The development of quantum mechanics (or the quantum theory) is a revolution. It not only overcame the existing paradigm of classical physics, but along its developmental path questioned the pervading philosophy of the universe and also reformed the use of mathematics in science. The fundamental question that arises is the actual nature of a revolution in science. A powerful definition arises from combining the theories of Kuhn, Bolwer and Morris. It states that in order to judge whether or not a particular event is revolutionary, the idea has to be radically different such that it successfully supplants existing ideas and excludes alternative approaches. Furthermore for an idea to be useful, it has to be readily accepted by the relevant community and used in new applications. Kuhn further exclaimed the chronological steps in the development of a revolution: first anomalies arise which old paradigms are unable to explain, then comes the development of a new paradigm that is incommensurable with the former, and finally the new paradigm supplants the older. All these events are seen in the development of quantum mechanics.
Quantum mechanics arose because of the need to explain and understand several anomalies, which are: the blackbody radiation, the photoelectric effect and the splitting of spectral lines. Blackbody radiation in its idealized form is a substance that absorbs all radiation incident upon it and releases it in another wavelength independent of the substance, but dependent only on its temperature. This phenomenon was first described by Robert Kirchhoff between 1859-60, and Josef Stefan further added that the heat radiation varied with the forth power of the absolute temperature (Kragh 1999, 58). Wilheim Wein later saw a problem with Stepan's law and further added that blackbody radiation does not depend on the absolute temperature, but is a product of the temperature and the wavelength (Kragh 1999, 58). This law was experimentally satisfying, but its theoretical basis on classical physics was deemed inadequate. This event clearly shows the early inadequacy of the existing paradigm of classical physics. Max Planck sought a sound theoretical explanation for this phenomenon based on first principles, and as a believer in the absolute truth of the second law of thermodynamics he used an expression of entropy to derive Wein's law. Much to his dismay Wein's law was proved to be only a rough representation, thus rendering it incorrect. From this example, one can observe that in order to provide an explanation of a new phenomenon the existing paradigm is first utilized rigorously, but is unable to describe it thus demonstrating the beginning of the fall of the old paradigm. Classical mechanics predicts that the radiation energy density of a blackbody would approach zero, while experiments conducted by Heinrich Rubens and Ferdinand Kurlbaum is the fall of 1900 showed that energy approached a nonzero value. Many new theories based on classical mechanics were put forward to solve this anomaly, but were of no importance (Kragh 1999, 59). This demonstrates that how ever hard scientists attempt to fix classical physics to conform to novel observations, it always failed.
Planck was more successful in developing a new theory based on entropy that was scarcely more than an inspired guess (Kragh 1999, 61), thus showing the radical new directions away from classical physics one had to take in order to explain such an anomaly. He introduced Boltzmann's equation of statistical mechanics, which undermined the absolute validity of one the fundamental tenets of classical physics - the second law of thermodynamics, but in order to find a constant, he had to calculate the energy of the oscillation of a black body divided into finite portions of energy. This value of energy defrauded classical physics because it theorized that energy could be found at any quantity, and not discrete multiples of a fundamental constant. Even through Planck did not notice it in December 1900; his theory was on the path to a revolution (Kragh 1999, 62). The problem of the blackbody radiation arose again in a new form as the ultraviolet catastrophe which was observed by Henrik Lorentz. Classical physics predicted that the energy density of a blackbody radiation would increase as a function of the second power, thus increasing infinitely as the radiation increased. This was not observed experimentally and the deviations were especially obvious in the ultraviolet frequencies. A few years later Planck realized that classical mechanics and his observations could not be reconciled. (Kragh 1999, 64). In 1909 Planck wrote to Lorentz that "the energy exchange between electrons and free ether occurs only in whole numbers of quanta hv" (Kragh 1999, 65). This was a radical departure from the established laws of physics, but also the beginning of the growing acceptance of quantum mechanics.
The idea of discrete quantities of energy was becoming more solidified with the problem of photoelectric effect. It was observed that when light with a minimum wavelength was shined onto a piece of metal, it began to emit electrons. What was truly puzzling about this new phenomenon was that there was a minimum wavelength where this happened and furthermore the electron would be emitted at an instant. The classical explanation for this would be that energy would heat up the metal and then the electron would jump, but it just could not account for the fact that this "jump" occurred without any delay. Albert Einstein decided to tackle this problem and deduced that the only thing that would solve this anomaly was the notion of quantized energy (Kragh 1999, 67). Unlike Planck, Einstein instantly discovered the revolutionary nature of this idea and in a letter to his friend Conrad Habicht he stated that the "radiation and the energetic properties of light" as "very revolutionary (Kragh 1999, 66)." Einstein's theory was considered extremely radical from the outset as Walther Nerst, a chemist quoted "he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light-quanta (Kragh 1999, 68)." Nerst's quote implies that he found it crazy. After this, Nerst himself introduced quantum mechanics into chemistry since no other theories existed that accounted for these anomalies. Furthermore, it again illustrates the growing acceptance of the new theory, not just among physicist, but among chemists as well (Kragh 1999, 68).
Thomas Kuhn in his book "The Structure of Scientific Revolutions" stated that in order for there to be a scientific revolution, two competing paradigms had to be incommensurable. This is aptly demonstrated by Neils Bohr, who earnestly attempted to convert the theories of classical physics into the new quantum theory by using his correspondence principle. This proved to be an extremely difficult proposition because of the differences in values of the two paradigms; while classical physics made the clear distinction between waves and particles, quantum mechanics stated that particles have wave-like properties and vice versa. The anomaly that Bohr was faced with that led to his theory of the quantization of energy was the splitting of spectral lines (Beller 1999, 215). Using this Bohr theorized of the stability atoms, which was unknown in the classical paradigm. Bohr's assistant Heisenberg was a big figure in the development of quantum mechanics. He was developmental in the in the advance of matrix calculus to describe and calculate models based on quantum mechanics. Matrix calculus was not used in classical physics and this further shows the incommensurability of classical physics and quantum mechanics because they use different tools (Beller 1999, 104). Heisenberg was instrumental in the new interpretation of quantum mechanics - the uncertainty principle. This stated that one cannot know the momentum and the position at the same time. This is a clear deviation of classical physics where both these quantities can be known simultaneously. Heisenberg along with Max Born proposed a model of the world based on a statistical chance alone. This means that there is only a certain chance that something observable exists (Beller 1999, 216). Once again this violates classical physics where objects exist and move in a definite path.
Matrix calculus developed by Heisenberg was difficult for many scientists to use. In order for an idea to be revolutionary, it has to be accessible and Erwin Schrödinger developed the mathematics of wave mechanics to make the theory less strenuous (Jones 2008, 225). This thus led to the new paradigm becoming more regular among scientists and led to its increasing use. Soon after 1909 quantum mechanics became to be an extremely powerful tool and it spread very rapidly as seen by the graph on page 65 on Kragh's book where from the 1900s to 1909 there were less than twenty publications on the matter a year, but in the succeeding years the numbers of new publications began to grow at a rapid rate. This clearly implies that development of quantum mechanics was being readily accepted by the community. Furthermore, quantum mechanics left its place of origin in Western Europe and in its second part of development to places such as the United States and Japan, and scientists from these countries were rapidly building on the foundations of quantum mechanics (Jones 2008, 226). As the century progressed, it is seen that quantum mechanics began to leave these peripheral counties to further countries such as Brazil, was seen with the emigration of David Bohm from the United States after an anti-communist purge there (Albert, 1994, 60). This closely follows the last stage of the development of a paradigm where research is done within it.
The development of quantum mechanics was a radical revolution. It overcame the fundamental notions of classical physics by the development of new mathematical tools, by questioning the nature of matter and completely destroyed the old paradigm. There was no competition in its development because no theory could match it accuracy, and classical physics was supplanted for its vast inadequacies.
Albert, David. "Bohm's Alternative to Quantum Mechanics." Scientific American (1994): 58-67. Print.
Beller, Mara. Quantum Dialogue the Making of a Revolution. Chicago: University of Chicago, 1999. Print
Kragh, Helge. Quantum Generations: a History of Physics in the Twentieth Century. Princeton, NJ: Princeton UP, 1999. Print.
Jones, Sheilla. The Quantum Ten: a Story of Passion, Tragedy, Ambition and Science. Oxford: Oxford UP, 2008. Print.