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Physics World

Life after Schrödinger

Published Apr 1, 1997• 0 citations
Publisher

Abstract

It is difficult to imagine how a discovery in physics could reverberate around the world in the same way that Dolly the cloned sheep has in recent weeks. As biologists clone sheep and monkeys – albeit with only one event in noisy backgrounds of several hundred failed attempts – physicists are still trying to "clone" the wave-functions of single atoms, and then only in special circumstances. Yet as medical and biological research garners larger amounts of the public funds available for science, physicists with the requisite expertise could do worse than follow the old adage: "If you can't beat them, join them".

DOI
10.1088/2058-7058/10/4/1

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Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...

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It is difficult to imagine how a discovery in physics could reverberate around the world in the same way that Dolly the cloned sheep has in recent weeks. As biologists clone sheep and monkeys – albeit with only one event in noisy backgrounds of several hundred failed attempts – physicists are still trying to "clone" the wave-functions of single atoms, and then only in special circumstances. Yet as medical and biological research garners larger amounts of the public funds available for science, physicists with the requisite expertise could do worse than follow the old adage: "If you can't beat them, join them".
In 1903 the physicist Albert Michelson made an astonishing pronouncement. Confident of the advances made by the great physicists of the Victorian era, such as Lord Kelvin, James Clark Maxwell and Thomas Edison, he declared that ‘the most important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplemented in consequence of new discoveries is exceedingly remote’.1 In so doing he followed what appeared to be a long-established tradition that eminent physicists should make bold and far-reaching statements on the nature of the universe and its physical laws.2 Unfortunately, Michelson’s timing could not be worse as early twentieth-century physicists were about to make a string of discoveries that would fundamentally alter our perceptions of the universe. The world as Michelson understood it was about to be turned on its head by the work of three men: Max Planck, Albert Einstein and Ernest Rutherford. The first, Planck, was a respected German physicist who had done work on entropy, but had done little to distinguish himself. Then in 1900 he developed his ‘quantum theory’ which posited that energy did not flow as a stream or wave as had been imagined before, but rather was carried by packets or quanta. This seemingly simple, yet deceptively complex, thesis was to have a profound effect upon our understanding of the physical universe. Planck’s thesis proved to be the foundation for the modern discipline of quantum physics, a discipline that first came to the attention of the wider public when in 1905 a young Swiss patents clerk called Albert Einstein wrote five papers for the Annalen der Physik. Three of these papers are widely accepted to be among the best in the history of physics and examined photoelectric effects by applying Planck’s new quantum theory, Brownian Motion and a ‘Special Theory of Relativity’. As Bill Bryson notes in his Short History of Nearly Everything, ‘the first won its author a Nobel Prize and explained the nature of light (and also helped make television possible among other things). The Second provided proof that atoms do indeed exist – a fact that had surprisingly, been in some dispute. The third merely changed the world’.3 Thus within two years of Michelson’s pronouncement much of our understanding of the physical universe had been turned on its head by this new development; but for Michelson worse was to follow. In 1895, a young South African named Ernest Rutherford had won a scholarship to the world famous Cavendish Laboratory at the University of Cambridge. By 1911, Rutherford had become obsessed with the nature of atoms, the basic building blocks that form the constituent parts of the universe. That year he proposed his ‘theory of atomic nuclei’, which suggested that all the positive charge and most of the mass of an atom must be contained in a tiny nucleus at the atom’s centre, with the negatively charged electrons ‘in orbit’ about this nucleus. To prove his thesis Rutherford had to ‘split’ the atom to prove that he could release matter from this nucleus, something which he finally succeeded in doing in 1919 when he showed that by firing alpha-particles into nitrogen gas a small amount of hydrogen could be produced. In so doing he also established that energy could be released from the nucleus of an atom, thereby proving an essential part of Albert Einstein’s Special Theory of Relativity: the unification of energy and mass, usually represented by the famous equation E=mc2.4 With Rutherford providing the link between quantum theory and nuclear physics the Newtonian view of the universe, which was at the heart of Michelson’s beliefs, had been rewritten in less that 20 years.
Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...