It is a previledge to be invited to this seminar, especially for someone whose specialty is not Philosophy of Science. One of the aims of the seminar is to create a better understanding of science by generating dialogue among people of different backgrounds. In the spirit of this goal, this contribution reports on some of the metaphysical inputs in a frontier area of science. Some of the justification for presenting such a report was provided by Prof. V. Singh's remarks in the keynote address. The remark being that Philosophy of Science must also be done in a scientific manner. The way science is done has itself been changing with the times. The scientist inherits the practice of science from his or her mentors and improvises upon it as demanded by circumstances. Thus the very subject matter of the Philosophy of Science has been evolving. The present contribution is an account some of this development. Some technically distinct notions, but which have all been philosophically called ``symmetry'' will be presented. They have been utilised for guessing the laws governing the fundamental interactions. The presentation is neither rigorous nor exhaustive, but hopefully will kindle some interest.
The notion of symmetry was used by Einstein to guess the General Theory of Relativity. This he did in the absence of any empirical evidence for the theory. In apparently unrelated developments, Heisenberg proposed in the '30s a symmetry as the basis for understanding the nuclear forces among protons and neutrons. This was extended by Yang and Mills and independently by Shaw. The extension made Heisenberg's idea closer in spirit to Einstein's postulate of General Relativity. At the time they did this, there was no empirical evidence to support the Yang-Mills theory as the theory of nuclear forces. A decade or so later, after more empirical evidence had accumulated and better understanding of collective quantum phenomena was obtained, the Yang-Mills theory could be suitably modified to account for all nuclear forces. The point is that the paradigm of symmetry principles was used to make fairly accurate guesses at theories for which scant or no empirical evidence existed. How is such a procedure justified? Is it always successful? Not all theories guessed in this way are successful. One example is of Kaluza-Klein theory. Similarly, there is no empirical evidence for a Supersymmetric theory. However, in the reductionist endeavour of theoretical physics, the symmetry principle has played a central role.
How useful has it been to understand the fundamental forces in this way? Do these theories allow us to calculate all the observed data from first principles? The answer is in the negative. While all the important features of the sub-nuclear world can be qualitatively explained, quantitative predictions are possible only for a limited class of phenomena. In the case of Gravity, Newtonian theory is sufficient for all but a few minuscule effects. The edifice of General Relativity may well appear to be a dispensable extravagance. With future technologies and techniques of computation, the theories will be surely exploited to their fuller potential. For the present, the overwhelming motivation is best expressed in Einstein's own words:
``I want to know how God created this world. I am not interested
in this or that phenomenon, in the spectrum of this or that element. I want
to know his thoughts, the rest are details".
This purist sentiment has been vindicated by the fact that the structure of the fundamental theories appears, with hindsight, to be remarkably elegant. One or two fundamental ideas coupled with powerful mathematical machinery suffice to deductively reconstruct the theory. Thus it is not utilitarian motives that drive the effort in fundamental Physics, but rather a deep belief in the existence of a deductive structure based on simple axioms. The symmetry principles to be described in the following are a concrete realisation of this paradigm.
The remainder of this talk is divided as follows. In section 2 the required mathematical and conceptual preliminaries are discussed. These include the ideas of a vector fields, symmetries, and the notion of a coupling constant. In section 3, the symmetry principles involved in each of General Theory of Relativity, Electromagnetic theory and Nuclear interactions are described. Section 4 discusses the efficacy of the approach and possible counterexamples. It also contains concluding remarks.