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 apparent even to him. In hindsight though, it is not surprising that his new description of space and time was to be extremely influential. The theory describes two of the inherent properties shared by everything in this universe; space and time. Everything must sit in space and ride on time. To date one has found any aspect of relativity to be inconsistent with experiments or observations.
When relativity made its quiet entry into the world, in June 1905, the time was ripe for a revolution. In the decade preceding Einstein's first paper on relativity the foundations on which previous thinking about the physical universe were beginning to crumble. As with many leaps in understanding 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 conceptual leap to the theory of relativity. Einstein, in isolation and working 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 then accepted 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 this revolution of ideas and, when Einstein's status as a twentieth century genius had been 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, especially size, time, mass etc. It is true that he developed a theory which better describes the relationship between these physical quantities than did Newton. It is also true that Newton's work is still fundamental in science and engineering today, and that the revolution he began was of a significant magnitude more profound than was Einstein's. Newton was able to describe the readily observable physical universe with his theories and mathematics in a way which accorded with human intuition. To do this Newton assumed the existence of absolute time and absolute space. Einstein went beyond the intuitive and introduced to us a description of the universe that is counterintuitive, and even seems bizarre, being 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 is self-consistet. A century since it was introduced to the world no one has managed to disprove it, or to find a better more elegant description.
In the following notes I wish to present a brief outline of the times, thinking and influences that led Einstein to develop his extraordinary theory.
Nineteenth Century Thinking.
In 1682 Newton published his laws of mechanics and gravity. His mathematical descriptions of the way things move here on Earth, and how the planets orbit the Sun, seemed to be perfect. His model was central to the discovery of Neptune in 1846. It was predicted to exist through the application of Newton's laws of gravity to the unusual motion of the planet Uranus. Uranus had been discovered 70 years prior, and its path was under continual examination. The unusual motion of Uranus about the Sun had led some to question Newton's law of gravity. While these laws described the motion of the other planets exceedingly well, Uranus was a disturbing exception. However, there were those within the scientific community who were not willing to part with Newtonian physics, and who sought to find an explanation through the application of his laws. Two such men were LeVerrier of France and Adams of England. They worked independently, and bother assumed that a planet of equal mass to Uranus was gravitationally pulling on it from a more distant orb. Their assumption proved to be correct, and by using Newtown's physics, and mathematics, they successfully predicted both the existence, and the location, of the unseen planet. Le Verrier was only just able to beat Adams to the discovery by using better equipped astronomers. This new planet was discovered on the same night the astronomers in at Berlin were given the predicted location. This further bolstered the confidence of the scientific community in their ability better to understand the universe.
The nineteenth century saw many discoveries in the realm of the previously unseen. The atom, for example, was at the beginning of the century thought of only as a possibility, and not embraced by many. By the end of the century by contrast the atom was a concept gaining strong support. Dalton, in 1808, introduced atomic theory, but it took a century for the diverse derivations it gave birth to finally crystallize into a uniform model. Ironically chemists were somewhat slow to accept the concept as a physical reality. It largely was in physics, that the model progressed, such as by Avagadro, 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 Avagadro's number. Its experimental measurement was a convincing proof of the reality of the atom. As an example of Einstein's other work, he examined 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 was observed to indeed be the case. Einstein developed mathematical formulae that described the random path of the small particles. This led to an independent derivation of Avagadro's number and a new measure of atomic size. The first published account of an experiment to measure this motion was by Brown, a century earlier. The random walk motion of such a particle bares his name, Brownian motion. While Einstein was not aware of this published work, he used his research to come up with three independent derivations of Avagadro's number. His work was one of many that eventually led to 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 preceding 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, called light quanta. This was the early days of the quantum theory. Thus Einstein was one of its founding scientists. The development and successes of the new quantum theory were to haunt Einstein for his remaining life, and somewhat ironically he was never comfortable with the deviation of the new theory from the more Newtonian, deterministic philosophy.
The nineteen century was also a period when mathematicians dared to think of introducing new geometries. Geometries were developed that deviated from those laid down both by the ancient Greeks, and those before them. The Greek Euclid, about 300BC, had a profound influence in this area, and his texts are still the primary reference for practical geometry today. By contrast the new geometries of the nineteenth century described new dimensions beyond the observable thress was see around us. Mathematicians such as Gauss and Reimann developed new mathematics to handle these new geometries. Abstract questions were also 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. Foucault built an enormous pendulum in Paris that, left swinging for an entire day could reveal the rotation of the Earth. What medium, therefore, beyond the Earth was the pendulum tapping into to permit it to swing in such a plane? The nature of the physical universe at the end of the nineteenth century was starting to pose awkward questions, about the best technique to use to describe space.
The nineteenth century was the century of light. Newton and Huygens, had begun the study, but it was left to scientists a century later to discover some of its more intriguing properties. It was the examination of light and its properties in the nineteenth century, for example, 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's laws had predicted. 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 of "what substance such a wave could be propagating through?". All other known waves had a medium through which they travel. Sound waves need air, ocean waves need water, a violin string wave needed a violin string. What was the material through which light travels? This invisible, all pervading medium was given a name the aether.
By the mid nineteenth century the velocity of light had been measured with a great degree of accuracy. Traveling at approximately 300 000 km/s through the aether, it was by far the fastest thing then 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 a different velocities relative to the Earth depending on which direction it was traveling. In the same way, for example, 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 measure these different relative velocities of light. The experiments however found no difference! Light was found to always have the same velocity independent of its direction through space, or the motion of the Earth. This 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 to be found in the theory of relativity.
It is intriguing that in the decade before relativity was published all the evidence necessary for its development was in place. Yet no one had made the necessary leap to a new physics. Some scientists 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 behind this was thought to be some type of resistance imposed by the aether and that 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 new expressions were considered 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 the development of relativity. It was Einstein however who independently derived the Lorentz 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 aether. It was an amazing achievement. It would also go onto predict many new peculiarities of the physical universe that had never before been observed.
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 at the top of his class. He was not good at French, however, although in later life he was known for his eloquence in German, his native tongue. He spent much of his teen years reading mathematics and physics for pleasure. A book on Euclidean geometry, given to him by a family friend, was to have a profound influence on him. Much of his early schooling was in Munich. He later took steps to leave school and to self-study in order that he could sit the entry exam for university in Zurich, partially 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 these 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, but it and it was subsequently rejected. In mid 1902 he accepted a position at the patent office in Bern. Grossman, through his father, was influential in Einstein receiving this job. It was a position that allowed Einstein the time necessary for him to pursue his research, and publish papers. From 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 now best known as also the year he published his theory of relativity.
The Lorentz transforms hinted at the need for relative time, a concept of time that made time dependent on the relative motion of objects. This also leads to the need for relative space. Poincare was hinting at this in the same year that Einstein published his new theory. The realization of both space and time seen as relative quantities was a thought ripe for the picking.
When Einstein published his theory of relativity he was a little known scientist living in academic 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 somewhat 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 quashed when he received a letter from the noted German physicist Max Planck. Planck 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 invited to give 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 entire theory is based on these two axioms. Most of what will be 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 equats mass with energy, and cleared the way to explaining how the interior of a star, such as our Sun, can create enormous amounts of energy for billions of years. However these axioms are restrictive in the extent of the set of natural processes they can explain. Soon after publishing his theory of special relativity Einstein started work on a more general theory. It took him a further ten years to complete this work. This new theory took considered the effects of acceleration and gravity. He called it the general relativity. It was a theory that could be used to explain the precession of Mercury's orbit, for example. 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 every 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.