first assume a model in which particles are visualized as moving in space and time. The model must begin by defining space and time.
The use of models, which are simplified pictures of observations, is not limited to the professional practice of science. They are often used to deal with the ordinary problems of life. For example, we model the sun as an orb rising in the east and setting in the west. Travelers heading to the west can point themselves each day in the direction of the setting sun and, correcting for some northward or southward drift (depending on season), arrive safely at their destination. No additional elements to the model are needed—in particular, no metaphysics. The ancient Greeks viewed the sun as the gold-helmeted god Apollo, driving a golden chariot across the sky. The ancient Chinese thought it was a golden bird. Neither metaphysical model offers any additional aid to our travelers in their navigation. And, that lack of necessity in the absence of any other evidence testifies strongly for the nonexistence of such a god or golden bird.
While utilizing models is a normal process in everyday life, scientific models objectify and, whenever possible, quantify the procedure—thus providing a rational means for distinguishing between what works and what does not. Whenever possible, mathematics and logic are used as tools to enforce a consistency that is not always found in commonplace statements, which are formulated in the vernacular. For example, instead of saying that your blood pressure is probably high, a physician will measure it and give you two numbers, say, 130 over 100. Then he might prescribe some calculated amount of medication to bring the 100 down to 80.
Scientific instruments that enhance the power of our senses commonly yield quantifiable measurements, enabling scientists to deal with variables having numerical values upon which all observers can agree—within equally quantifiable measurement errors. While some sciences may deal with nonnumerical variables, physical models are almost always quantitative and the logical power of mathematics is put to great use in their utilization.
Most scientific models begin by defining their observables operationally, that is, by characterizing them in terms of a well-prescribed, repeatable measuring procedure. For example (as Einstein emphasized), time is defined as what you read on a clock.
Temperature is what you read on a thermometer. Specific instruments are chosen as standards. A mathematical framework is then formulated that defines other variables as functions of the observables and postulates connections between these quantities.
The term
model
usually applies to the preliminary stages of a scientific process when considerable testing and further work still need to be done. The “theories” that arise from this effort are not the unsupported speculations that they are often accused of being by those unfamiliar with the scientific method or by those wishing to demean it. To be accepted into the ranks of scientific knowledge, theories must demonstrate their value by passing numerous, risky empirical tests and by showing themselves to be useful. Theories that fail these tests, or do not prove useful, are discarded.
In this book we will make frequent reference to the
standard models
of fundamental physics and cosmology. By now these have sufficiently advanced to the level where they can be honestly recognized as standard
theories,
although their prior designations as models continue to be used in the literature, presumably to maintain familiarity. I find it amusing and ironic that opponents of evolution think they are undermining it by calling it “just a theory.”
The validity of the scientific method is justified by its immense success. However, we must recognize and acknowledge that scientific models and theories, no matter how well established, are still human contrivances and subject to change by future developments. This is in