Physical Theory and Empirical Verification

A theory is generally a logical formulation of a phenomenon or process, which is capable of making predictions of the future events. Such a theory is usually constructed on the basis of actual observations in a laboratory or of the particular phenomenon. A good and robust theory should be capable of explaining observed phenomenon accurately and predicting the future events deducible from it. When the data are collected about the predicted events, they are used to test the veracity of that theory. If the theoretical predictions are not in reasonably good agreement with the data, theory stands falsified and there is a need for a new and more general theory, which should be capable of verifying all the existing data and making new predictions thus opening the way for further development.

As an example, Galileo formulated theoretical relationships for bodies moving under the influence of gravity (balls rolling down the inclined planes, swinging pendulums, etc.) and Kepler similarly developed empirical relationships for the movement of the solar planets. With a stroke of genius, Newton deduced his laws of motion from this work and the existing data and knit these relationships into a beautiful theory of gravitation, which embodied Galileo’s and Kepler’s formulas naturally. This theory not only predicted the dynamics of moving solid objects, it was able to predict the characteristics of the tides in the oceans and estuaries. Newton’s theory held unchallenged sway for more than two centuries and is still in good stead for the moving bodies at a speed sufficiently smaller than the speed of light.

Similar success was also achieved in the field of electricity and magnetism. Faraday had done the experimental work and made several original discoveries and Clark Maxwell was able to successfully formulate his theory of electromagnetism which not only unified the electric and magnetic forces into one theory but also showed that light consisted of electromagnetic waves. Such is the power of a theory that it unifies and explains various apparently unrelated phenomena. But the unified theory did not attain the status of a successful theory until it was verified by all kinds of pertinent data. Verification is the ultimate test of a theory; it is the touchstone. A theory not verified by empirical evidence is metaphysics.

As more and more diverse phenomena were related in the threads of mathematical theories, these theories became ever more sophisticated and complex. For this reason, they were getting farther and farther away from the comprehension of a common literate person. In order to be able to comprehend Maxwell’s theory of electromagnetism and Newton’s theory of gravity, for instance, disciplined education in a school and college is required for many years. Without such formal education, it becomes very difficult to understand the essence of, and use these theories intelligently.

With the advent of theories of special and general relativity, mathematical sophistication increased by several orders of magnitude. They also produced several paradoxes, e.g. twin paradox, etc., which still baffle the mind of a common person. Although the theories were produced and verified to the satisfaction of majority of the physicists and cosmologists, I have read dissident discussion at least up till early 1970’s. At least one of the dissidents had Ph.D’s in philosophy and physics. And some implications of these theories are still difficult to discuss intelligently in our daily language.

Einstein published his theory of general relativity in 1916 and predicted bending of light rays in the vicinity of the massive objects. The verification came in 1919 when the celebrated Cambridge cosmologist and astronomer, Arthur Eddington, measured the deflection of light rays from a distant star in the vicinity of the sun, during solar eclipse. Since then numerous verifications have been found and the theory is still valid and unmodified.

A curious aspect of the theory of relativity was that it unified the time with the three space dimensions and wove a continuum which was called the space-time. Time was considered absolute before Einstein’s formulation of relativity and mankind was happy and content with the three dimensions of space. Now the number of dimensions was increased to four.

Theory Overtakes the Empirical Observations

The advent of quantum mechanics at the turn of the twentieth century manifested the powers of a mathematical theory which were not evidenced in the past. Around 1930, Paul Dirac predicted the existence of an antiparticle on the basis of his theory. This particle had the mass of an electron but had a positive charge. It was called positron. Nobody had ever suspected the existence of such a particle of matter. But true enough, positron was discovered in a cloud chamber experiment soon afterwards. Dirac’s theory was vindicated. His theory also predicts the existence of monopoles (magnets having only one pole) which have not yet been detected and discovered. Now it’s known that every particle of matter has an anti-particle which means there is antimatter side by side with the matter. Theory was thus ahead of the experimental observation. This happened on several occasions when theory predicted the existence of new particles which were discovered later on. This gave so much confidence to the scientists that now a days actual experimental verification can be suspended and the theoretical work carried on ahead without feeling any qualms of doubt and skepticism. If a theory is logically sound and seems coherent with the previous work, chances are that it will receive experimental support in due time. The scientists can often intuitively feel assured of the soundness of such a theory.

As an example, electro-weak theory, which was independently developed by Steven Weinberg and Abdus Salam can be quoted. The theory was published in 1960’s. In the beginning, the theory did not attract much attention. Then, in 1971, Gerard t’Hooft showed that the Salam-Weinberg theory was indeed renormalizable, which accorded a great deal of confidence to the theory. Weinberg (1) stated the status of the theory in these words, “It was not clear that this theory was mathematically consistent, although Abdus Salam and I argued that it was. Then in 1971, a previously unknown graduate student, Gerard t’Hooft (see note at the end) at the University of Utrecht, showed that theories of this type are, in fact, mathematically consistent. Immediately the world of theorists began to take this theory seriously and write many papers about it. ..experimental evidence began to emerge showing that the theory was valid.” And the rest is history now.

We have come a long way since the early 1900’s when it was an article of faith of the logical positivists that without any empirical verification, a theory is not worthy of consideration. We have reached a stage now when the new cosmological theories are so far ahead of any experimental verification that the theorists keep on slugging onward undauntedly without worrying too much about verification at the present time. Brian Greene, a noted physicist and the author of the book “The Elegant Universe, Superstrings, Hidden dimensions, and the Quest for the Ultimate Theory”, stated gingerly, “..it is a very strange research career, in a way. So far I’ve spent something like 17 years working on a theory for which there is essentially no direct experimental support. It’s a very precarious way to live and to work,” (2).

Einstein, Dirac and many other scientists had intuitive kind of faith in the correctness of their theories without empirical evidence. They implicitly believed that a good theory has internal beauty and exclusive elegance, on the basis of which it can be determined whether it has any merit or not. Be it so, such a test, in the last resort, is only subjective. It can be argued that very few theorists will accept that their theories are flawed. Ultimate criterion of acceptability is still empirical verification.

Theory in Wilderness

Attempts to unify the fundamental forces of nature opened up new vistas of theoretical investigation and adventurism. First attempt was made by Kaluza who unified Einstein’s theory of general relativity with Maxwell’s theory of electromagnetism. He realized that it was possible only when the number of space dimensions was increased to four. His space-time would thus consist of five dimensions. His mathematics was elegant and persuasive and he felt encouraged to submit his work to Einstein (for publication) in the first quarter of the twentieth century.

Einstein was impressed by the beauty of the mathematical formulation but his spirit was dampened by the requirement of the additional dimension. Kaluza believed that the extra dimension did as a matter of fact exist but it was compactified to extremely small magnitude and could not be detected. The extra dimensions and their compactification would haunt us ever incessantly after Kaluza. May be they have the key for the ultimate unification.

Work on unification slowed down when exciting discoveries were made in quantum mechanics which attracted most of the research physicists because it offered a fertile field for research work. Interest however did not completely wane in the unification arena and it gained a fresh and much invigorated infusion of life after the publication of Salam’s and Weinberg’s work on the unification of the weak and electromagnetic forces. At about the same time, string theory came into life and the prediction of ‘graviton’ raised hopes for string theory to be the tool of unification. The graviton was considered to be the link between quantum mechanics and theory of relativity.

Initial attempts at unification using string theory were not encouraging. For one thing, it needed twenty six dimensions and for another, there were several anomalies embedded in it. One of them was ‘tachyon’, a particle with imaginary rest mass and superluminal speed. Many physicists lost interest in string theory. Interest revived in it again in early 1980’s when it was combined with super-symmetry (susy); the resultant theory was called the theory of superstrings. The theory needed ten dimensions and the anomalies disappeared naturally. In the ensuing intellectually tumultuous work on superstrings, the theorists were not bothered by the requirement of the extra dimensions because they implicitly believed that they could be appropriately compactified in due time. To cut the long story short, we are now working with the M-theory which has shown that all the five apparently different superstring theories are included in it, which requires eleven dimensions instead of ten that the superstring theories needed. The theorists have also moved away from the one dimensional strings and are working with ‘branes’ which are multi-dimensional.

Even if the theory succeeds in its self-specified objective of unification, is there any chance of its experimental verification? Views on this issue vary depending on who is talking?

Davies and Brown published their book “Superstrings: A Theory of Everything” in 1988 in which they published the interviews of several eminent physicists who were actually working on the theory and several others who had significant insights into the superstring theory and had made number of milestone contributions to quantum mechanics. Although their comments are somewhat outdated now (M-theory was formulated after the publication of the book), the basic argument is still valid.

One of them, Richard Feynman, who was considered as great a scientist as Einstein, said, “May be theoretical physics is degenerating but I don’t know into what. Let me say something first. I have noticed when I was younger, that lots of old men in the field couldn’t understand new ideas very well, and resisted them with one method or another, and that they were very foolish in saying these ideas were wrong – such as Einstein not being able to take quantum mechanics. I’m an old man now, and these are new ideas, and they look crazy to me, and they look they’re on wrong track. Now I know that other old men have been very foolish in saying things like this, therefore, I would be very foolish to say this is nonsense. I am going to be very foolish, because I do feel that this is nonsense! I can’t help it, even though I know the danger in such a point of view. So perhaps I could entertain future historians by saying I think all this superstring stuff is crazy and is in the wrong direction,” (3).

Abdus Salam who was excited about the promise that the string theory held for unification, said, “After all, no theory should be believed in beyond what one can test. The claim of the present Theory of Everything is that it can tell us about all phenomena up to Planck energies (about 10^10 GeV). Now, to test a theory directly at Planck energy, we would need accelerators delivering such energies. On any foreseeable future design such accelerators would have to be at least 10 light years in length! So we can never have a direct test of any Theory of Everything, valid for energies higher than, say, 10^7 GeV. Only indirect tests can be possible, but these can never be all-embracing,” (4).

Sheldon Glashow who is still a severe critic of the superstrings theory, said, “I’m particularly annoyed with my friends, the theorists, because they cannot say anything about the physical world. Some of them are convinced in the uniqueness and beauty, and therefore truth, of their theory; and since it is unique and true it obviously includes a description of the entire physical world. It does not seem to them to be necessary to do any experiments to prove such a self-evident truth, so they begin to attack the value of experiments…,” (5).

Michio Kaku wrote in his book “Hyperspace” in support of the theory, “Personally, I don’t think that we have to wait a century until our accelerators, space probes, and cosmic ray counters will be powerful enough to probe the tenth dimension indirectly. Within a span of years, and certainly within the lifetime of today’s physicists, some one will be clever enough to either verify or disprove the ten-dimensional theory by solving the field theory of strings or some other non-perturbative formulation. The problem is thus theoretical and not experimental,” (6).

The juncture where physics finds itself at present is strange. The only way to go ahead and make progress is by way of theory and the predictions which the theory is making are nearly impossible to verify by direct experimentation. So how are we going to determine if the proposed theory is sound and trustworthy?

The same kind of situation exists in cosmology. The predictions that the string theory is making are outlandish. According to the theory, our universe is among a million of other universes that exist in the megaverse. Many of them come into being and die out every now and then.

According to http://www.edge.org/3rd_culture/susskind03_index.html, “On the theoretical side, an outgrowth of inflationary theory called eternal inflation is demanding that the world be a megaverse full of pocket universes that have bubbled up out of inflating space like bubbles in an uncorked bottle of Champaigne. At the same time string theory, our best hope for a unified theory, is producing a landscape of enormous proportions. The best estimates of theories are that 10^500 distinct kinds of environments are possible….This landscape of possibilities is a mathematical space representing all of the possible environments that theory allows. Each possible environment has its own laws of physics, elementary particles and constants of nature. Some environments are similar to our own corner of the landscape but slightly different….The old 20th century question, ‘What can you find in the universe?’ is giving way to ‘What can you not find?’”

Can the theory be its own best judge?

Note: Gerard t’Hooft shared the Nobel Prize in 1999 with his teacher, Martinus J.G. Veltman for elucidating the quantum structure of electroweak interaction.

References

1.Steven Weinberg, “Facing Up,” Harvard University Press, Cambridge, Massachusetts, 2001, p. 88.
2.“A Conversation with Brian Greene,” The Elegant Universe Homepage, Nova Science Programming, wysiwyg://25/http:www.pbs.org/wgbh/nova/elegant/greene.htm, July, 2003.
3.P.C.W. Davies and J. Brown, “Superstrings: A Theory of Everything,” Cambridge University Press, 1988, pp. 193-194.
4.Ibid., pp. 170-171.
5.Ibid., p. 182.
6.Michio Kaku, “Hyperspace,” Anchor Books Doubleday, New York, 1994, p. 189.