The Three Physics

I. A synergy of the most unreasonable utility

Except for the simplest of cases, the equations describing the state of a reasonably complex physical system are, very often, not soluble theoretically by conventional analytical means. In order to understand how the system behaves,  then, the only recourse is to start from a known initial state and calculate numerically the changes in the various  physical quantities.

Large physical environments such as the global weather system and stellar clusters, complex devices such as tokamaks, semiconductor circuits and supersonic aircraft, and microscopic systems such as genes, crystal structures, and interactions between molecules in new medicines and drugs are currently being investigated using various computational techniques. The common factor binding them is the non-linear  nature of the phenomena of interest, putting them beyond the scope of analytical methods, and the complexity of the systems themselves.

Technology in many fields has advanced to the stage where many important problems cannot be solved by analytical techniques. This is because systems being studied have become complex. Complexity emerges when the description of the system becomes sufficiently detailed. This may happen by employing, for example, partial differential equations instead of ordinary differential equations; when moving from simple one-dimensional models to realistic three-dimensional representations; when incorporating higher orders in a mathematical expansion scheme; when moving from scalar to vector or tensor systems, and extending a linear approximation to a non-linear one. One sees in many fields of physics important problems whose solutions can be found only by computational means.

The advances made in computational techniques coupled with the wide availability of high speed computers and the consequent lowering of computational costs has made computational physics a feasible addition to modern research programs. There is no area which cannot benefit from its application.

The interaction amongst the three fields leads to a more unified approach in the investigation of natural phenomena. Not only does computation help theory by generating numerical solutions to existing problems, it also helps theoreticians test new theories (or modifications to old theories) by generating numerical solutions to proposed models.

With respect to experiment, the help that computation renders the scientist in controlling experiments and analyzing data is augmented by generation of new data through modeling. When the physical system is inaccessible to scientists, or whose creation under controlled laboratory conditions is hazardous, difficult, very expensive or just plain impossible, computation is the only recourse. What is more, by identifying areas for experimental study which have better probability of yielding desired results, computation can lead to significant savings in time and money - both very important resources when research is competitive and funds in short supply.

This is the reason why scientists working in the field of computational physics have the confidence to stand apart from both theoreticians and experimentalists and claim equal footing.

II. Computers, Computation and the Physicist

The other is computational science - the science of computing rather than computers. It is the elder of the two, having established itself much earlier under the name of "numerical methods". This deals with the various means by which functions may be evaluated approximately, or differentiated and integrated; it concerns itself with optimization techniques, finding roots to equations, solving systems of linear, ordinary and partial differential equations - in fact, wherever analytical methods face a brick wall, numerical methods attempt to provide an answer.

Computational science forms the mathematical backbone of computational physics. By casting the mathematics of the physical problem into a framework which can be tackled by some of these methods, a computational physicist tries to get approximate solutions to problems which are otherwise difficult to obtain. For a system in a steady state a computational solution would normally be a graph depicting the relationship between two or more parameters. For a dynamic, time-varying system, the calculations may trace its behavior over time and space, in effect re-creating the system itself. Such a re-creation is commonly called a "computer simulation", and if the simulation is sufficiently complete it is referred to as a "computer experiment".

The ease with which computers can be used has enabled the current generation of scientists to meet the demands of engineers for solutions to complex problems and extend the limits of what is technologically possible. There is now a class of scientists which does not look at the computer merely as a sophisticated calculator, but as an extension of what the mind can visualize.

A computational physicist is somewhat different from the normal breed of physicists. Firstly, he has to have a sound knowledge of theory and the analytical techniques used by theoreticians. Along with physical insight, this is required in order to properly formulate the problem and test the computational procedures being used, as well as to interpret the results. It is also necessary to know how good a mathematical approximation is and how it affects the physics of the phenomenon being studied.

Secondly, he must have the practical skills of an experimentalist. This is needed to push the computational apparatus to its limits and understand the many sources of error, some of which may be a feature of the hardware, and some of the computational method.

Thirdly, he must have an in-depth knowledge of computers and programming. The computational physicist interacts with the hardware at a level which is more fundamental than anyone else. He is relying on its power as an extension of his mind's ability to imagine theoretical models and detect complex and subtle patterns within huge volumes of data. Not only does he need to know the nature of the computer being used, but also the software which controls it has to be understood in detail.

Experiment and computation has many similarities. Just as an experimentalist spends hours in tinkering with his apparatus, repeating his experiment with minor changes in various settings, so also does the computational physicist spends equally long hours running his program repeatedly with minor changes in input parameters or boundary conditions. The job of tracking down subtle programming errors is equivalent to finding out why an experiment did not "work" as it should have. For the experimentalist, an unexpected experimental result could be a genuine new finding, but more often it is due to an error in measurement. Similarly, in a computation very often it is difficult to decide if an unexpected result is a genuine consequence of the theory or an artifact of the method of calculation itself.

III. The bottom line

Whatever be the case, both theoretical and experimental physics have been extended by computational physics in a manner significant enough to be essential to the future progress of both. Computational physics has come of age, and its importance in any research program cannot be overlooked.

IV. References

NRC, 1986. "Scientific Interfaces and Technological applications". A volume in the series Physics
through the 1990s, National Academy Press, 1986.