Number of words: 296<\/p>\n\n\n\n
Studying a limited group of phenomena can also mean studying their physical properties only over a limited range, which may be another reason for the theory to be approximate. This aspect of the approximation is quite subtle because we never know beforehand where the limitations of a theory lie. Only experience can tell. Thus the image of classical mechanics was further eroded when twentieth-century physics showed its essential limitations. Today we know that the Newtonian model is valid only for objects consisting of large numbers of atoms, and only for velocities which are small compared to the speed of light. When the first condition is not given, classical mechanics has to be replaced by quantum theory; when the second condition is not satisfied, relativity theory has to be applied. This does not mean that Newton\u2019s model is \u2018wrong\u2019, or that quantum theory and relativity theory are \u2018right\u2019. All these models are approximations which are valid for a certain range of phenomena. Beyond this range, they no longer give a satisfactory description of nature and new models have to be found to replace the old ones-or, better, to extend them by improving the approximation. <\/p>\n\n\n\n
To specify the limitations of a given model is often one of the most difficult, and yet one of the most important tasks in its construction. According to Geoffrey Chew, whose \u2018bootstrap models\u2019 will be discussed at great length later on, it is essential that one should always ask, as soon as a certain model or theory is found to work: why does it work? what are the model\u2019s limits? in what way, exactly, is it an approximation? These questions are seen by Chew as the first step towards further progress.<\/p>\n\n\n\n