.
Consequently, no information is available to predict the amounts
of spin in the two horizontal directions (x and y
axes), so they are of necessity entirely random. If you then
measure the spin in one of these directions, there is an equal
chance of its pointing right or left, forward or back. This
fundamental randomness is what we call Heisenberg's uncertainty
In order to progress beyond a single elementary
system, Zeilinger's principle has to be generalised. He proposes
simply that two elementary systems carry exactly two bits of
information, and N systems carry N bits. This gives
us a natural explanation for one of the most fundamental and
puzzling features of quantum mechanics--entanglement.
When, say, two electrons are entangled, it is
impossible even in principle to describe one without the other.
They have no independent existence. This seems bizarre until you
use Zeilinger's principle. Concentrating on their spins, a
two-electron system contains two bits. For example, they might be
"The spins in the z direction are parallel," and "The spins
in the x direction are antiparallel". The two bits are
thereby used up, and the state is completely described--yet no
statement is made about the direction of spin of one electron or
the other. The entire description consists of relative statements,
or correlations. This means that as soon as one spin is measured
along a certain direction, the other one is fixed, even if it
happens to be far away.
Zeilinger's single, simple principle leads to
these three cornerstones of quantum mechanics: quantisation,
uncertainty and entanglement. What, then, of the more formal
elements of quantum mechanics such as wave functions and
Schrödinger's equation--the bread and butter of atomic
physicists? The road promises to be long and steep, but Zeilinger
and his student `´Caslav Brukner, have now begun the ascent.
Physicists use Schrödinger's equation to
work out how a particle will behave in a given situation. It
governs the evolution of things called wave functions, inside a
bizarre abstract arena called Hilbert space. Because Hilbert space
makes use of imaginary numbers, based on the square root of minus
one, these numbers--the amplitudes of the wave functions--have to
be squared to produce a real, observable quantity, such as the
probability of a particle being in a given place. It is not an
intuitively obvious way of describing things.
Illustration: Aude Van Ryn
Zeilinger and Brukner discard it.
Instead, they introduce a three-dimensional space they call
information space. The relationship between 2D Hilbert space and
3D information space is a bit like the relationship between an
accurate perspective drawing and a real, three-dimensional object.
This new space is much closer to our reality, as its axes
correspond to the answers of yes or no questions about an
elementary system. An electron's spin can be measured, or
quantised, along the x, y, or z axes of real
space, which gives the three dimensions of information space a
clear correspondence with reality. In other two-state systems the
connections are not so obvious, but three independent propositions
will always exhaust the possibilities.
Any quantum system has to describe how states
change over time, so the point in information space has to move.
It seemed natural to Zeilinger and Brukner to have the point move
as if it were a real, classical object. So they used the
mechanical equation that governs the motion of bullets and
billiard balls. When translated back into its equivalent form in
Hilbert space, it turns out to be none other than
Their next aims are to generalise this approach
from one elementary system to many, and to find a way to include
continuous variables such as position and speed. Eventually, they
must find a way to account for the information contained in
quantities like mass and charge.
Even if this programme succeeds, physicists may
dismiss it as old wine in new bottles. Why should they adopt the
principle if it doesn't tell us anything new? But in fact it
already does. In October 1999, Zeilinger and Brukner turned their
theory around to propose a new measure of information.
A new theory of quantum information is needed
if we are to handle the quantum computers of the future. This
technology promises one day to perform calculations far faster
than ordinary computers can, by exploiting the ability of quantum
systems to be in more than one state at a time.
Physicists call the building blocks of their
planned quantum computers "qubits". A qubit is simply an
elementary system such as an electron spin. Because a qubit can be
in a superposition of 1 and 0, it must hold not only classical
information, but some more elusive quantum kind of information
too. Many practitioners feel that ordinary information theory must
be contained in quantum information theory.
The number of classical bits in a system has
traditionally been evaluated using a formula derived by the
American engineer Claude Shannon. Say your system is a hand of
cards. If you wanted to e-mail a friend to describe your hand,
Shannon's formula gives the minimum amount of information you'd
need to include. But Zeilinger and Brukner noticed that it doesn't
take into account the order in which different choices or
measurements are made.
This is fine for a classical hand of cards. But
in quantum mechanics, information is created in each
measurement--and the amount depends on what is measured when--so
the order in which different choices or measurements are made does
matter, and Shannon's formula doesn't hold. Zeilinger and Brukner
have devised an alternative measure that they call total
information, which includes the effects of measurement. For an
entangled pair, the total information content in the system always
comes to two bits.
Without Shannon's theory, progress in
telecommunications during the second half of the 20th century
would have been far slower. Perhaps total information will become
as important in the 21st century.
Zeilinger's principle is a newborn baby. If its
fate is anything like that of Planck's century-old energy quantum,
years will pass before it grows up and gains acceptance in the
mainstream of physics. But if it does, it will transform physics
as thoroughly as its venerable predecessor.
- "A Foundational Principle for Quantum Mechanics" by Anton Zeilinger, Foundations of Physics, vol 29, p 631 (April 1999)
Two becomes one
According to Richard Feynman, there is one
experiment that exposes "the only mystery" of quantum mechanics.
Light from a single source is split into two beams that travel
along different paths. Where the beams recombine, two detectors
measure how the two waves interfere with each other: detector S
fires if the beams interfere constructively and detector D fires
if they interfere destructively, cancelling each other out. For a
beam with no interference, either S or D will fire, each with a
50-50 probability. When the two paths have the same length, the
waves will be in phase where they recombine and the beams will
interfere constructively, so detector S keeps firing and D never
Now suppose the light is so feeble that photons can only travel
through the apparatus one at a time. That interference remains.
The startling implication is that each photon has to travel along
both paths simultaneously. The same goes for beams of electrons,
neutrons, atoms, or molecules. Zeilinger has even seen this
happening to buckyballs--big, football-shaped carbon molecules.
But if instruments are installed to measure which path the photons
travel down, the detectors start firing randomly: interference is
destroyed. How, except by magic, can this be reconciled with the
previous experiment on the same apparatus? How do photons know
whether to go down only one path, or both?
Zeilinger's answer is that our choice of measurement is putting
that information into the photon. But it can only carry one bit.
So if we arrange the experiment so that the photon is destined to
trigger detector S, that bit is used up, and we can have no
knowledge of which path it traversed. On the other hand, if we
decide to know which path it travelled, we cannot predict whether
S or D will fire.
This experiment highlights another troubling aspect of quantum
mechanics, called the measurement problem. Each photon seems to
undergo a mysterious metamorphosis from a quantum wave to a
classical particle in the act of measurement. But according to
Zeilinger's principle, we simply cannot know enough about the
photon to call it either wave or particle. Zeilinger's elementary
system is no more than a carrier of information.