Werner Heisenberg
One cannot fully appreciate the work of Werner Heisenberg unless one examines his contributions in the context of the time in which he lived. Werner Karl Heisenberg was born in Wuerzburg, Germany, on December 5, 1901, and grew up in academic surroundings, in a household devoted to the humanities. His father was a professor at the University of Munich and undoubtedly greatly influenced young Werner, who was a student at the Maximilian Gymnasium.
Heisenberg had the opportunity to work with many of the top physicists in the world including Niels Bohr and Max Born. Like many of the top physicists of the time Heisenberg received his doctorate at an early age. In Heisenberg's case he received it at the young age of twenty three. Heisenberg was not just a researcher. He was also a professor and author. During his career he taught at many prestigious universities, including the Universities of Leipzig, Goettingen, and Berlin. He also wrote many important books including, Physical Principles of the Quantum Theory, Cosmic Radiation, Physics and Philosophy, and Introduction to the Unified Theory of Elementary Particles. In 1932 he won the Nobel Prize in Physics for his work in Quantum Mechanics.
With the Nazi's in power, and World War two on the horizon it was inevitable that his German heritage would play a crucial role in his career. Before Germany's blitzkrieg on Poland Heisenberg decided to make one final visit of his friends in the West. Many tried to convince him to stay and accept a professorship at Columbia, but Heisenberg declined. He felt that it was his duty to preserve the foundation of science in Germany during the war. He also believed that by staying in Germany during the war, he could help individual German scientists. In fact, he did offer jobs to Jewish scientists when they were fired from their posts at other universities. As time passed, Heisenberg found that he was powerless to protect his friends. Heisenberg himself was personally attacked, and his appointment at the University of Munich was blocked. For over a year Heisenberg was attacked in the SS newspaper, which referred to him as a "white Jew." The attack became so threatening that Heisenberg's mother, who had a slight connection to Himmler's family, wrote to Himmler's mother asking Himmler to intercede. Himmler personally cleared Heisenberg of the charges leveled against him a year later, but he was told to study science and avoid discussing scientists. The strain of the investigation surely affected Heisenberg's creativity.
During the war Heisenberg worked on the German A-bomb project along with a number of other German scientists. It has been proposed in the novel Heisenberg's War, written by Thomas Powers, that Heisenberg deliberately sabotaged this project to keep the bomb out of Hitler's hands. After the war was over, all of the scientists in Germany working on the A-bomb project, including Heisenberg, were interned in England to be questioned about their work on the project.
Heisenbergs nationalism eventually ruined many of his academic friendships. His close relationship with Neils Bohr was destroyed by his decision to remain in Germany during the war. His failure to be more specific about his stand in whether or not to seriously work to develop a German bomb played an important part in his inability to reestablish ties with friends who moved to the West. The creative interaction with many leading scientists prior to the war was not resumed at the war's end.
Heisenberg's most important finding, the Uncertainty Principle is the corner stone of Quantum Mechanics. However, many advances in Quantum Mechanics had to be made before Heisenberg found it. Everything started with Rutherford's model of the atom. Consisting of a positively charged central nucleus, surrounded by orbiting planetary electrons. Around the same time that Rutherford was discovering the basic structure of the atom, Plank did some important work also. Finding that energy from an oscillating particle is emitted not continuously, but in packets of energy he developed the Quantum Theory of Radiation. From this came the universal constant h which played a large role in Heisenbergs uncertainty principle. Neils Bohr then made a new model of the atom, which combined both Rutherford's and Plank's work. This new model accounted for known patterns of atomic radiation as seen in spectra. However, what Bohr wrote on paper about the electron activity and what other physicists were observing were two different things. Bohr had developed his quantum theory of the atom by discarding the idea of a classical frequency associated with the orbit of an electron, but he still retained the concept of the classical orbit. Heisenberg went one step further and discarded the concept of the orbit itself. Rather than the classical idea of the position and the motion, or momentum, of the electron at each instant in time, Heisenberg introduced his square arrays or matrices, which depict the electron as existing simultaneously in all possible Bohr orbits. After Heisenberg's discovery, the classical concept of the electron as a particle was no longer justifiable.
Heisenberg was led to these revolutionary ideas by his insistence on utilizing only those quantities in a theory that are directly observable. Since the orbit of an electron is not observable, it can have no place in a theory. Only the spectral lines are observed, and, since these involve pairs of orbits, all quantities that are used to describe the electron inside the atom should be associated with such pairs.
Such thinking led to Heisenberg's matrices. One of the important features of matrices is that it is not commutative. If the array representing the position of an electron is q and an array representing its momentum is p, then the product pq is not the same as the product qp.
This showed Heisenberg that the uncertainty relationship is purely an algebraic consequence of his matrix theory. If you picture the product pq as representing a measurement of the position of the electron followed by a measurement of its momentum; qp, on the other hand, represents the measurement of the momentum of a particle followed by at the measurement of its position. That these two sets of measurements give different results simply means that the measurement of the momentum of a particle destroys our knowledge of its position, and vice versa. It follows that it is impossible to obtain or to have precise knowledge of the position and the momentum of a particle simultaneously; this is the essence of the uncertainty principle.
Its significance for the structure of the atom is that we have no way of determining the orbit of an electron inside the atom observationally. As Heisenberg pointed out in his analysis of the Copenhagen interpretation of quantum theory, an electron can be observed inside an atom only with a gamma-ray microscope which, because of the short wavelength of gamma rays, has a high resolving power. This microscope shows us where the electron is at any moment, but at least one gamma-ray photon must be reflected from the electron. In this very process the electron is knocked out of the atom. It is senseless then to speak of its orbit.
Although the uncertainty relations can be derived mathematically from theory, it is much more instructive to derive them from the physical picture. This method shows clearly the interrelationship between the wave and the particle. In fact, it is clear from Heisenberg's analysis that wave and particle are complementary aspects, as are position and momentum. It was from considerations such as these that Bohr developed his theory of complementarily, which is essential for an understanding of modern atomic theories.
The uncertainty relations completely change our ideas of causality. If we cannot determine the position and the momentum of a particle simultaneously to any desired degree of accuracy, we cannot determine its future course. We can solve equations for the motion of the particle. However, these solutions can tell us its future history only if at some moment in the past or at the present instant we know its position and momentum. The farther we try to look into the future, the less accurate our predictions become because our present uncertainty, however small leads to greater deviations from the predicted pattern of the motion as the time increases. We can understand this situation by considering the lunar missile probes carried out by the United States and Soviet Union. To hit a target as gar away as the moon involves extreme accuracy in aiming the rocket and giving it the correct initial momentum; if we wish to hit targets at greater distances, our accuracy will have to be increased considerably because the further the distance, the greater the multiplication of any initial error.
Today we use the term quantum mechanics for the entire mathematical scheme that is used to treat problems in atomic, nuclear, elementary-particle, and field physics. The mathematics of quantum mechanics stems directly from Heisenberg's matrix mechanics and is a consequence of his uncertainty principle. If anyone were to prove his uncertainty principle wrong the foundations of quantum mechanics would fall.
Heisenberg spent the final years of his career trying to derive the properties of such elementary particles as electrons, protons, and so on, from a departure from quantum field theory by having the field itself construct its own particles. Unfortunately, this approach led to a very complex mathematical formulation which some say spoiled the great beauty of quantum mechanics.
Sunday, 1 September 2013
Werner Heisenberg 4
Werner Heisenberg
One cannot fully appreciate the work of Werner Heisenberg unless one examines his contributions in the context of the time in which he lived. Werner Karl Heisenberg was born in Wuerzburg, Germany, on December 5, 1901, and grew up in academic surroundings, in a household devoted to the humanities. His father was a professor at the University of Munich and undoubtedly greatly influenced young Werner, who was a student at the Maximilian Gymnasium.
Heisenberg had the opportunity to work with many of the top physicists in the world including Niels Bohr and Max Born. Like many of the top physicists of the time Heisenberg received his doctorate at an early age. In Heisenberg's case he received it at the young age of twenty three. Heisenberg was not just a researcher. He was also a professor and author. During his career he taught at many prestigious universities, including the Universities of Leipzig, Goettingen, and Berlin. He also wrote many important books including, Physical Principles of the Quantum Theory, Cosmic Radiation, Physics and Philosophy, and Introduction to the Unified Theory of Elementary Particles. In 1932 he won the Nobel Prize in Physics for his work in Quantum Mechanics.
With the Nazi's in power, and World War two on the horizon it was inevitable that his German heritage would play a crucial role in his career. Before Germany's blitzkrieg on Poland Heisenberg decided to make one final visit of his friends in the West. Many tried to convince him to stay and accept a professorship at Columbia, but Heisenberg declined. He felt that it was his duty to preserve the foundation of science in Germany during the war. He also believed that by staying in Germany during the war, he could help individual German scientists. In fact, he did offer jobs to Jewish scientists when they were fired from their posts at other universities. As time passed, Heisenberg found that he was powerless to protect his friends. Heisenberg himself was personally attacked, and his appointment at the University of Munich was blocked. For over a year Heisenberg was attacked in the SS newspaper, which referred to him as a "white Jew." The attack became so threatening that Heisenberg's mother, who had a slight connection to Himmler's family, wrote to Himmler's mother asking Himmler to intercede. Himmler personally cleared Heisenberg of the charges leveled against him a year later, but he was told to study science and avoid discussing scientists. The strain of the investigation surely affected Heisenberg's creativity.
During the war Heisenberg worked on the German A-bomb project along with a number of other German scientists. It has been proposed in the novel Heisenberg's War, written by Thomas Powers, that Heisenberg deliberately sabotaged this project to keep the bomb out of Hitler's hands. After the war was over, all of the scientists in Germany working on the A-bomb project, including Heisenberg, were interned in England to be questioned about their work on the project.
Heisenbergs nationalism eventually ruined many of his academic friendships. His close relationship with Neils Bohr was destroyed by his decision to remain in Germany during the war. His failure to be more specific about his stand in whether or not to seriously work to develop a German bomb played an important part in his inability to reestablish ties with friends who moved to the West. The creative interaction with many leading scientists prior to the war was not resumed at the war's end.
Heisenberg's most important finding, the Uncertainty Principle is the corner stone of Quantum Mechanics. However, many advances in Quantum Mechanics had to be made before Heisenberg found it. Everything started with Rutherford's model of the atom. Consisting of a positively charged central nucleus, surrounded by orbiting planetary electrons. Around the same time that Rutherford was discovering the basic structure of the atom, Plank did some important work also. Finding that energy from an oscillating particle is emitted not continuously, but in packets of energy he developed the Quantum Theory of Radiation. From this came the universal constant h which played a large role in Heisenbergs uncertainty principle. Neils Bohr then made a new model of the atom, which combined both Rutherford's and Plank's work. This new model accounted for known patterns of atomic radiation as seen in spectra. However, what Bohr wrote on paper about the electron activity and what other physicists were observing were two different things. Bohr had developed his quantum theory of the atom by discarding the idea of a classical frequency associated with the orbit of an electron, but he still retained the concept of the classical orbit. Heisenberg went one step further and discarded the concept of the orbit itself. Rather than the classical idea of the position and the motion, or momentum, of the electron at each instant in time, Heisenberg introduced his square arrays or matrices, which depict the electron as existing simultaneously in all possible Bohr orbits. After Heisenberg's discovery, the classical concept of the electron as a particle was no longer justifiable.
Heisenberg was led to these revolutionary ideas by his insistence on utilizing only those quantities in a theory that are directly observable. Since the orbit of an electron is not observable, it can have no place in a theory. Only the spectral lines are observed, and, since these involve pairs of orbits, all quantities that are used to describe the electron inside the atom should be associated with such pairs.
Such thinking led to Heisenberg's matrices. One of the important features of matrices is that it is not commutative. If the array representing the position of an electron is q and an array representing its momentum is p, then the product pq is not the same as the product qp.
This showed Heisenberg that the uncertainty relationship is purely an algebraic consequence of his matrix theory. If you picture the product pq as representing a measurement of the position of the electron followed by a measurement of its momentum; qp, on the other hand, represents the measurement of the momentum of a particle followed by at the measurement of its position. That these two sets of measurements give different results simply means that the measurement of the momentum of a particle destroys our knowledge of its position, and vice versa. It follows that it is impossible to obtain or to have precise knowledge of the position and the momentum of a particle simultaneously; this is the essence of the uncertainty principle.
Its significance for the structure of the atom is that we have no way of determining the orbit of an electron inside the atom observationally. As Heisenberg pointed out in his analysis of the Copenhagen interpretation of quantum theory, an electron can be observed inside an atom only with a gamma-ray microscope which, because of the short wavelength of gamma rays, has a high resolving power. This microscope shows us where the electron is at any moment, but at least one gamma-ray photon must be reflected from the electron. In this very process the electron is knocked out of the atom. It is senseless then to speak of its orbit.
Although the uncertainty relations can be derived mathematically from theory, it is much more instructive to derive them from the physical picture. This method shows clearly the interrelationship between the wave and the particle. In fact, it is clear from Heisenberg's analysis that wave and particle are complementary aspects, as are position and momentum. It was from considerations such as these that Bohr developed his theory of complementarily, which is essential for an understanding of modern atomic theories.
The uncertainty relations completely change our ideas of causality. If we cannot determine the position and the momentum of a particle simultaneously to any desired degree of accuracy, we cannot determine its future course. We can solve equations for the motion of the particle. However, these solutions can tell us its future history only if at some moment in the past or at the present instant we know its position and momentum. The farther we try to look into the future, the less accurate our predictions become because our present uncertainty, however small leads to greater deviations from the predicted pattern of the motion as the time increases. We can understand this situation by considering the lunar missile probes carried out by the United States and Soviet Union. To hit a target as gar away as the moon involves extreme accuracy in aiming the rocket and giving it the correct initial momentum; if we wish to hit targets at greater distances, our accuracy will have to be increased considerably because the further the distance, the greater the multiplication of any initial error.
Today we use the term quantum mechanics for the entire mathematical scheme that is used to treat problems in atomic, nuclear, elementary-particle, and field physics. The mathematics of quantum mechanics stems directly from Heisenberg's matrix mechanics and is a consequence of his uncertainty principle. If anyone were to prove his uncertainty principle wrong the foundations of quantum mechanics would fall.
Heisenberg spent the final years of his career trying to derive the properties of such elementary particles as electrons, protons, and so on, from a departure from quantum field theory by having the field itself construct its own particles. Unfortunately, this approach led to a very complex mathematical formulation which some say spoiled the great beauty of quantum mechanics.
One cannot fully appreciate the work of Werner Heisenberg unless one examines his contributions in the context of the time in which he lived. Werner Karl Heisenberg was born in Wuerzburg, Germany, on December 5, 1901, and grew up in academic surroundings, in a household devoted to the humanities. His father was a professor at the University of Munich and undoubtedly greatly influenced young Werner, who was a student at the Maximilian Gymnasium.
Heisenberg had the opportunity to work with many of the top physicists in the world including Niels Bohr and Max Born. Like many of the top physicists of the time Heisenberg received his doctorate at an early age. In Heisenberg's case he received it at the young age of twenty three. Heisenberg was not just a researcher. He was also a professor and author. During his career he taught at many prestigious universities, including the Universities of Leipzig, Goettingen, and Berlin. He also wrote many important books including, Physical Principles of the Quantum Theory, Cosmic Radiation, Physics and Philosophy, and Introduction to the Unified Theory of Elementary Particles. In 1932 he won the Nobel Prize in Physics for his work in Quantum Mechanics.
With the Nazi's in power, and World War two on the horizon it was inevitable that his German heritage would play a crucial role in his career. Before Germany's blitzkrieg on Poland Heisenberg decided to make one final visit of his friends in the West. Many tried to convince him to stay and accept a professorship at Columbia, but Heisenberg declined. He felt that it was his duty to preserve the foundation of science in Germany during the war. He also believed that by staying in Germany during the war, he could help individual German scientists. In fact, he did offer jobs to Jewish scientists when they were fired from their posts at other universities. As time passed, Heisenberg found that he was powerless to protect his friends. Heisenberg himself was personally attacked, and his appointment at the University of Munich was blocked. For over a year Heisenberg was attacked in the SS newspaper, which referred to him as a "white Jew." The attack became so threatening that Heisenberg's mother, who had a slight connection to Himmler's family, wrote to Himmler's mother asking Himmler to intercede. Himmler personally cleared Heisenberg of the charges leveled against him a year later, but he was told to study science and avoid discussing scientists. The strain of the investigation surely affected Heisenberg's creativity.
During the war Heisenberg worked on the German A-bomb project along with a number of other German scientists. It has been proposed in the novel Heisenberg's War, written by Thomas Powers, that Heisenberg deliberately sabotaged this project to keep the bomb out of Hitler's hands. After the war was over, all of the scientists in Germany working on the A-bomb project, including Heisenberg, were interned in England to be questioned about their work on the project.
Heisenbergs nationalism eventually ruined many of his academic friendships. His close relationship with Neils Bohr was destroyed by his decision to remain in Germany during the war. His failure to be more specific about his stand in whether or not to seriously work to develop a German bomb played an important part in his inability to reestablish ties with friends who moved to the West. The creative interaction with many leading scientists prior to the war was not resumed at the war's end.
Heisenberg's most important finding, the Uncertainty Principle is the corner stone of Quantum Mechanics. However, many advances in Quantum Mechanics had to be made before Heisenberg found it. Everything started with Rutherford's model of the atom. Consisting of a positively charged central nucleus, surrounded by orbiting planetary electrons. Around the same time that Rutherford was discovering the basic structure of the atom, Plank did some important work also. Finding that energy from an oscillating particle is emitted not continuously, but in packets of energy he developed the Quantum Theory of Radiation. From this came the universal constant h which played a large role in Heisenbergs uncertainty principle. Neils Bohr then made a new model of the atom, which combined both Rutherford's and Plank's work. This new model accounted for known patterns of atomic radiation as seen in spectra. However, what Bohr wrote on paper about the electron activity and what other physicists were observing were two different things. Bohr had developed his quantum theory of the atom by discarding the idea of a classical frequency associated with the orbit of an electron, but he still retained the concept of the classical orbit. Heisenberg went one step further and discarded the concept of the orbit itself. Rather than the classical idea of the position and the motion, or momentum, of the electron at each instant in time, Heisenberg introduced his square arrays or matrices, which depict the electron as existing simultaneously in all possible Bohr orbits. After Heisenberg's discovery, the classical concept of the electron as a particle was no longer justifiable.
Heisenberg was led to these revolutionary ideas by his insistence on utilizing only those quantities in a theory that are directly observable. Since the orbit of an electron is not observable, it can have no place in a theory. Only the spectral lines are observed, and, since these involve pairs of orbits, all quantities that are used to describe the electron inside the atom should be associated with such pairs.
Such thinking led to Heisenberg's matrices. One of the important features of matrices is that it is not commutative. If the array representing the position of an electron is q and an array representing its momentum is p, then the product pq is not the same as the product qp.
This showed Heisenberg that the uncertainty relationship is purely an algebraic consequence of his matrix theory. If you picture the product pq as representing a measurement of the position of the electron followed by a measurement of its momentum; qp, on the other hand, represents the measurement of the momentum of a particle followed by at the measurement of its position. That these two sets of measurements give different results simply means that the measurement of the momentum of a particle destroys our knowledge of its position, and vice versa. It follows that it is impossible to obtain or to have precise knowledge of the position and the momentum of a particle simultaneously; this is the essence of the uncertainty principle.
Its significance for the structure of the atom is that we have no way of determining the orbit of an electron inside the atom observationally. As Heisenberg pointed out in his analysis of the Copenhagen interpretation of quantum theory, an electron can be observed inside an atom only with a gamma-ray microscope which, because of the short wavelength of gamma rays, has a high resolving power. This microscope shows us where the electron is at any moment, but at least one gamma-ray photon must be reflected from the electron. In this very process the electron is knocked out of the atom. It is senseless then to speak of its orbit.
Although the uncertainty relations can be derived mathematically from theory, it is much more instructive to derive them from the physical picture. This method shows clearly the interrelationship between the wave and the particle. In fact, it is clear from Heisenberg's analysis that wave and particle are complementary aspects, as are position and momentum. It was from considerations such as these that Bohr developed his theory of complementarily, which is essential for an understanding of modern atomic theories.
The uncertainty relations completely change our ideas of causality. If we cannot determine the position and the momentum of a particle simultaneously to any desired degree of accuracy, we cannot determine its future course. We can solve equations for the motion of the particle. However, these solutions can tell us its future history only if at some moment in the past or at the present instant we know its position and momentum. The farther we try to look into the future, the less accurate our predictions become because our present uncertainty, however small leads to greater deviations from the predicted pattern of the motion as the time increases. We can understand this situation by considering the lunar missile probes carried out by the United States and Soviet Union. To hit a target as gar away as the moon involves extreme accuracy in aiming the rocket and giving it the correct initial momentum; if we wish to hit targets at greater distances, our accuracy will have to be increased considerably because the further the distance, the greater the multiplication of any initial error.
Today we use the term quantum mechanics for the entire mathematical scheme that is used to treat problems in atomic, nuclear, elementary-particle, and field physics. The mathematics of quantum mechanics stems directly from Heisenberg's matrix mechanics and is a consequence of his uncertainty principle. If anyone were to prove his uncertainty principle wrong the foundations of quantum mechanics would fall.
Heisenberg spent the final years of his career trying to derive the properties of such elementary particles as electrons, protons, and so on, from a departure from quantum field theory by having the field itself construct its own particles. Unfortunately, this approach led to a very complex mathematical formulation which some say spoiled the great beauty of quantum mechanics.
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