快猫短视频

WHERE do the laws of physics come from? It鈥檚 the sort of question only
children and geniuses ask鈥攃ertainly most physicists are far too busy
putting the laws to work.

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鈥檛 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.

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鈥檛 heard the first of it. For Frieden believes he
has found the Law of Laws, the principle underpinning physics itself.

The laws of electricity, magnetism, gases, fluids, even Newton鈥檚 laws of
motion鈥攁ll 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 鈥渜uest for information鈥� is no empty
philosophical pose. It can be made solid, and leads to a way of deriving all the
major laws of fundamental physics鈥攁long with some new ones.

The sheer power of Frieden鈥檚 approach is beginning to catch the eye of
other researchers. 鈥淭he results already obtained are extremely spectacular and
I鈥檓 an enthusiastic supporter,鈥� 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.

In the early 1970s, he pioneered techniques to 鈥渃lean up鈥� 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. 鈥淔or 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鈥�. Someday, I thought, I was
going to investigate that鈥攁nd now the time was ripe.鈥�

Named after the Cambridge statistician Ronald Aylmer Fisher in the mid-1920s,
Fisher information鈥攗sually contracted to I鈥攃aptures 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鈥攖hey all come with a certain amount of error. What鈥檚 more there
are inherent 鈥渆rrors鈥� in the system鈥攔andom disorder, jitters associated
with the temperature of the gas and the 鈥渏olts鈥� 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.

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. 鈥淚 came across a 1959 paper by the Dutch mathematician A.
J. Stam, who showed that I could be used to derive Heisenberg鈥檚 famous
uncertainty principle,鈥� recalls Frieden. 鈥淎nd being a physicist, this set me
迟丑颈苍办颈苍驳.鈥�

Studying Stam鈥檚 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.

It鈥檚 a relationship strikingly similar to the uncertainty principle. Multiply
together the uncertainties in your knowledge of a particle鈥檚 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鈥攁nd vice versa.

The similarity between the Cramer-Rao inequality and the uncertainty
principle started Frieden wondering whether information鈥攁nd Fisher
information in particular鈥攈ad a much deeper role in physics. 鈥淪ince
Heisenberg鈥檚 principle is so basic, it occurred to me that perhaps every
physical phenomenon occurs in reaction to measurement鈥攖hat measurement
acts as a kind of catalyst for the effect,鈥� says Frieden. 鈥淎nd the possibility
that physical laws occur as answers to questions excited my curiosity.鈥�

Digging into this possibility, Frieden soon found another mathematical
鈥渃oincidence鈥�. Whenever he did calculations using the Fisher information, the
final results were differential equations. 鈥淲hat struck me,鈥� he recalls, 鈥渋s
that virtually all of physics can also be expressed in terms of differential
别辩耻补迟颈辞苍蝉.鈥�

Differential equations are formulae showing how the rate of change of a
certain quantity changes under outside influences. For instance, Newton鈥檚 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 Schr枚dinger鈥檚 famous wave equation and
Dirac鈥檚 relativistic equation for the electron. The same format shows up across
the whole of physics.

Again, it鈥檚 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.

Put simply, Lagrangians are made up of the difference between two quantities
which together form something called the 鈥渁ction鈥�. For reasons as yet utterly
mysterious, this quantity stays as small as possible under all circumstances.
This curiosity鈥攌nown as the principle of least action鈥攊s reflected
in the fact that the fundamental laws of physics are differential equations,
since that鈥檚 what you need to minimise the action.

In Newton鈥檚 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鈥檚 mass times its acceleration always
has to equal the force applied. Minimising this particular action leads to
Newton鈥檚 second law of motion.

Beyond action

Theorists are convinced that action must be incredibly important鈥攕o
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鈥檚 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.

It is the puzzle of action鈥攁nd thus the origin of the laws of
physics鈥攖hat Frieden now reckons he has solved. And, he says, it all comes
down to information鈥攖he information we try to prise from nature by making
observations and the information nature has, but is reluctant to part with.

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鈥檙e trying to measure.

It is from this that Frieden has built his radically new vision of physics
based not on the mysterious 鈥渁ction鈥�, 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鈥擨 minus J鈥攖o 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.

Frieden鈥檚 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. 鈥淭hrough the
very act of observing, we thus actually define the physics of the thing
measured,鈥� says Frieden. He adds that while unfamiliar, the idea that
鈥渞eality鈥濃�攐r, at least, the laws of physics鈥攁re 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.
鈥淥bserver participancy gives rise to information and information gives rise to
physics,鈥� he says.

That鈥檚 not to say Frieden鈥檚 approach implies that the laws of physics are
鈥渁ll in the mind鈥�. Rather, it means that any physical attempt to extract
information about nature determines the answer we obtain鈥攁nd the best
information we can ever extract is what we call the laws of physics.

So Frieden鈥檚 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鈥檚 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.

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 鈥渞eal鈥� world. To derive each
law鈥攐r, more accurately, each Lagrangian鈥攚e have to ask an
incredibly simple yet fundamental question, such as 鈥渨hat is the precise
location of a particle in space and time?鈥�

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
鈥渆merges鈥�. No reverse engineering, no fancy use of mathematical tricks, no
inspired guesses.

Take that question about the precise location of a particle in space and
time. Frieden鈥檚 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鈥檚 approach
leads to Schr枚dinger鈥檚 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.

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鈥檚 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.

The quantum world offers an equally demanding challenge that has effectively
defeated the world鈥檚 best theorists for decades. Quantum theory鈥攚hich sees
everything in terms of discrete jerks, jumps and packets鈥攋ust does not sit
easily with Einstein鈥檚 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.

Until now, however, the principles behind Wheeler-deWitt have been far from
clear. Frieden鈥檚 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. 鈥淧art of the reason is
probably simple inertia to learning about a new concept like Fisher
information,鈥� he says.

But others are more enthusiastic. 鈥淔rieden鈥檚 shown that a host of what used
to be regarded as fundamental equations of physics are actually capable of
derivation,鈥� says Hawkes. Cocke agrees: 鈥淚t is a sort of unifying principle, and
I see it as a method of solving tough problems in statistical physics.鈥�

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. 鈥淲hat I and my co-workers have done
so far is by no means the final word, but it does offer a systematic way to
finding laws for new phenomena. And it seems that information is what physics is
all about.鈥�