We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates.First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory quantum mechanics textbook. (...) For example, the trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical.We then examine higher-dimensional approximations, i.e., eigenstates Ψ α of the Hamiltonian in this truncated basis, and show that ∇ i S α =0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the same, regardless of the accuracy of the eigenfunction approximation.The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii) execute circular orbits around the z-axis with constant velocity. (shrink)

The two-electron atom is the simplest nontrivial quantum system not amenable to exact solutions. Today, its relevance in the development of quantum mechanics and its pedagogical value within the realm of atomic physics are widely recognized. In this work, an historical review of the known different methods and results devised to study such a problem is presented, with an emphasis to the calculations of the ground state energy of helium. Then we discuss several, related, unpublished results obtained around (...) the same years by Ettore Majorana, which remained unknown till recent times. Among them a general variant of the variational method appears to be particularly interesting, even for current research in atomic and nuclear physics: it takes directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Further relevant contributions, specialized to the two-electron problem, include the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results) and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable. Finally a survey of results, relevant mainly for pedagogical reasons, is given; in particular we focus on simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as on a simple alternative to Hylleraas’ method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas. (shrink)

The known facts of quantum physics and biology strongly suggest the following hypotheses: atoms and the fundamental particles have a rudimentary degree of consciousness, volition, or self-activity; the basic features of quantum mechanics are a result of this fact; the quantum mechanical wave properties of matter are actually the conscious properties of matter; and living organisms are a direct result of these properties of matter. These hypotheses are tested by using them to make detailed predictions of new facts, and then (...) by showing that the predictions can be verified. The hypotheses are used to predict successfully that the quantum wave properties of matter are strongly predominant in proteins, to explain the presence and relative abundance of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur in proteins, and to explain diffraction phenomena, the behavior of helium II, the exclusion principle, and causality and determinism in modern science, thus closely relating physics and biology. (shrink)

Some recent work in mathematical chemistry is discussed. It is claimed that quantum mechanics does not provide a conclusive means of classifying certain elements like hydrogen and helium into their appropriate groups. An alternative approach using atomic number triads is proposed and the validity of this approach is defended in the light of some predictions made via an information theoretic approach that suggests a connection between nuclear structure and electronic structure of atoms.

The article begins with a response to a recent contribution by Jensen, in which he has criticized several aspects of the use of triads of elements, including Döbereiner’s original introduction of the concept and the modern use of atomic number triads by some authors including myself. Such triads are groups of three elements, one of which has approximately the average atomic weight of the other two elements, as well as having intermediate chemical reactivity. I also examine Jensen’s attempted reconstruction Mendeleev’s (...) use of triads in predicting the atomic weights of three hitherto unknown elements, that were subsequently named gallium, germanium and scandium. The present article then considers the use of atomic number triads, in conjunction with the phenomenon of first member anomaly, in order to offer support for Janet’s left-step periodic table, in which helium is relocated into group 2 of the table. Such a table features triads in which the 2nd and third elements of each group, without fail, fall into periods of equal length, a feature that is absent in the conventional 18-column or the conventional 32-column table. The dual sense of the term element, which is the source of much discussion in the philosophy of chemistry, is alluded to in further support of such a relocation of helium that may at first appear to contradict chemical intuition. (shrink)

The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with (...) experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect, and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra. (shrink)

In this paper we study some of the methodological problems associated with the development of the various theoretical schema devised to explain the phenomenon of superfluidity. The physical behaviour of supercooled helium defied explanation in terms of the known atomic laws for helium and their ‘natural’ extrapolations. We show that the basic conceptual difficulties involved were circumvented by the development of intermediate intermediaries through a process of contextual reinterpretation.

It is with good reason that the name Rutherford is closely linked with the early history of the alpha particle. He discovered them, determined their nature, and from 1909 used them to probe the structure of the atom. From 1898 to 1902 Rutherford construed alpha radiation as a type of non-particulate Röntgen radiation. On his theory of the locomotion of radioactive particles Rutherford proposed that alpha radiation consisted of negatively charged particles. During 1902 he confirmed the particulate nature of (...) alpha radiation but discovered that these alpha particles were positively charged. Although Rutherford suspected from 1903 that these alpha particles were related somehow with helium, the proof required six long years of investigation. By mid-1908 it seemed certain that the alpha particle possessed two units of the elementary charge. Since the e/m ratio had already been determined for alpha particles, this evidence enhanced the suspected connection with helium. However, this gain and loss of charge was still construed as an ionization effect. Since as late as 1908 gaseous ionization was assumed to involve the gain or loss of a single unit of charge, Rutherford's alleged case of doubly ionized alpha particles was presumably an exception. Yet helium was known to be an inert gas and thus hardly a likely candidate for such exceptional ionization behaviour. To establish the connection, therefore, Rutherford resorted to a spectroscopic test. He collected spent alpha particles shot into a thin glass tube and gradually observed the spectrum of helium. Rutherford had thus been correct in his assumption, but a proper explanation was possible only after the confirmation of the nuclear structure of the atom. (shrink)

In a recent paper in this Journal, one of us argued against placing He above Be in Mendeleiev’s system of the elements. In it the goal was to dispute the notion that in Mendeleiev’s system of the elements the location of He should in fact lie above Be, which has a very similar electronic configuration, rather than above the noble gas column. That paper was based on rather old, Hartree–Fock limit studies on the strikingly limited non-additive contributions in the He3 (...) and He4 systems in contrast with the much larger non-additivity obtained for the Be3, Be4 and Be5 oligomers. In a recent benchmark multireference Averaged Quadratic Coupled Cluster results on Be2 and Be3 we showed that the delocalized non-additive contribution comprises 94 % of the binding energy of Be3. Here we use this and other pertinent information (drawn from the same paper) to conclude that He may not be associated with Be in Mendeleiev’s Table, despite their quite similar spectroscopic ground states. Furthermore, we use the new results to show that the large non-additivity implies that less than 2 % of the Be3 binding is located in each Be pair contained within the Be trimer. The rest of the interaction energy is necessarily delocalized over all three Be atoms. This might actually announce the bulk properties (i.e. “the electron gas”) that in solid-state physics explain the large electric and heat conduction for the solid Be metal. Thus, in the case of beryllium the metallic characteristics are already evident in Be3, a far cry from the monoatomic helium gas. (shrink)

Introductory survey -- Atomic theory and mechanics -- The quantum postulate and the recent development of atomic theory -- The quantum of action and the description of nature -- The atomic theory and the fundamental principles underlying the description of nature.

These articles and speeches by the Nobel Prize-winning physicist date from 1934 to 1958. Rather than expositions on quantum physics, the papers are philosophical in nature, exploring the relevance of atomic physics to many areas of human endeavor. Includes an essay in which Bohr and Einstein discuss quantum and_wave equation theories. 1961 edition.

Helium and neon, the two lightest noble gases, have been traditionally positioned by IUPAC in the Group 18 of the Periodic Table of Elements, together with argon, and other unreactive or moderately reactive gaseous elements (krypton, xenon, radon), and oganesson. In this account we revive the old discussion on the possible placement of helium in the Group 2, while preserving the position of neon in Group 18. We provide quantum-chemical arguments for such scenario—as well as other qualitative and (...) quantitative arguments—and we describe previous suggestions in the literature which support it or put it into question. To this author’s own taste, He should be placed in Group 2. (shrink)

Although continued investments in nanotechnology are made, atomically precise manufacturing (APM) to date is still regarded as speculative technology. APM, also known as molecular manufacturing, is a token example of a converging technology, has great potential to impact and be affected by other emerging technologies, such as artificial intelligence, biotechnology, and ICT. The development of APM thus can have drastic global impacts depending on how it is designed and used. This paper argues that the ethical issues that arise from APM (...) - as both a standalone technology or as a converging one - affects the roles of stakeholders in such a way as to warrant an alternate means furthering responsible innovation in APM research. This paper introduces a value-based design methodology called Value Sensitive Design (VSD) that may serve as a suitable framework to adequately cater to the values of stakeholders. Ultimately, it is concluded that VSD is a strong candidate framework for addressing the moral concerns of stakeholders during the preliminary stages of technological development. (shrink)

Hydrogen is troublesome in any periodic table classification. This being so it may as well be placed in a position that confers desirable attributes to the arrangement of the elements, while notionally recognising its lineage to the group 1 alkali metals and the group 17 halogens. Since the noble gases bridge the halogens and the alkali metals, and hydrogen encompasses the transition from the alkali metals to the halogens, there is more to the idea of hydrogen over helium. (Meyer (...) 1870, p. 357) (Proust 1927, p. 559). (shrink)

The quantum theory of atoms in molecules (QTAIM) uses physics to define an atom and its contribution to observable properties in a given system. It does so using the electron density and its flow in a magnetic field, the current density. These are the two fields that Schrödinger said should be used to explain and understand the properties of matter. It is the purpose of this paper to show how QTAIM bridges the conceptual gulf that separates the observations of (...) chemistry from the realm of physics and do so in a manner that is both rigorous and conceptually simple. Since QTAIM employs real measurable fields, it enables one to present the findings of complex quantum mechanical calculations in a pictorial manner that isolates the essential physics. The time has arrived for a sea change in our attempts to predict and classify the observations of chemistry, time to replace the use of simplified and arbitrary models with the full predictive power of physics, as applied to an atom in a molecule. (shrink)

This book reexamines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Bohr. In particular, it gives a detailed study of the development and the interpretation given to Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927.

This paper argues that the field of chemistry underwent a significant change of theory in the early twentieth century, when atomic number replaced atomic weight as the principle for ordering and identifying the chemical elements. It is a classic case of a Kuhnian revolution. In the process of addressing anomalies, chemists who were trained to see elements as defined by their atomic weight discovered that their theoretical assumptions were impediments to understanding the chemical world. The only way to normalize the (...) anomalies was to introduce new concepts, and a new conceptual understanding of what it is to be an element. In the process of making these changes, a new scientific lexicon emerged, one that took atomic number to be the defining feature of a chemical element. (shrink)

We provide a detailed history of the concepts of atomic number and isotopy before the discovery of protons and neutrons that draws attention to the role of evolving interplays of multiple aims and criteria in chemical and physical research. Focusing on research by Frederick Soddy and Ernest Rutherford, we show that, in the context of differentiating disciplinary projects, the adoption of a complex and shifting concept of elemental identity and the ordering role of the periodic table led to a relatively (...) coherent notion of atomic number. Subsequent attention to valency, still neglected in the secondary literature, and to nuclear charge led to a decoupling of the concepts of elemental identity and weight and allowed for a coherent concept of isotopy. This concept received motivation from empirical investigations on the decomposition series of radioelements and their unstable chemical identity. A new model of chemical order was the result of an ongoing collaboration between chemical and physical research projects with evolving aims and standards. After key concepts were considered resolved and their territories were clarified, chemistry and physics resumed autonomous projects, yet remained bound by newly accepted explanatory relations. It is an episode of scientific collaboration and partial integration without simple, wholesale gestalt switches or chemical revolutions. (shrink)

Philosophers routinely invoke self‐control in their theorizing, but major questions remain about what exactly self‐control is. I propose a componential account in which an exercise of self‐control is built out of something more fundamental: basic intrapsychic actions called cognitive control actions. Cognitive control regulates simple, brief states called response pulses that operate across diverse psychological systems (think of one's attention being grabbed by a salient object or one's mind being pulled to think about a certain topic). Self‐control ostensibly seems quite (...) different because it regulates complex, temporally extended states such as emotions and cravings. But critically, these complex states also exhibit important componential structure: They rely on response pulses as a key means by which they bring about action. The overall picture is that self‐control consists of skilled sequences of cognitive control directed against extended streams of response pulses that arise from states such as emotions and cravings, thus preventing these states from being effective in action. The account clarifies the “atoms” of self‐control—the elemental units that get combined in complex ways to produce different kinds of self‐control actions. Surprisingly, the account, which is derived from research in cognitive science, aligns nicely with the commonsense conception of self‐control. (shrink)

The intention of Atomic Order is to encourage and contribute to the dialogue between philosophers and scientists by discussing a concrete example of scientific discovery according to a method acceptable and understandable to both sides. This discussion takes simultaneously into account the scientific and philosophical methodologies and mentalities. By regarding "pure" science or "pure" philosophy as limiting cases, it becomes evident that basic questions are best posed and answered by emphasiz ing the deeply embedded complementary relationship between the two. The (...) example chosen is atomic physics, and a systematic method is developed to illuminate the philosophical structure of this science--and science generally--from within.The book consists of two parts. The first part is devoted to the problem of atomic order as discovered and verified by physics, from the speculations of Dalton to the consequences of modern quantum mechanics. These chapters will afford a telescopic, historical review to the scientific reader and a reliable, understandable account of the physical discoveries and theories to the nonscientist. The second part analyzes the presuppositions, guiding principles, and implications that made possible the development of atomic physics and that impart a humanistic meaning to it. In separate chapters are discussed the epistemological structure of atomic physics, the new conception of matter implicit in the quantum theory, and the ontological implications of atomic order. It is seen that, in this area, science and philosophy are inextricably interpenetrated. A philosophic problematic is immanent in creative atomic science, as is evidenced by the numerous reflections and speculations of scientists that are quoted in the book. Conversely, an interest in scientific research is indispensable for a modern philosopher, and the philosopher may well be surprised and encouraged on recognizing the role already being played by philosophy in the supposedly pragmatic world of science.Dr. Cantore brings an ecumenical cast Lof mind to the healing of the bjcultural split between the humanists and the scientists. The recipient of a doctorate in physics and another in philosophy, he has drawn from both fields in a book dedicated to "making the educated public more aware of the need and method for a new synthesis between the two cultures.". (shrink)

In this paper I discuss some consequences and manifestations of a mereology of structured wholes in chemistry, with particular reference to the concept of atoms in molecules.

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)

This paper suggests that the cases made for atoms and the aether in nineteenth-century physical science were analogous, with the implication that the case for the atom was less than compelling, since there is no aether. It is argued that atoms did not play a productive role in nineteenth-century chemistry any more than the aether did in physics. Atoms and molecules did eventually find an indispensable home in chemistry but by the time that they did so they were different (...) kinds of entities to those figuring in the speculations of those natural philosophers who were atomists. Advances in nineteenth-century chemistry were a precondition for rather than the result of the productive introduction of atoms into chemistry. (shrink)

In this paper I shall explore a novel alternative to these familiar views. In his recent book Sub ects of Ex erience, E. J. Lowe argues, as many others have done before, that you and I are not animals. It follows from this, he says, that we must be simple substances without parts. That may sound like Cartesian dualism. But Lowe is no Cartesian. He argues from premises that many present-day materialists accept. And he claims that our being mereologically simple (...) is consistent with our having such paradigmatically physical properties as being six feet tall and weighing 160 pounds. You and I, he claims, are mereological atoms shaped like human beings. (shrink)

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability domain) (...) provide consistent definitions which accommodate chemistry and quantum mechanics. (shrink)

"Atom," "byte" and "gene" are metonymies for techno-scientific developments of the 20th century: nuclear power, computing and genetic engineering. Resistance continues to challenge these developments in public opinion. This book traces historical debates over atoms, bytes and genes which raised controversy with consequences, and argues that public opinion is a factor of the development of modern techno-science. The level and scope of public controversy is an index of resistance, examined here with a "pain analogy" which shows that just as (...) pain impacts movement, resistance impacts techno-scientific mobilization: it signals that something is wrong, and this requires attention, elaboration and a response to the challenge. This analysis shows how different fields of enquiry deal with the resistance of social-psychological mentalities in the face of industrial, scientific and political activities inspired by projected futures. (shrink)

In this paper I address two important objections to the theory called ‘ Composition as Identity’ : the ‘wall-bricks-and-atoms problem’, and the claim that CAI entails mereological nihilism. I aim to argue that the best version of CAI capable of addressing both problems is the theory I will call ‘Atomic Composition as Identity’ which consists in taking the plural quantifier to range only over proper pluralities of mereological atoms and every non-atomic entity to be identical to the plurality of atoms (...) it fuses. I will proceed in three main steps. First, I will defend Sider’s Composition as identity. Oxford University Press, Oxford, pp 211–221, 2014) idea of weakening the comprehension principle for pluralities and I will show that :219–235, 2016a) it can ward off both the WaBrA problem and the threat of mereological nihilism. Second, I will argue that CAI-theorists should uphold an ‘atomic comprehension principle’ which, jointly with CAI, entails that there are only proper pluralities of mereological atoms. Finally, I will present a novel reading of the ‘one of’ relation that not only avoids the problems presented by Yi Composition as identity. Oxford University Press, Oxford, pp 169–191, 2014) and Calosi :429–443, 2016b, Am Philos Q 55:281–292, 2018) but can also help ACAI-theorists to make sense of the idea that a composite entity is both one and many. (shrink)

: This paper examines the debate in the late 19th and early 20th centuries over the acceptability of atomic and molecular physics. It focuses on three prominent figures: Maxwell, who defended atomic physics, Ostwald, who initially rejected it but changed his mind as a result of experiments by Thomson and Perrin, and Duhem, who never accepted it. Each scientist defended the position he did in the light of strongly held methodological views concerning empirical evidence. The paper critically evaluates each of (...) these methodological positions. (shrink)

although mostly known to specialists nowadays, Kenelm Digby was a remarkable figure on the intellectual scene of the early seventeenth century. He has been described as “one of the most influential natural philosophers” of his time,1 and corresponded with many of the great scholars of his days, including Descartes, and the French pioneer of atomism, Pierre Gassendi. In the later years of his life, Digby, alongside men like Robert Boyle, became one of the founding members of the Royal Society.2Digby authored (...) one major work of philosophy: the Two Treatises of 1644. This work consisted of a long First Treatise on bodies, and a shorter, Second Treatise on the human soul. In the First Treatise, Digby argued... (shrink)

A possible atomic mechanism underlying the Re- and Ru-induced strengthening effects on the n - n ' interface in Ni-based single-crystal superalloys has been investigated using the DMol3 molecular orbital package based on density functional theory. The calculation of bonding properties has been performed on a cluster designed to model Re and Ru strengthening effects within the interface. The stronger Re--Ni bonds are formed mainly as a result of d- hybridization, while the Ni--Ni bonding become weaker accompanying the Re substitution. (...) The vertical and horizontal bond orders for a local environmental cluster are proposed and developed for the description of the strengthening effect on the n - n ' interface, with larger bond order values achieving better effect. Results show that both Re and Ru significantly strengthen the interface. It is also shown that the strengthening effect of Re is better than that of Ru, and this is explained in terms of the charge transfer of electrons between orbitals of Ru atom according to Mulliken population analysis. The calculation results provide a basis for understanding the atomic mechanism of Re- and Ru-induced n - n ' interfacial strengthening. (shrink)

Event concepts are unstructured atomic concepts that apply to event types. A paradigm example of such an event type would be that of diaper changing, and so a putative example of an atomic event concept would be DADDY'S-CHANGING-MY-DIAPER.1 I will defend two claims about such concepts. First, the conceptual claim that it is in principle possible to possess a concept such as DADDY'S-CHANGING-MY-DIAPER without possessing the concept DIAPER. Second, the empirical claim that we actually possess such concepts and that they (...) play an important role in our cognitive lives. The argument for the empirical claim has the form of an inference to the best explanation and is aimed at those who are already willing to attribute concepts and beliefs to infants and nonhuman animals. Many animals and prelinguistic infants seem capable of re-identifying event-types in the world, and they seem to store information about things happening at particular times and places. My account offers a plausible model of how such organisms are able to do this without attributing linguistically structured mental states to them. And although language allows adults to form linguistically structured mental representations of the world, there is no good reason to think that such structured representations necessarily replace the unstructured ones. There is also no good reason for a philosopher who is willing to explain the behavior of an organism by appealing to atomic concepts of individuals or kinds to not use a similar form of explanation when explaining the organism's capacity to recognize events. -/- We can form empirical concepts of individuals, kinds, properties, event-types, and states of affairs, among other things, and I assume that such concepts function like what François Recanati calls ‘mental files’ or what Ruth Millikan calls ‘substance concepts’ (Recanati 2012; Millikan 1999, 2000, 2017). To possess such a concept one must have a reliable capacity to re-identify the object in question, but this capacity of re-identification does not fix the reference of the concept. Such concepts allow us to collect and utilize useful information about things that we re-encounter in our environment. We can distinguish between a perception-action system and a perception-belief system, and I will argue that empirical concepts, including atomic event concepts, can play a role in both systems. The perception-action system involves the application of concepts in the service of (often skilled) action. We can think of the concept as a mental file containing motor-plans that can be activated once the individual recognizes that they are in a certain situation. In this way, recognizing something (whether an object or an event) as a token of a type, plays a role in guiding immediate action. The perception-belief system, in contrast, allows for the formation of beliefs that can play a role in deliberation and planning and in the formation of expectations. I distinguish between two particular types of belief which I call where-beliefs and when-beliefs, and I argue that we can model the formation of such perceptual beliefs in nonlinguistic animals and human infants in terms of the formation of a link between an empirical concept and a position on a cognitive map. According to the account offered, seemingly complex beliefs, such as a baby's belief that Daddy changed her diaper in the kitchen earlier, will not be linguistically structured. If we think that prelinguistic infants possess such concepts and are able to form such beliefs, it is likely that adults do too. The ability to form such beliefs does not require the capacity for public language, and we can model them in nonlinguistic terms; thus, we have no good reason to think of such beliefs as propositional attitudes. Of course, we can use sentences to refer to such beliefs, and thus it is possible to think of such beliefs as somehow relations to propositions. But it is not clear to me what is gained by this as we have a perfectly good way to think about the structure of such beliefs that does not involve any appeal to language. (shrink)

The characteristic features of ortho- and para-helium are investigated within the framework of Relativistic Schrödinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the $\mathfrak{u}(2)$ -valued bundle connection $\mathcal{A}_{\mu}$ into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for (...) their exchange interactions. The electromagnetic interactions are mediated by the usual four-potentials A μ and thus are essentially the same for both types of field configurations, where naturally the electrostatic forces (described by the time component A 0 of A μ) dominate their magnetostatic counterparts (described by the space part A of A μ). Quite analogously to this, the exchange forces are as well described in terms of a certain vector potential (B μ), again along the gauge principles of minimal coupling, so that also the exchange forces split up into an “electric” type ( $\rightsquigarrow B_{0}$ ) and a “magnetic” type ( $\rightsquigarrow {\bf B}$ ). The physical difference of ortho- and para-helium is now that the first (ortho-) type is governed mainly by the “electric” kind of exchange forces and therefore is subject to a stronger influence of the exchange phenomenon; whereas the second (para-) type has vanishing “electric” exchange potential (B 0 ≡ 0) and therefore realizes exclusively the “magnetic” kind of interactions ( $\rightsquigarrow {\bf B}$ ), which, however, in general are smaller than their “electric” counterparts. The corresponding ortho/para splitting of the helium energy levels is inspected merely in the lowest order of approximation, where it coincides with the Hartree–Fock (HF) approximation. Thus RST may be conceived as a relativistic generalization of the HF approach where the fluid-dynamic character of RST implies many similarities with the density functional theory. (shrink)