According to the Rayleigh criterion of classical optics, the finite resolving power of a microscope is due to the width of the central peak of the Fraunhofer diffraction pattern produced by the microscope's finite lens aperture. During the last few decades, theories and techniques for superresolution beyond the Rayleigh criterion have been developed in classical optics. Thus, Heisenberg's microscope could also in principle be made to give superresolution and thereby appear to violate the uncertainty relation. We believe that this paradox (...) is due to the inappropriate use of a definition, based purely on experimental convenience, to support a quantum mechanical theorem. (shrink)

"Sir Hermann Bondi, NatureThe late S. Chandrasekhar was best known for his discovery of the upper limit to the mass of a white dwarf star, for which he received ...

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.Representing a decade's work from (...) a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London, the National Medal of Science in the United States, and the Copley Medal from the Royal Society. His many publications include Radiative transfer, Hydrodynamic and hydromagnetic stability, and The mathematical theory of black holes, each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable. (shrink)

About the Book : Several years ago, on a fateful night in a colonial house in Yercaud, Tamil Nadu, UG Krishnamurthi made a bonfire of Chandrasekhar's dreams.

The success of India's democracy hinges on the pivotal role played by its auxiliary institutions in negotiating major challenges through slow and persistent transformation. However, an objective audit of the performance of these institutions in the recent past would indicate a decline in operations and an acute crisis of corruption. Key institutions responsible for governance have been put under the spotlight by an alert and mobilized civil society, urging immediate measures for ensuring their operational efficiency and integrity. This essay undertakes (...) a critical examination of the present performance and efficiency of major democratic institutions in India, in the light of their prescribed roles and the malaise of corruption that plagues them. It argues that in order to articulate a comprehensive institutional response to the problem, relevant measures of political reform and constant vigil by civil society would prove crucial. The article is divided into six sections; first, a brief outline of the structure and changing nature of the institutional political set-up in India is provided; the second section examines the existing literature on , and the third section highlights the increasing incidence of corruption in India at various politico-administrative tiers. The fourth section delineates the inception and role of anti-corruption institutions in India, signifying the early response to corruption. The fifth section critically reviews the theoretical and statistical evidence of performance-decline in the major institutions at present and gauges the potency of corruption; the sixth section explores the existing and prospective institutional responses for tackling corruption and the final section presents concluding observations. (shrink)

Using the linearized Einstein gravitational field equations and the Maxwell field equations it is shown that the plane of polarization of an electromagnetic wave is rotated by the gravitational field created by the electromagnetic radiation of a ring laser. It is further shown that this gravitational Faraday effect shares many of the properties of the standard electromagnetic Faraday effect. An experimental arrangement is then suggested for the observation of this gravitational Faraday effect induced by the ring laser.

Summary The 1935 conflict on the nature of relativistic degeneracy that pitted Subrahmanyan Chandrasekhar against Arthur Stanley Eddington is part of astronomical lore. In recountings of the events surrounding the dispute, the complaint is frequently aired that Chandrasekhar, who faced the pre-eminent astrophysicist of his time, did not enjoy the support of the astronomical community, which opted to side instead with Eddington. We reconsider these statements in the light of the published record and argue that the reception of (...) Chandrasekhar's ideas was, if anything, rather favourable and that any perceived lack of support may have been due in great part to the inability to distinguish, on an observational basis, between the predictions of the competing theories. We further argue that the observational situation improved little over the subsequent thirty years, but that this did not prevent Chandrasekhar's version of relativistic degeneracy, and associated theory of electron-degenerate stars, from gaining a central position within the realm of stellar structure and evolution. We briefly compare this status to that enjoyed by general relativity before 1960. (shrink)

Contemporary biologists are not agreed on the question of whether there are any human races, despite the widespread scientific consensus on the underlying genetics. For most purposes, however, we can reasonably treat this issue as terminological. What most people in most cultures ordinarily believe about the significance of “racial” difference is quite remote, I think, from what the biologists are agreed on. Every reputable biologist will agree that human genetic variability between the populations of Africa or Europe or Asia is (...) not much greater than that within those populations; though how much greater depends, in part, on the measure of genetic variability the biologist chooses. If biologists want to make interracial difference seem relatively large, they can say that “the proportion of genic variation attributable to racial differences is … 9 – 11%.”1 If they want to make it seem small, they can say that, for two people who are both Caucasoid, the chances of difference in genetic constitution at one site on a given chromosome are currently estimated at about 14.3 percent, while for any two people taken at random from the human population, they are estimated at about 14.8 percent. The statistical facts about the distribution of variant characteristics in human populations and subpopulations are the same, whichever way the matter is expressed. Apart from the visible morphological characteristics of skin, hair, and bone, by which we are inclined to assign people to the broadest racial categories—black, white, yellow—there are few genetic characteristics to be found in the population of England that are not found in similar proportions in Zaire or in China; and few too which are found in Zaire but not in similar proportions in China or in England. All this, I repeat, is part of the consensus . A more familiar part of the consensus is that the differences between peoples in language, moral affections, aesthetic attitudes, or political ideology—those differences which most deeply affect us in our dealings with each other—are not biologically determined to any significant degree.[…]In this essay, I want to discuss the way in which W. E. B. Du Bois—who called his life story the “autobiography of a race concept”—came gradually, though never completely, to assimilate the unbiological nature of races. I have made these few prefatory remarks partly because it is my experience that the biological evidence about race is not sufficiently known and appreciated but also because they are important in discussing Du Bois. Throughout his life, Du Bois was concerned not just with the meaning of race but with the truth about it. We are more inclined at present, however, not to express our understanding of the intellectual development of people and cultures as a movement toward the truth; I shall sketch some of the reasons for this at the end of the essay. I will begin, therefore, by saying what I think the rough truth is about race, because, against the stream, I am disposed to argue that this struggle toward the truth is exactly what we find in the life of Du Bois, who can claim, in my view, to have thought longer, more engagedly, and more publicly about race than any other social theorist of our century. 1. Masatoshi Nei and Arun K. Roychoudhury, “Genetic Relationship and Evolution of Human Races,” Evolutionary Biology 14 : 11; all further references to this work, abbreviated “GR,” will be included in the text. Anthony Appiah is associate professor of philosophy, African studies, and Afro-American studies at Yale. He is the author of Assertion and Conditionals and For Truth in Semantics . In addition, he is at work on African Reflections: Essays in the Philosophy of Culture. (shrink)

In this dialogue, Mileva and Albert start to talk about physics and its subject matter, the physical. They end up in a situation that permits causal dependence between separate ontological domains. In this possible world, they continue talking. First, they Socratically agree that the physical is physical and only physical. Then, they call the physical an ontologically homogeneous domain. They then generalise the principle that the physical is causally unaffected by anything non-physical, into the principle that ontologically homogeneous domains do (...) not cause ontologically homogeneous domains. From a modern point of view talking about black hole singularities, they continue discussing the Chandrasekhar limit and the collapse of the physical laws as we know them. Mileva carries a burden and Albert stands up and carries it with her. The burden is an implication of the generalised principle. Relying on parsimony, only ontologically homogeneous domains are forbidden to cause ontologically homogeneous domains. This leaves the door open for ontologically heterogeneous domains to cause ontologically homogeneous domains. Also relying on parsimony, only ontologically homogeneous domains are forbidden to be caused by ontologically homogeneous domains and this allows ontologically heterogeneous domains to be caused by ontologically homogeneous domains. Ontologically heterogeneous domains, thus, are allowed to causally link ontologically homogeneous domains. Albert realises that the mathematical could qualify as an ontologically homogeneous domain and that the theoretical difficulties that are foreseen beyond the Chandrasekhar limit could be addressed by expanding physics into a context that contains also an ontologically heterogeneous domain. The theoretical difficulties beyond the Chandrasekhar limit would be due to an emergent mathematical-physical domain. Mileva concludes that Albert’s theory is not faulty but regional. A global theory would have to include the explanation of the mathematical-physical. (shrink)

Gödel's conclusion that time-travel is possible in his models of Einstein's gravitational theory has been questioned by Chandrasekhar and Wright, and treated as doubtful in the recent philosophical literature. The present note is intended to remove this doubt: a review of Gödel's construction shows that his arguments are entirely correct; and the objection is seen to rest upon a misunderstanding. Computational points treated succinctly by Gödel are here presented in fuller detail. The philosophical significance of Gödel's results is briefly (...) considered, and a set of technical questions is posed whose answers would clarify this significance. (shrink)

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the “quanta” of the cosmological (...) constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 1055 g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of ‘classical’ fundamental constants. (shrink)

Lanczos, C. Einstein's path from special to general relativity.--Balazs, N. L. The acceptability of physical theories: Poincaré versus Einstein.--Ellis, G. F. R. Global and non-global problems in cosmology, by G. F. R. Ellis and D. W. Sciama.--Ehlers, J. The geometry of free fall and light propagation, by J. Ehlers, F. A. E. Pirani and A. Schild.--Trautman, A. Invariance of Lagrangian systems.--Penrose, R. The geometry of impulsive gravitational waves.--Exact solutions of the Einstein-Maxwell equations for an accelerated charge.--Taub, A. H. Plane-symmetric similarity (...) solutions for self-gravitating fluids.--Robinson, I. Equations of motion in the linear approximation, by I. Robinson and J. R. Robinson.--Florides, P. W. Rotating bodies in general relativity.--Chandrasekhar, S. A limiting case of relativistic equilibrium.--Israel, W. The relativistic Boltzmann equation.--Thompson, W. B. The self-consistent test-particle approach to relativistic kinetic theory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Feminist Studies 41, no. 3. © 2015 by Feminist Studies, Inc. 509 Mytheli Sreenivas Birth Control in the Shadow of Empire: The Trials of Annie Besant, 1877–1878 In March 1877, two London activists provoked a debate about poverty and overpopulation that reverberated across metropole and colony. These activists, Annie Besant and Charles Bradlaugh, republished a book by the American physician Charles Knowlton that outlined methods to prevent conception. TheFruitsofPhilosophy,which (...) Bradlaugh and Besant provocatively subtitled An Essay on the Population Question, had been in limited circulation in Britain since 1833, but the book’s legality was called into question when its previous publisher was charged with obscenity in early 1877.1 Determined to establish the legal right to publish information about contraception, on March 23rd, 1877, Bradlaugh and Besant delivered copies of The Fruits of Philosophy to the police department, the city solicitor, and local magistrates, and they announced their intent to sell the book from their premises at the Freethought Publishing Company on Stonecutter Street in East London. The following day, a crowd filled the narrow space outside the publishing house, and the two activists sold hundreds of copies of Knowlton’s book. When no arrests were made, Besant and Bradlaugh renotified the authorities that they were selling a supposedly obscene book and were informed in turn that papers were 1. S. Chandrasekhar, “A Dirty, Filthy Book”: The Writings of Charles Knowlton and Annie Besant on Reproductive Physiology and Birth Control and an Account of the Bradlaugh-Besant Trial (Berkeley: University of California Press, 1981), 26. 510 Mytheli Sreenivas being prepared for their arrest and prosecution. On the 7th of April, 1877, Besant and Bradlaugh were arrested and taken into custody.2 In their subsequent trial, the two activists linked birth control advocacy to a Malthusian worldview. They argued that the urban working classes and the rural poor in Britain labored under the burden of overpopulation. Humanitarian concern for impoverished people, and not intent to promote obscenity, drove them to disseminate information about birth control. Besant and Bradlaugh were eventually acquitted on a legal technicality, and Bradlaugh moved on to other issues. Besant, however, was dissatisfied with The Fruits of Philosophy because its methods were outdated by the science of the day. She was determined to write a more up-to-date guide explaining contraceptive methods and went on to found a Malthusian League to disseminate birth control information. These events—the trial and Besant’s further campaigns promoting contraception —mark a watershed moment in the history of birth control activism.3 They would shape how reproduction came to be understood not as a private matter, but as a particular sort of social problem, whose implications reverberated from London to the empire in India and back again. To outside observers, Bradlaugh and Besant may have seemed an unlikely pair to set these events into motion. Bradlaugh, at age forty-four, had a long history of association with radical causes. A celebrated atheist and antimonarchical republican, he helped to shape a tradition of mid-nineteenth-century English radicalism that developed in the wake of Chartist decline. As a member of the National Reform League in the 1860s, he had participated in public demonstrations to extend the franchise. His leadership of the National Secular Society made him a popular lecturer among Freethinkers on issues of political democracy, anticlericalism, and occasionally on neo-Malthusianism.4 2. Anne Taylor, Annie Besant: A Biography (Oxford: Oxford University Press, 1992), 110–12. 3. The term “birth control” was coined in a meeting of Margaret Sanger and her associates in 1914, and thus would not have been in use in the late nineteenth century. The term contraception was not unknown, but had only limited circulation in scientific discourses. Nevertheless, I use both “birth control” and “contraception” interchangeably to mean methods to prevent conception. See Peter C. Engelman, A History of the Birth Control Movement in America (Santa Barbara, CA: Praeger, 2011), xviii. 4. Taylor, Annie Besant, 80–81. Mytheli Sreenivas 511 In comparison to Bradlaugh’s prominence, Besant was relatively unknown. Her public career began after a separation from her husband, the Anglican vicar Frank Besant. Perhaps the couple were ill-suited to each other from... (shrink)

According to prevailing theory, relativistic degenerate stars with masses beyond the Chandrasekhar and Oppenheimer–Volkoff (OV) limits cannot achieve hydrostatic equilibrium through either electron or neutron degeneracy pressure and must collapse to form stellar black holes. In such end states, all matter and energy within the Schwarzschild horizon descend into a central singularity. Avoidance of this fate is a hoped-for outcome of the quantization of gravity, an as-yet incomplete undertaking. Recent studies, however, suggest the possibility that known quantum processes may (...) intervene to arrest complete collapse, thereby leading to equilibrium states of macroscopic size and finite density. I describe here one such process which entails pairing (or other even-numbered association) of neutrons (or constituent quarks in the event of nucleon disruption) to form a condensate of composite bosons in equilibrium with a core of degenerate fermions. This process is analogous to, but not identical with, the formation of hadron Cooper pairs that give rise to neutron superfluidity and proton superconductivity in neutron stars. Fermion condensation to composite bosons in a star otherwise destined to collapse to a black hole facilitates hydrostatic equilibrium in at least two ways: (1) removal of fermions results in a decrease in the Fermi level which stiffens the dependence of degeneracy pressure on fermion density, and (2) phase separation into a fermionic core surrounded by a self-gravitating condensate diminishes the weight which must be balanced by fermion degeneracy pressure. The outcome is neither a black hole nor a neutron star, but a novel end state, a “fermicon star,” with unusual physical properties. (shrink)