Observer Research Foundation Mumbai

Ideas and Action for a Better India

100 years after Einstein’s happiest thought – Quantum space-time and string theory

In the third lecture of the ORF lecture series ‘Gurus of Science’ Dr Spenta Wadia explains the basics of Einstein’s theories and the progress in the field of physics since the General Theory of Relativity.

Dr Spenta Wadia is a professor at the Tata Institute of Fundamental Research (TIFR) in Mumbai, and Chairman of the Department of Theoretical Physics at TIFR. He is also Director of the International Centre for Theoretical Sciences, Bangalore. Having completed his Masters at the Indian Institute of Technology (IIT) Kanpur, he went on to do his doctoral research at City University, New York. Professor Wadia is a J.C. Bose Fellow with the Department of Sci-ence and Technology, Government of India and a recipient of the TWAS (The Academy of Sci-ences of the Developing World) Physics Prize (2004). He has won the Steven Weinberg Prize of the Abdus Salam International Center for Theoretical Physics, Trieste, Italy in 1995. His efforts are instrumental in establishing a world class research group in string theory (and related areas) at the Tata Institute.

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Albert Einstein was one of the foremost thinkers of the 20th century and of all times. He made profound contributions to the Quantum Theory of Light, to Statistical Mechanics and to the Special and General Theory of Relativity.  A change so significant had not occurred since Isaac Newton in the 17th century – his ideas changed our entire view of the world.  Einstein’s Special Theory of Relativity gave rise to the famous equation E = mc2 which says that mass can transmute into energy. As is well known this has applications to nuclear energy. His General Theory of Relativity changed our conception of space-time and explained the force of gravity as resulting from the undulations of the geometry of space-time. This theory forms the basis of the Big-Bang theory of the origin and evolution of the Universe. It also predicts the existence of Black Holes of enormous size which are abundantly present in the Universe.

Dr. Spenta Wadia began his talk by discussing the development of the framework of physical theory from the time of Galileo and Newton to the present. He referred to  the notion of the inertial reference frames and the universality of time within which Newton formulated his laws of motion and the universal law of gravitation. He emphasized the importance of the development of time measuring devices that preceded the formulation of Newton’s theory and stressed the fact that great generalizations in physics, with some exceptions, go hand-in-hand with advances in the technology of measurements and experiments.  Even though Newton’s laws were usually expressed in terms of equations involving point particles, their adaptation to multi-particle systems and fluids were developed by Euler, Navier and Stokes.

Dr.Wadia then discussed the concept of the electric and magnetic fields introduced by Faraday and the great synthesis of the laws of electro-magnetism by Maxwell, who predicted electro-magnetic waves and identified light as an electro-magnetic wave. He explained how Maxwell’s equations contain the seeds of the revision of the Newtonian framework because the velocity of light was finite and same in all inertial frames (which move at constant velocity with respect to each other). This simple fact leads to time dilation for observers moving with uniform velocity with respect to each other. This is the basis of Einstein’s Special Theory of Relativity (1905). 

Einstein then puzzled over accelerating reference frames and also about the fact that the gravitational interaction, in Newton’s law of gravitation, is instantaneous. In 1907 he had `the happiest thought of his life’, which is the Principle of Equivalence. It says that the effects of gravity can always be simulated by an accelerating reference frame (over short distances and short times).  The effect of people falling forward when a bus, in which they are travelling, brakes sharply is, by the principle of equivalence, exactly the same phenomenon as a person tripping and falling on to the floor. Dr. Wadia explained how this idea eventually led to the formulation of the General Theory of Relativity in 1915, in which gravity is understood as deviations and warps of the fabric of space-time caused by the mass of an object (e.g., a heavy ball on a trampoline) to which another object responds.  Einstein’s solitary struggle, between 1907 and 1915, to formulate the General theory of Relativity is described by Richard Feynman, another very well-known Physicist, as ‘trying to swim with his hands tied behind his back’.  Einstein’s theory is experimentally well tested and is also used in the Global Positioning Systems (GPS) which are commonly in use today.

The discovery of Quantum Mechanics in the early 20th century is one of the most important scientific discoveries of all times. It is the framework for theories of atoms, molecules, electrons, nuclei, quarks and other elementary particles, which has been experimentally verified to extremely short distances (one part in 10^{-21} cms) in high energy physics experiments at CERN. All electronic devices and computers work on the basis of quantum mechanics.

Dr. Wadia discussed the implication of Quantum Mechanics on the fabric of space-time that emerged from Einstein’s theory and said that such a description breaks down at very short distances (one part in 10^{-32} cms as a rough estimate). He also said that there is a logical difficulty in reconciling the physics of Black Holes with Quantum Mechanics. This issue is serious because Black Holes besides being predictions of Einstein’s General Relativity exist in the universe!

String Theory is a framework which contains General Relativity as an approximate description, provides a new framework for fundamental physics. It conforms to the laws of quantum mechanics but its basic building blocks are extended objects of dim. 0,1,2,….,9. The one dimensional object is the string. The theory is called String Theory for historical reasons. String theory leads to a radical change in our concepts of space-times at very short distances. The smooth fabric of space-time of the Einstein theory is gone! The paradoxes of black hole physics are also gone because string theory models black holes in terms of its building blocks very much like we model a piece of coal in terms of its atoms and molecules. 

In the last part of the talk Dr. Wadia described the Maldacena Conjecture in which gravitational phenomena, is coded in a more conventional gauge theory (a generalization of Maxwell’s theory) on the boundary of space-time. This conjectured correspondence is called holography and has been verified for various processes. He explained how these ideas have led to the connection of fluid dynamics with black holes in one higher dimension. There are also some interesting applications to the physics of the quark-gluon plasma, to superconductivity and the problem of the confinement of quarks in protons and neutrons (which are the constituents of atomic nuclei). He ended by saying that String Theory, because of the richness of its structures, seems to unify previously disparate phenomena in physics.      

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  In his introductory remarks, Sudheendra Kulkarni, Chairman of ORF Mumbai, said that the quest for understanding the mysteries of nature and the meaning of existence had engaged the human mind since time immemorial. Contemplation about the architecture of the material universe and the laws governing its functioning began with the birth of the first thinking man. Referring to the subject of Dr. Wadia’s talk, he said that, like modern physics, India’s ancient philosophy had also tried to understand the reality in an integral way, both in its material and non-material aspects and also in its ‘big’ and ‘small’ dimensions. In this context, he cited the question posed in Katha Upanishad: Anor aniyam mahato mahiyan – What is smaller than the smallest, and larger than the largest? The answer given by the ancient rishis is, “It is the soul that animates the heart of man and also everything else in this Infinite Universe”.

In his closing remarks, Kulkarni thanked Dr. Wadia for delivering a fascinating lecture that paid tribute to the countless scientists who had contributed to physics’ journey from Newton to Einstein and beyond. Dr. Wadia’s talk, he observed, proved that no true scientific discovery is fully invalidated by a new discovery; rather, the new discovery sets the boundary conditions for the validity of the old one. Einstein himself, he said, had recognized this truth by stating, way back in 1916, “No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.”

Kulkarni remarked that the journey from Newtonian physics to String Theory demonstrated man’s quest to gain unified knowledge of the universe bereft of contradictions. In spite of his successes in the “Search for a Theory of Everything”, man finds that there is still so much more that is mysterious and incomprehensible. The predicament of this never-ending search had made even Einstein, one of the greatest scientists of all time, to state: “The eternal mystery of the world is its comprehensibility…The fact that it is comprehensible is a miracle.”

Voicing happiness over the fact that Indian scientists in the String Theory group rank among the Top 5 in the world, Kulkarni expressed confidence that India would soon stand at the forefront of cutting-edge advances in various branches of science and technology. “It should be our endeavour and determination to become a nation of creators – and not just remain consumers — of new knowledge in science and technology,” he said. ORF’s ‘GURUS OF SCIENCE’ Lecture Series, he added, is guided by this national goal.

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About ‘The Happiest Thought in Einstein’s Life’

The initial inkling of how to generalize relativity struck Einstein in1907, and it is a moment reminiscent of Newton’s contemplation of the falling apple, though trickier to comprehend. “I was sitting in a chair in my patent office in Bern. Suddenly a thought struck me: if a man falls freely, he would not feel his weight.” If you were to jump off a rooftop or better still a high cliff, you would not feel gravity. “I was taken aback. The simple thought experiment made a deep impression on me. It was what lead to my theory of gravity,” Einstein wrote later. He called this “the happiest thought of my life.”

To drive the point home, he imagined that as you fall, you let go of some rocks from your hand. What happens to them? They fall at the same rate as you, side by side. If you were to only concentrate on the rocks (admittedly difficult!) you would not be able to tell if they were falling to the ground. An observer on the ground would see you and the rocks accelerating together for a smash, but to you the rocks, relative to your reference frame, would appear to be ‘at rest’.

Or imagine being inside a moving lift while standing on a weight scale. As the life descends, the faster it accelerates, the less you will feel your weight and the lighter will be the weight reading on the scale. If the lift cable were to snap and the lift were to go into freefall, your weight according to the scales would be zero. Then gravity would not exist for you in your immediate vicinity. In other words, the existence of gravity is relative to acceleration. From such thinking, Einstein restated a venerable idea that has become known as his ‘equivalence principle’ – the idea that gravity and acceleration are in a sense, equivalent.

(From EINSTEIN: A Hundred Years of Relativity by Andrew Robinson)

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WHAT IS STRING THEORY?

String theory is the idea that the fundamental particles we observe are not point-like dots, but rather tiny strings!

We live in a wonderfully complex universe, and we are curious about it by nature. Time and again we have wondered— why are we here? Where did we and the world come from? What is the world made of? It is our privilege to live in a time when enormous progress has been made towards finding some of the answers. String theory is our most recent attempt to answer the last (and part of the second) question.

So, what is the world made of? Ordinary matter is made of atoms, which are in turn made of just three basic components: electrons whirling around a nucleus composed of neutrons and protons. The electron is a truly fundamental particle (it is one of a family of particles known as leptons), but neutrons and protons are made of smaller particles, known as quarks. Quarks are, as far as we know, truly elementary.

Our current knowledge about the subatomic composition of the universe is summarized in what is known as the Standard Model of particle physics. It describes both the fundamental building blocks out of which the world is made, and the forces through which these blocks interact. There are twelve basic building blocks. Six of these are quarks— they go by the interesting names of up, down, charm, strange, bottom and top. (A proton, for instance, is made of two up quarks and one down quark.) The other six are leptons— these include the electron and its two heavier siblings, the muon and the tauon, as well as three neutrinos.

There are four fundamental forces in the universe: gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force. The most familiar of these is the photon, a particle of light, which is the mediator of electromagnetic forces. (This means that, for instance, a magnet attracts a nail because both objects exchange photons.) The graviton is the particle associated with gravity. The strong force is carried by eight particles known as gluons. Finally, the weak force is transmitted by three particles, the W+, the W- , and the Z.

The behavior of all of these particles and forces is described with impeccable precision by the Standard Model, with one notable exception: gravity. For technical reasons, the gravitational force, the most familiar in our everyday lives, has proven very difficult to describe microscopically. This has been for many years one of the most important problems in theoretical physics– to formulate a quantum theory of gravity.

In the last few decades, string theory has emerged as the most promising candidate for a microscopic theory of gravity. And it is infinitely more ambitious than that: it attempts to provide a complete, unified, and consistent description of the fundamental structure of our universe. (For this reason it is sometimes, quite arrogantly, called a ‘Theory of Everything’).

The essential idea behind string theory is this: all of the different ‘fundamental ‘ particles of the Standard Model are really just different manifestations of one basic object: a string. How can that be? Well, we would ordinarily picture an electron, for instance, as a point with no internal structure. A point cannot do anything but move. But, if string theory is correct, then under an extremely powerful ‘microscope’ we would realize that the electron is not really a point, but a tiny loop of string. A string can do something aside from moving— it can oscillate in different ways. If it oscillates a certain way, then from a distance, unable to tell it is really a string, we see an electron. But if it oscillates some other way, well, then we call it a photon, or a quark, or a … you get the idea. So, if string theory is correct, the entire world is made of strings!

Perhaps the most remarkable thing about string theory is that such a simple idea works— it is possible to derive (an extension of) the Standard Model (which has been verified experimentally with incredible precision) from a theory of strings. But it should also be said that, to date, there is no direct experimental evidence that string theory itself is the correct description of Nature. This is mostly due to the fact that string theory is still under development. We know bits and pieces of it, but we do not yet see the whole picture, and we are therefore unable to make definite predictions. In recent years many exciting developments have taken place, radically improving our understanding of what the theory is.

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To know more about String Theory, one of the highly recommended popular science books is “The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for The Ultimate Theory” by Prof. Brian Greene.

Other resources are:

The Official String Theory Website: An excellent introductory site for the non-specialist, including RealAudio interviews with leading string theorists, and a tour of the Big Bang.

Particle Adventure: A very nice tour through the main ideas of the Standard Model of particle physics.

The Science of Matter, Space and Time: Another nice presentation of the concepts of particle physics.

Einstein’s Unfinished Symphony: An article on string theory that appeared in TIME magazine, on occasion of TIME’s designation of Einstein as the person of the 20th century.

Black Holes, Strings and Quantum Gravity: A public lecture by Prof. Juan Maldacena, undoubtedly the most influential string theorist in the last few years.

Duality, Spacetime and Quantum Mechanics: A public lecture by Prof. Edward Witten, a leading contributor to string theory

The Theory of Strings— A Detailed Introduction: An extensive description of the basic ideas of the theory, by Prof. Sunil Mukhi, a leading string theorist.

Black Holes, Quantum Mechanics and String Theory: A series of 10 lectures on string theory, intended for the general public, by Prof. Finn Larsen.

ITP Teachers’ Educational Forum on String Theory: Is it the Theory of Everything?: A set of lectures on string theory, intended for highschool teachers.

 

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This entry was posted on 27/05/2010 by in Science and Technology and tagged , , , , , .
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