The Relativity Revolution
Einstein introduced a radically new way of thinking about space and time. He called his theory Relativity. Initially the enormous repercussions of these ideas were not even apparent to him. Though, in hindsight, it is not surprising that his new description of space and time was going to be extremely influential. The theory describes two of the inherent properties that everything in this universe shares; space and time. Everything must sit in space and ride on time. Change our concept of space and time and it changes the way we view almost everything.
When relativity made its quiet entry into the world, in June 1905, the time was ripe for a revolution. During the decade proceeding Einstein's first paper on Relativity the foundations on which previous thinking was based were beginning to crumble. As with many leaps of understand before, and since, the main protagonist worked independently, not constrained by the current dogma. It is a tribute to the mind of Einstein that many of the foundations of Relativity had already been derived and discussed within the scientific community before the publication of his theory. No one however had made the leap to Relativity. Einstein, in his isolation, as a technical expert third class in a patent office in Bern, independently derived the fundamental equations of Relativity, and saw the need to change the preconceived nature of the universe. His leap of genius can only be compared with the work two centuries previously of Isaac Newton. In the decades that followed the revolution, when Einstein's status as a twentieth century genius was well established, he reflected on the changes he had introduced.
"Newton, forgive me; you found the only way which in your age was just about possible for a man with the highest powers of thought and creativity. The concepts which you created are guiding our thinking in physics even today, although we now know that they have to be replaced by other farther removed from the sphere of immediate experience, if we aim at a profounder understanding of relationships."
Einstein was referring to the relationship between measurable physical quantities; size, time, mass etc. It is true he developed a theory that better describes the relationship between these physical quantities. It is also true that Newton's work is still fundamental in science and engineering today, and that the revolution he founded was of a significant magnitude more profound that Einstein's. Newton was able to describe the intuitive physical universe with his theories and mathematics. Newton assumed the existence of absolute time and absolute space. Einstein went beyond the intuitive and introduced to us a description of the universe which is counterintuitive, and seems bizarre, based on relative time and space. It is this aspect of Relativity that I find particularly fascinating. It is a theory that has changed every aspect of the way we view the physical universe. It is an enormous theory, and yet it is extremely self-consistent. A century since it was introduced to the world no one has managed to disprove it, or find a better, more elegant description.
In the following notes I wish to present a brief outline of the times, the thinking and influences that led Einstein to his extraordinary theory.
Nineteenth Century Thinking.
In 1682 Newton published his laws of mechanics and gravity. His mathematical descriptions of the way things moved here on earth, and how the planets orbit the sun, seemed to be perfect. He was further exonerated in 1846 when the planet Neptune was discovered. It was predicted to exist through the application of Newton's laws of gravity. This prediction was derived from the unusual motion of the planet Uranus. Uranus had been discovered 70 years previous, and its path was under continual examination. The unusual motion of Uranus about the sun had led some to bring Newton's law of gravity into question. These described the motion of the other planets exceeding well. Uranus was a disturbing exception. However, there were those within the scientific community who were not willing to part with Newtonian physics, and sort to find an explanation through his laws. Two such men were LeVerrier of France and Adams of England. They worked independently, and assumed a planet of equal mass to Uranus may be gravitationally pulling on it from a more distant orb. Their assumption proved to be good, and using Newtown's physics, and mathematics, they predicted the existence, and location, of the unseen planet. Le Verrier was only just able to beat Adams to the discovery by simply using better equipped astronomers. The new planet was discovered the same night the astronomers at Berlin astronomers were given the predicted location. This further bolstered the confidence the scientific community had in their ability to understand the universe.
The nineteenth century made many discoveries into the realm of the unseen. The atom, for example, at the beginning of the century was only a possibility, not embraced by many. By the end of the century the atom was a concept gaining strong support. Dalton, in 1808, introduced atomic theory and it took a century for the diverse derivations it gave birth to finally crystallize into a uniform model. Ironically the chemists were slow to accept the concept as a physical reality. It was the physicists, like Avagardro, who imagined the atoms physical nature and stated that any litre of gas at a standard temperature and pressure would have the same number of atoms. This quantity is called Avagardro's number. Its experimental measurement was a convincing proof of the reality of the atom. As an example of Einstein's independent work he looked into the effects a fluid of atoms should have on small particles floating within it. A very small particle suspended in a fluid should be jostled about by the random motion of the neighbouring atoms. This is indeed the case. Einstein developed mathematical formulae that described the random path of the small particles. This led to an independent derivation of Avagardo's number and a measure of atomic size. The first published account of an experiment to measure the motion was by Brown, a century earlier. The random walk motion of the particle bares his name, Brownian motion. Einstein was not aware of the published work. He used his research to come up with three independent derivations of Avagardo's number. His work was one of many that eventually led to the support of the atomic theory. His PhD thesis was on the deviation of atomic dimensions, and of all his papers, it is his most cited.
In the decade preceeding relativity the electron was discovered. One of Einstein's early contributions to physics was a study that involved stripping electrons from atoms using light. It was through this study that he deduced that light comes in the form of little packets of energy, light quanta. This was the early days of the quantum theory. Einstein was one of its founding scientists. The development and successes of the quantum theory were to haunt Einstein all his life. He was ironically never comfortable with the deviation of the theory from a more Newtonian, deterministic philosophy.
The nineteen century was also a period when mathematicians dared to think of introducing new geometries. Geometries that deviated from those laid down by the ancient Greeks, and before. The Greek Euclid, about 300BC, has had a profound influence, and his texts are still the reference for practical geometry today. The new geometries of the nineteenth centruy described new dimensions beyond the third dimension. Mathematicians such as Gauss and Reimann developed new mathematics to handle these new geometries. Also some abstract questions were beginning to be asked about the nature of space and its geometry. Mach, a German physicist asked the profound question, if the earth was the only thing in the universe would it be possible to determine if it were rotating. Faucault build an enormous pendulum in Paris that left swinging for a day could reveal the rotation of the earth. What medium beyond the earth was the pendulum taping into to permit it to swing in a fixed plain? The nature of the physical universe, at the end of the nineteen century, was starting to pose awkward questions, about the best technique to use to describe space, for the enquiring minds.
The nineteenth century was the century of light. Newton and Huygen, had began the study, but it was left to scientists a century later to find some of its more intriguing properties. It was the examination of light and its properties which lay the foundation for Relativity at the beginning of the twentieth century. In 1851 Fizeau developed experimental confirmation for Fresnel's equations which showed that, multiple velocities cannot be added together, as Newton would have expected. In 1873 light was found to be a wave of oscillating electric and magnetic fields, described very elegantly by James Maxwell's empirical equations. This raised the question "what did this wave propagate through?". All other waves had a medium through which they traveled. Sound waves need air, ocean waves need water, a violin string wave needed a violin string. What was the material through which light traveled? This invisible, all pervading medium was called the aether.
The velocity of light had been measured to great accuracy by the mid nineteenth century. Traveling at approximately 300 000 km/s through the aether, it was by far the fastest thing known, though some were surmising that gravity was substantially faster. An experiment was devised to measure the motion of Earth through the aether, using light as a reference. If the aether was like an ocean filling the universe, and was absolutely stationary, then light should have different velocities relative to the earth depending on which direction the light was traveling. Just like a bird flying through the air will have a different velocity when viewed from, or relative to, a moving car depending on weather the bird is flying with or against the motion of the car. Michelson and Morley devised an extremely accurate experiment to try and measure these difference relative velocities of light. The experiments found no difference. Light was found to always have the same velocity independent of its direction through space, or the motion of the earth. The conclusion sat very uncomfortably with the experimenters. It was impossible to measure the motion of the earth through the aether. The aether did not seem to be there. But what then is the light traveling through? It would take a quarter of a century before an answer was found.
It is intriguing that in the decade before relativity all the evidence necessary for its development were in place. Yet no one made the necessary leap to a new physics. Some scientists though were taking steps in the right direction. George Francis Fitzgerald predicted that all objects contract in length, in the direction they are traveling. The reasoning for the contraction was thought to be some type of resistance imposed by the aether and the contraction was absolute not relative. Lorentz independently came up with empirical mathematical descriptions for these properties, developing them from the results of the Michelson and Morley experiment. The mathematics hinted at a new geometry for space, but the mathematical expressions were considered to be only a convenient description of what was happening in the experiment. It was difficult to associate any physical reason for the equations. The French scientist Poincare was on the verge of seeing the need for a new mechanics that did not depend on absolute time, a definite requirement for Relativity. It was however Einstein who independently derived the Lorentzian transformations, and imagined the need for time to be a relative quantity. If time and space were made flexible then a self consistent theory could describe the peculiar properties of light without the need for the aether. It was an amazing achievement. It would also go onto predict many new peculiarities of the physical universe that had never been observed before.
Then came Einstein
One of Albert Einstein's greatest traits was his independence. As a child he was a loner, not interested in the stringent schooling system. A teacher once remarked to Einstein that he would prefer if he were not in his class. He said to a bemused Albert
"... you sit in the back row and smile, and that violates the feeling of respect which a teacher needs from his class"
Aside from this Einstein was a brilliant student, often topping his class. He was not good at French, though in later life he was know for his eloquence in German, his native talk. He spent much of his teen years reading mathematics and physics for pleasure. A profound moment was when he received a book on Euclidian Geometry. Much of his early schooling was in Munich. He later took steps to leave school and do self study so that he could sit the entry exam for a university in Zurich, partially in a move to avoid military service in Germany. He was eventually accepted into the ETH Zurich. It was during these Zurich years that he started to develop friendships that would last his lifetime. One of the notable friendships was with Marcel Grossman, a fellow student. However for the most part he remained a loner, relying on his own interests to drive his independent study.
Einstein finished university at the turn of the century. For a year he worked in a few teaching jobs while writing his PhD thesis on the kinetic theory of gases. In 1901 he submitted it and it was subsequently rejected. Mid 1902 he accepted a position at the patent office in Bern. Grossman, through his father, was influential in Einstein receiving this job. A position that allowed Einstein the time necessary for him to pursue his research, and publish papers. 1903 to 1904 he published papers on statistical mechanics. In 1905 he published a paper on the photoelectric effect, for which he was to receive the Nobel Price fifteen years later. 1905 was also the year he resubmitted his doctorate thesis, which was finally accepted by the university in Zurich. As great as these achievements are, 1905 was also the year he published his theory of relativity.
The Lorentzian transforms hinted at the need for relative time. A concept of time that made time dependent on the relative motion of objects. This led to the need for relative space. Poincare was hinting at this in the same year that Einstein published his theory. It would seem that the realization that space and time should be seen as relative quantities was a thought ripe for the picking.
When Einstein published his theory he was a little know scientist living in effective isolation. The library in Bern had limited resources which made accessing recent research papers difficult. This being said it seems that Einstein had little interest in literature surveys, and rarely cited other research within his works. When relativity made its quiet entry into the world, Einstein was a little concerned about the immediate lack of interest. This lack of interest was not surprising considering the magnitude of the work and the number of people capable of understanding it. His disappointment was quickly squashed when he received a letter from the German physicist Max Plank. Plank was a world leader in his field, and he wrote to Einstein to acknowledge his interest in the work and to ask some questions. Einstein was delighted. He was soon giving invited lectures on his new theory.
Another astounding aspect of this first paper on relativity was that it presented a complete theory. In its few pages the paper contained a self-consistent theory without mistakes or any need for extension. Within it was all that was necessary to place physics on a new path in the twentieth century. The paper defined two axioms
the velocity of light is always a constant
all uniform motion is relative.
The whole theory is based on these two axioms. Most of what is presented in this course over the following weeks shall be derived directly from these axioms, and it is the objective of this course to illustrate many of the effects that result from them. For example, Einstein eventually derived his most famous equation E = mc2 from these axioms. This equated mass with energy, and cleared the way to explaining how the interior of a star, like our Sun, can create enormous energies for billions of years. However these axioms are restrictive in the extent of natural processes they can explain. Soon after publishing his Special Theory of Relativity Einstein started work on a more general theory. It took him a further ten years work. This theory took into account the effects of acceleration and gravity. He called it the General Theory of Relativity. It was a theory that could be used to explain the precession of Mercury's orbit. Today in astronomy General Relativity is a constant companion when trying to explain the nature of the cosmos and the path of light through it. It is essential when explaining the time dilation effects of a black hole, and the orbits of neutron stars. We would not have GPS without the General Theory of Relativity.
Though Einstein's theory may seem remote and not relevant, it is here in the passing of very second, in the fall of a leaf, and in the rising of the Sun. In the coming weeks we shall explore many of its fascinating details and see examples of its presence in our everyday lives.