Hello,
I have a burning question, kinda...
I've often wondered if physicl systems can be described purely in terms of
the transfer of information. I recently found an article in New Scientist
magazine (see below) about recasting physics in just such terms. This, to
me, seems like it might be related to the idea of Quality, for what is
information but patterns of value? Does this seem like a reasonable
suggestion?
(Sorry if this has been asked before, I'm new here)
Ross.
In the beginning was the bit
17 Feb 01
And after that came the rest of the weird world, says Hans Christian von
Baeyer
"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 world.
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 debatable philosophy.
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 principle.
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.
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 SchrÖdinger's equation.
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.
-----------------------------------
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 fires.
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.
-----------------------------------
Further reading:
A Foundational Principle for Quantum Mechanics by Anton Zeilinger,
Foundations of Physics, vol 29, p 631 (April 1999) www.quantum.at
-----------------------------------
Hans Christian von Baeyer is a physicist and writer based at the College of
William & Mary in Williamsburg, Virginia.
>From New Scientist magazine, vol 169 issue 2278, 17/02/2001, page 26
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