Mathematical Aspects Of Einstein's General Relativity Theory example essay topic

Albert Einstein: Great Scientist, Curious Man In the study of a scientist's life, it is important to recognize several key elements. Scientific contributions are of utmost importance. Following mention of those, it is then possible to look at his or her life, family, and religion as well. However, for Albert Einstein, these elements must all be looked at collectively. Einstein will no doubt go down in history as a great theoretical physicist. His work is compared in importance to that of scientists such as Galileo Galilei, Nicolas Copernicus, Johannes Kepler, and Isaac Newton.

Some would even say that his contributions to science were greater. However, it is impossible to paint a complete picture of Einstein without examining his life, his religion, and his personality. His science was his life, and his religion gave him insights as to how to approach science. By observing his innate curiosity, desire for simplicity and elegance, humble outlook, and desire to seek answers, we can see what elements reached the center of his being. Though Einstein was one of the greatest contributors to physical science of our times, he was by no means the most brilliant theorist or experimenter. Competent specialists within the field of physics could have better accomplished some of his mathematical deductions.

In fact, he needed the assistance of a friend, mathematician Marcel Grossman, to wield the tools necessary to develop his general theory of relativity. Einstein shined brightest within a theoretical context, but, despite the fact that his relativistic theories were most revolutionary, the study of quantum mechanics made a larger impact on the way physics is studied today. What, then, set Einstein apart? Curiosity was the key factor. As Einstein said, "I have no special gift – I am only passionately curious' (Hoffmann 7). His curiosity gave him the ability to immediately get to the center of a problem, search with vigor for a satisfactory solution, and then find a new question to address.

Einstein's desire to find new questions and their answers surfaced in his youth. He was born on March 14, 1879, in the small town of Ulm, Germany. His father, Hermann Einstein, was a practical and thoughtful man whose ambitions led him to set up an electrotechnical factory in Munich after Albert's birth. His mother, Pauline Einstein (nee Koch), looked after the family and was a very talented musician. The move to Munich occurred when Albert was a year old, and his sister Maja was born a year after that. Both children attended a Catholic elementary school.

However, the Einstein family was Jewish, and Albert took his Jewish beliefs very seriously. He often observed the dietary practices more strictly than his father, and neither he nor his sister let go of those beliefs. His belief in God was important to his science, since he often asked himself the question, "How much choice did God have in constructing the universe?' (Hawking 174). By contemplating whether or not God would have designed the universe a certain manner, Einstein could use his sharp intuition to develop simple and elegant ideas. At the age of 10, Einstein began attending school at the Luitpold Gymnasium. Although he was typically bright in school, his teachers did not think kindly of him, and the school's promotion of rote learning adversely affected his learning.

In fact, one teacher, Albert's Greek teacher, told him "You will never amount to anything' (Hoffmann 20). Because of Einstein's formal schooling difficulties, much of his early study was independent. At age twelve, he learned of the Pythagorean Theorem, developed a method of proving it, and began to study in depth a booklet on Euclidean geometry. A consequence of his scientific awakenings, though, was that he became extremely skeptical of religion, noting conflicts between religion and science. He did not abandon Judaism; he just became a skeptic of authority. He later recalled that "To punish me for my contempt for authority, Fate made me an authority myself' (Hoffmann 24).

This skepticism did nothing to improve the impressions he made on his teachers. At the age of fifteen, he decided to rejoin his parents, who had since left for Italy. After a year spent in Italy, he decided to continue his education by applying to the Zurich Polytechnic in Switzerland. However, he failed the entrance exams and instead entered a cantonal school in Aarau, Switzerland. Heinrich Weber, a physics professor at the Polytechnic, also agreed to let Einstein attend his lectures there, providing further encouragement. At the Aarau school, Einstein found a much better atmosphere for learning.

After completing his studies, he entered the Polytechnic, but found he was more preoccupied with independent excursions into science. Lectures were a bore to him, and he had to cram from a friend's notes to pass a few of them. By utter coincidence, this friend was Marcel Grossman, the man who would help shape the mathematical aspects of Einstein's general relativity theory. Einstein graduated from the Polytechnic at the age of twenty-one. With his graduation, Einstein had to seek means to continue his research. Finding no teaching positions, he settled for positions tutoring and performing calculations.

In the meantime, he wrote a research article on capillarity that was his first to be published. The important journal Annalen der Physik published it, and though Einstein declared it worthless, it was his first of a series of many that would revolutionize physics. This paper was sent out to many professors to aid Einstein in getting a job, but it yielded no results. Though he remained content with life through his two other passions, music and the violin, he had to find other means. In 1901, his friend Grossman again came to his aid. He recommended Einstein for a position in the Bern Patent Office, where Einstein was to spend many years working efficiently to make time for his private research and calculations.

He was hired at this office because the interviewers were impressed with his knowledge of Maxwell's electromagnetic theory, a rare mastery. While waiting to start, he wrote a research paper on thermodynamics that was published in Annalen der Physik, but this was rejected as a Ph. D. thesis. Despite this, Einstein's steady job was all he really needed to continue his work, which continued to blossom. Einstein used tutoring as another source of income. An important phase of his life occurred when Maurice Solovine, a philosophy student, sought Einstein to learn more about a concrete subject such as physics. An involved discussion ensued, and when a mathematician friend, Konrad Habicht, joined them, they named the group the "Olympia Academy.

' This group would discuss topics in all disciplines, and was a source of inspiration and amusement for Einstein. Later, Solovine would be the man responsible for translating Einstein's books into French. This Academy provided Einstein with many fond memories for the rest of his days. In late 1902, Einstein's father died, a loss that he described as the deepest shock he ever experienced. Once again, Einstein turned to science.

In that year, he completed another scientific paper that was published in Annalen der Physik. Within the next two years, he published two more papers that also dealt with thermodynamics. This thermodynamic work aided him with his work in the Patent Office. He often had to examine models of perpetual motion machines, which are thermodynamically impossible. Meanwhile, he married Mile va Magic, a former classmate at the Zurich Polytechnic, in 1903. She bore him two sons: Hans Albert in 1904 and Eduard in 1910.

Finally, in the year 1905, Einstein wrote four major papers that are among his most revolutionary. These were to be exchanged with his Academy friend Habicht, who had lost touch with Einstein over the years. As Einstein promised, the impact of these papers on science was quite dramatic. Einstein's first paper was quite revolutionary. In it, he examined an ever-present conflict in physics involving light. Isaac Newton studied it and devised a corpuscular theory stating that light is made of particles.

Introduction of electromagnetic concepts, however, led scientists to explore the possibility that radiated light behaves in a wavelike manner. What Einstein realized was that since matter possesses atomicity and radiation doesn't, a clash occurs if they are treated collectively. He theorized that light should be thought of as consisting of particles. He found that the entropy of radiation is best described by the entropy of gas particles, and then he showed that the ratio of energy vs. frequency would equal Planck's constant. Next, he applied his particle ideas to the phenomenon of the photoelectric effect. He showed that the higher the energy of incident light, the faster electrons would be ejected from a metal.

This made no Maxwell ian sense at all, but Einstein was able to derive extremely simple photoelectric formula that transcended the current knowledge of his time on the subject. Another consequence of Einstein's quantum research in this area was interest of the scientific community in quantum mechanics, a science Einstein would dismiss as too in deterministic. From these discoveries, Einstein was to receive a Nobel Prize. Einstein regarded his second paper of 1905 as relatively unimportant. In it, he calculated a way of determining the size of molecules and found a value for Avogadro's number.

By analyzing diffusion rates of particles through liquids, he devised a simple model that facilitated his calculations. He submitted this paper for a Ph. D. thesis, and upon being told it was too short, added a sentence. It was thus accepted, and Einstein finally earned his Ph. D. His third 1905 paper was more important. In it, Einstein pondered the interactions of particles in air and the related statistical consequences. He did not realize that he observed Brownian motion, but what he found was that the molecular theory of gases and Brownian motion both posses a key quantity that shares the same numerical value. Einstein had found an important symmetry, and his inspirations to find this symmetry were his curiosity and his need to find answers.

Even at an early age, Einstein contemplated what light would look like if one moved alongside it. In Einstein's fourth 1905 paper, "On the Electrodynamics of Moving Bodies,' he introduced his revolutionary special theory of relativity and addressed this curiosity. Relativity is an especially revolutionary idea because some basic assumptions about the nature of light had to be ignored, and new ones made. Previously, space, time, and distance were considered absolute, and Newton made his laws in accordance with these assumptions.

Einstein asserted, instead, that space and time are not absolute, but the speed of light is. This implies that there will be disagreement between observers at different velocities on the distance light travels and the time it takes, but each set of calculations should yield the same constant speed of light. To explain this warping of time, Einstein determined a formula using a simple coordinate transformation that quantifies time dilation. This formula is: T = To / (1- (v^2/c^2) ) ^. 5 This equation shows two major things. First, if there is any velocity difference between two moving observes, there will be a difference in their perceptions of time.

Second, it shows that the speed of light is a universal limit. If one were to travel at velocity c, the time passed on a "stationary' Earth would be infinite... Einstein finally showed that Maxwell's equations conform to relativity, and after mathematically verifying all of this, he concluded the revolutionary work. More revolutionary work was to come. Einstein's next paper, published in 1907, showed that all mass consists of energy. Using his electromagnetic equations, he found that if a body releases E in energy, its mass decreases by E / c^2.

He then finalized his theory that E = mc^2, showing that all matter possesses a proportionately large amount of energy. Only later in his life would Einstein realize the true significance of this mass-energy conversion. Einstein soon became well known in the world of science. He took a teaching position in Bern, but quickly became a professor at Zurich University. He shortly moved to the Zurich Polytechnic, but this was not to last. He was elected to the Prussian Academy of Science and was assigned the directorship of the Kaiser Wilhelm Institute in Germany.

Soon afterward, though, World War One began, and Einstein quickly made his beliefs known. He was still of Jewish faith, but he supported the ideas of Spinoza, a man who accepted all nature as God, as Einstein did. In each of Einstein's ideas, he always gave thought to how God would have planned the universe. Also Einstein vocally supported pacifism. All his life, he sought to encourage nonviolent solutions to problems, and war ran against this belief. Again, he turned to his science to maintain focus.

Since the world of politics brought him no answers, science had to once again. During the war years, Einstein expanded his theory of relativity to a general case. Since he revolutionized the concept of space-time in his previous works, he decided to look into how gravity, light, and acceleration behave relativistically. Ultimately, he asserted that acceleration is relative, one can't tell the difference between a gravitational force and a uniform acceleration, and that gravitation bends light rays. This bending was experimentally verified by observing an eclipse of the sun, and is also evident in the apparent "red shift' of electromagnetic radiation. Einstein then used tensor calculus (with the help of his friend Grossman) to determine sixteen field equations: ten which are gravitational and six of an electromagnetic nature.

Einstein considered his relativity theories to be his true life's work. For a large part of his life, he would travel the world in support of these theories. In 1919, Einstein's mother died, providing yet another shock in Albert's life. Also, in that year, he divorced his wife and remarried five months later. His second wife, widow Elsa Einstein (a second cousin), had two daughters from her first marriage, Ilsa and Margot. Meanwhile, in the political arena, the German Kaiser abdicated, and the new nationalistic ideals of Germany began to operate against Einstein due to his pacifism and Jewish beliefs.

Einstein traveled to America in 1921 to raise funds for a university in Jerusalem, again showing his convictions. He was well received, and lectured at length on relativity there. He then returned to Germany, but left his home temporarily due to death threats. A trip to Japan followed, where again he was well received. While there, he learned of his Nobel Prize, awarded to him because of his contributions on the photoelectric effect. At his acceptance, though, he spoke on relativity.

Evidently, he felt compelled to promote this aspect of his work. Einstein's fiftieth birthday soon arrived. This was widely celebrated, much to Albert's dismay. He and Elsa were "given' land in Caput h where the family lived away from the academic atmosphere of Berlin. However, he moved back to Princeton in 1933 upon the Nazi incursion. At that time, the Germans seized his possessions, and revoked Einstein's citizenship after he had already done so.

He lived in Princeton for the remainder of his life. In 1939, again supporting his pacifist ideals, Einstein signed a note sent to President Roosevelt noting the reality of atomic power as well as its deadly potential. Numerous verifications of his mass-energy conversion theory prompted this action. Its deadly potential was realized when, in August of 1945, Hiroshima and Nagasaki became the first targets of an atomic bomb. "Alas' (Hoffmann 210) doesn't adequately express Einstein's dismay upon these occurrences. Einstein's next main concern was continuing his activistic and scientific work.

In 1945, he began a study on the age of the universe, refuting the current estimate. Also, he developed the idea of a cosmological constant. He later acknowledged this as being the biggest mistake of his life. He spent the rest of his days searching for a unified field theory that connected gravity, electromagnetism, and the nuclear forces. This search was unsuccessful, as the current knowledge of nuclear forces was inadequate. This search continues even today.

Einstein continued to speak politically. He made several public gestures supporting Zionism and pacifism, and he was even offered the presidency of Israel in 1952. He declined, citing inexperience in politics. Possessing a stronger duty to science, he stated that "Equations are more important to me, because politics is for the present, but an equation is something for eternity' (Hawking 178). Shortly thereafter, he fell ill, and on April 18, 1955, Albert Einstein died. He left behind the legacy of a man who altered the face of physics as we know it.

What he didn't leave behind was a shrine or place of burial. Even in death, Einstein existed humbly, showing the manner of man he was. Albert Einstein's lifelong quest was to seek the answers to questions his curiosity posed. His religious inspirations and intuitive nature helped set him apart from other scientists, and aided him in finding the solutions he sought. He was just as unique a man, possessing a world view many have come to respect. In short, Einstein was a man who was much greater than the sum of his equations.

It is in this light that he will be forever remembered. It is also because of this truth that Einstein is considered one of the most revolutionary men of our time.

Bibliography

Duxbury, Philip. "Physics concepts, physics careers' lecture notes. East Lansing, 1996.
Hawking, Stephen. A Brief History of Time. New York: Bantam, 1988.
Hoffmann, Banish (with Helen Dukas as collaborator). Albert Einstein: Creator and Rebel. New York: Viking, 1972.