The Physics Process

Before discussing the various tools used by physicists for solving some of the most complicated problems known to man (understanding nature), it is prudent to overview the general process physicists use to solve problems.

We begin with the overall goal of the scientific method:

The scientific method is the process by which scientists, collectively and over time, endeavor to construct an accurate (that is, reliable, consistent and non-arbitrary) representation of the world.

More specifically, the scientific method involves these steps^4.1:

1. Observation and description of a phenomenon or group of phenomena.
2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.
3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.
4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.

If the experiments bear out the hypothesis it may come to be regarded as a theory or law of nature (more on the concepts of hypothesis, model, theory and law below). If the experiments do not bear out the hypothesis, it must be rejected or modified. What is key in the description of the scientific method just given is the predictive power (the ability to get more out of the theory than you put in; see Barrow, 1991) of the hypothesis or theory, as tested by experiment. It is often said in science that theories can never be proved, only disproved. There is always the possibility that a new observation or a new experiment will conflict with a long-standing theory.

However, the process often looks more like

1. Take (usually quantitative) experimental data on a phenomenon or group of phenomena.
2. Develop a mathematical model (often based on first principles) for the phenomena.
3. Solve the mathematical model (often using a Computer Simulation).
4. Test the Simulation via a numerical control. Tweak Simulation until numerical controls are validated.
5. Compare the results to the experimental data. If results agree with data, go on to step 6, otherwise go back to either of steps 1, 2, 3, or 4, depending on your judgement!
6. Use your model to predict other behavior of the system of interest.
7. Solve the mathematical model and see if your model successfully predicts the new behavior. If yes, move on to step 8, otherwise, restart entire process!
8. If you're a physicist, publish results - gain esteem of your colleagues! If you're an engineer, make new gadget - get rich!

What I want to emphasize here is the iterative nature of the process (see step 5), which can be seen in the following figure:

Figure 4.1: How does this end, again?