Stephen P. King (firstname.lastname@example.org)
Wed, 05 May 1999 23:07:14 -0400
Do Questions Asked Define The Laws Of Physics?Most scientists assume that the laws of physics can answer all their questions about the physical world. But recent work by B. Roy Frieden, professor of optical sciences at The University of Arizona in Tucson, suggests that the reverse is true: it is their questioning of the world that defines the laws of physics.
Frieden's newly-released book, "Physics from Fisher Information," has quickly become a hot seller in science. In it, Frieden demonstrates how all the laws of physics -- everything from classical electrodynamics to quantum gravity -- arise from the attempt to extract information from a system that only grudgingly yields it.
Every physical system contains a certain amount of information; scientists use measurements to extract this information. But all measurements have errors, and all measuring devices eventually reach the limit of their accuracy.
And there are intrinsic errors, too, associated with the random motions of the particles in the system. Together, the measurement errors and the intrinsic uncertainties limit the amount that can be learned about a system to only a fraction of the system's total information content.
In the 1920s, Cambridge statistician Ronald Aymler Fisher calculated exactly how much information could potentially be extracted from a system, given the inevitable uncertainties. He called this quantity "I" -- we now call it "Fisher information."
An optical scientist by trade, Frieden first used Fisher information to clean up blurry images. But in the course of this work, a serendipitous encounter with a paper by A.J. Stam, a Dutch mathematician, turned his thoughts in a new direction.
Stam showed that Fisher information could be used to derive the famous Heisenberg uncertainty principle. This principle states that one can never simultaneously know the exact position and momentum of a subatomic particle: The more closely you pin down its location, the less you know about how fast it is moving -- and vice versa.
In his derivation, Stam used an analogous property of Fisher information, the Cramer-Rao inequality, which says that the larger the error in a given measurement, the less Fisher information can be obtained from the measured system. Then, by mathematically associating the Fisher information with the uncertainty in a particle's momentum, and the measurement error with the uncertainty in its position, Stam reproduced the uncertainty principle.
In most textbooks, Heisenberg's relation is described as a direct consequence of quantum mechanics, which says that all particles are made of waves and measurements are uncertain because the particle doesn't have an exact location or momentum.
Stam's derivation turns this interpretation on its head. It says that the act of measuring "causes" the uncertainty principle, and therefore "causes" quantum mechanics.
"The possibility that physical laws occur as the answers to questions excited my curiosity", says Frieden.
Frieden's next clue was that the results of his Fisher information calculations always came in the form of differential equations. Differential equations express the rate of change of the state of a physical system in terms of the current state of the system.
This observation intrigued Frieden, since all the laws of physics, from simple kinematics to Einstein's General Theory of Relativity, can be written as differential equations. But unless some way to derive these equations from Fisher information could be found, it would remain nothing but an interesting coincidence.
Oddly enough, Frieden found that the solution is to subtract information. Or, more specifically, to subtract another Fisher information term. The second term, "J", represents the Fisher information that is available "inside" the system, and can potentially be measured.
It turns out that "J" is proportional to "I", the maximum amount of information that actually is extracted by the measurement. Since it is impossible to get more information from a system than the system contains, "I" is always less than or equal to "J".
Frieden and his colleagues then argued that physical laws arise when scientists attempt to extract the most possible information from a system. Therefore, to derive a law from the Fisher information, the difference between "I" and "J" should be made as small as possible. When they did this, they found that the behavior of the system must be governed by differential equations. And, depending on the system, these equations corresponded exactly to the known laws of physics.
In his book, Frieden uses this method to derive virtually all the laws of physics, beginning with classical mechanics and ending with the Wheeler-DeWitt equations of quantum gravity.
Along the way, he has found several fascinating curiosities. For example, in all the quantum theories, "I" and "J" are exactly equal, but the classical "I" is always one-half of "J". "I guess the quantum half is missing", Frieden speculates.
Frieden's next challenge is to derive all of thermodynamics from Fisher information. In classical thermodynamics, all systems tend to become more disordered -- in other words, their entropy, a measure of the "ordered-ness" of a system, always increases.
In Frieden's theory, "I" should also act as a universal measure of disorder and should decrease with time. But this conjecture remained unproven until a father-and-son team from the University of La Plata, Argentina, Angelo and Angelo R. Plastino, delivered a powerful mathematical proof, opening the door for Frieden to try to replace entropy with Fisher information. Although his team hasn't derived the whole of thermodynamics from "I", a confident Frieden says "we are a good way towards proving the hypothesis."
Although very few physicists receive formal training in the techniques of Fisher information, Frieden's work seems to have sparked their interest. "Sales have soared to produce the largest concentration of sales of any title since our online catalog went live", says an enthusiastic Harriet Millward, a marketing controller at Cambridge University Press.
The first printing is nearly gone and a second printing has been scheduled for next month to meet the surprising demand. "I haven't even received my author's discounted copies yet," Frieden happily complains.
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