Bohr’s atomic model is one of the better known examples of empirically successful, albeit inconsistent, theoretical schemes in the history of physics. For this reason, many philosophers use this model to illustrate their position for the occurrence and the function of inconsistency in science. In this paper, I proceed to a critical comparison of the structure and the aims of Bohr’s research program – the starting point of which was the formulation of his model – with (...) some of its contemporary philosophical readings. My study comes to conclude that the attempt of certain philosophers to accommodate Bohr’s model to a form of paraconsistent logic obliterates essential aspects of scientists' actual practice and reasoning. (shrink)

Niels Bohr’s model of the hydrogen atom is widely cited as an example of an inconsistent scientific theory because of its reliance on classical electrodynamics together with assumptions about interactions between matter and electromagnetic radiation that could not be reconciled with CED. This view of Bohr’s model is controversial, but we believe a recently proposed approach to reasoning with inconsistent commitments offers a promising formal reading of how Bohr’s model worked. In this paper we present this new (...) way of reasoning with inconsistent commitments and compare it with other approaches before applying it to Bohr’s model and offering some suggestions for how it might be extended to account for subsequent developments in old quantum theory. (shrink)

Zollinger wants to show that Bohr's principle of complementarity is applicable to human social interaction as well as to the sub-atomic realm. He therefore spends much time laying the foundations of his thesis, explaining the principle in its microphysical context. The human socio-political matrix is not merely analogous to the microphysical realm, for Zollinger, but is an evolutionary extension of it. Both are subject to complementarity in differing degrees of complexity. From a discussion of the tiny organism, he (...) moves through an account of primitive societies to a short review of the history of civilization to the present era. He toys with themes like male and female complementarity as a factor in human evolution. He describes the emergence of male characteristics from subordination to dominance, with the "new male" breaking the matriarchal order to build "the revolutionary rational order of dynamic political masculinity." His historical and anthropological accounts are on the whole superficial and stated in generalities that are long on speculation and short on research. Throughout, the book is plagued by obscurities caused by clumsy phrasing, private jargon, questions raised but not dealt with, and non sequiturs. Toward the end of the book, as he gets into the modern era, Zollinger finds himself in more familiar territory, and what he has to say is more solid than at the beginning. He suggests ways in which modern political man might better take into account the interdependency of the disparate elements of his society and integrate them into a whole of superior order. This is perhaps an important point, but here, as in other places in the book, the connection with Bohr is contrived, and Zollinger's model seems more properly to be Hegelian Aufhebung than Bohr's complementarity.--S. O. H. (shrink)

Niels Bohr was a central figure in quantum physics, well known for his work on atomic structure and his contributions to the Copenhagen interpretation of quantum mechanics. In this book, philosopher of science Slobodan Perović explores the way Bohr practiced and understood physics, and analyzes its implications for our understanding of modern science. Perović develops a novel approach to Bohr’s understanding of physics and his method of inquiry, presenting an exploratory symbiosis of historical and philosophical analysis that uncovers the (...) key aspects of Bohr’s philosophical vision of physics within a given historical context. -/- To better understand the methods that produced Bohr’s breakthrough results in quantum phenomena, Perović clarifies the nature of Bohr’s engagement with the experimental side of physics and lays out the basic distinctions and concepts that characterize his approach. Rich and insightful, Perović’s take on the early history of quantum mechanics and its methodological ramifications sheds vital new light on one of the key figures of modern physics. (shrink)

We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T$ is a theory of size $\lambda$ where the principal types are dense, yet $T$ has no atomic model.

Research into learners' ideas aboutscience suggests that school and collegestudents often hold alternative conceptionsabout `the atom'. This paper discusses whylearners acquire ideas about atoms which areincompatible with the modern scientificunderstanding. It is suggested that learners'alternative ideas derive – at least in part –from the way ideas about atoms are presented inthe school and college curriculum. Inparticular, it is argued that the atomicconcept met in science education is anincoherent hybrid of historical models, andthat this explains why learners commonlyattribute to atoms properties (...) (such as beingthe constituent particles of all substances, orof being indivisible and conserved inreactions) that more correctly belong to otherentities (such as molecules or sub-atomicparticles). Bachelard suggested that archaicscientific ideas act as `epistemologicalobstacles', and here it is argued thatanachronistic notions of the atom survive inthe chemistry curriculum. These conceptualfossils encourage learners to develop an`atomic ontology' (granting atoms `ontologicalpriority' in the molecular model of matter); tomake the `assumption of initial atomicity' whenconsidering chemical reactions; and to developan explanatory framework to rationalisechemical reactions which is based on thedesirability of full electron shells. Theseideas then act as impediments to thedevelopment of a modern chemical perspective onthe structure of matter, and an appreciation ofthe nature of chemical changes at the molecularlevel. (shrink)

We believe that physics education has to meet today’s requirement for a qualitative approach to Quantum Mechanics (QM) worldview. An effective answer to the corresponding instructional problem might allow the basic ideas of QM to be accessed atan early stage of physics education. This paper presents part of a project that aims at introducing a sufficient, simple, and relevant teaching approach towards QM into in-/preservice teacher education, i.e., at providing teachers with the indispensable scientific knowledge and epistemological base needed for (...) a reform of science education along the aforementioned line. The investigation of teacher–learners’ (t-ls’) initial knowledge indicated that their main misconceptions appear to be the result of their pre-/in university traditional instruction, which causes the overlapping/mix-up of the conceptual frameworks of Classical Physics (CP) and QM. Assuming that these misconceptions form by nature epistemological obstacles to the acquisition of QM knowledge, the educational strategy proposed here aims at leading t-ls to form a conceptual structure that includes CP and QM as two totally independent conceptual systems. Accepting, furthermore, that the complete distinction of these systems demands a radical reconstruction of t-ls’ initial knowledge, we present here an instructional model that bases the required reconstruction on the juxtaposition of two models that constitute the signal point of twentieth century’s “paradigm shift”: (a) Bohr’s semiclassical atom model, and (b) the model of the atom accepted by modern physics theory. (shrink)

Summary This paper presents an immanent criticism of Lakatos' reconstruction of the degenerating phase of Bohr's atomic theory. That is to say, the historiographical methods used are exclusively of a Lakatosian kind. Such a closer Lakatosian look at the historical episode in question shows that Lakatos' own reconstruction is incorrect on three essential points. These are the role of the correspondence principle, the position of the hard core in Bohr's programme, and the presence of important novel predicted (...) facts. I conclude that these defects are irreparable within the framework of Lakatos' methodology of scientific research programmes. (shrink)

Scientific models invariably involve some degree of idealization, abstraction, or nationalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations, which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by applying it to (...) the case of Bohr's model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models. (shrink)

In this paper we analyse the approach to interpreting atomic spectra in the framework of classical physics from the discovery of the electron in 1897 to Bohr's atomic model of 1913. Taken as a whole, efforts in this direction are part of a remarkable intellectual endeavour in which the classical theoretical framework seems to have been exploited to its full potential. By demonstrating the limits and weaknesses of classical physics in solving the problem of spectral emissions, (...) these attempts opened the way to a complete break from traditional thought and the introduction of the new quantum ideas. (shrink)

Counterfactual reasoning has been used to account for many aspects of scientific reasoning. More recently, it has also been used to account for the scientific practice of modeling. Truth in a model is truth in a situation considered as counterfactual. When we reason with models, we reason with counterfactuals. Focusing on selected models like Bohr’s atom model or models of population dynamics, I present an account of how the imaginative development of a counterfactual supposition leads us from reality (...) to interesting model assumptions; how it guides our reasoning from these assumptions to interesting consequences for the model scenario via counterfactual entailment; and how it leads us back to conclusions on real target phenomena. (shrink)

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.

Summary The emergence of quantum theory in the early decades of the twentieth century was accompanied by a wide range of popular science books, all of which presented in words, and a few in images, new scientific ideas about the structure of the atom. The work of physicists such as Ernest Rutherford and Niels Bohr, among others, was pivotal to the so-called planetary model of the atom, which, still today, is used in popular accounts and in science textbooks. In (...) an attempt to add to our knowledge about the popular trajectory of the new atomic physics, this paper examines one book in particular, co-authored by Danish science writer Helge Holst and Dutch physicist and close collaborator of Niels Bohr, Hendrik A. Kramers. Translated from Danish into four European languages, the book not only explained contemporary ideas about the quantum atom, but also discussed unresolved problems. Moreover, the book was quite explicit in identifying the quantum atom with the atom as described by Bohr's theory. We argue that Kramers and Holst's book, along with other ‘atomic books’, was a useful tool for physicists and science popularisers in trying to understand the new quantum physics. (shrink)

Presented in this study is an analysis of the electronic properties of doped diamond calculated using the Vienna ab initio simulation package, employing density functional theory within the generalized-gradient approximation. The dopants studied here have been inserted substitutionally into a 64-atom diamond supercell and include the single-electron acceptors boron and aluminium, the single-electron donors nitrogen and phosphorus and the double-electron donors oxygen and sulphur. Co-doping of diamond with sulphur and boron has also been briefly examined. The doped supercells have been (...) relaxed, followed by calculation of electronic properties from the electronic density of states such as the indirect bandgap E g , the valence bandwidth and an examination of the acceptor and donor states in the bandgap. It is anticipated that this study will provide a useful comparison of the third- and fourth-row donors and acceptors in diamond. (shrink)

ArgumentJ. Robert Oppenheimer was a complex person. His work in physics during the 1930s, at Los Alamos during the 1940s, and as governmental advisor in the immediate postwar period, gave him a deep sense of connection with communities that had distinctive purposes. But he found it difficult to conceive an overall creative vision for himself or to devise a compelling objective for the community he belonged to if one had not been formulated at the time he assumed its leadership. I (...) analyze the reasons for his successes: the vision and demands of physics during the 1930s, the make-up of Los Alamos, and the challenges of the postwar atomic world. In each of these enterprises he assumed a distinctive role and came to represent a distinctive persona – but he could not integrate his activities into a coherent whole that might be a model for the intellectual in the new world he had helped to shape. (shrink)

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world (...) of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT. (shrink)

This work utilizes examples from chemical sciences to present fundamentals of dialectics and synergetics. The laws of dialectics remain appropriate at the level of atoms, at the level of molecules, at the level of the reactions, and at the level of ideas. The law of the unity and conflict of opposites is seen, for instance, in the relationships between the ionization energy and electron affinity of atoms, between the forward and back reactions, as well as in the differentiation and integration (...) between the various areas of chemistry. The law of the passage of quantitative changes into qualitative changes describes the transformation properties of the compounds when the number and arrangement of atoms in the molecule undergoes changes. According to this law, the development is accompanied by breaks and jumps. This paper suggests equations for the description of these relationships. The law of the negation of the negation is manifested in the Periodic Law, in the evolution of ideas about the mutual transformation of chemical elements, in the development the concept of triads of elements, etc. Small changes in the conventional Periodic Table on the basis of previously rejected versions allow reflecting secondary and additional periodicity. Synergetics, similarly to dialectics, is dedicated to the studies of general laws of evolution. Synergetics includes highly advanced and specified ideas of dialectics. The cornerstone of synergetics is the principles of self-organization and nonlinearity. Mathematical development of these concepts was substantially facilitated by considering oscillating chemical reactions as an example. These reactions are quite complex and therefore provide adequate models for self-organization. Oscillations may exist only upon execution of specific thermodynamic, mathematical, and chemical conditions. Mechanisms of several oscillatory reactions are briefly reviewed. The construction of novel biomimetic or smart materials based on oscillating reactions is described. (shrink)

Quasi-set theory????\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {Q}$$\end{document} is a first order theory which allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that x = x is not a formula, if x is an arbitrary term. The terms of????\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {Q}$$\end{document} are either collections or atoms (empty terms who are not collections), in a precise sense. (...) Within this context,????\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {Q}$$\end{document} is supposed to be some sort of generalization of ZFU (ZF with atoms). Strangely enough, no one published any permutation model of quasi-set theory until now, although this theory is already 30 years old. In this paper I introduce a class of permutation models of????′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {Q}'$$\end{document} defined as????−{Axiom of Choice and all axioms involving quasi-cardinality}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {Q}-\{\text{Axiom of Choice and all axioms involving quasi-cardinality}\}$$\end{document}. I show, for example, that all permutation models of????′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {Q}'$$\end{document} are models of ZFU−{Axiom of Choice}. (shrink)

A pair of harmonic oscillators come in contact and then separate. This could be a model of an atom encountering an electromagnetic field. We explore the coherence properties of the resulting state as a function of the sort of initial condition used. A surprising result is that if one imagines a large collection of these objects repeatedly coming in contact and separating, the asymptotic distribution functions are not Boltzmann distributions, but rather exponentials with the same rate of dropoff.

Werner Heisenberg's 1925 paper ‘Quantum-theoretical re-interpretation of kinematic and mechanical relations’ marks the beginning of quantum mechanics. Heisenberg famously claims that the paper is based on the idea that the new quantum mechanics should be ‘founded exclusively upon relationships between quantities which in principle are observable’. My paper is an attempt to understand this observability principle, and to see whether its employment is philosophically defensible. Against interpretations of ‘observability’ along empiricist or positivist lines I argue that such readings are philosophically (...) unsatisfying. Moreover, a careful comparison of Heisenberg's reinterpretation of classical kinematics with Einstein's argument against absolute simultaneity reveals that the positivist reading does not fit with Heisenberg's strategy in the paper. Instead the appeal to observability should be understood as a specific criticism of the causal inefficacy of orbital electron motion in Bohr's atomic model. I conclude that the tacit philosophical principle behind Heisenberg's argument is not a positivistic connection between observability and meaning, but the idea that a theory should not contain causally idle wheels. (shrink)

A complete theoretical model describing artificial disintegration of nuclei by bombardment with α-particles, developed by Majorana as early as 1930, is discussed in detail jointly with the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear process, (...) which is the directly measurable quantity of interest in the experiments. Although this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana work anticipates by several years the related seminal paper by Fano on Atomic Physics. (shrink)

Erwin Schrödinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics” or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived at his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen Bohr's atom model for example, as a structure in space—time, but (...) instead, following the lead of Einstein's 1905 theory of relativity, representing only empirically observable properties, such as the transition amplitudes between the stationary states of the atom. These amplitudes can be arranged in square arrays of numbers. In Heisenberg's scheme these arrays, and other like them, are combined according to certain rules that were later recognized by Max Born to be the rules of matrix multiplication. The whole scheme is abstract and mathematical, and avoids using any space—time picture of what is going on at the atomic level. Schrödinger, on the other hand, represented the electron in an atom by a cloudlike wave surrounding the nucleus. This is a space—time structure that, superficially at least, is more in line with the classical physical theories of the eighteenth and nineteenth centuries. -/- Niels Bohr invited Schrödinger to come to Copenhagen to present his ideas, and to discuss this subject with himself, Heisenberg, and others. Schrödinger arrived in Copenhagen on October 1st, 1926, and was immediately intensively engaged by Bohr and the others in a “debate” that lasted for days. Eventually, Schrödinger become ill, and was confined in Bohr's home to a bed, upon which Bohr sat, continuing the discussion. Schrödinger finally exclaimed “If all the quantum jumping is here to stay, then I am sorry that I ever became involved in quantum mechanics”. Bohr replied, “But we are glad that you did!”. (shrink)

William Haas (1883-1956) was born in Nuremberg and received his PhD. at Munich in 1910. He traveled widely throughout the Middle East and taught at universities in Germany, Iran and the United States. After a lifetime studying the thoughts and cultures of the East, he formulated the thesis laid out here in his final book: that East and West are not mere geographical or even racial distinctions, but two radically different types of consciousness, two fundamentally different orientations and ways of (...) thinking. "Professor Haas attacks-and I believe, demolishes-an assumption that underlies almost all modern theories of history: that the minds of all human beings, if not defective or disordered, work in essentially the same way.... [He] has, I believe, done for the study of comparative history what Böhr did for atomic physics." - Revilo Oliver. (shrink)

We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates. BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ’learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of (...) the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system. (shrink)

This paper analyses Bohr’s complementarity framework and applies it to biosemiotic studies by illustrating its application to three existing models of living systems: mechanistic biology, Barbieri’s version of biosemiotics in terms of his code biology and Markoš’s phenomenological version of hermeneutic biosemiotics. The contribution summarizes both Bohr’s philosophy of science crowned by his idea of complementarity and his conception of the phenomenon of the living. Bohr’s approach to the biological questions evolved – among other things – from the consequences of (...) an epistemological lesson of quantum theory and in light of complementarity of observer as a priori living creature and ex post scientific explanation of the living. In a manifestation of the phenomenon of the living, each model of living system and its description makes accessible – from its own presuppositions, contexts and concepts – some features which are not accessible from the others. Nevertheless, for a general understanding of that phenomenon, incompatible sophisticated approaches are equally necessary. Bohr’s epistemology of complementarity turns out to be a heuristic and methodical framework for testing the extent to which biosemiotics can become one of the special sciences or its potential as a cross-disciplinary branch of study. (shrink)

We have conducted an experimental study of V-type electromagnetically induced transparency in sodium. Its principles are elucidated by a simple model. Measurements show decreased fluorescence and absorption depending on the detuning of the driving and probe fields, which is in agreement with the results of numerical simulation.

Nucleation and motion of kink pairs on partial dislocations are examined by elasticity theory for materials with a high Peierls stress. Two approaches are used: one considers the change in average stacking-fault energy due to alloying elements and the other considers the change in local SFE due to a nearby solute atom. Both approaches highlight the role of SFE on kink nucleation, propagation and annihilation and both furnish strain rate as a function of stress, temperature and SFE. Model predictions (...) are compared with yield stress data for two systems: firstly, an intermetallic, MoSi 2 , which softens for alloying elements that decrease the SFE and hardens for Re additions that increase the SFE; secondly, a ceramic oxide, MgO-Al 2 O 3 spinel, which softens with increasing addition of excess alumina and at the same time exhibits a decrease in SFE. The average SFE approach agrees qualitatively with the data while quantitative agreement is obtained with the local SFE approach. The possibility is considered that the model applies to other materials, such as TiAl, HfV 2 and Fe 3 Al, which show softening with certain alloying additions. One requirement is that the dislocations are dissociated more than a few atomic distances; otherwise kink nucleation occurs on the perfect dislocation . Hence the model does not apply to materials such as bcc metals which only have a core dissociation. Normal hardening effects of solutes from size and modulus misfits are additive with any softening effects from a decrease in SFE and so may mask the latter, as occurs for W additions to MoSi 2. (shrink)

Although many philosophers of religion have claimed support for continuing to live with paradoxes in theology from the existence of basic paradoxes in scientific theory, few have probed the validity of this claim. This monograph fills the gap. After a useful chapter surveying the current status of the wave-particle theories in physics and Bohr's principle of complementarity, Austin abstracts from the discussion the idea of complementary models and uses this to propose a "complementarist interpretation" of paradoxes in religion. This (...) he favors over the "paradox-minimizing approach" and the "sui generis interpretation" found in such writers as Bochenski and G. E. Hughes, on the one hand, and Pseudo-Dionysius and classical Indian mystics, on the other. The former approach fails to do justice to the element of mystery in religion while the latter makes too much of it. In his account of the latter, Austin relies especially on Ninian Smart's Reasons and Faiths, the theses of which are rather uncritically adopted as the key to understanding religious discourse. Regrettably, Austin has to depend on secondary sources in his treatment of Indian thought and this makes his handling of it less masterly than his discussion of contemporary physics. Likewise, the concept of "model" needs more critical scrutiny than is possible here if it is to serve a subinterest of the book in the status of theology as a "science." But generally the work is replete with qualifications and illustrations and is a welcome addition to the literature on religion and science.—C. P. S. (shrink)

Traditional nomological accounts of scientific explanation have assumed that a good scientific explanation consists in the derivation of the explanandum’s description from theory (plus antecedent conditions). But in more recent philosophy of science the adequacy of this approach has been challenged, because the relation between theory and phenomena in actual scientific practice turns out to be more intricate. This critique is here examined for an explanatory paradigm that was groundbreaking for 20th century physics and chemistry (and their interrelation): Bohr’s first (...) model of the atom and its explanatory relevance for the spectrum of hydrogen. First, the model itself is analysed with respect to the principles and assumptions that enter into its premises. Thereafter, the origin of the model’s explanandum is investigated. It can be shown that the explained “phenomenon” is itself the product of a host of modelling accomplishments that stem from an experimental tradition related to 19th century chemistry, viz. spectroscopy. The relation between theory and phenomenon is thus mediated in a twofold way: by (Bohr’s) theoretical model and a phenomenological model from spectroscopy. In the final section of the paper an account is outlined that nevertheless permits us to acknowledge this important physico-chemical achievement as a case of (nomological) explanation. (shrink)

Berichte zur Wissenschaftsgeschichte, EarlyView.

A simple model for the description of atomic and ionic species with spectra exhibiting a quantum defect is solved using the Lie algebra su(1, 1). The quantum defect of bound states is related to the phase shift of scattering states. The resonances are discussed in terms of the nonunitary representations of this algebra.

There exists a countable structure of Scott rank where and where the -theory of is not ω-categorical. The Scott rank of a model is the least ordinal β where the model is prime in its -theory. Most well-known models with unbounded atoms below also realize a non-principal -type; such a model that preserves the Σ1-admissibility of will have Scott rank . Makkai [M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 301–318. [4]] produces a hyperarithmetical (...) model of Scott rank whose -theory is ω-categorical. A computable variant of Makkai’s example is produced in [W. Calvert, S.S. Goncharov, J.F. Knight, J. Millar, Categoricity of computable infinitary theories, Arch. Math. Logic . [1]; J. Knight, J. Millar, Computable structures of rank J. Math. Logic . [2]]. (shrink)

Falsificationism has dominated 20th century philosophy of science. It seemed to have eclipsed all forms of inductivism. Yet recent debates have revived a specific form of eliminative inductivism, the basic ideas of which go back to F. Bacon and J.S. Mill. These modern endorsements of eliminative inductivism claim to show that progressive problem solving is possible using induction, rather than falsification as a method of justification. But this common ground between falsificationism and eliminative inductivism has not led to a detailed (...) investigation into the relationship, if any, which may exist between these two methodologies. This paper reviews several versions of eliminative inductivism, establishes a natural relation between eliminative inductivism and falsificationism, which derives from the distinction between models and theories, and carries out this investigation against a case study of the construction of atom models. The result of the investigation is that falsificationism is a form of eliminative inductivism in the limit of certain constraints. (shrink)

The ternary xV2O5–(40 − x)Li2O–60B2O3 glass system, where x = 1, 2, 3, 4 and 6 mol%, was prepared by normal quenching. Ultrasonic velocities and attenuation were measured at room temperature using a pulse-echo technique. Various parameters, such as elastic moduli, micro-hardness, Poisson's ratio and Debye temperature, were determined from the measured densities and velocities. The composition dependence of these parameters, in addition to the glass-transition temperature, suggested that vanadium ions were incorporated into these glasses as a network modifier, resulting (...) in the reconversion of BO4 tetrahedra to BO3 triangles by the breaking of B–O–B linkages and the formation of nonbridging oxygens (NBOs). The outcome was a reduction in network connectivity and rigidity with increasing V2O5 content. The results are explained quantitatively in terms of fractal bond connectivity, average atomic volume, network dimensionality, packing density, number of network bonds per unit volume, cross-link density and atomic ring size. The Makishima and Mackenzie model appears to be valid for the studied glasses when the fate of BO4 tetrahedra and creation of NBOs are taken into account. (shrink)

In this study Arun Bala examines the implications that Niels Bohr's principle of complementarity holds for fields beyond physics. Bohr, one of the founding figures of modern quantum physics, argued that the principle of complementarity he proposed for understanding atomic processes has parallels in psychology, biology, and social science, as well as in Buddhist and Taoist thought. But Bohr failed to offer any explanation for why complementarity might extend beyond physics, and his claims have been widely rejected by (...) scientists as empty speculation. Scientific scepticism has only been reinforced by the naïve enthusiasm of postmodern relativists and New Age intuitionists, who seize upon Bohr's ideas to justify anti-realist and mystical positions. Arun Bala offers a detailed defence of Bohr's claim that complementarity has far-reaching implications for the biological and social sciences, as well as for comparative philosophies of science, by explaining Bohr's parallels as responses to the omnipresence of grown properties in nature. (shrink)

Kuhn’s view of science is as follows. Science involves two key phases: normal and extraordinary. In normal science, disciplinary matrices (DMs) are large and pervasive. DMs involve “beliefs, values, techniques, and so on shared by the members of a given community” (Kuhn 1996, 175). “And so on” is regrettably vague, but Kuhn (1977, 1996) mentions three other key elements: symbolic generalizations (such as F=dp/dt), models (such as Bohr’s atomic model), and exemplars. These components of DMs overlap somewhat. For (...) instance, symbolic generalizations may feature in techniques and beliefs, and models may exhibit values. To be a (genuine) scientist, in the normal science phase, is to puzzle solve within the boundaries of the DM. It is to buy into the ruling dogma (Kuhn 1963) and to accept that “failure to achieve a solution discredits only the scientist ... ‘It is a poor carpenter who blames his tools’” (Kuhn 1996, 80). Puzzle solving involves a wide variety of activities, including. (shrink)

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent (...) on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. -/- I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it. -/- . (shrink)

In the present paper I aim to discuss the philosophical foundations of the early correspondence principle, by comparing the conceptual structure underlying the first correspondence principle with the procedure of analogy that Immanuel Kant introduced in the Critique of Judgment from 1790. On such a comparison, I will seek to demonstrate the consistency of the conceptual ratio according to which the correspondence principle is to the classical "concepts" of space and time, as these a priori forms of intuition, in Kant, (...) are related to the separate faculty of pure intuition. As a result, it will turn out that the conceptual structure of the correspondence principle suits to the Kantian doctrine of a separate faculty of pure intuition, which is divided from the faculty of understanding. The aim is to shed new light on the line of reasoning underlying Niels Bohr's analogical thinking in quantum physics. (shrink)

E. Schrödinger's ideas on interpreting quantum mechanics have been recently re-examined by historians and revived by philosophers of quantum mechanics. Such recent re-evaluations have focused on Schrödinger's retention of space–time continuity and his relinquishment of the corpuscularian understanding of microphysical systems. Several of these historical re-examinations claim that Schrödinger refrained from pursuing his 1926 wave-mechanical interpretation of quantum mechanics under pressure from the Copenhagen and Göttingen physicists, who misinterpreted his ideas in their dogmatic pursuit of the complementarity doctrine and the (...) principle of uncertainty. My analysis points to very different reasons for Schrödinger's decision and, accordingly, to a rather different understanding of the dialogue between Schrödinger and N. Bohr, who refuted Schrödinger's arguments. Bohr's critique of Schrödinger's arguments predominantly focused on the results of experiments on the scattering of electrons performed by Bothe and Geiger, and by Compton and Simon. Although he shared Schrödinger's rejection of full-blown classical entities, Bohr argued that these results demonstrated the corpuscular nature of atomic interactions. I argue that it was Schrödinger's agreement with Bohr's critique, not the dogmatic pressure, which led him to give up pursuing his interpretation for 7 yr. Bohr's critique reflected his deep understanding of Schrödinger's ideas and motivated, at least in part, his own pursuit of his complementarity principle. However, in 1935 Schrödinger revived and reformulated the wave-mechanical interpretation. The revival reflected N. F. Mott's novel wave-mechanical treatment of particle-like properties. R. Shankland's experiment, which demonstrated an apparent conflict with the results of Bothe–Geiger and Compton–Simon, may have been additional motivation for the revival. Subsequent measurements have proven the original experimental results accurate, and I argue that Schrödinger may have perceived even the reformulated wave-mechanical approach as too tenuous in light of Bohr's critique. (shrink)