TA 19 (Nunn / Frieden)

Commentary 2

I IS THE LAW

by Robert Matthews

30 January 1999, posted 17 August 1999

(The following is the book review from the New Scientist which Lindley (TA19C1) refers to - Paragraph numbers added - HFJM)

It's the ultimate big idea, the source of everything we know

about the physical world. And it all comes from

one simple question, says Robert Matthews

Where do the laws of physics come from? It's the sort of question only children
and geniuses ask -- certainly most physicists are far too busy putting the
laws to work.

`<2>
Take quantum theory, the laws of the subatomic world. Over the past century
it has passed every single test with flying colours, with some predictions
vindicated to 10 places of decimals. Not surprisingly, physicists claim
quantum theory as one of their greatest triumphs. But behind their boasts
lies a guilty secret: they haven't the slightest idea why the laws work,
or where they come from. All their vaunted equations are just mathematical
lash-ups, made out of bits and pieces from other parts of physics whose
main justification is that they seem to work.
<3>
Now one physicist thinks he knows where the laws of quantum theory come
from. More amazingly still, Roy Frieden thinks he can account for all the
laws of physics, governing everything from schoolroom solenoids to space
and time. Sounds incredible? You haven't heard the first of it. For Frieden
believes he has found the Law of Laws, the principle underpinning physics
itself.
<4>
The laws of electricity, magnetism, gases, fluids, even Newton's laws of
motion -- all of these, Frieden believes, arise directly from the same basic
source: the information gap between what nature knows and what nature is
prepared to let us find out. Using sophisticated mathematics, Frieden has
shown that this notion of physics as a 'quest for information' is no empty
philosophical pose. It can be made solid, and leads to a way of deriving
all the major laws of fundamental physics--along with some new ones.
<5>
The sheer power of Frieden's approach is beginning to catch the eye of other
researchers. 'The results already obtained are extremely spectacular and
I'm an enthusiastic supporter,' says theorist Peter Hawkes from the CNRS
laboratories in Toulouse, France.
Unlike most of the mathematical Schwarzeneggers now trying to unify the
whole of physics, Frieden does not normally spend his waking hours wrestling
with 26-dimensional space-time. As a researcher at the Optical Sciences
Center of the University of Arizona, he has an international reputation
in the more practical field of optical image enhancement.
<6>
In the early 1970s, he pioneered techniques to 'clean up' fuzzy images of
everything from distant galaxies to stolen car number plates. He was put
on the trail of a radical new view of physics while investigating alternative
ways of capturing the information content of images. 'For years, I had kept
in the back of my mind a passage I had read in a textbook on information
theory, which talked about something called 'Fisher Information'. Someday,
I thought, I was going to investigate that -- and now the time was ripe.'
<7>
Named after the Cambridge statistician Ronald Aylmer Fisher in the mid-1920s,
Fisher information -- usually contracted to I -- captures how much information
you can squeeze out of a physical system. Suppose you want to know where
a gas molecule is. You can try measuring it, but no measurements are perfect
-- they all come with a certain amount of error. What's more there are inherent
'errors' in the systemm -- random disorder, jitters associated with the
temperature of the gas and the 'jolts' caused by the very act of observing,
made famous by quantum theory. All of these errors are governed by statistical
distributions, such as the famous bell-shaped curve. Plugging these distributions
into a formula worked out by Fisher, you end up with a measure of how much
information you can extract from a physical system, given all the errors.
<8>
At first, Frieden simply used Fisher information calculations as a way of
prising more information out of blurry images. But it was while he was reading
around the subject that he found himself being pointed in another, more
profound, direction. 'I came across a 1959 paper by the Dutch mathematician
A. J. Stam, who showed that I could be used to derive Heisenberg's famous
uncertainty principle,' recalls Frieden. 'And being a physicist, this set
me thinking.'
<9>
Studying Stam's work, Frieden noticed that it made use of a result from
information theory called the Cramer-Rao inequality. This little-known mathematical
result shows, roughly speaking, that when the error in a measurement is
multiplied by the amount of Fisher information in the measurement, the result
is a number that is never less than one.
<10>
It's a relationship strikingly similar to the uncertainty principle. Multiply
together the uncertainties in your knowledge of a particle's position and
its momentum, and the result is never less than a certain value. The more
precisely you know the position, the less precisely you can know the momentum.
Or put another way, the act of measuring the position influences the measured
value of the momentum -- and vice versa.
<11>
The similarity between the Cramer-Rao inequality and the uncertainty principle
started Frieden wondering whether information -- and Fisher information
in particular -- had a much deeper role in physics. 'Since Heisenberg's
principle is so basic, it occurred to me that perhaps every physical phenomenon
occurs in reaction to measurement -- that measurement acts as a kind of
catalyst for the effect,' says Frieden. 'And the possibility that physical
laws occur as answers to questions excited my curiosity.'
<12>
Digging into this possibility, Frieden soon found another mathematical 'coincidence'.
Whenever he did calculations using the Fisher information, the final results
were differential equations. 'What struck me,' he recalls, 'is that virtually
all of physics can also be expressed in terms of differential equations.'
<13>
Differential equations are formulae showing how the rate of change of a
certain quantity changes under outside influences. For instance, Newton's
second law of motion relates the acceleration of an object to the force
applied: F = ma . The acceleration in this formula is the rate of change
of velocity, which in turn is the rate of change of distance. Quantum theory
has its own, more abstract, examples, such as Schroedinger's famous wave
equation and Dirac's relativistic equation for the electron. The same format
shows up across the whole of physics.
<14>
Again, it's the kind of observation that is apt to provoke a shrug of the
shoulders. But now Frieden was sure he was on to something really deep.
The ubiquity of these types of equation, he believed, is intimately linked
to one of the most profound mysteries in science: despite the vast range
of phenomena covered by the fundamental laws of physics, all of those laws
can be made to drop out of mathematical objects known as Lagrangians. And
no one knows why.
<15>
Put simply, Lagrangians are made up of the difference between two quantities
which together form something called the 'action'. For reasons as yet utterly
mysterious, this quantity stays as small as possible under all circumstances.
This curiosity -- known as the principle of least action -- is reflected
in the fact that the fundamental laws of physics are differential equations,
since that's what you need to minimise the action.
<16>
In Newton's laws of motion, for example, the relevant action turns out to
be the difference between the kinetic energy and the potential energy of
a body. Kinetic energy is the energy associated with how fast something
is moving, and potential energy with its location. It turns out that to
keep the difference between these two to a minimum, the object's mass times
its acceleration always has to equal the force applied. Minimising this
particular action leads to Newton's second law of motion.
<17>
BEYOND ACTION
Theorists are convinced that action must be incredibly important -- so much
so that the discovery of any new fundamental law prompts a race to work
out the particular action needed to produce it. The trouble is that no one
understands the principles behind nature's infatuation with action, and
so no one can calculate it directly. Instead, they have to reverse-engineer
it, working backwards from the newly discovered law.
<18>
It is the puzzle of action -- and thus the origin of the laws of physics
- that Frieden now reckons he has solved. And, he says, it all comes down
to information -- the information we try to prise from nature by making
observations and the information nature has, but is reluctant to part with.
<19>
If you look at Lagrangians for gravity or electromagnetism, says Frieden,
they all have more or less the same mathematical form. They are all made
up of the difference between I, the Fisher information from observing the
phenomenon, and another statistical quantity, J, which is the amount of
information bound up in the phenomenon you're trying to measure.
<20>
It is from this that Frieden has built his radically new vision of physics
based not on the mysterious 'action', but on something more intuitive: our
attempt to come up with the best possible description of phenomena. All
the information needed for such a description exists, in the form of J,
and we want as much of it as possible to be extracted by our measurements,
in the form of I. In other words, we want the information difference --
I minus J -- to be as small as possible. And it turns out that for this
difference to be as small as possible, the phenomenon must obey a differential
equation.
<21>
Frieden's information-based methods provide a stunningly clear interpretation
of the laws of physics: they represent the best we can possibly do in our
quest to extract information using our inevitably error-prone methods. 'Through
the very act of observing, we thus actually define the physics of the thing
measured,' says Frieden. He adds that while unfamiliar, the idea that 'reality'
-- or, at least, the laws of physics -- are created by observation is not
new. During the 18th century, empiricist philosophers such as Bishop Berkeley
were raising similar ideas. Much more recently, John Wheeler, a physicist
at Princeton University who is widely regarded as one of the deepest thinkers
on the foundations of physics, has championed remarkably similar views.
'Observer participancy gives rise to information and information gives rise
to physics,' he says.
<22>
That's not to say Frieden's approach implies that the laws of physics are
'all in the mind'. Rather, it means that any physical attempt to extract
information about nature determines the answer we obtain -- and the best
information we can ever extract is what we call the laws of physics.
So Frieden's achievement is to give a philosophical view of physics a solid
mathematical foundation. For any given system, I and J are statistical quantities
which can be calculated using Frieden's methods. And the payoff is spectacular:
with these two quantities, you can fulfil the 200-year-old dream of deriving
the Lagrangian for that system, and thus of deriving the physical law that
rules it.
<23>
Over the past 10 years, in a series of papers in such journals as Physical
Review , Frieden and colleagues including Bernard Soffer of the Hughes Research
Laboratories in Malibu, California, have been steadily working their way
through physics, showing that all of its laws are the result of a kind of
cosmic game between ourselves and the 'real' world. To derive each law --
or, more accurately, each Lagrangian -- we have to ask an incredibly simple
yet fundamental question, such as 'what is the precise location of a particle
in space and time?'
<24>
Any attempt to answer such questions requires the same two quantities: the
information that exists in any given thing or system, J, and the information
we can acquire, I. Frieden has developed methods of calculating both for
a wide range of phenomena in physics. Subtracting J from I then leads straight
to the appropriate Lagrangian, and when this is made as small as possible,
the appropriate law of physics 'emerges'. No reverse engineering, no fancy
use of mathematical tricks, no inspired guesses.
<25>
Take that question about the precise location of a particle in space and
time. Frieden's approach leads directly to the Lagrangian for the Klein-Gordon
equation. This is the central law of relativistic quantum theory which describes
the way particles move through space and time. If, on the other hand, you
want to know about the location of a particle in space alone, Frieden's
approach leads to Schroedinger's wave equation.
That this one principle can act as a key to unlock the fundamental laws
is impressive enough, but if it really is the key to all physics, it should
do more than reproduce what physicists already know. It should also reveal
the secrets of unsolved mysteries.
<26>
TURBULENCE TAMED
Some researchers are finding that it can. Take turbulence, the roiling motion
of fast-moving fluids whose understanding Einstein himself regarded as the
biggest challenge to classical physics. In 1996, John Cocke at the University
of Arizona showed that using Frieden's approach on the question of what
is the flow of mass at a particular time and place leads to a law governing
the size of density fluctuations in turbulent fluids. This law makes sense
of otherwise baffling results from studies of fluid behaviour.
<27>
The quantum world offers an equally demanding challenge that has effectively
defeated the world's best theorists for decades. Quantum theory -- which
sees everything in terms of discrete jerks, jumps and packets -- just does
not sit easily with Einstein's concept of smooth expanses of curved space-time.
Yet Frieden found last year that by asking what space-time like is, he arrives
at a Lagrangian which leads straight to the Wheeler-deWitt equation: a formula
giving a quantum description of space-time. The Wheeler-deWitt equation,
now more than 30 years old, is one of the few concrete results in quantum
gravity theory.
<28>
Until now, however, the principles behind Wheeler-deWitt have been far from
clear. Frieden's theory not only shows how to derive the Wheeler-deWitt
equation, but also seems to shed light on what the equation means. Frieden
is already examining these clues to see how they may help theorists go beyond
the equation to a full-blown theory of quantum gravity.
Frieden is still struggling to spread his message among other theorists,
many of whom are reluctant even to study his approach. 'Part of the reason
is probably simple inertia to learning about a new concept like Fisher information,'
he says.
<29>
But others are more enthusiastic. 'Frieden's shown that a host of what used
to be regarded as fundamental equations of physics are actually capable
of derivation,' says Hawkes. Cocke agrees: 'It is a sort of unifying principle,
and I see it as a method of solving tough problems in statistical physics.'
Frieden hopes that his new book, which shows in detail how to apply Fisher
information to physical problems, will help to convince others how powerful
his approach is, and encourage them to join in. 'What I and my co-workers
have done so far is by no means the final word, but it does offer a systematic
way to inding laws for new phenomena. And it seems that information is what
physics is all about.'
---------------------
Robert Matthews is science correspondent of The Sunday Telegraph
From New Scientist, 30 January 1999
(c) Copyright New Scientist, RBI Limited 1999
(I have no e-mail address for Robert Matthews. You may try to contact him
through the mentioned newspapers. - HFJM)`