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Review of Einstein's Theories of Relativity.

Byline: Dr. Gulfaraz Ahmed

1905 was a historical year for Einstein as well as science. A relatively unknown clerk in the Swiss patents office in Bern, Einstein, published four papers; each paper changed the course of science. Prior to Einstein's work light was regarded as an electromagnetic wave and the wave nature of light was considered an established fact. Einstein expounded that light was not a continuous wave but consisted of localized particles. In the first paper he applied the newly developed Max Planck's quantum theory to light to explain the phenomenon of photoelectric effect, by which a material emits electrically charged particles when light beam hits it. He wrote in his paper that, "According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of energy quanta that are localized in points in space and move without dividing, and can be absorbed or generated only as a whole".

In the second paper Einstein produced an experimental proof of the existence of atoms by analyzing the Brownian motion of tiny particles suspended in water which is caused by the chaotic motion of the air molecules above and water molecules below the surface. This proof laid the base for the Standard Model of Physics which is the foundation of the modern science.

The third and most famous paper was on the "Electrodynamics of Moving Bodies". Einstein confronted the apparent contradiction between two principal theories of physics: Isaac Newton's concept of absolute space and time and James Clerk Maxwell's idea that light travelled at constant speed through ether. The concept of ether was proven unnecessary by the famous Michelson-Morley experiment in 1887 which established that speed of light was not affected by direction of its travel with respect to the movement of the earth. A Dutch physicist Lorentz explained the results of Michelson-Morley by suggesting that the space contracted and time slowed down along the direction of motion through the ether. Knowledge grows at the edges through a slow and progressive buildup, but every now and then the expanded base of knowledge provides a springboard for a quantum jump that pales the history of knowledge growth.

Such a quantum jump occurred when, to resolve the prevailing contradiction in the theory, Einstein introduced his Theory of Special Relativity, which postulated that the laws of physics were same even for objects moving in different inertial frames (which move at constant speed relative to each other), and that the speed of light was constant in all inertial frames and there was no ground for the existence of ether. Accordingly, all observers should measure the same speed of light no matter how fast they are moving.

The fourth paper expounded the fundamental relationship between mass and energy, which is a natural consequence of the Theory of Special Relativity. Ether to mass and energy were regarded two different entities. Einstein's famous equation E=mc2 (where "c" is the constant speed of light) provides a mathematical relationship for precisely calculating the conversion. It established the interchangeability of mass and energy and explained the amount of energy released during nuclear fission or fusion. This equation is also at the heart of the destructive power of the atomic bombs. At one point in time Einstein had written a letter to President Roosevelt as well as encouraged the U.S. Government to fund research into the development of nuclear weapons which were later used in the Second World War against Japan.

In particle accelerators protons are accelerated to almost the speed of light and thereby becoming much more massive, following Einstein's Theory of Special Relativity, and then smashed into each other creating more massive particles than the original protons such as the Higgs Boson discovered very recently.

The Theory of Special Relativity changed the fundamentals of theoretical physics and cosmology forever. Time and space were no more absolute and independent fundamentals, both changed relative to a fast moving observer. The speed of light became the only immutable entity that would remain constant in all inertial frames that move at constant speed with respect to each other, regardless of the motion of the source or the observer. Einstein was awarded the Nobel Prize in 1921 for his pioneering work on photoelectric effect, but the remaining three papers in their own right were also worthy of Nobel prizes. Special relativity explained the gravitational phenomenon for objects moving at constant speeds and was not applicable to accelerating bodies involving the force of gravity. It provided that time did not pass identically for everyone.

If one of the identical twins undertakes a relativistic fast travel in a spacecraft his time will pass quicker and he would look younger than his twin on his return to earth as the time, near a massive body like earth, slows down. Time dilates and slows down and length shrinks along the direction of motion at relativistic speed close to that of light. As an object moves with a speed close to the speed of light it acquires immense amount of kinetic energy and its equivalent mass increases immensely. With further increase in speed the equivalent mass tends to become infinite and it requires infinite energy to increase the speed further. Consequently, no object with a finite mass can achieve the speed of light and this places a limit on the superluminal motion. Only waves like the light electromagnetic waves, that have no mass, travel at the speed of light.

These papers brought Einstein into prominence and he started getting job offers from various universities. Despite his monumental success Einstein realized that his theory did not fit with the concept of gravity of how things fell and he came to a conclusion that the universal law of gravity developed by the father of physics, Isaac Newton, needed a revision. Newton had postulated that the force of gravity between two bodies emerged instantaneously but Einstein's Theory of Special Relativity had established that nothing, no signal and no effect, could move faster than the speed of light. Building on the Special Relativity Theory Einstein realized that he could include the effect of gravity in his theory if he could capture the effect of acceleration of moving bodies. Guided by his powerful intuition and mathematical techniques, Einstein embarked on the development of the Theory of General Relativity by analyzing the accelerating frames of motion to capture the effect of gravity.

This was a tough nut to crack and Einstein endeavored to pursue it for nearly a decade. Searching through mathematical literature he came upon the formulation of two dimensional curved surfaces like the sides of a hill by the nineteenth century legendary mathematician Carl Friedrich Gauss. Gauss had assigned the task of extending his work to a brilliant student named Bernard Riemann. The latter did groundbreaking work and extended the curvature to three dimensional surfaces in his doctoral thesis. His mathematics described a three dimensional curvature tensor that came to be known as Riemann Curvature and is generally denoted by R in mathematical formulations. Einstein was intrigued by Riemann's mathematics and spent a long time in understanding and extending it to four dimensions of space-time fabric to study the curvature caused by nearby massive bodies at a specific time. He published the Theory of General Relativity in November 1915 which became a masterpiece of modern physics.

It was received with awe and skepticism across the scientific world. The field theory still remains a powerful and radical concept that has put to rest the conjectures that gravity was some mysterious innate and instantaneous force between bodies having mass.

The theory not only provided the basis of working out the gravitational force in relation to fast moving massive bodies it also explained the origin of it as the bending of time-space fabric. As a special case of relative motion at ordinary speed it validated the work of Newton done some 250 years earlier of calculating the gravitational force between two bodies. It is this force that gives the cosmos the given structure, keeps the planets in their orbits and causes the tidal motion. The Theory of General Relativity still remains a tough and challenging concept to grasp and few contemporaries had a thorough understanding of it and the circle of understanding expands as the time passes.

In its original formulation the theory had predicted an expanding universe, but sensing that it would go counter to the commonly held belief of a stable and static universe Einstein fudged the equation by introducing a cosmological constant. But as would happen later in 1929, Mr. Hubble proved incontrovertibly the fact of expanding universe while observing the phenomenon of Red Shift of the distant galaxies through his telescope. Embarrassed, Einstein recanted calling the manipulation of the cosmological constant as the biggest blunder of his life.

Einstein's general relativity had predicted bending of light rays while passing by massive stars. A couple of British expeditions were sent to two different locations in Africa and Brazil in November 1919 to observe the path of light emanating from stars located close or behind the sun during a predicted complete solar eclipse. An iconic British astronomer, Mr. Eddington, heading the African team precisely measured the path of light emanating from seven selected stars and waited for final analysis. The eclipse enabled the scientists to observe the rays of light coming from the stars close to the sun, which would otherwise not be visible due to the bright light of the sun.

There existed three possibilities: If there was found no bending Einstein would be proven wrong and the Theory of General Relativity would be invalid; if the bending was much less than the prediction of the theory, England would win as the model by Newton would hold good in explaining the behavior of the universe and; if the bending was in line with the prediction of the Theory of General Relativity Einstein would have been successful in giving the world a new model of the universe. The field observations supported the third possibility which catapulted Einstein into global acclaim and put him in front of the leading scientists of the time. The theory would continue to explain new phenomena bringing into open the secrets of the cosmos. In due course the scientists would label the field theory as the God's equation, as it came close to reading the mind of God about the architecture of the universe.

The General Relativity Theory also predicted the existence of gravitational waves. Gravitational waves are ripples in the space-time fabric and are created by fast moving massive bodies like the motion of fast spinning massive binary stars revolving around each other or the collision of massive stars or black holes. This prediction had eluded proof for nearly a century. But in 2013, scientists studied precisely the motion of two massive binary stars, a neutron and a white dwarf, revolving around each other 300 times per second at a relatively closer distance of about 7.5 million light years from the earth. Einstein had explained that the loss of energy caused by the motion would reduce the time period of the revolution which would indirectly prove the occurrence of the gravitational waves.

A number of scientists conducted precise measurements of the binary system for a year and concluded that time-period had reduced by eight millionth of a second in one year which was exactly in accordance with the prediction of the General Relativity Theory. This was the toughest test yet of Einstein's epoch changing theory. Even though it proved the existence of the gravitational waves indirectly, no one had ever actually observed these waves. The world did not have to wait much longer as in February 2016 gravitational waves were physically detected as well as heard.

Using four kilometer laser light waves interferometer in LIGO Lab, the underground scientists detected the signal of the gravitational waves generated by the old clash of two massive black holes over a billion-and-a half light years before. The amount of energy released by the clash was equivalent to 3 times the mass of the sun. The gravitational waves travel with the speed of light twisting and compressing the space in their path. The latest achievement will enable scientists to look to the events further behind in time closer to the Big Bang for a better understanding of the early moments of the universe! The Big Bang was the explosion of an extremely young, small and hot universe. The detection of the Cosmic Background Radiation which is a diffuse glare from the remnant of the heat generated by the original explosion proved the concept of Big Bang. The Theory of General Relativity has met every test so far with success and the stature of the genius of Einstein keeps increasing as the time passes.

It is amazing how the mere thoughts on paper by a genius continue to be proven right through the precise field measurements of the cosmos. Here I would like to quote the genius himself, "How is it possible that mathematics, a product of human thought that is independent of experience, fits so exactly the objects of physical reality". A famous astrophysicist, Mario Livio, in his book titled "Is God a Mathematician?" published in 2009 seeks an answer to an eternal question: Does mathematics hold the key to understanding the mysteries of the physical world? He puzzles over the mystery of how God created reality follows so prophetically the creation of human thought. He argues, how does mathematics have omnipotent powers; is it woven into the fabric of nature and meant for the human being to discover it? At times it gives an illusion of a virtual universe and a perspective of the human mind.

Take for example the simple Law of Gravity envisioned by Newton in 1660s that force of gravity equals the product of masses divided by the square of the distance between the two masses and multiplied by a gravitational constant. This very simple but prophetic mathematical formulation has been providing the basis for precisely calculating the trajectories of all space missions, even beyond the solar system, undertaken to-date. It remains an area of mathematical romanticism for challenging the conventional wisdom.

Another proof for the Theory of General Relativity came from explaining the peculiarities in the orbit of Mercury, the first planet of the solar system that feels the maximum effect of solar gravity. The theory successfully explains the anomalous precession of the planet's perihelion which is the rotation of the line joining the sun to the point of the closest approach of the planet. Newton's Universal Law of Gravitation had not been able to predict this effect.

Einstein's work remained very challenging in common understanding and very few people understood it well. It may be useful to highlight some related fundamentals for aiding common understanding. Newton, around 1667, had realized that all material bodies attracted each other with a force that he named as gravity. However, Newton continued to puzzle unsuccessfully as to how this force acted between bodies through empty space between them. Newton's laws had assumed that gravity was an innate force of an object with an ability to act over a distance instantaneously. On the contrary, Einstein's General Relativity is based on a wave equation and the force of gravity propagates with the speed of light. The gravitational waves emanating from the clash of two black holes in the distant past had taken 1.5 billion light years to reach the earth.

It would be mind boggling to imagine the infinite number and extent of time-space warps that might have been set in motion by infinite cosmic events over the whole life of the universe. The world would continue to discover them as generated gravitational waves keep reaching the earth labs. Although Newton believed that space was not absolute but he didn't believe that space could be affected by the objects in it. Einstein, however, changed that as he believed that space was affected by the presence of matter which appeared in the form of bending of the time-space fabric which he called time-space warp. Einstein had theorized that mass can warp, bend, push, or pull the space. Gravity was thus a natural outcome of the presence of mass in the space. According to General Relativity warping is not independent of time since gravity or the effect of matter on space propagates with the speed of light therefore there is a time-space warp.

Contrary to this Newton had believed that time was absolute and therefore not affected by gravity. Following the Theory of General Relativity at any one point in space the space-time warp changes with time and at any one time the warp changes with space. Had Newtonian contention of instantaneous gravity been true we would have been seeing the simultaneous effect of cosmic events by sensing the gravitational waves in real-time.

Reviewing the prevailing scientific concepts before the unfolding of the General Relativity there had existed no concept of any field pervading the empty space. But just before Einstein was born, two British scientists Michael Faraday and James Maxwell had developed the concept of an electromagnetic field in the space that Newton had considered empty. This field fills the space and vibrates and oscillates like a flexible surface and carries the electrical force across the space. Einstein built on the concept of electromagnetic field and visualized the existence of a likewise gravitational field filling the space and carrying the force of gravity. He was seized with trying to unravel the working of this field and expressing it in the form of a mathematical equation. At some point down the creativity lane, he hit upon a Eureka moment that the gravitational field did not just fill the space like that of the electromagnetic field but that the gravitational field was the space itself.

Space and matter were not two different things but features of the same fabric. The time-space-matter fabric, that contains space and matter and that twists, turns, undulates, flexes and curves with time, is actually the gravitational field itself. The extent of the expanding gravitational field means the edge of the space that contains matter and the motion of it is the flow of time.

Time started as the movement of the universe started at the time of the initial explosion of the Big Bang. Time is a consequential effect of movement and is not an independent entity and its flow is affected by mass as well as speed of motion. The sun curves the space around and the earth revolves around it to follow the curvature of the gravitational field like a marble rolling in a funnel. There are no mysterious forces working on the earth or the marble, they simply follow the curved path while rolling around. Planets circle round the sun and things fall because of the bending of the gravitational field. Force of gravity originates from the dynamic gravitational warp. What we commonly call space is actually the pervading gravitational field. It extends up to where matter extends and that sets the edge of the universe. As the universe or the gravitational field is accelerating while expanding, the density of the matter continues to reduce and so does the curvature of the universe.

There is a lingering conundrum, if the time-space fabric extends only up to the extension of the gravitational field there can be no vacuum beyond the edges. For vacuum to exist beyond the gravitational waves the space has to be pre-existing before the start of the gravitational waves at the time of the Big Bang. How did the pre-existing empty space devoid of matter or energy and thus having complete vacuum come about cosmologically needs to be explained outside of the Big Bang concept? If time, space and matter/energy are inter-woven in the physical fabric of the universe, we need to find the mathematics that can provide a way out. This may explain the search for the Modern String Theory which is seeking to combine the dimensions of time, three normal space dimensions and seven folded quantum space dimensions that take care of the effect of gravity at quantum level as well.

Another conundrum relates to the growing difference of scales of the extent of the expanding universe and the maximum speed of transmitting signals from one part to others. The speed of light is woefully inadequate to map the dynamism of the universe. There is a need to discover a faster messenger whose speed relates compatibly to the extent of travels involved in the expanding universe. Otherwise the reality of the present day cosmos will forever remain a mystery elusive to the mankind.

In Einstein's magical formulation of the Theory of General Relativity he started with equating the Riemann's curvature known as Ricci Tensor denoted by Ruv with the gravity tensor Tuv and added the metric tensor guv which provides measurement of infinitesimal distances along the curved space. The resultant equation can be described in half a line:


Normally in mathematical equations space and time dimensions are denoted separately by different symbols as both are treated as different entities. In this case the space and time dimensions are combined together in the Ricci Tensor and represent the space-time fabric. This equation does not have the term for the infamous Cosmological Constant which Einstein had later dropped but the scientists are again bringing it in for defining an open universe expanding faster and faster. The equation reveals how a given amount of mass and/or energy warp the space-time. The left-hand side of the equation describes the curvature of space-time whose effect is felt as the gravitational force. is termed as the energy-momentum tensor which describes the way mass, energy, momentum and pressure are distributed throughout the universe. The constant is the Newton's gravitational constant and c is the speed of light.

The Greek letters and are 4 dimensional parameters, three of space and fourth of time and can each take on the values of 0, 1, 2 or 3. It is symmetric tensor known as Riemann Manifold and has only 10 effective terms.

If and both take the value 0, then the equation relates only to time. The term now stands for energy, which causes time to speed up or slow down. The left-hand side of the equation describes the change in the flow of time at one point in space. The flow of time, for example, will slow down near a black hole due to the massive gravitational effect and time will stop to flow at the surface of a black hole as the escape velocity is equal to the speed of light which is in line with Einstein's Theory of Special Relativity.

Developments in Physics generally follow the developments in the mathematical techniques. The Theory of General Relativity followed the developments in mathematics of the curved spaces by the famous mathematicians like Carl Friedrich Gauss, Bernard Riemann and Ricci for the technique using 4-dimensional tensors. The space and time are interwoven through a single 4-dimensional tensor represented by R in earlier equation. Tracing the history's successive developments, the Greek philosopher Aristotle gave his model of the physical universe by holding space and time absolute in 340 BC. Newton published his famous book titled "Phiolsophiae Naturalis Principia Mathematica" in 1687 and gave a new model of the universe replacing that of Aristotle. According to Newton time alone was considered absolute.

The current challenges facing physics of merging the big and small are awaiting further breakthroughs in mathematics for some future Einstein to visualize the missing pieces of the jigsaw puzzle of the working of the universe. The modern String Theory postulates eleven dimensional branes which include three common dimensions of space, one of time and seven folded dimensions of quantum scale which would require mathematical techniques involving 11 dimensional tensors presenting hitherto unsurmountable mathematical challenges. It is for this reason that eminent physicists like Stephen Hawking commonly undertake crash courses in new mathematical developments for expounding new theories to handle the challenges facing Physics.

It takes a determined effort to master the mathematics of Riemann Curvature for understanding and using the most famous and beautiful equation of the Theory of General Relativity. The equation presents serious computational challenges requiring supercomputers for real life general cosmological solutions. The growing understanding as well as mounting evidence of its correct predictions is leading to the unlocking of the new secrets of the universe. In some romantic sense the three attributes of simplicity, beauty and truth are interrelated. In the words of the romantic Poet Laureate John Keats: beauty is truth and truth beauty. Einstein's equation of General Relativity with inspiring mathematical lyrics is a befitting measure of truth and beauty.

Einstein did have his share of frustration after he had achieved worldwide fame in 1920s. He differed with mainstream physicists and made pointed criticism of quantum mechanics calling it incomplete. According to Einstein extrapolating the quantum mechanics mathematics predicted the bizarre phenomena of quantum entanglement that particles separated in space could still interact among themselves instantaneously. He wrote to Max Born in 1926, "Quantum mechanics is certainly imposing but an inner voice tells me that it is not yet the real thing.... I, at any rate am convinced that (God) is not playing at dice". He had even dubbed entanglement as a spooky action at a distance which after his death, was confirmed experimentally in 1982 by the French physicist Alain Aspect. This concept is now being used successfully in a number of applications like the quantum cryptography and information technology.

Although no particle or a signal can travel at more than the speed of light according to the Theory of Special Relativity, the instantaneous interaction between entangled particles at great distance apart remains a conundrum in physics. On September 29, 2017 President Academy of Sciences China made the first ever totally secure and hack-free call over 7000 kilometers away to an Austrian physicist using quantum cryptography based on the quantum entanglement. This was made possible by the launch of the very first quantum satellite by China in August 2016. But none of Einstein's frustrations can eclipse the far reaching contributions to physics that he was able to make in the earlier part of his life. In December 1999 the Time Magazine splashed his picture on the cover page choosing him as the Man of the 20th Century. It is very likely that he would also be the Man of the Second Millennium when Time or any other institution comes to defining the millennial personality.

The greatest challenge confronting Physics of uniting the Theory of the Big, Einstein's Theory of Gravity, with the theory of the small, the Quantum Theory, has remained elusive although the best of scientific brains have been trying endlessly for several decades. If the universe is the continuum of the dynamic gravitational field, it physically combines the worlds of the big and the small together. The jiggling of the field by the elephants distorts the effect of the quantum world owing to astronomically smaller curvature of the quantum particles on the dynamic global gravitational field. The motion of the gravitational field swamps the effect of the very small. For this reason gravity is the weakest force in the everyday world yet it is the strongest force in the universe. The scale gets infinitely more distorted at the quantum level. The recent discovery of the Higgs particle of 125 billion electron volts mass establishes the permeation of Higgs field in the universe.

Higgs field is the field of mass/energy provided by the interacting particles which fills every region of the universe. It appears natural that the Higgs field merges or meshes with the gravitational field enveloping the time and space continuum. As a particle interacts with the Higgs field it gains mass or energy. Light particles, photons gain no mass but only energy and are thus able to travel with the speed of light. A particle gaining mass loses ability to travel at the speed of light.

Were there an achievable chance of uniting the worlds of the big and the small, the creative genius of Einstein might have hit upon it in the later decades of his searching life. Einstein as a man died on April 18, 1955 at age 76 in Princeton, but Einstein as an icon continues to live on to see his work gain greater credibility. A picture taken of his office hours after he died shows a blackboard full of mathematical scribble and a dozen or so books opened and piled a product of mathematical poetry randomly on the table suggesting that the search for a complete theory of everything went on till the last moment of his calling.
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Date:Apr 30, 2018
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