Infrared metaphysics: radiation and theory-choice. Part 2

We continue our discussion of the competing arguments in favour of the unified theory and the pluralistic theory of radiation advanced by three nineteenth-century pioneers: Herschel, Melloni, and Draper. Our narrative is structured by a consideration of the epistemic criteria relevant to theory-choice; the epistemic focus highlights many little-known aspects of this relatively well-known episode. We argue that the acceptance of light-heat unity (and of the unified theory of radiation more generally) in this period cannot be credibly justified on the basis of common evaluative criteria such as simplicity and standard notions of explanatory power. Whether the consensus was justified by some other criteria remains an open question.     

How to think about shared norms and pluralism without circularity: A reply to Anna Leuschner

Anna Leuschner argues that there is problematic circularity in Helen Longino's approach that postulates the existence of some shared norms as a necessary precondition for well-functioning pluralistic communities. As an alternative, Leuschner proposes to approach the establishing of more pluralistic communities through political means on a case-by-case basis, taking relevant epistemic and political factors into account. In this paper, I argue that there is an alternative understanding of norms that avoids circularity. I do so by drawing on Isabelle Peschard's discussion of shared practice. I go on to show that norms, so understood, are important in the cases where a political decision may not alone be sufficient for establishing a successful community. Specifically, I discuss pluralistic communities that include laypersons in possession of relevant expertise as an example.     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part two

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a 1924 paper by John H. Van Vleck in The Physical Review as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking that led to Heisenberg’s Umdeutung paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr’s correspondence principle to construct their quantum counterparts both for the special case of a charged harmonic oscillator (Sect. 5) and for arbitrary non-degenerate multiply-periodic systems (Sect. 6). We then rederive these results in modern quantum mechanics (Sect. 7). This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin. The authors gratefully acknowledge support from the Max Planck Institute for History of Science. The research of Anthony Duncan is supported in part by the National Science Foundation under grant PHY-0554660.     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part one

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.     

Effective Field Theories,Reductionism and Scientific Explanation

Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation.     

The many faces of unification and pluralism in economics: The case of Paul Samuelson's Foundations of Economic Analysis

The history of modern economics abounds with pleas for more pluralism as well as pleas for more unification. These seem to be contradictory goals, suggesting that pluralism and unification are mutually exclusive, or at least that they involve trade-offs with more of one necessarily being traded off against less of the other. This paper will use the example of Paul Samuelson's Foundations of Economic Analysis (1947) to argue that the relationship between pluralism and unification is often more complex than this simple dichotomy suggests. In particular, Samuelson's Foundations is invariably presented as a key text in the unification of modern economics during the middle of the twentieth century; and in many ways that is entirely correct. But Samuelson's unification was not at the theoretical (causal and explanatory) level, but rather at the purely mathematical derivational level. Although this fact is recognized in the literature on Samuelson, what seems to be less recognized is that for Samuelson, much of the motivation for this unification was pluralist in spirit: not to narrow scientific economics into one single theory, but rather to allow for more than one theory to co-exist under a single unified derivational technique. This hidden pluralism will be discussed in detail. The paper concludes with a discussion of the implications for more recent developments in economics.     

A historical review of the problem of mitogenetic radiation

The 'miracle of caryokinesis' was the starting point that stimulated Alexander G. Gurwitsch to carry out his famous 'mitogenetic' experiments in 1923. The results obtained confirmed his hypothesis of a weak radiation from cells, which is able to trigger the growth of other cells. Extensive experimental work within the first two decades after this discovery indicated that the problem of mitogenetic radiation is generally related to the biological significance of UV-radiation. Both 'energetic' and 'informational' aspects have to be considered, namely radiation effective in activating molecules, and that involved in arranging them into larger units. The molecular organization of biological structures is evidently governed by nonequilibrium conditions needing the uptake or emission of radiation. These concepts of A. G. Gurwitsch can be linked with modern approaches based on hypotheses of coherence in biology, 'synergetics' and 'dissipative structures'. However, the question of causal interrelationships between this part of non-equilibrium radiation and biological matter on different levels of evolution has to be solved now.     

Spacetime Models for the World

In this paper I take a sceptical view of the standard cosmological model and its variants, mainly on the following grounds: (i) The method of mathematical modelling that characterises modern natural philosophy—as opposed to Aristotle's—goes well with the analytic, piecemeal approach to physical phenomena adopted by Galileo, Newton and their followers, but it is hardly suited for application to the whole world. (ii) Einstein's first cosmological model (1917) was not prompted by the intimations of experience but by a desire to satisfy Mach's Principle. (iii) The standard cosmological model—a Friedmann–Lemaı̂tre–Robertson–Walker spacetime expanding with or without end from an initial singularity—is supported by the phenomena of redshifted light from distant sources and very nearly isotropic thermal background radiation provided that two mutually inconsistent physical theories are jointly brought to bear on these phenomena, viz the quantum theory of elementary particles and Einstein's theory of gravity. (iv) While the former is certainly corroborated by high-energy experiments conducted under conditions allegedly similar to those prevailing in the early world, precise tests of the latter involve applications of the Schwarzschild solution or the PPN formalism for which there is no room in a Friedmann–Lemaı̂tre–Robertson–Walker spacetime.     

Holism and structuralism in U(1) gauge theory

After decades of neglect philosophers of physics have discovered gauge theories—arguably the paradigm of modern field physics—as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism—in the eyes of its proponents the best suited realist position towards modern physics—has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories—in particular U(1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov–Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed.     

Unified science as political philosophy: positivism, pluralism and liberalism

Logical positivism is widely associated with an illiberal technocratic view of politics. This view is a caricature. Some members of the left Vienna circle were explicit in their criticism of this conception of politics. In particular, Neurath’s work attempted to link the internal epistemological pluralism and tolerance of logical empiricism with political pluralism and the rejection of a technocratic politics. This paper examines the role that unified science played in Neurath’s defence of political and social pluralism. Neurath’s project of unified science addressed problems that lie at the centre of recent debates around liberalism concerning the possibility of social co-operation in conditions of pluralism. His response is distinctive in calling upon an empiricist tradition that differs from Kantian proceduralist approaches that have predominated in recent liberalism. While Neurath’s position has problems, it deserves reconsideration, especially in so far as it questions the Kantian assumption that a thin language of abstract rights provides the best basis for the cosmopolital lingua franca required by conditions of social pluralism. An investigation of the role that unified science plays in Neurath’s politics also gives reasons for revising common misconceptions about the nature of the unity of science programme itself.     

地貌分类指标的钢柔性探索

争对目前地貌类型基本概念的极度混乱现象,文章提出了地貌分类指标的钢柔性方法。该法把直接影响地貌类型基本概念的指标定为钢性指标,把与地貌类型基本概念不密切的指标定为柔性指标,并在此基础上建立了地貌钢柔性分类系统的参考模式,解决了地貌概念的混乱问题,同时增强了地貌分类的灵活性。该结果对促动地貌的生产利用和科学普及有一定作用。     

The rhetorical strategy of William Paley’s Natural theology (1802): Part 1, William Paley’s Natural theology in context

This article reconstructs the historical and philosophical contexts of William Paley’s Natural theology (1802). In the wake of the French Revolution, widely believed to be the embodiment of an atheistic political credo, the refutation of the transmutational biological theories of Buffon and Erasmus Darwin was naturally high on Paley’s agenda. But he was also responding to challenges arising from his own moral philosophy, principally the psychological quandary of how men were to be kept in mind of the Creator. It is argued here that Natural theology was the culmination of a complex rhetorical scheme for instilling religious impressions that would increase both the virtue and happiness of mankind. Philosophy formed an integral part of this strategy, but it did not comprise the whole of it. Equally vital were those purely rhetorical aspects of the discourse which, according to Paley, were more concerned with creating ‘impression’. This facet of his writing is explored in part one of this two-part article. Turning to the argumentative side of the scheme, part two examines Paley’s responses to David Hume and Erasmus Darwin in the light of the wider strategy of inculcation at work throughout all his writings.     

The emergence of selection rules and their encounter with group theory, 1913–1927

In today's quantum mechanics and quantum field theory, the observable signature of a symmetry is often sought in the form of a selection rule: a missing radiation frequency, a particle that does not decay in another one, a scattering process which fails to take place. The connection between selection rules and symmetries is effected thanks to the mathematical discipline of group theory. In the present paper, I will offer an overview of how the productive synergy between selection rules and group theory came to be. The first half of the work will be devoted to the emergence of the idea of spectroscopic selection rules in the context of the old quantum theory, showing how this notion was linked with an interpretive scheme of theoretical nature which, once combined with group theory, would bear many fruits. In the second part of the paper, I will focus on the actual encounter between selection rules and group theory, and on the person largely responsible for it: Eugene Wigner. I will attempt to reconstruct the path which led Wigner, of all people, to be the agent effecting this connection.     

The rhetorical strategy of William Paley’s Natural theology (1802): Part 2, William Paley’s Natural theology and the challenge of atheism

The first part of this two-part article suggested that William Paley’s Natural theology (1802) should be viewed as the culmination of a complex psychological strategy for inculcating religious and moral sentiments. Having focused in Part 1 on Paley’s rhetoric, we now turn our attention to the philosophical part of the programme. This article attempts to settle the vexed question of how far Paley responded to the devastating critique of the teleological argument contained in Hume’s posthumously published Dialogues concerning natural religion (1779). It also identifies tensions that arose in Natural theology between the rhetorical and intellectual sides of the stratagem. In response to Erasmus Darwin’s evolutionary theories, Paley asserted that the divinely designed architecture of nature had remained unchanged since the creation. But the more he emphasized the preordained nature of providence, its effectuation through mechanical dispositions, the less room there appeared to be for particular interventions. Section 2 concentrates on Paley’s efforts to reconcile this model of a law-governed, mechanical universe, with the belief in a personal God who was active in worldly affairs. It therefore challenges the view, long unquestioned in the historical literature, that Paley’s Deity was merely a watchmaker, who had remained idle since the Creation.     

在非线性系统中的微观粒子的特性和非线性量子力学理论(下)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

A lost chapter in the pre-history of algebraic analysis: Whittaker on contact transformations

In the early 1930s W. O. Kermack and W. H. McCrea published three papers in which they attempted to prove a result of E. T. Whittaker on the solution of differential equations. In modern parlance, their key idea consisted in using quantized contact transformations over an algebra of differential operators. Although their papers do not seem to have had any impact, either then or at any later time, the same ideas were independently developed in the 1960–1980s in the framework of the theory of modules over rings of microdifferential operators. In this paper we describe the results of Kermack and McCrea and discuss possible reasons why such promising papers had no impact on the mathematics of the twentieth century.     

A probabilistic foundation of elementary particle statistics. Part I

The long history of ergodic and quasi-ergodic hypotheses provides the best example of the attempt to supply non-probabilistic justifications for the use of statistical mechanics in describing mechanical systems. In this paper we reverse the terms of the problem. We aim to show that accepting a probabilistic foundation of elementary particle statistics dispenses with the need to resort to ambiguous non-probabilistic notions like that of (in)distinguishability. In the quantum case, starting from suitable probability conditions, it is possible to deduce elementary particle statistics in a unified way. Following our approach Maxwell-Boltzmann statistics can also be deduced, and this deduction clarifies its status.Thus our primary aim in this paper is to give a mathematically rigorous deduction of the probability of a state with given energy for a perfect gas in statistical equilibrium; that is, a deduction of the equilibrium distribution for a perfect gas. A crucial step in this deduction is the statement of a unified statistical theory based on clearly formulated probability conditions from which the particle statistics follows. We believe that such a deduction represents an important improvement in elementary particle statistics, and a step towards a probabilistic foundation of statistical mechanics.In this Part I we first present some history: we recall some results of Boltzmann and Brillouin that go in the direction we will follow. Then we present a number of probability results we shall use in Part II. Finally, we state a notion of entropy referring to probability distributions, and give a natural solution to Gibbs' paradox.     

On classical cloning and no-cloning

It is part of information theory folklore that, while quantum theory prohibits the generic (or universal) cloning of states, such cloning is allowed by classical information theory. Indeed, many take the phenomenon of no-cloning to be one of the features that distinguishes quantum mechanics from classical mechanics. In this paper, we argue that pace conventional wisdom, in the case where one does not include a machine system, there is an analog of the no-cloning theorem for classical systems. However, upon adjoining a non-trivial machine system (or ancilla) one finds that, pace the quantum case, the obstruction to cloning disappears for pure states. We begin by discussing some conceptual points and category-theoretic generalities having to do with cloning, and proceed to discuss no-cloning in both the case of (non-statistical) classical mechanics and classical statistical mechanics.