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Max Planck was an expert on classical thermodynamics and turned his attention to the understanding of black-body radiation in 1895. He worked out the form the radiation formula had to have from the emission and absorption of radiation of a dipole in thermal equilibrium with the radiation it emits. The formula related the mean energy density of radiation to the average energy of the oscillator. Using new precision measurements of the black-body spectrum, Planck derived the primitive form of the black-body spectrum by a combination of theory and the empirical results of experiment, but without any physical interpretation of the significance of the formula.
The birth of physics can be traced to the Copernican, Galilean and Newtonian revolutions of the seventeenth century. The Copernican picture of the world was to replace the geocentric Ptolemaic model. Tycho Brahe's innovations in observation brought about an order of magnitude improvement in the determination of the motions of the planets. These observations resulted in the formulation of Kepler's laws of planetary motion, which were to be crucial in Newton's discovery of the laws of motion. At the same time, Galileo's pioneering telescopic discoveries provided support for the Copernican picture of the world.
The opening chapter sets out the aims of the book in more detail. There is a contrast between the way in which physics is taught and how it is used in a research context. Lecture courses provide a streamlined presentation of the material that every physicist ought to know, but this does not necessarily reflect the actual process of discovery and innovation in physics. The book is intended to bring to life the process of carrying out research in physics. The roles of creativity and imagination are emphasised and illustrated by seven case studies of key areas of physics. Tracing how giants like Maxwell and Einstein came to their revolutionary innovations brings to life the process of discovery in physics. Theoretical analyses are given at a level accessible to undergraduates in experimental and theoretical physics. The book should be considered complementary to standard physics courses and is intended to enrich the appreciation of the content of physics and theoretical physics courses.
Maxwell's equations are derived starting with a mathematical structure which is then given physical meaning with the minimum of assumptions. From these, all the laws of electromagnetism, such as Ampère’s law, Faraday’s law of electromagnetic induction, Coulomb’s law and the Biot-Savart law are derived. It is shown how the equations can be applied to electromagnetic phenomena in material media. It is demonstrated that, in the presence of electromagnetic fields, there is an electromagnetic energy density in the vacuum.
The success of the standard cosmological model with a finite cosmological constant raises many problem for fundamental physics. The inflationary model of the very early Universe provides a solution to a number of these problems but it requires the introduction of new physics. There is no physical realisation of the inflaton field. The model has, however, had a notable success in accounting for the origin of the fluctuations from which galaxies and the large-scale structure of the Universe formed. A solution to the origin of the baryon asymmetry of the Universe has yet to be found. Many cosmologists believe that the solution to these problems lies in the very earliest epochs, the Planck era, when gravity itself has to be quantised.
With the development of general relativity, Einstein realised that he had a theory which for the first time could be used to create fully self-consistent cosmological models. In 1917, he introduced the cosmological constant to create a static closed Universe. The standard world models were discovered by Friedman in 1922 and 1924 and rediscovered by Lemaitre a few years later. The expansion of the Universe was discovered by Hubble in 1929. A key discovery was that of the cosmic microwave background radiation by Penzias and Wilson in 1965. The resulting hot big bang scenario for the large-scale structure and evolution of the Universe became the preferred cosmological model. With the development of precision cosmology through precise measurements of the cosmic microwave background radiation, it was established that the cosmological constant has a finite value and that the Universe is geometrically flat.
Newton codified the laws of motion and gravity, their primitive forms being enunciated in 1665-66. Using Kepler's laws, he discovered the inverse square law of gravity and went on to show that gravity is the same force which holds the planets in their orbits, as well as that which causes apples to fall to the ground. Newton was a brilliant experimentalist who invented the Newtonian, reflecting telescope which eliminated the aberrations of refracting telescopes such as those built by Galileo. Newton's researches culminated in the publication of his revolutionary Principia Mathematica of 1687. He devoted as much effort to chemical (or alchemical) analyses and to the interpretation of ancient texts and the scriptures. He was also the inventor of differential and integral calculus.
Planck immediately set about attempting to understand the significance of his formula for black-body radiation. He began by using Boltzmann's procedure in statistical mechanics, an approach he had previously rejected, but then adopted empirically a definition of the entropy of the oscillators which introduced the concept of quantisation. HIs derivation was not understood by his contemporaries, including Einstein, because of the lack of a theoretical motivation for the definition of entropy. Despite a major effort to understand his formula, Planck found no classical solution to the meaning of h, Planck's constant.
Einstein never deviated from his belief in the reality of light quanta. In 1909, he published a remarkable paper in which he showed that fluctuations in the intensity of black-body radiation consisted of the statistical sum of the wave and particle properties of light. Following the 1911 Solvay conference, most of the participants were converted to the existence of light quanta. Bohr first applied the concepts of quanta to the structure of atoms. The experiment which finally convinced everyone of the light quantum hypothesis was Compton's demonstration of the energy change of X-rays in their scattering by electrons. This resulted in the concept of the wave-particle duality of light, one of the major foundation stones of quantum mechanics.
Galileo's brilliant experiments laid the foundations for the development of Newton's laws of motion. His experimental skill led to the derivation the law of acceleration as well as constructing the best telescopes for terrestrial and astronomical observations. His observations of the satellites of Jupiter provided an analogue for the motions of the planets about the Sun. His advocacy of the Copernican system of the world led to his trial and condemnation for heresy. His great realisation, the foundation of modern scientific enquiry, was that the laws of physics can be expressed in mathematical form.
The preface describes how the book came about and its objectives. The aim is to illuminate the process of discovery in physics and how the discipline really works through a number of case studies in key areas of classical and early quantum physics. The case studies span the whole of classical physics and bring out the connections between the different strands of the subject. The book is a revised and updated version of the first and second editions, with three new chapters and additional insights in all chapters.
In 1905, Einstein published three of the greatest papers in physics on the subjects of Brownian motion, special relativity and light quanta. The third of the series is the most revolutionary of the three and asserts that, under certain circumstances, light can be considered to consist of particles rather than waves. Using his deep understanding of entropy and statistics, he showed that, in the Wien region of the spectrum, light behaves as if it consisted of light quanta with energies hn. He then showed that, if Planck had followed the proper Boltzmann procedure, he would have obtained the Planck formula for black-body radiation. He proposed three test of his hypothesis, the most important being the energy dependence of the photoelectric effect upon the frequency of the incident radiation. He could also account for discrepancies between the classical and quantum expressions for the specific heat capacities of gases.
Maxwell's great paper of 1865 on the theory of the electromagnetic field is analysed in detail, emphasising the revolutionary nature of its contents. Building on his discovery of the equations for the electromagnetic field, he reformulated the theory without recourse to a mechanical model of the field, although his thinking was still strongly influenced by Newtonian mechanics. He emphasised the primacy of fields as the vehicle for transmitting forces and abolished the Newtonian concept of action at a distance. Fields pervaded the aether, endowing empty space with physical properties. In the new formalism, he demonstrated again that light is electromagnetic radiation.
In 1905, Einstein published his paper on the special theory of relativity. Although Lorentz and Poincaré had introduced a number of the essential feature of the special theory, Einstein's' paper went much deeper and showed that we live in four-dimensional space-time. A consequence of this approach was the derivation of the mass-energy relation E = mc2. The route to the special theory of relativity was not straightforward, but Einstein's approach was quickly adopted and the mass energy relation confirmed by the Cockcroft and Walton experiment of 1932. In this chapter, the theory of special relativity is developed through the use of four-vectors, providing a robust framework for carrying out calculations in special relativity.
The story of the discovery of quantisation and quanta begins with the numerous problems facing physicists at the end of the nineteenth century. A number of experimental results did not fit naturally into the scheme of classical physics. Among the most important of these was the spectrum of black-body radiation, which was being determined much more precisely experimentally in the last decade of the nineteenth century and which had to be explained theoretically. Important clues came from the pioneering studies of the origin of the Stefan-Boltzmann law and Wien's displacement law, the latter involving the clever use of dimensional methods.