To the fourth dimension and beyond

by Hilarian Codippily

As we commemorate the anniversary of Albert Einstein's birthday on March 14, 1879 and celebrate the detection of gravitational waves predicted by him over 100 years ago, it may be opportune to revisit the major paradigm shift the formulated in our quest for understanding the universe. This was done mainly in terms of the special and general theories of relativity.

Monuments erected in honour of this great man are well preserved, as witnessed during my visits both to his birthplace in the City of Ulm in Germany, as well as to his last office at the Institute for Advanced Study at Princeton, New Jersey, USA. His office could be accessed through Maxwell Lane and Einstein Drive. A memorial square adorns the original site of his house in Germany destroyed during the war, and is circled by two fast food outlets and two book stores. His much-photographed house at Princeton is a tourist attraction, even though it is un-numbered at the request of the current owners.

The literature on Einstein is phenomenal - stretching across the past century from recent works such as Walter Isaacson's classic on Einstein to one of the earliest publications by Lincoln Barnett in 1948 with a foreword by Einstein himself. The aim here is to restrict this article to a few glimpses of a man who became a legend in his own lifetime. As noted by Barnett, when names of fourteen greatest names in scientific history, for the iconography of Manhattan's most famous Riverside Church, every list had the name of Einstein - in his own lifetime.

The past century has witnessed perhaps the most profound and far-reaching developments in physics and in particular, our perceptions and concepts of the physical world. At the turn of the century, observed phenomena in the physical world were explained largely by classical physics. The sense of complacency prevailing at that time was soon shattered by radical shifts in our worldview. These consisted of the formulation of the theory of relativity and the development of quantum mechanics - the two main pillars of modern physics. While the former explained the fundamentals of the macroscopic physical world of the stars, planets, and the universe at large, the latter explained processes of the microscopic world of elementary particles. A challenge for the rest of the past century was to unify these two fundamental theories into a single coherent framework - a challenge that Einstein began to work on from the 1920s and continued later in his years at Princeton from the 1930s. One approach was the development of string theory in the latter part of the past century.

The special theory of relativity

Albert Einstein's special theory of relativity published in 1905 revolutionised our concepts of space and time, which were considered absolute in terms of the Newtonian model. Special relativity unified space and time into a four-dimensional continuum of space-time. The springboard for this revolution was provided by another revolution by James Clerk Maxwell who paved the way for the subsequent unification our concepts of electricity and magnetism into one of an electromagnetic field, within a four dimensional space-time framework. Maxwell's equations provided the answer to Einstein's question as a teenager: "what would a beam of light look like if one rides alongside at the speed of light?" Could one observe a stationary wave? Maxwell's equations showed, in particular, that they do not admit stationary waves, and predicted that light would travel at the same relative velocity, no matter how close to the velocity of light the observer would be travelling. To explain this null result, Hendrik Lorentz and George Fitzgerald had proposed a formulae for contraction of lengths and slowing down of clocks when they moved through "ether". Henri Poincaré had also developed a mathematical structure to explain these results, but only in terms of classical physics.But it was Einstein, while working in the Swiss Patent Office at that time, who pointed out that it was unnecessary to assume all-pervading ether if one could abandon the notion of absolute time, as assumed by Newton. Putting together these concepts into a coherent theory in physics was indeed the work of a genius.

The special theory of relativity is based on two postulates: (a) that the laws of nature are the same for observers in uniform translatory motion, and (b) that the velocity of light c is constant for all observers;c is also the upper limit for velocities within the universe. In the words of Hermann Minkowski "...henceforth space by itself, and time by itself are doomed to fade away into mere shadows, and the only a kind of union of the two will preserve an independent reality". The special theory of relativity also unified our concepts of mass and energy through the well-known equation:, where E denotes energy, c the velocity of light and m denotes mass. This equation laid the foundation for the harnessing of nuclear energy. In 1905, known as the "Miracle Year", Einstein provided a physical interpretation to the lumpiness or the discreteness of energy through his investigations of the photoelectric effect for which he was awarded the 1921 Nobel Prize in Physics.

The general theory of relativity

Einstein's general theory of relativity, published in 1915 further revolutionised our concepts of the physical world by showing that motion under gravity was is not caused by a gravitational force as such, but by the geometry or curvature of space time arising from the distribution of mass. Einstein realised that the instantaneous impact of gravity over long distances was a direct contradiction to the upper limit of velocity in the universe, i.e. the velocity of light. Einstein concluded in 1907 that the force one experiences from gravity and the force one experiences from acceleration are, in fact, the same. Thus, the cornerstone of general relativity is the principle of equivalence or the symmetry between a gravitational field and a frame of reference that experiences acceleration. This together with the principle of covariance that the laws of nature are the same for observers, regardless whether they are accelerating or not, form the basis of general relativity.

Using Riemannian geometry developed by Georg Bernard Riemann in the nineteenth century, Einstein linked up the curvature of spacetime with the distribution of matter. Einstein's equation for the orbit of a planet round the sun is essentially a geodesic in curved spacetime or a natural path round the sun. This equation differs from the Newtonian equation only by the last term on the right hand side, which explains the behaviour of the perihelion of Mercury (not explained by the Newtonian equation).General relativity was experimentally verified in during 1919 solar eclipse, through the observations concerning the bending of light rays when passing the Sun.

The theory of relativity provides the framework for physics at the macroscopic level and for modern cosmology. The consequences of general relativity include the slowing down of clocks in gravitational fields, the existence of black holes from which light cannot escape and the big bang and other models of the universe. The fine-tuned GPS we use today for driving also owes its existence to general relativity.

The microscopic world

Perhaps the most significant landmark in this field is the formulation of Heisenberg's uncertainty principle - which basically overthrew the notion of ultimate precision associated with physical science. In essence, the uncertainty principle states that the more accurately we try to measure the position of a particle, the less accurately we can measure its momentum and vice versa. As Einstein once remarked, "the more we try to find it, the more it hides". The main implication of this principle is that one cannot measure all the characteristics of a physical state, without altering what is being measured.

Max Planck laid the foundation for quantum mechanics and the eventual development of the Standard Model. The formulation of Schrödinger's wave equation and Heisenberg's landmark achievement opened up vast areas of research in particle physics. Notable milestones amongst a vast number include those of Paul Dirac, Wolfgang Pauli and Richard Feynman. All these milestones were in the direction towards the standard model of particle physics in a framework concerning the electromagnetic, weak, and strong nuclear interactions. The current formulation includes a coherent classification of subatomic particles based on the experimental confirmation of the existence of quarks, as well as the discoveries of the top quark (1995), the tau neutrino (2000), and more recently the Higgs boson (2012).

However, a major problem was encountered when one tried to incorporate gravity into the standard model. It was found to be almost impossible to construct a theory that is partly classical and partly quantum.

String theory

String theory, notwithstanding its controversies and lack of experimental verification, offers an extraordinary framework for incorporating general relativity and quantum mechanics into one unified theory. In essence, string theory postulates that all elementary particles are not point particles as assumed in the standard model, but infinitely thin strings with a length of the order of the Planck length (about vibrating in 11 dimensional space. Seven of these dimensions are assumed to have curled in at the time of the big bang, leaving the familiar three spatial dimensions and the time dimension to expand after the big bang.

Thus, the properties of the photon, the electric charge, the weak charge, the strong charge, and all other elementary particles are determined by the precise way in which the corresponding strings vibrate. This represents the ultimate unification in the world of physics, as all matter (fermions) and all forces (bosons) in the universe arise from the same kind of vibrating strings. Brian Greene calls this a 'Cosmic Symphony'.

String theory also represents a major leap from the standard model. Gravity is an integral part of it, which arises from the model. The more vigorous the vibration, the greater will be its energy. Therefore, the pattern of vibration will determine the response of the particle to a gravitational force. Furthermore, according to string theory, one of the vibrational patterns perfectly matches the properties of the graviton. We thus see that gravity arises as an integral part of string theory - and not imposed upon it.

String theory was developed through the collaborative efforts of a large number of scientists across the world. They include notable figures such asJohn Schwarz, Michael Green and Edward Witten, and a large number of others. A major landmark was a lecture by Edward Witten was given in 1995, who showed that five superstring theories in 10 dimensions were equally valid though the introduction of an 11th dimension. These five theories were shown to be different facets of a more fundamental theory called M-Theory - another step in the direction of unification. Stephen Hawking has called this the "ultimate theory of the universe".

Gravitational Waves

The detection of gravitational waves announced on February 11, 2016 has been hailed as the biggest scientific breakthrough of the century. For the first time, researchers have detected the warping of spacetime originating from the collision of two black holes some 1.3 billion light years from the Earth. This historic announcement, based on signals from two Laser Interferometer Gravitational Observatories (LIGO), was made by David Reitze of the California Institute of Technology. The actual observation was made by Marco Drago of the Max Planck Institute. The significance of this discovery lies in the fact that it is the first signal that we have received from a non-electromagnetic source - thus opening a new window into the universe. Hitherto, all our observations have been from electromagnetic sources such as visible light, X - rays, and gamma rays.

As we all know, there is enough empirical evidence in support of the standard model of cosmology, in terms of which the universe started at a definite moment of time, some 13.8 billion years ago. As the universe cooled over time, the spacetime coordinates and forms of matter and energy began to emerge, leading up eventually to the observable universe of stars and galaxies as we know today. There is evidence to show that only 4.6 percent of the universe consists of matter as we know it, while the balance is made up of dark energy (71.4%) and dark matter (24%).

Sensation of the mystical

Albert Einstein died on April 18, 1955, at the age of 76, but his works live on. Let me conclude this article with his immortal words: "The most beautiful and most profound emotion we can experience is the sensation of the mystical. It is the sower of all true science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their primitive forms - this knowledge, this feeling is at the centre of true religiousness".

(The writer is a Visiting Lecturer, University of Colombo)