Empirical and Theoretical Laws

Empirical and Theoretical Laws

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Kepler’s laws of planetary motion which specify the nature of planetary orbits (elliptical) and their quantitative aspects (rate of motion and time periods) were arrived by generalizing data of observations which had been carefully collected by another astronomer (Tycho Brahe). Boyle’s law of gases which enunciated the relationship between the volume and pressure of a given quantity of gas at a certain temperature was derived from the results of careful experimentation with confined gases using measuring devices. So was Ohm’s law of electrical resistance which states the relationship between the current through a wire and the potential difference between its end points. Laws of this kind which follow directly from observational or experimental data are empirical laws. They are essentially insightful generalizations from a series of particular observations. As one author put it, “By the warp and woof of experiment, the man of science weaves a pattern of threads of evidence, and presents the result to the world for anyone to use and improve.”

But this was not how Newton’s law of gravitation was discovered. Newton did not collect experimental data to arrive at this law. His discovery resulted from his attempt to account for Kepler’s laws. His goal was to explain, rather than to generalize. Newton said that he deduced “that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve….” The law of gravitation is thus a theoretical or concept-derived law. The notions of force and attraction are concepts which were introduced into a theory in terms of which the law is formulated.

Of course, empirical laws also rely on conceptual constructs. Without the notion of pressure, there can be no Boyle’s law. Without the notions of mass and acceleration, there can be no second law of motion. Empirical laws generalize. But they don’t say what makes nature behave in a particular manner. Concept-derived laws explain what empirical laws state in terms of entities and principles that are not directly observed or perceived. Experimentalists discover empirical laws. Theoreticians discover concept-derived laws.

Empirical laws may be explained by concept driven laws, but how are we to explain concept-derived laws? Why, one may ask, do bodies attract each other, as stated in the law of gravitation? If told that this is the property of all masses, one may ask, why is this is a property of all masses? Clearly, one can continue asking such questions at every step. Often, a concept-driven law is taken to be the ultimate answer to such questions, for it gives the most fundamental reason for nature’s behavior as due to a particular property. This is the reason why some have maintained that on final analysis science describes, rather than explains the physical world. This is why Karl Popper said that “There can be no explanation which is not in need of a further explanation.”

However, it is important to recognize that descriptions of natural phenomena through the scientific mode are different in essence from descriptions in the language of art or poetry. A poet’s description of the blue sky or the artist’s painting of a running stream may be beautiful, insightful, and aesthetically satisfying. But scientific descriptions explain, i.e. provide causal connections. The physicist can tell us why the sky is blue and not green or red.  Scientific descriptions also endow us with the power to predict a course of events, at least at the classical level. At the quantum level, it can give non-trivial probabilistic predictions. Science can tell us why the stream takes that particular course, how that course might change as a result of winds and other external factors. Often, scientific descriptions also enable us to manipulate features of nature which other kinds of description don’t and can’t. From a description of how moving magnets induce electric currents, one can construct electric generators.