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There is hardly another principle in physics with wider scope of applicability and more far-reaching consequences than Pauli's exclusion principle. This book explores the principle's origin in the atomic spectroscopy of the early 1920s, its subsequent embedding into quantum mechanics, and later experimental validation with the development of quantum chromodynamics. The reconstruction of this crucial historic episode provides an excellent foil to reconsider Kuhn's view on incommensurability. The author defends the prospective rationality of the revolutionary transition from the old to the new quantum theory around 1925 by focusing on the way Pauli's principle emerged as a phenomenological rule 'deduced' from some anomalous phenomena and theoretical assumptions of the old quantum theory. The subsequent process of validation is historically reconstructed and analysed within the framework of 'dynamic Kantianism'. The variety of themes skilfully interwoven in this book will appeal to philosophers, historians, scientists and anyone interested in philosophy.
The 250 years from the second half of the 17th century saw the birth of modern physics and its growth into one of the most successful of the sciences. The reader will find here the lives of 55 of the most remarkable physicists from that era described in brief biographies. All the characters profiled have made important contributions to physics, either through their ideas, through their teaching or in other ways. The emphasis is on their varied life-stories, not on the details of their achievements, but when read in sequence the biographies, which are organised chronologically, convey in human terms something of the way in which physics was created. Scientific and mathematical detail is kept to a minimum, so the reader who is interested in physics, but perhaps lacks the background to follow technical accounts, will find this collection an inviting and easy path through the subject's modern development.
A new era in solar spectroscopy was launched in the late 1860s when a series of solar eclipses provided an opportunity to study the solar chromosphere. This is the hot tenuous layer lying above the photosphere, which is the region of the Sun that emits the vast proportion of the visible light. At the time of a total solar eclipse, it was well known by the 1860s that the light from the thin chromospheric layer (with a height of ∼ 10 to 12 arc seconds or 8000 to 10 000 km) became briefly visible. Moreover, the solar prominences are large structures of chromospheric material extending out from the limb, often a minute of arc or more in height. They too were seen at times of eclipse, and the question of the physical conditions in the chromosphere and prominences arose. The spectroscope was the natural tool to settle the issue. If they were comprised of hot low density gas, then bright emission lines would be expected, as William Huggins pointed out, and hence they should have spectra similar to those of the gaseous nebulae, such as the Orion nebula. Huggins also believed that if bright lines were present, then perhaps they could be observed with suitable glass filters to isolate the line radiation, even outside of eclipse, but attempts to do so did not come to fruition.
Few astronomers would dispute the pivotal rôle that the astronomical spectrograph has played in the development of astrophysics. Of all astronomical instruments other than the telescope itself, none other can compete with the spectrograph for the range of new astronomical knowledge it has provided, and for the insights it has given on the physical nature of the celestial bodies in the Universe. Together with the predecessor of the spectrograph, the visual spectroscope, these instruments have revolutionized our knowledge of the Sun, the planets, stars, gaseous nebulae, the interstellar medium, galaxies and quasars.
Without the spectrograph, we would know nothing of solar or stellar composition, nothing about stellar rotation rates, and much less than we do on stellar space motions and binary stars. Even the real nature of the stars themselves would be a matter of conjecture and debate. And we would have rudimentary knowledge of the conditions prevailing in gaseous and planetary nebulae and of the nature of external galaxies beyond the Milky Way. There would be no Hubble's law, and hence no direct knowledge of the expansion of the Universe other than indirect inference based on Olbers' paradox or on theoretical prediction. Quasars would not be easily distinguished from stars, and the study of radio galaxies and active galactic nuclei would be limited to their morphological properties in optical or radio images. In short, optical spectrographs have underpinned almost every branch of astrophysics in the past century and a half.
A new era in solar spectroscopy was launched in the late 1860s when a series of solar eclipses provided an opportunity to study the solar chromosphere. This is the hot tenuous layer lying above the photosphere, which is the region of the Sun that emits the vast proportion of the visible light. At the time of a total solar eclipse, it was well known by the 1860s that the light from the thin chromospheric layer (with a height of ∼ 10 to 12 arc seconds or 8000 to 10 000 km) became briefly visible. Moreover, the solar prominences are large structures of chromospheric material extending out from the limb, often a minute of arc or more in height. They too were seen at times of eclipse, and the question of the physical conditions in the chromosphere and prominences arose. The spectroscope was the natural tool to settle the issue. If they were comprised of hot low density gas, then bright emission lines would be expected, as William Huggins pointed out, and hence they should have spectra similar to those of the gaseous nebulae, such as the Orion nebula. Huggins also believed that if bright lines were present, then perhaps they could be observed with suitable glass filters to isolate the line radiation, even outside of eclipse, but attempts to do so did not come to fruition.
Henry Draper and William Huggins, pioneers in ultraviolet stellar spectroscopy
Observational studies of the near ultraviolet region of stellar spectra have a long history, which goes back to the early days of stellar spectrum photography. The very first spectrum ever recorded by photography was by Henry Draper in 1872. He used his 28-inch reflector and a spectrograph with a quartz prism, and the then relatively new innovation of a dry emulsion glass plate. He noted:
In the photographs of the spectrum of Vega there are eleven lines, only two of which are certainly accounted for, two more may be calcium, the remaining seven, though bearing a most suspicious resemblance to the hydrogen lines in their general characters, are as yet not identified.
The key to Draper's success was in part his use of the new dry plates, which were so much more convenient than the wet collodion plates used previously in astronomical photography. But also his use of a silvered-glass reflecting telescope and a spectrograph with a quartz prism allowed him not only to go below the approximately 400 nm wavelength limit of the human eye, but below the approximately 380 nm limit for the transmission of flint glass used in the lenses of achromatic refractors.
A spectrograph is an instrument that receives light from a source, disperses the light according to its wavelength into a spectrum, and focusses the spectrum onto a detector, which records the spectral image. In the astronomical case the source might be a star or galaxy, and the light will first be collected by a telescope. Many telescopes produce an image of the source on a spectrograph slit (although slitless objective prism instruments are also possible). After the slit, a collimator renders the rays almost parallel, and a dispersing element, usually a grating or a prism, sends photons of different wavelengths into different directions. A camera then records a continuous succession of monochromatic slit images, each displaced in the dispersion direction according to its wavelength. This array of slit images constitutes the spectrum.
The simplest possible slit spectrograph (Fig. 2.1) therefore comprises a slit, a collimator (either a mirror or a lens system), a dispersing element (typically a grating or a prism) and a camera (again a mirror or lens system) and finally a detector (perhaps a charge-coupled device or CCD, perhaps a photographic plate, but in early instruments it was the human eye in conjunction with an eyepiece).
INTRODUCTION TO SPECTROGRAPHS OF THE LATE TWENTIETH CENTURY
In this chapter, ten outstanding spectrographs which had their first light in the late twentieth or early twenty-first centuries are presented. The section covers five high resolution instruments, four at low resolution and one spectrograph with multiple capabilities that includes low, medium and high resolution modes. All were commissioned between 1984 and 2003 and they are presented in chronological order of their entry into service.
The choice of ten representative spectrographs from the several dozen commissioned over this two decade period was a matter of some difficulty. The final choice was my own personal one. I wanted to show that spectrograph design has become a pursuit of great innovation, ingenuity and also complexity, at times verging towards a creative art-form involving cutting edge optical technology. In this period, huge developments were made in the use of optical fibres, larger and improved efficiency CCD detectors, the production of large mosaic gratings, the development of grisms and volume phase holographic gratings, the design and manufacture of multi-element dioptric cameras with specialized antireflection coatings, high reflection coatings on mirrors, and the extension of the wavelength range both down into the near ultraviolet at the atmospheric limit and also to the far red near one micrometre.
For almost a century since the objective prism spectrograph was first used at Harvard in 1885, this was the only solution available to astronomers for multi-object spectroscopy – the simultaneous recording of the spectra of more than one object. All other astronomical spectroscopy was undertaken sequentially, one object at a time. The limitations of the objective prism caused by overlapping spectra and sky brightness, as well as variable resolving power (dependent on the seeing) have already been discussed.
From about 1980, two new solutions for multi-object spectroscopy, which overcame some of the problems of the objective prism, were introduced. One is the aperture plate combined with a low dispersion element, which is often a combined prism and transmission grating (or ‘grism’ – see Section 2.8). The other is the use of optical fibres. The early history (roughly the first decade) of both these techniques is described here.
APERTURE PLATE MULTI – OBJECT SPECTROSCOPY
The aperture plate was introduced by Harvey Butcher (b. 1947) at Kitt Peak in 1980 as a way of undertaking multi-object spectroscopy of faint objects, all of which lay within the 5 arc minute field of view at the Cassegrain focus of the 4-m Mayall telescope. The aperture plate is a black anodized aluminium sheet in the focal plane, with holes drilled in it, typically with a diameter corresponding to 2.5 arc seconds on the sky.
The concepts of colour, refrangibility and wavelength have been crucial for the development of spectroscopes and spectroscopy. Indeed the first prism spectroscopes were built partly for measuring the refractive indices or refrangibility of different glasses, while diffraction gratings were used for early measurements of wavelength.
The refraction of light
The Dutch astronomer Willebrord Snell (1591–1626) is usually credited with the discovery of the law of refraction, in the early seventeenth century in Leiden. René Descartes (1596–1650) later included the law in his treatise Dioptrics of 1637 (without however acknowledging Snell), and he used it to account for the formation of a rainbow, but not explicitly for the colours that the rainbow produces.
Isaac Newton's (1642–1726) first paper, published by the Royal Society in 1672, but based on his optical experiments undertaken six years earlier, came to important conclusions on the relationship between refrangibility and colour. Newton studied the refraction of the Sun's rays in a glass prism, and projected the resulting spectrum onto a wall of his room. He concluded: ‘… light consists of rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.’ He found that the Sun's light was composed of rays of different primary colours, each with its different refrangibility, which gave rise to the dispersive power of the prism.
There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.
Shakespeare, Hamlet, Act 1 Scene 5
The challenge of semiclassical mechanics: Reassessing the views
Semiclassical mechanics significantly broadens our understanding of the relationship between classical and quantum mechanics. It reveals that there is much more to the relation between these theories than simply showing that classical behavior can be recovered from quantum systems in the limit of large actions (ħ → 0) or large quantum numbers (n → ∞). Although these limits are an important piece of the puzzle, the usual reductionist account of the quantum–classical relation in terms of these limits alone does not tell the whole story.
More specifically, research in semiclassical mechanics has uncovered a number of surprising theoretical and experimental correspondences. Indeed the program of semiclassical research can be broadly understood as the theoretical and experimental task of uncovering these correspondences and extending them in new ways. On the theoretical side, semiclassical methods such as EBK quantization, Gutzwiller's trace formula, and closed orbit theory show how classical structures can be used to construct quantum quantities. These semiclassical methods have proven to be not just useful calculational tools, but also important investigative tools, in that they are often able to provide physical insight into the structure of the quantum dynamics, and hence lead to new discoveries.
The principles of the old quantum theory were first articulated by Niels Bohr in 1913 in a three-part paper titled “On the Constitution of Atoms and Molecules.” Bohr had adopted Ernest Rutherford's model of the atom, according to which the mass of the atom is concentrated in a small central nucleus, while the electrons orbit the nucleus in planetary trajectories. The key challenge facing Rutherford's model was that it was unstable: according to classical electrodynamics, the electron, which is a moving charged body, should radiate energy and so eventually collapse into the nucleus. Bohr's solution was to incorporate Max Planck's theory of radiation, according to which “the energy radiation from an atomic system does not take place in the continuous way assumed in ordinary electrodynamics, but that it, on the contrary, takes place in distinctly separated emissions” (Bohr 1913, p. 4; BCW 2, p. 164). In this early paper, and most subsequent accounts, Bohr summarized his quantum theory by means of two assumptions or postulates. According to the first postulate, electrons cannot travel in any path they like around the nucleus, rather atomic systems can only exist in a series of discrete “stationary states,” in which the electron is in a particular allowed stable periodic orbit and is not emitting radiation.