Sunday, 17 May 2015

Published Elsewhere: One Hundred Years of Exactitude

[I had written this article in article earlier this year, for the souvenir of the 42nd Reunion of the Physics Department of my university.]

Most Distant Gravitational Lens J1000+0221
[Credit: NASA, ESA, and A. van der Wel (Max Planck Institute for Astronomy)]

One Hundred Years of Exactitude

A look at the scientific method in the centenary year of Einstein’s general relativity

What does a genius look like? With pictures of Einstein at our disposal, this question has been rather easy to answer for the past hundred years or so. We think we know what makes a genius: an apparently unorthodox “brilliance” coupled with myriad eccentricities – or in other words, a madman who got lucky. We often mistake complicated for complex and the notion that Einstein’s achievements are profound because of their seeming indecipherability is so widespread that it has become absolutely essential to rescue Einstein from the tag of “genius”. Otherwise, how do we distinguish between Einstein and the kind of “genius” who philosophises about space, time, existence, human condition and whatnot in a state of intoxication? (It is not uncommon, even in the second decade of the 21st century, to find Einstein equated to that other sort of “genius”, even in many “reputed” quarters.) Why then does Einstein’s work deserve our respect? The answer is not very difficult to understand at all.

In 1905, arguably the most sacred year in the history of physics, Einstein published four papers (known as the Annus mirabilis papers) which would change the way we look at physics. It is often emphasised that Einstein shook the very foundation of all that went before him. What almost invariably goes unmentioned is the fact that his new foundation was based on the old one. It is often claimed that Einstein introduced the principle of relativity in physics with his special theory of relativity. This is laughably wrong. The principle of relativity was a cornerstone even in Newtonian mechanics, which went by the name of Galilean relativity. In fact, special relativity had to be formulated because the principle of relativity was threatened. In the words of Steven Weinberg, “the principle of relativity was not originated by the special theory of relativity, but rather restored by it”. Many think that Einstein’s theory tells us that everything is relative and tend to apply this ill-defined (also completely false) notion to different fields, usually with disastrous consequences. If special relativity tells us anything, it is the absoluteness of physical laws which retain the same form for all observers moving with uniform velocity with respect to one another.

Even if Einstein had published any one of his Annus mirabilis papers (actually, two of the four papers were closely linked), it can be said with certainty that we would still be paying tributes to him today. What he did next was even more astounding. Einstein’s formulation of general relativity, a generalisation of the principle of relativity to include gravitation, is justly celebrated as the peak of human intellectual achievement. General relativity perfectly illustrates how simple physical ideas, rigorous theoretical framework and extremely sophisticated experiments can come together to form a grand unified totality (pun unintended).

Einstein developed his theory of general relativity on one simple idea, based on one experimental fact. It appeared from several accurate experiments that inertial and gravitational masses (these are two different definitions of mass) of a body are always equal, although there is absolutely no reason for them to be so. This fact led Einstein to formulate what is known as the principle of equivalence in 1907, which asserts that it is impossible to distinguish between a gravitational field and an accelerated reference frame locally. It is remarkable that Einstein was not able to achieve what he wanted with this principle. It shows that even the most powerful physical idea is of little use to us unless we have the right tools to express this idea. And what is a better medium of expression for a theoretical physicist than mathematics?

History of science shows that collaboration between people of different branches often leads to path-breaking results. We should be thankful to the Swiss mathematician Marcel Grossman, Einstein’s friend, for giving Einstein just the tool he needed. Bernhard Riemann, a nineteenth-century German mathematician developed the so-called Riemannian geometry, describing spaces which are Euclidian (flat) locally, but not globally. Einstein realised the deep connection between the properties of this geometry and his principle of equivalence. Armed with the formalism of tensor calculus developed by the Italian mathematician Tulio Levi-Civita, Einstein was able to formulate his elegant theory of gravity in a coordinate-independent way. In November 1915, Einstein presented his findings to the Prussian Academy of Sciences.

At this point, one may rightly ask what good is any theory, however elegant, if it cannot describe nature as she appears before us? In this respect, too, general relativity has been a grand success. So far, it has passed every experimental test with full marks. Ironically enough, the experiment that first claimed to verify the validity of general relativity (the bending of light by the Sun) later turned out to be highly imprecise. But all other subsequent experiments, which were very accurate, indicated that Einstein was certainly a true genius.

So, a hundred years later, where do we stand? Research in general relativity is still a very active field, both in terms of theory and experiment. The Einstein equations predict gravitational waves, just as the Maxwell equations predict electromagnetic ones. Enormous experimental efforts to find such waves are currently underway, in which our country is a proud participant. Quantising gravity is a major challenge in theoretical physics.

It is quite possible that general relativity would eventually be proven “wrong” by some other better theory. But that does not mean we should abandon it altogether. Again, history of science shows that we need to push a “wrong” theory to its extreme in order to discover the “correct” ones: Newtonian mechanics, for example. Richard Feynman said that American Civil War would eventually pale into “provincial insignificance” in comparison to the discovery of the Maxwell equations in the same era. The same can perhaps be said for the First World War and general relativity. It is worth remembering the achievements of Einstein as a guide for our unending exploration.

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