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Werner Heisenberg and the Heisenberg Uncertainty Principle Werner Heisenberg, born in the dawn of the twentieth century became one of its greatest physicists; he is also among its most controversial. While still in his early twenties, he was among the handful of bright, young men who created quantum mechanics, the basic physics of the atom, and he became a leader of nuclear physics and elementary particle research. He is best known for his uncertainty principle, a component of the so-called Copenhagen interpretation of the meaning, and uses of quantum mechanics. Through his successful life, he lived through two lost World Wars, Soviet Revolution, military occupation, two republics, political unrest, and Hitler’s Third Reich. He was not a Nazi, and like most scientists of his day he tried not to become involved in politics. He played a prominent role in German nuclear testing during the World War II era. At age twenty-five he received a full professorship and won the Nobel Prize in Physics in 1932 at the age of thirty-two. He climbed quickly to the top of his field beginning at the University of Munich when his interest in theoretical physics was sparked Heisenberg was born the son of August Heisenberg in Würzburg, Germany on December 5, 1901. August Heisenberg was a professor of Greek at the University of Munich. His grandfather was a middle-class craftsman who’s hard work paid enough to afford a good education for August Heisenberg. The successfulness of August Heisenberg allowed him to support his family well. The professorship at the University of Munich put them in the upper middle-class elite, and was paid three times the salary of skilled workers. Through his life Werner Heisenberg was pestered with health problems. At the age of five, he nearly died with a lung infection which helped him get a little preferential treatment from his parents. During his early years, Werner was in constant competition with his brother Erwin which caused friction. The Heisenberg family were accomplished musicians. Every evening they would sit and practice together. August was on the piano, Erwin played the violin, and Werner played the cello. Their mother insisted that she had no musical talent as an excuse to not be involved in the male competition. Later Werner also learned the piano and used his musical talents as a social vehicle during the course of his life. This manly competition carried out in many other activities in the house. Sometimes August Heisenberg would make games out of difficult homework problems that the boys had. Werner once said when reflecting back on his childhood, "Our father used to play all kinds of games with [us] …. And since he was a good teacher, he found that the games could be used for the educating the children. So when my brother had some mathematical problems in his schoolwork …. he tried to use these problems as a kind of game and find out who could do them quickly, and so on. Somehow, I discovered that I could do that kind of mathematics rather quickly, so from that time on I had a special interest in mathematics." This constant competition caused many fights between the brothers. As they grew older the fights became more vicious. One time the fight became particularly bloody where they beat each other with wooden chairs. After this confrontation the brothers called a truce and hardly interacted with each other except for occasional family get togethers when they were adults. In school, Werner began to show his amazing ability early on. He excelled through school and always received complementary remarks from his teachers. As a result from the competition with his brother he developed a hard work ethic and a strong drive to succeed. Even though Werner was not a good runner he would run around the track timing himself with a stopwatch trying to improve his running times. A teacher of his once said, "The pupil is also extraordinary, self-confident and always wants to excel." Werner Heisenberg excelled in math, physics, and religion in which he consistently received 1’s (the equivalent of A’s). The subjects that he did not fair as well in were German and Athletics which he usually received 2’s (or B’s). At the age of thirteen one of his teachers noted that his interests were moving to more "physical-technical things". This change in interests moved Heisenberg along the path from the geometry of objects into the realm of theoretical physics, especially the mathematical analysis of physical objects and data. As a pupil at the Gymnasium, he was intrigued by Einstein’s theory of relativity and it’s explanation. He later recalled that mastering the mathematics in Einstein’s book gave him no difficulty. At the age of sixteen he tutored a 24 year old university calculus student to pass her final examination. Having no previous knowledge in calculus, he set out to teach himself so in turn he could teach the woman(by 1903 women were accepted to study at the University of Munich with the equal opportunities of men). During the three month time period he was able to teach the woman enough to pass her examination. Heisenberg said, "And in that time I didn’t know whether she had learned it, but I certainly had." In the Summer of 1920 Werner Heisenberg graduated Munich’s Maximiliams-Gymnasium and entered the University of Munich the following Fall. Not yet knowing which field of study he wished to commit to, his father arranged an appointment for Werner with Ferdinand von Lindemann, the professor of mathematics at the University of Munich. When he arrived for the appointment he saw the older professor sitting in his dimly lit office with his poodle hiding under his desk. When Heisenberg began to speak, the dog started to bark. For the duration of the entire conversation, the dog kept yapping. In the brief conversation Lindemann only asked a few questions of Heisenberg, one of which was what books he had been reading. Heisenberg responded with Weyl’s Space, Time and Matter, through the noise of the dog Lindemann closed the conversation with, "In that case you are completely lost in mathematics." Rejected by Lindemann, Werner’s father decided that he should try his hand in theoretical physics. In his first meeting with Sommerfeld, he also asked Heisenberg which books he had recently been reading. Werner replied with the same answer but Sommerfeld’s response was completely different, saying, "You are too demanding… You can’t possibly start with the most difficult part and hope that the rest will automatically fall into your lap." The first semester that he attended at the University of Munich, Werner was conscientious not to sign up for too many theoretical physics classes just in case he found out that he was not cut out for it. He took a couple theoretical physics courses and the rest were math classes. By the next semester, it was not an issue anymore and he signed up for all of Sommerfeld’s course offerings. When Heisenberg first devoted himself in Sommerfeld’s department, Sommerfeld was struggling, trying to find an explanation for the behavior of optical spectrums emitted by atoms. When white light is sent through a spectrum, each color corresponds to a different band of frequencies. If the atom if one element are stimulated by heat or high voltage they will emit not an entire spectrum of radiation but only certain colored lines corresponding to certain definite frequencies of light characteristic of that element. One year later, Heisenberg presented his atomic "core model" of complicated atoms that resolved every spectroscopic riddle in one stroke and still saved the phenomena. This model worked only because he disregarded all other previous explanations. This model was way too controversial for widespread acceptance of his theory. In the duration of the first two years that he attended the University of Munich he published four physics research papers, submitting the first one eighteen months after graduating at the Gymnasium. Three of the papers dealt with atomic spectroscopy and one with hydrodynamics. These papers thrust Heisenberg at the ripe age of twenty to the forefront of quantum atomic physics research. This extraordinary achievement was largely due to the marvelous training that he received from his university mentor, physics professor Arnold Sommerfeld who was well respected in his field. Sommerfeld was the first of many men to influence Heisenberg and his research of quantum mechanics. During that time period Bohr-Sommerfeld made a quantum theory of the atom that utilized a puzzling combination of classical and quantum notions that only somewhat seemed to work. By the conclusion of World War I experimental techniques improved and many physicists tried to improve the inadequate theory and overcome its limitations. Heisenberg fully participated in all of these experiments. These new mechanics and its Copenhagen interpretations achieved by the end of 1927 were combined with other innovations such as the electron spin and the exclusion principle. These new innovations opened up the realm of the atom and enabled entirely new and profound advances in understanding all aspects of the physical world, from nuclei and quarks to the big-bang theory which had profound implications for the world in which we live, from philosophy to the technology of nuclear reactors, atomic bombs, semiconductors and superconductivity. Heisenberg played a leading role in many of these developments from the moment he entered the University of Munich as an eighteen year old student. In October of 1921, Heisenberg traveled to Jena for his first physics conference. He was able to briefly meet many top physicists in the world at that time such as Max Planck, and Max von Laue. Unfortunately, to his dismay, Albert Einstein was unable to attend this conference. During the nineteenth century German physicists concerned themselves more with the experimental side of physics such as Newtonian Physics. By the twentieth century the transformation from experimental physics to theoretical physics such as Einstein’s theory of relativity were slowly taking place. Sommerfeld accepted a guest professorship at the University of Wisconsin the second year that Heisenberg attended the University of Munich. With his mentor in the United States, Werner decided to travel to Götingen to study with Professor Born. While in Götingen, his parents supported him monetarily while he experienced much more knowledge in the field of theoretical physics. After a while he was offered a job as an assistant with a generous salary of twenty-thousand marks a month. As an example of inflation and political unrest inflation had brought the average wage of a skilled worker twenty years prior from a little over one-thousand marks a year to twenty-thousand a month for a professor’s assistant. In May 1923, Professor Sommerfeld returned to the University of Munich and so did Heisenberg. During Heisenberg’s time in Götingen Born and Heisenberg did extensive studies on the helium atom. This research yielded a strictly orthodox helium calculation that gained widespread recognition which was the beginning of the end for the earlier successful Bohr-Sommerfeld quantum theory of the atom. They modeled this research off of the Balmer formula for the case of the outer helium electron and treated the excited helium electron the same as a hydrogen electron. After a very successful three years of study at the University of Munich, Heisenberg prepared for his oral examination for his doctorate. The format had four professors to ask four questions on three subjects. These subjects were Math, Astronomy, and Physics. The physics department at the University of Munich was split between experimental physics and theoretical physics and therefore he would be asked two physics questions and would only receive one grade in which both professors would have to agree on. In math Perron gave him a I for his explanation of the mathematical question. Seeliger asked the astronomical question that he received a II. For physics, Sommerfeld, head of theoretical physics, gave Heisenberg a I and Wein, head of experimental physics, gave him a V which is not passing. Heisenberg had had a confrontation with Wein the previous semester when he made his final project for the class out of cigar boxes and cardboard. During the final examination he was biased in his question as well as his grade. The average of his physics score became a III which was fairly disappointing. The final score for Heisenberg’s oral examination was a III which is equaled to a ‘C’ in the American grading system. August Heisenberg was troubled by Werner’s low score and wondered if physics was the correct field for him to be in. Werner shocked by his surprising score and caught a late train to Götingen. The next morning he appeared in Born’s office. When he left Götingen he was promised a job the next winter, in Born’s office Heisenberg asked if the job was still out on the table because of his low score on his examination. Born asked what Wein’s question was and they went over it together. Born said that it was a very tricky question and that he could understand his answer. On September 1925 Heisenberg published a fifteen page article with the title "On a Quantum Theoretical Reinterpretation of Kinematic and Mechanical Relations". The intent of this paper was to establish a basis for theoretical quantum mechanics, founded exclusively on relationships between quantities which in principle, are observable. It dealt with observed frequencies and intensities of emitted and absorbed light, and in doing it enabled a momentous breakthrough in physics, ensuring Heisenberg’s place in modern physics. Heisenberg then laid the groundwork for the new theoretical "matrix mechanics". The next semester, Heisenberg wrote a paper on the topic but was not sure if he should publish it. He gave it to Born to read, and while he was away at Cambridge, England Born sent the paper to the "Zeitschrift für Physik", a leading German physics journal. The principle of matrix mechanics utilized the same principle of the multiplication of matrices. On March 22, 1927, Heisenberg submitted a paper to the "Zeitschrift für Physik" entitled "On the perceptual content of quantum theoretical kinematics and mechanics" This twenty-seven page paper forwarded from Copenhagen contained Heisenberg’s most famous and far-ranging achievement in physics, his formulation of the uncertainty or indeterminacy principle in quantum mechanics. This uncertainty principle formed a fundamental component of the Copenhagen interpretation of quantum mechanics. The other two portions were Bohr’s complementary principle and Born’s statistical interpretation of Schrödinger’s wave function. The Copenhagen Interpretation was an explanation of the uses and limitations of the mathematical apparatus of quantum mechanics the fundamentally altered our understanding of nature and our relationship to it. This was the most controversial and profound transformation in physics that has not been equaled since. Heisenberg compared this to how Newtonian mechanics had to be replaced by a new relativistic mechanics such as how the effects of Einstein’s theory of relativity transformed our notions of space and time under certain conditions, which are high speeds, and enormous expanses of space and time. Heisenberg continued how a similar transformation is required in the realm of small masses and short distances such as the order of atoms and electrons. It was impossible to observe the individual workings of atoms, only the external workings of large numbers of atoms. Prior to the Heisenberg Uncertainty Principle it was common belief that it was able to describe the electron’s motion by noting its position and velocity at any given moment. In his essay, Heisenberg argued this belief and stated that this concept would not work; the previous belief would only be accurate if the object were macroscopic and in the ‘viewable’ world. When objects are sill viewable and measurable, Newtonian physics still applies, but when objects become so minute they are not able to be measured with an accurateness. It is impossible for the physicists to know any more than it is possible for them to measure. This is his explanation for this concept, "If one seeks to measure the exact position of an electron, one could use a microscope of very high resolving power, which would require the illumination of the electron with the light of very short wavelengths. But the shorter the wavelength, the grater the energy of the light quantum (or the greater the pressure of the light wave) hitting the electron - thus the greater the recoil velocity of the electron." He noted that there seemed to be a reciprocal relationship between the uncertainties with which it is possible to simultaneously measure velocity and the position of the electron in any given instant. "The more precisely we determine the position, the more imprecise the determination is the determination of velocity in this instant, and vice versa" This statement had profound implications on the way physicists would look at the quantum world. In the essay, Heisenberg also stated that with the new boundary of precision, the causalty theory became invalid. The causalty theory stated that with every action or effect, there is a cause for that action or effect. In Heisenberg expressed, "In the strict formulation of the causal law - if we know the present, we can calculate the future - it is not the conclusion that is wrong but the premise." This basically states that without knowing the precise location and velocity of the electron, it is only possible to calculate a range of possibilities for the location and velocity of the electron at any point in the future. The uncertainty relations that Heisenberg used to mathematically explain are: DpDq ³ h/2p DEDt ³ h/2p This first equation expresses the relationship when the position q, and the velocity p are measured simultaneously. The error in the precision of p and q are expressed as Dp and Dq at a given instant. The product of these uncertainties have to be at least equal to h/2p. This number is very small, (h represents the number 6.6 X 10-27 erg-sec). In the remote possibility that Dp would equal zero, then Dq would become infinite and vice versa. Heisenberg was also able to not only show these mathematical relations but it was also consistent with other experimental data which pointed all evidence to show that this theorem was true. Heisenberg also said that even if you could accurately measure the position of the electron, it would disrupt the velocity of the electron because the light necessary for ‘seeing’ the electron would interrupt the electron’s previous course, thus changing all future motion of the electron and making it impossible to predict its position and velocity. This principle would change the course of the way physicists looked at quantum mechanics and further experiments with the electron. After the publication of his paper, Heisenberg realized that it contained some errors. Born advised Heisenberg to write a post-script describing these errors; Heisenberg did write "Essential points that I had overlooked" to describe his error. In this post-script it mentioned, "uncertainty in the observation - arises not exclusively from discontinuous particles or continuous waves but also from the attempt to encompass simultaneously the phenomenon that arises from both wave and corpuscular origins." This error was noticed when experimental data was not congruent with his original writing and other physicists began to realize this. In response to the new advances in quantum mechanics, Einstein wrote, " Above all …. The reader should be convinced that I fully recognize the very important progress that the statistical quantum theory has brought to theoretical physics …. This theory and the (testable) relations, which are contained in it, are within the natural limits of the indeterminacy relation, complete …. What does not satisfy me in that theory, from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation)." It was Einstein’s opinion that the quantum theory was heading in the right direction, but they were not quite there yet. Physicists could not yet explain or fully prove the inner workings of an atom. During the year of 1927, Heisenberg was offered a full professorship at both Leipzig and Zurich. He chose to teach at Leipzig for the opportunity to work with a great experimental physicist, Peter Debye. The first seminar that Heisenberg taught was only attended by one student. He still remained optimistic that he would become more accepted with perseverance. Before taking over this new position, he was granted a year’s leave of absence to go on a lecture tour to the United States. In February of 1929, Heisenberg boarded a ship leaving Bremerhaven for New York. In the United States, Heisenberg had been offered to teach at a number of schools, giving him the opportunity to see all aspects of the country. He found it refreshing to see the open-mindedness of the young American students. At the end of his one-year term, he returned to his original post at Leipzig. At Leipzig, Heisenberg enjoyed the academic variety of teaching. Heisenberg published "The Physical Principles of Quantum Theory" in 1928 which described his work in matrix mechanics beginning from 1925. In 1932, Werner Heisenberg won the Nobel Prize in Physics for his development of matrix mechanics and his early development in the. During that same year, Heisenberg wrote a three part paper which describes the modern picture of the nucleus of an atom. He explained the structure of various nuclear components discussing their binding energies and their stability. This helped opened the door for further study of the atomic nucleus using the quantum theory. Hitler came to power during 1933 and began to expel all Jews from the universities. From this time on, war was immanent and it was impossible to separate the scientific world from the political world. In September of 1939, Hitler began his war with Poland. Heisenberg had moved his wife and child to Urfeld, in the mountains of Southern Germany, hoping to keep them safe for the duration of the war. Heisenberg was a member of mountain troop reserves, the Alpenjäger, and felt that he soon would be called to report for duty. A few days after the war had begun with Poland, he got orders to report to Berlin. To his surprise he did not meet his fellow Alpenjäger troops but the Heereswaffenamt, the Army Ordinance Research Department. Along with himself, he was met by other well known theoretical physicists. The Germans wanted these top physicists to develop the technology for a nuclear weapon. The Germans wanted all of the research to take place under one roof in Berlin, but Heisenberg protested and persuaded them to allow each scientist to conduct their research in their own laboratories. Already with the technology of fission, the first plan was to allow the bomb to simply be a runaway reactor, but it did not prove to be as easy as they had first imagined. Through 1940 and 1941, the Heereswaffenamt was concentrating on two line of research, how to make a chain-reacting pile, and how to separate U-235. Heisenberg wrote two papers for each subject. Both papers regarding separating U-235 suggested using heavy water as a moderator. He conceded that other pure substances such as various forms of carbon and other likewise pure elements. He recommended using heavy water because of its low neutron absorption rate and would therefore require less uranium. On June 23, 1942, Heisenberg’s laboratory in Leipzig underwent a slight catastrophe. Near six o’ clock, Heisenberg’s assistant interrupted his weekly seminar to tell him that he should come to see his laboratory. Once they arrived, Heisenberg noticed that bubbles were emerging from the pile called L-IV. All had gone as expected for the twenty days that the sphere had already been emerged. They tested the gas that was leaking, and discovered that it was hydrogen. Both men concluded that the seal in the sphere containing the uranium oxide had been broken. The lab mechanic helped lift the sphere out of the moderator. He then unscrewed the metal cover to remove the uranium oxide and there was a hissing sound like air rushing into a vacuum. For a couple seconds nothing happened, then flames and gas bust out around the cover, spewing burning particles of uranium around the laboratory. They dowsed the flames, and they slowly subsided. Then the lab assistant, Robert Döpel, tried to salvage the precious heavy water from inside the sphere. Heisenberg concluded that oxygen must have seeped into the sphere, so not knowing what else to do Heisenberg had his assistant lower the sphere back into the tank to keep it away from oxygen and to keep it cool. Later when observing the sphere, Heisenberg and Döpel noticed the steam threateningly rise from the water in the tank. Next they saw the pile within shudder, then swell. Without having to say anything, both men leapt for the door in one motion. Seconds later, the sound of an explosion rushed from the laboratory. Burning uranium flew around the laboratory and set the whole building on fire. The force of the explosion split the sphere apart which severed a hundred bolts. The fire within the sphere continued for two days until it finally died away. With extensive damage done to his laboratory, many of his experiments in effect were delayed. Despite all of his hard work for the development of nuclear weapons, he was not able to produce a successful model by the end of World War II. After the war, Heisenberg was interned in Britain with other leading German scientists. In 1946, he returned to Germany where he was appointed director of the Max Planck Institute for Physics and Astrophysics at Göttingen. In 1958, the institute moved to Munich and Heisenberg continued to be its director. Werner Heisenberg was an exceptional physicist that made many leaps forward in the knowledge of quantum mechanics. From a young prodigy growing up in Munich through his very successful career in the field of theoretical physics. His unsuccessfulness of creating powerful nuclear weapons ended up benefiting man kind. Through his career, Heisenberg remained controversial on many of his theories because he did not always follow the orthodox laws of physics. This allowed him to be able to develop his uncertainty principle and other models of the atom that he created throughout his life. On the first day of February 1976, Werner Heisenberg the renowned physicist died in Munich Germany. His work is still highly regarded by physicists today and his notoriety will continue years to come. This essay is only for research purposes. If used, be sure to cite it properly! |
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