|MadSci Network: Physics|
Hello Kirstin, YOUR QUESTION: 1. What is the relationship between Quatum Theory & Super- Symmetry Theory? Is it true that even the smallest sub-atomic particles have an invisible "pair"? What does this mean in terms of energy/mass relationships? ie. if we understand the Universe at the sub-atomic level, does this knowledge necessarily explain the larger whole? ANSWER PART 1) Since I am not sure what you know about Quantum physics: Let me first tell you a little about Quantum theory: THE origin of quantum theory is connected with a well-known phenomenon, which did not belong to the central parts of atomic physics. Any piece of matter when it is heated starts to glow, gets red hot and white hot at higher temperatures. The colour does not depend much on the surface of the material, and for a black body it depends solely on the temperature. Therefore, the radiation emitted by such a black body at high temperatures is a suitable object for physical research; it is a simple phenomenon that should find a simple explanation in terms of the known laws for radiation and heat. The attempt made at the end of the nineteenth century by Lord Rayleigh and Jeans failed, however, and revealed serious difficulties. It would not be possible to describe these difficulties here in simple terms. It must be sufficient to state that the application of the known laws did not lead to sensible results. When Planck, in 1895, entered this line of research he tried to turn the problem from radiation to the radiating atom. This turning did not remove any of the difficulties inherent in the problem, but it simplified the interpretation of the empirical facts. It was just at this time, during the summer of 1900, that Curlbaum and Rubens in Berlin had made very accurate new measurements of the spectrum of heat radiation. When Planck heard of these results he tried to represent them by simple mathematical formulas which looked plausible from his research on the general connection between heat and radiation. One day Planck and Rubens met for tea in Planck's home and compared Rubens' latest results with a new formula suggested by Planck.(See Planck below) The comparison showed a complete agreement. This was the discovery of Planck's law of heat radiation. It was at the same time the beginning of intense theoretical work for Planck. What was the correct physical interpretation of the new formula? Since Planck could, from his earlier work, translate his formula easily into a statement about the radiating atom (the so-called oscillator), he must soon have found that his formula looked as if the oscillator could only contain discrete quanta of energy - a result that was so different from anything known in classical physics that he certainly must have refused to believe it in the beginning. But in a period of most intensive work during the summer of 1900 he finally convinced himself that there was no way of escaping from this conclusion. It was told by Planck's son that his father spoke to him about his new ideas on a long walk through the Grunewald, the wood in the suburbs of Berlin. On this walk he explained that he felt he had possibly made a discovery of the first rank, comparable perhaps only to the discoveries of Newton. So Planck must have realised at this time that his formula had touched the foundations of our description of nature, and that these foundations would one day start to move from their traditional present location toward a new and as yet unknown position of stability. Planck, who was conservative in his whole outlook, did not like this consequence at all, but he published his quantum hypothesis in December of 1900. The idea that energy could be emitted or absorbed only in discrete energy quanta was so new that it could not be fitted into the traditional framework of physics. An attempt by Planck to reconcile his new hypothesis with the older laws of radiation failed in the essential points. It took five years until the next step could be made in the new direction. This time it was the young Albert Einstein, a revolutionary genius among the physicists, who was not afraid to go further away from the old concepts. There were two problems in which he could make use of the new ideas. One was the so-called photoelectric effect, the emission of electrons from metals under the influence of light. The experiments, especially those of Lenard, had shown that the energy of the emitted electrons did not depend on the intensity of the light, but only on its colour or, more precisely, on its frequency. This could not be understood on the basis of the traditional theory of radiation. Einstein could explain the observations by interpreting Planck's hypothesis as saying that light consists of quanta of energy travelling through space. The energy of one light quantum should, in agreement with Planck's assumptions, be equal to the frequency of the light multiplied by Planck's constant. The other problem was the specific heat of solid bodies. The traditional theory led to values for the specific heat which fitted the observations at higher temperatures but disagreed with them at low ones. Again Einstein was able to show that one could understand this behaviour by applying the quantum hypothesis to the elastic vibrations of the atoms in the solid body. These two results marked a very important advance, since they revealed the presence of Planck's quantum of action - as his constant is called among the physicists - in several phenomena, which had nothing immediately to do with heat radiation. They revealed at the same time the deeply revolutionary character of the new hypothesis, since the first of them led to a description of light completely different from the traditional wave picture. Light could either be interpreted as consisting of electromagnetic waves, according to Maxwell's theory, or as consisting of light quanta, energy packets travelling through space with high velocity. But could it be both? Einstein knew, of course, that the well- known phenomena of diffraction and interference can be explained only on the basis of the wave picture. He was not able to dispute the complete contradiction between this wave picture and the idea of the light quanta; nor did he even attempt to remove the inconsistency of this interpretation. He simply took the contradiction as something which would probably be understood only much later. In the meantime the experiments of Becquerel, Curie and Rutherford had led to some clarification concerning the structure of the atom. In 1911 Rutherford's observations on the interaction of a-rays penetrating through matter resulted in his famous atomic model. The atom is pictured as consisting of a nucleus, which is positively charged and contains nearly the total mass of the atom, and electrons, which circle around the nucleus like the planets circle around the sun. The chemical bond between atoms of different elements is explained as an interaction between the outer electrons of the neighbouring atoms; it has not directly to do with the atomic nucleus. The nucleus determines the chemical behaviour of the atom through its charge which in turn fixes the number of electrons in the neutral atom. Initially this model of the atom could not explain the most characteristic feature of the atom, its enormous stability. No planetary system following the laws of Newton's mechanics would ever go back to its original configuration after a collision with another such system. But an atom of the element carbon, for instance, will still remain a carbon atom after any collision or interaction in chemical binding. The explanation for this unusual stability was given by Bohr in 1913, through the application of Planck's quantum hypothesis. If the atom can change its energy only by discrete energy quanta, this must mean that the atom can exist only in discrete stationary states, the lowest of which is the normal state of the atom. Therefore, after any kind of interaction the atom will finally always fall back into its normal state. By this application of quantum theory to the atomic model, Bohr could not only explain the stability of the atom but also. in some simple cases, give a theoretical interpretation of the line spectra emitted by the atoms after the excitation through electric discharge or heat. His theory rested upon a combination of classical mechanics for the motion of the electrons with quantum conditions, which were imposed upon the classical motions for defining the discrete stationary states of the system. A consistent mathematical formulation for those conditions was later given by Sommerfeld. Bohr was well aware of the fact that the quantum conditions spoil in some way the consistency of Newtonian mechanics. In the simple case of the hydrogen atom one could calculate from Bohr's theory the frequencies of the light emitted by the atom, and the agreement with the observations was perfect. Yet these frequencies were different from the orbital frequencies and their harmonies of the electrons circling around the nucleus, and this fact showed at once that the theory was still full of contradictions. But it contained an essential part of the truth. It did explain qualitatively the chemical behaviour of the atoms and their line spectra; the existence of the discrete stationary states was verified by the experiments of Franck and Hertz, Stern and Gerlach. Bohr's theory had opened up a new line of research. The great amount of experimental material collected by spectroscopy through several decades was now available for information about the strange quantum laws governing the motions of the electrons in the atom. The many experiments of chemistry could be used for the same purpose. It was from this time on that the physicists learned to ask the right questions; and asking the right question is frequently more than halfway to the solution of the problem. What were these questions? Practically all of them had to do with the strange apparent contradictions between the results of different experiments. How could it be that the same radiation that produces interference patterns, and therefore must consist of waves, also produces the photoelectric effect, and therefore must consist of moving particles? How could it be that the frequency of the orbital motion of the electron in the atom does not show up in the frequency of the emitted radiation? Does this mean that there is no orbital motion? But if the idea of orbital motion should be incorrect, what happens to the electrons inside the atom? One can see the electrons move through a cloud chamber, and sometimes they are knocked out of an atom- why should they not also move within the atom? It is true that they might be at rest in the normal state of the atom, the state of lowest energy. But there are many states of higher energy, where the electronic shell has an angular momentum. There the electrons cannot possibly be at rest. One could add a number of similar examples. Again and again one found that the attempt to describe atomic events in the traditional terms of physics led to contradictions. Gradually, during the early twenties, the physicists became accustomed to these difficulties, they acquired a certain vague knowledge about where trouble would occur, and they learned to avoid contradictions. They knew which description of an atomic event would be the correct one for the special experiment under discussion. This was not sufficient to form a consistent general picture of what happens in a quantum process, but it changed the minds of the physicists in such a way that they somehow got into the spirit of quantum theory. Therefore, even some time before one had a consistent formulation of quantum theory one knew more or less what would be the result of any experiment. One frequently discussed what one called ideal experiments. Such experiments were designed to answer a very critical question irrespective of whether or not they could actually be carried out. Of course it was important that it should be possible in principle to carry out the experiment, but the technique might be extremely complicated. These ideal experiments could be very useful in clarifying certain problems. If there was no agreement among the physicists about the result of such an ideal experiment, it was frequently possible to find a similar but simpler experiment that could be carried out, so that the experimental answer contributed essentially to the clarification of quantum theory. The strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification; on the contrary, they became even more marked and more exciting. There was, for instance, the experiment of Compton on the scattering of X-rays. From earlier experiments on the interference of scattered light there could be no doubt that scattering takes place essentially in the following way: The incident light wave makes an electron in the beam vibrate in the frequency of the wave; the oscillating electron then emits a spherical wave with the same frequency and thereby produces the scattered light. However, Compton found in 1923 that the frequency of scattered X-rays was different from the frequency of the incident X-ray. This change of frequency could be formally understood by assuming that scattering is to be described as collision of a light quantum with an electron. The energy of the light quantum is changed during the collision; and since the frequency times Planck's constant should be the energy of the light quantum, the frequency also should be changed. But what happens in this interpretation of the light wave? The two experiments - one on the interference of scattered light and the other on the change of frequency of the scattered light - seemed to contradict each other without any possibility of compromise. By this time many physicists were convinced that these apparent contradictions belonged to the intrinsic structure of atomic physics. Therefore, in I924 de Broglie in France tried to extend the dualism between wave description and particle description to the elementary particles of matter, primarily to the electrons. He showed that a certain matter wave could 'correspond' to a moving electron, just as a light wave corresponds: to a moving light quantum. It was not clear at the time what the word 'correspond' meant in this connection. But de Broglie suggested that the quantum condition in Bohr's theory should be interpreted as a statement about the matter waves. A wave circling around a nucleus can for geometrical reasons only be a stationary wave; and the perimeter of the orbit must be an integer multiple of the wave length. In this way de Broglie's idea connected the quantum condition. which always had been a foreign element in the mechanics of the electrons, with the dualism between waves and particles. In Bohr's theory the discrepancy between the calculated orbital frequency of the electrons and the frequency of the emitted radiation had to be interpreted as a limitation to the concept of the electronic orbit. This concept had been somewhat doubtful from the beginning. For the higher orbits, however, the electrons should move at a large distance from the nucleus just as they do when one sees them moving through a cloud chamber. There one should speak about electronic orbits. It was therefore very satisfactory that for these higher orbits the frequencies of the emitted radiation approach the orbital frequency and its higher harmonics. Also Bohr had already suggested in his early papers that the intensities of the emitted spectral lines approach the intensities of the corresponding harmonics. This principle of correspondence had proved very useful for the approximative calculation of the intensities of spectral lines. In this way one had the impression that Bohr's theory gave a qualitative but not a quantitative description of what happens inside the atom; that some new feature of the behaviour of matter was qualitatively expressed by the quantum conditions, which in turn were connected with the dualism between waves and particles. The precise mathematical formulation of quantum theory finally emerged from two different developments. The one started from Bohr's principle of correspondence. One had to give up the concept of the electronic orbit, but still had to maintain it in the limit of high quantum numbers, i.e., for the large orbits. In this latter case the emitted radiation, by means of its frequencies and intensities, gives a picture of the electronic orbit; it represents what the mathematicians call a Fourier expansion of the orbit. The idea suggested itself that one should write down the mechanical laws not as equations for the positions and velocities of the electrons but as equations for the frequencies and amplitudes of their Fourier expansion. Starting from such equations and changing them very little one could hope to come to relations for those quantities which correspond to the frequencies and intensities of the emitted radiation, even for the small orbits and the ground state of the atom. This plan could actually be carried out; in the summer of 1925 it led to a mathematical formalism called matrix mechanics or, more generally, quantum mechanics. The equations of motion in Newtonian mechanics were replaced by similar equations between matrices; it was a strange experience to find that many of the old results of Newtonian mechanics, like conservation of energy, etc., could be derived also in the new scheme. Later the investigations of Born, Jordan and Dirac showed that the matrices representing position and momentum of the electron did not commute. This latter fact demonstrated clearly the essential difference between quantum mechanics and classical mechanics. The other development followed de Broglie's idea of matter waves. Schrödinger tried to set up a wave equation for de Broglie's stationary waves around the nucleus. Early in 1926 he succeeded in deriving the energy values of the stationary states of the hydrogen atom as 'Eigenvalues' of his wave equation and could give a more general prescription for transforming a given set of classical equations of motion into a corresponding wave equation in a space of many dimensions. Later he was able to prove that his formalism of wave mechanics was mathematically equivalent to the earlier formalism of quantum mechanics. Thus one finally had a consistent mathematical formalism, which could be defined in two equivalent ways starting either from relations between matrices or from wave equations. This formalism gave the correct energy values for the hydrogen atom: it took less than one year to show that it was also successful for the helium atom and the more complicated problems of the heavier atoms. But in what sense did the new formalism describe the atom? The paradoxes of the dualism between wave picture and particle picture were not solved; they were hidden somehow in the mathematical scheme. A first and very interesting step toward a real understanding Of quantum theory was taken by Bohr, Kramers and Slater in 192,+. These authors tried to solve the apparent contradiction between the wave picture and the particle picture by the concept of the probability wave. The electromagnetic waves were interpreted not as 'real' waves but as probability waves, the intensity of which determines in every point the probability for the absorption (or induced emission) of a light quantum by an atom at this point. This idea led to the conclusion that the laws of conservation of energy and momentum need not be true for the single event, that they are only statistical laws and are true only in the statistical average. This conclusion was not correct, however, and the connections between the wave aspect and the particle aspect of radiation were still more complicated. But the paper of Bohr, Kramers and Slater revealed one essential feature of the correct interpretation of quantum theory. This concept of the probability wave was something entirely new in theoretical physics since Newton. Probability in mathematics or in statistical mechanics means a statement about our degree of knowledge of the actual situation. In throwing dice we do not know the fine details of the motion of our hands which determine the fall of the dice and therefore we say that the probability for throwing a special number is just one in six. The probability wave of Bohr, Kramers, Slater, however, meant more than that; it meant a tendency for something. It was a quantitative version of the old concept of 'potentia' in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a~~ strange kind of physical reality just in the middle between possibility and reality. r Later when the mathematical framework of quantum theory was fixed, Born took up this idea of the probability wave and gave a clear definition of the mathematical quantity in the formalism. which was to be interpreted as the probability wave. It X as not a three-dimensional wave like elastic or radio waves, but a wave in the many-dimensional configuration space, and therefore a rather abstract mathematical quantity, Even at this time, in the summer of I926, it was not clear in every case how the mathematical formalism should be used to describe a given experimental situation. One knew how to describe the stationary states of an atom, but one did not know how to describe a much simpler event - as for instance an electron moving through a cloud chamber. When Schrödinger in that summer had shown that his formalism of wave mechanics was mathematically equivalent to quantum mechanics he tried for some time to abandon the idea of quanta and 'quantum jumps' altogether and to replace the electrons in the atoms simply by his three-dimensional matter waves. He was inspired to this attempt by his result, that the energy levels of the hydrogen atom in his theory seemed to be simply the eigenfrequencies of the stationary matter waves. Therefore, he thought it was a mistake to call them energies: they were just frequencies. But in the discussions which took place in the autumn of I926 in Copenhagen between Bohr and Schrödinger and the Copenhagen group of physicists it soon became apparent that such an interpretation would not even be sufficient to explain Planck's formula of heat radiation. During the months following these discussions an intensive study of all questions concerning the interpretation of quantum theory in Copenhagen finally led to a complete and, as many physicists believe, satisfactory clarification of the situation. But it was not a solution which one could easily accept. I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed to us in these atomic experiments? The final solution was approached in two different ways. The one was a turning around of the question. Instead of asking: How can one in the known mathematical scheme express a given experimental situation? the other question was put: Is it true, perhaps, that only such experimental situations can arise in nature as can be expressed in the mathematical formalism? The assumption that this was actually true led to limitations in the use of those concepts that had been the basis of classical physics since Newton. One could speak of the position and of the velocity of an electron as in Newtonian mechanics and one could observe and measure these quantities. But one could not fix both quantities simultaneously with an arbitrarily high accuracy. Actually the product of these two inaccuracies turned out to be not less than Planck's constant divided by the mass of the particle. Similar relations could be formulated for other experimental situations. They are usually called relations of uncertainty or principle of indeterminacy. One had learned that the old concepts fit nature only inaccurately. lie other way of approach was Bohr's concept of complementarity. Schrödinger had described the atom as a system not of a nucleus and electrons but of a nucleus and matter waves. This picture of the matter waves certainly also contained an element of truth. Bohr considered the two pictures - particle picture and wave picture - as two complementary descriptions of the same reality. Any of these descriptions can be only partially true, there must be limitations to the use of the particle concept as well as of wave concept, else one could not avoid contradictions. If one takes into account those limitations which can be expressed by the uncertainty relations, the contradictions disappear. In this way since the spring of I927 one has had a consistent interpretation of quantum theory, which is frequently called the 'Copenhagen interpretation'. This interpretation received its crucial test in the autumn of 1927 at the Solvay conference in Brussels. Those experiments which had always led to the worst paradoxes were again and again discussed in all details, especially by Einstein. New ideal experiments were invented to trace any possible inconsistency of the theory, but the theory was shown to be consistent and seemed to fit the experiments as far as one could see. The details of this Copenhagen interpretation will be the subject of the next chapter. It should be emphasised at this point that it has taken more than a quarter of a century to get from the first idea of the existence of energy quanta to a real understanding of the quantum theoretical laws. This indicates the great change that had to take place in the fundamental concepts concerning reality before one could understand the new situation. PLANCK and QUANTUM THEORY Quantum Theory, also quantum mechanics, in physics, a theory based on using the concept of the quantum unit to describe the dynamic properties of subatomic particles and the interactions of matter and radiation. The foundation was laid by the German physicist Max Planck, who postulated in 1900 that energy can be emitted or absorbed by matter only in small, discrete units called quanta. Also fundamental to the development of quantum mechanics was the uncertainty principle, formulated by the German physicist Werner Heisenberg in 1927, which states that the position and momentum of a subatomic particle cannot be specified simultaneously. II.EARLY HISTORY In the 18th and 19th centuries, Newtonian, or classical, mechanics appeared to provide a wholly accurate description of the motions of bodies-for example, planetary motion. In the late 19th and early 20th centuries, however, experimental findings raised doubts about the completeness of Newtonian theory. Among the newer observations were the lines that appear in the spectra of light emitted by heated gases, or gases in which electric discharges take place. From the model of the atom developed in the early 20th century by the English physicist Ernest Rutherford, in which negatively charged electrons circle a positive nucleus in orbits prescribed by Newton's laws of motion, scientists had also expected that the electrons would emit light over a broad frequency range, rather than in the narrow frequency ranges that form the lines in a spectrum. Another puzzle for physicists was the coexistence of two theories of light: the corpuscular theory, which explains light as a stream of particles, and the wave theory, which views light as electromagnetic waves. A third problem was the absence of a molecular basis for thermodynamics. In his book Elementary Principles in Statistical Mechanics (1902), the American mathematical physicist J. Willard Gibbs conceded the impossibility of framing a theory of molecular action that reconciled thermodynamics, radiation, and electrical phenomena as they were then understood. IIIPLANCK'S INTRODUCTION OF THE QUANTUM At the turn of the century, physicists did not yet clearly recognize that these and other difficulties in physics were in any way related. The first development that led to the solution of these difficulties was Planck's introduction of the concept of the quantum, as a result of physicists' studies of blackbody radiation during the closing years of the 19th century. (The term blackbody refers to an ideal body or surface that absorbs all radiant energy without any reflection.) A body at a moderately high temperature-a "red heat"-gives off most of its radiation in the low frequency (red and infrared) regions; a body at a higher temperature-"white heat"-gives off comparatively more radiation in higher frequencies (yellow, green, or blue). During the 1890s physicists conducted detailed quantitative studies of these phenomena and expressed their results in a series of curves or graphs. The classical, or prequantum, theory predicted an altogether different set of curves from those actually observed. What Planck did was to devise a mathematical formula that described the curves exactly; he then deduced a physical hypothesis that could explain the formula. His hypothesis was that energy is radiated only in quanta of energy hu, where u is the frequency and h is the quantum action, now known as Planck's constant. IVEINSTEIN'S CONTRIBUTION The next important developments in quantum mechanics were the work of German-born American physicist and Nobel laureate Albert Einstein. He used Planck's concept of the quantum to explain certain properties of the photoelectric effect-an experimentally observed phenomenon in which electrons are emitted from metal surfaces when radiation falls on these surfaces. According to classical theory, the energy, as measured by the voltage of the emitted electrons, should be proportional to the intensity of the radiation. The energy of the electrons, however, was found to be independent of the intensity of radiation-which determined only the number of electrons emitted-and to depend solely on the frequency of the radiation. The higher the frequency of the incident radiation, the greater is the electron energy; below a certain critical frequency no electrons are emitted. These facts were explained by Einstein by assuming that a single quantum of radiant energy ejects a single electron from the metal. The energy of the quantum is proportional to the frequency, and so the energy of the electron depends on the frequency. VTHE BOHR ATOM In 1911 Rutherford established the existence of the atomic nucleus. He assumed, on the basis of experimental evidence obtained from the scattering of alpha particles by the nuclei of gold atoms, that every atom consists of a dense, positively charged nucleus, surrounded by negatively charged electrons revolving around the nucleus as planets revolve around the sun. The classical electromagnetic theory developed by the British physicist James Clerk Maxwell unequivocally predicted that an electron revolving around a nucleus will continuously radiate electromagnetic energy until it has lost all its energy, and eventually will fall into the nucleus. Thus, according to classical theory, an atom, as described by Rutherford, is unstable. This difficulty led the Danish physicist Niels Bohr, in 1913, to postulate that in an atom the classical theory does not hold, and that electrons move in fixed orbits. Every change in orbit by the electron corresponds to the absorption or emission of a quantum of radiation. The application of Bohr's theory to atoms with more than one electron proved difficult. The mathematical equations for the next simplest atom, the helium atom, were solved during the 1910s and 1920s, but the results were not entirely in accordance with experiment. For more complex atoms, only approximate solutions of the equations are possible, and these are only partly concordant with observations. VIWAVE MECHANICS The French physicist Louis Victor de Broglie suggested in 1924 that because electromagnetic waves show particle characteristics, particles should, in some cases, also exhibit wave properties. This prediction was verified experimentally within a few years by the American physicists Clinton Joseph Davisson and Lester Halbert Germer and the British physicist George Paget Thomson. They showed that a beam of electrons scattered by a crystal produces a diffraction pattern characteristic of a wave (see Diffraction). The wave concept of a particle led the Austrian physicist Erwin Schrödinger to develop a so-called wave equation to describe the wave properties of a particle and, more specifically, the wave behavior of the electron in the hydrogen atom. Although this differential equation was continuous and gave solutions for all points in space, the permissible solutions of the equation were restricted by certain conditions expressed by mathematical equations called eigenfunctions (German eigen,"own"). The Schrödinger wave equation thus had only certain discrete solutions; these solutions were mathematical expressions in which quantum numbers appeared as parameters. (Quantum numbers are integers developed in particle physics to give the magnitudes of certain characteristic quantities of particles or systems.) The Schrödinger equation was solved for the hydrogen atom and gave conclusions in substantial agreement with earlier quantum theory. Moreover, it was solvable for the helium atom, which earlier theory had failed to explain adequately, and here also it was in agreement with experimental evidence. The solutions of the Schrödinger equation also indicated that no two electrons could have the same four quantum numbers- that is, be in the same energy state. This rule, which had already been established empirically by Austro-American physicist and Nobel laureate Wolfgang Pauli in 1925, is called the exclusion principle. VIIMATRIX MECHANICS Simultaneously with the development of wave mechanics, Heisenberg evolved a different mathematical analysis known as matrix mechanics. According to Heisenberg's theory, which was developed in collaboration with the German physicists Max Born and Ernst Pascual Jordan, the formula was not a differential equation but a matrix: an array consisting of an infinite number of rows, each row consisting of an infinite number of quantities. Matrix mechanics introduced infinite matrices to represent the position and momentum of an electron inside an atom. Also, different matrices exist, one for each observable physical property associated with the motion of an electron, such as energy, position, momentum, and angular momentum. These matrices, like Schrödinger's differential equations, could be solved; in other words, they could be manipulated to produce predictions as to the frequencies of the lines in the hydrogen spectrum and other observable quantities. Like wave mechanics, matrix mechanics was in agreement with the earlier quantum theory for processes in which the earlier quantum theory agreed with experiment; it was also useful in explaining phenomena that earlier quantum theory could not explain. VIIITHE MEANING OF QUANTUM MECHANICS Schrödinger subsequently succeeded in showing that wave mechanics and matrix mechanics are different mathematical versions of the same theory, now called quantum mechanics. Even for the simple hydrogen atom, which consists of two particles, both mathematical interpretations are extremely complex. The next simplest atom, helium, has three particles, and even in the relatively simple mathematics of classical dynamics, the three-body problem (that of describing the mutual interactions of three separate bodies) is not entirely soluble. The energy levels can be calculated accurately, however, even if not exactly. In applying quantum-mechanics mathematics to relatively complex situations, a physicist can use one of a number of mathematical formulations. The choice depends on the convenience of the formulation for obtaining suitable approximate solutions. Although quantum mechanics describes the atom purely in terms of mathematical interpretations of observed phenomena, a rough verbal description can be given of what the atom is now thought to be like. Surrounding the nucleus is a series of stationary waves; these waves have crests at certain points, each complete standing wave representing an orbit. The absolute square of the amplitude of the wave at any point is a measure of the probability that an electron will be found at that point at any given time. Thus, an electron can no longer be said to be at any precise point at any given time. IXTHE UNCERTAINTY PRINCIPLE The impossibility of pinpointing an electron at any precise time was analyzed by Heisenberg, who in 1927 formulated the uncertainty principle. This principle states the impossibility of simultaneously specifying the precise position and momentum of any particle. In other words, the more accurately a particle's momentum is measured and known, the less accuracy there can be in the measurement and knowledge of its position. This principle is also fundamental to the understanding of quantum mechanics as it is generally accepted today: The wave and particle character of electromagnetic radiation can be understood as two complementary properties of radiation. Another way of expressing the uncertainty principle is that the wavelength of a quantum mechanical principle is inversely proportional to its momentum. As atoms are cooled they slow down and their corresponding wavelength grows larger. At a low enough temperature this wavelength is predicted to exceed the spacing between particles, causing atoms to overlap, becoming indistinguishable, and melding into a single quantum state. In 1995 a team of Colorado scientists, led by National Institutes of Standards and Technology physicist Eric Cornell and University of Colorado physicist Carl Weiman, cooled rubidium atoms to a temperature so low that the particles entered this merged state, known as a Bose-Einstein condensate. The condensate essentially behaves like one atom even though it is made up of thousands. XRESULTS OF QUANTUM THEORY Quantum mechanics solved all of the great difficulties that troubled physicists in the early years of the 20th century. It gradually enhanced the understanding of the structure of matter, and it provided a theoretical basis for the understanding of atomic structure (see Atom and Atomic Theory) and the phenomenon of spectral lines: Each spectral line corresponds to the energy of a photon transmitted or absorbed when an electron makes a transition from one energy level to another. The understanding of chemical bonding was fundamentally transformed by quantum mechanics and came to be based on Schrödinger's wave equations. New fields in physics emerged-condensed matter physics, superconductivity, nuclear physics, and elementary particle physics (see Physics)-that all found a consistent basis in quantum mechanics. XIFURTHER DEVELOPMENTS In the years since 1925, no fundamental deficiencies have been found in quantum mechanics, although the question of whether the theory should be accepted as complete has come under discussion. In the 1930s the application of quantum mechanics and special relativity to the theory of the electron (see Quantum Electrodynamics) allowed the British physicist Paul Dirac to formulate an equation that referred to the existence of the spin of the electron. It further led to the prediction of the existence of the positron, which was experimentally verified by the American physicist Carl David Anderson. The application of quantum mechanics to the subject of electromagnetic radiation led to explanations of many phenomena, such as bremsstrahlung (German, "braking radiation," the radiation emitted by electrons slowed down in matter) and pair production (the formation of a positron and an electron when electromagnetic energy interacts with matter). It also led to a grave problem, however, called the divergence difficulty: Certain parameters, such as the so-called bare mass and bare charge of electrons, appear to be infinite in Dirac's equations. (The terms bare mass and bare charge refer to hypothetical electrons that do not interact with any matter or radiation; in reality, electrons interact with their own electric field.) This difficulty was partly resolved in 1947-49 in a program called renormalization, developed by the Japanese physicist Shin'ichirô Tomonaga, the American physicists Julian S. Schwinger and Richard Feynman, and the British physicist Freeman Dyson. In this program, the bare mass and charge of the electron are chosen to be infinite in such a way that other infinite physical quantities are canceled out in the equations. Renormalization greatly increased the accuracy with which the structure of atoms could be calculated from first principles. XIIFUTURE PROSPECTS Quantum mechanics underlies current attempts to account for the strong nuclear force (see Quantum Chromodynamics) and to develop a unified theory for all the fundamental interactions of matter (see Physics: Modern Physics: Unified Field Theories). Nevertheless, doubts exist about the completeness of quantum theory. The divergence difficulty, for example, is only partly resolved. Just as Newtonian mechanics was eventually amended by quantum mechanics and relativity, many scientists-and Einstein was among them-are convinced that quantum theory will also undergo profound changes in the future. Great theoretical difficulties exist, for example, between quantum mechanics and chaos theory, which began to develop rapidly in the 1980s. Ongoing efforts are being made by theorists such as the British physicist Stephen Hawking, to develop a system that encompasses both relativity and quantum mechanics. Now to the SUPERSYMMETRY and to answer what connects it to the Quantum theory: Supersymmetry (SUSY) is a generalization of the space time symmetrics of quantum field theory tthat performs fermions into bosons and vice versa.It also provides a frame work for the unification of particle physics and gravity,which is governed by the Planck Scale (please see my scans for equations)(definded to be the enegery scale where the gravitational interactions of elementary particles become compareable to their gauge interactions) If supersymmetry were an exact symmetry of nature,then particles and their superpartners(which differ in spin by half a unit) would be degenerate in mass. Thus supersummetry cannot be an exact symmetry of nature and must be broken . In theories of "low energy" supersymmetry the effective scale of supersymmetry breaking is tied to the electroweak scale which is characterized by the Standard Model Higgs vaccum expectaions value v=246GeV. It is thus possible that supersymmetry will ultimatley explain the origin of the large hirachy of energy scales from W and Z masses to the Planck Scale. At present there is no unambiguous eperimental results that require the existence of low-energy supersymmetry. However if experimentation at future colliders uncovers evidence for supersymmetry,this would have a profoiund effect on the study of Te-scale physicsand the development of a more fundamentaltheory of mass and symmetry breaking phenomena in particle physics. Now back to your other questions: If we would completly understand the uuniverse on it's supernatural level...would we understand the Universe? I honestly don't know but it woudl surley deepen our understanding a great deal. For every answer there is at least two new questions. For example we need a whole new set of physics to describe what goes on in a Singularity ... . How does the Mandelbrot set help in understanding our Universe? It is a start to tackle the "CHASO THEORY" and I recommend that you check out CHAOS COMPLEXITY THEORY WEB SITE
Try the links in the MadSci Library for more information on Physics.