Atomic and Molecular Physics

The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The (...) Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant. (shrink)

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other (...) estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or “Dutch book”) in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent. (shrink)

Cartea abordează bazele fenomenlogice din fizica atomică, fizica nucleară, radioactivitatea, fizica particulelor, fisiunea, fuziunea și energia nucleară. Conținutul oferă o perspectivă modernă a domeniului, simultan cu o retrospectivă istorică a dezvoltării sale. Fiecare capitol pune accent pe explicațiile fizice ale fenomenelor, ocurența naturală, măsurare, și utilizarea practică a fenomenelor respective. CUPRINS: Fizica atomică - Natura atomică a materiei - - Ipoteze atomice - - Proprietățile atomilor - - - Proprietăți nucleare - - - Masa - - - Forma și dimensiunea (...) - - - Dezintegrarea radioactivă - - - Momentul magnetic - - - Nivelurile energetice - - - Valența și comportamentul legăturilor - - - Stări - - Imagistica atomică - - Structura atomului - - - Particule subatomice - - - Nucleul - - - Norul de electroni Atomul și cuanta - Descoperirea nucleului atomic - Descoperirea electronului - - Descoperirea - Spectroscopia atomică - Linii spectrale - - Teorie - - Atomii - - Linii spectrale - - - Tipuri de spectre de linii - Modelul Bohr al atomului - - Origine - - Mărimea relativă a atomilor (Raza atomilor) - - - Definiții - - - Raze atomice măsurată empiric - - - Raze atomice calculate - - Nivele energetice cuantificate: Undele electronilor (Nivele energetice) - - - Explicație - - - Tranziții ale nivelelor de energie - Mecanica cuantică - - Istorie - - Formulări matematice - Principiul corespondenței - - Mecanica cuantică Nucleul atomic și radioactivitatea - Razele X - - Istorie - - Proprietăți - - - Interacțiunea cu materia - - Producere - - - Detectoare - - - Utilizări medicale - Radiații alfa, beta și gama - Radiații ionizante - - Radiația alfa - - - Utilizări - - Radiația beta - - - Utilizări - - Radiația gama - - - Utilizări - Nucleul atomic - - Structura nucleară - - Compoziție și formă - - Forțe - - - Forța nucleară slabă - - - Forța nucleară tare - Izotopi - - Izotop vs. nuclid - - Definiția - - Notație - - Izotopi radioactivi, primordiali și stabili - Dezintegrarea radioactivă - - Baza teoretică a fenomenelor de dezintegrare - - Apariție și aplicații - - Originea nuclizilor radioactivi - Timpul de înjumătățire - - Detectoare de radiații (Detectoare de particule) - - Detectoare de ionizare gazoasă - - Detector de urme nucleare în stare solidă - - Calorimetre - - Detectoare plate cu microcanale - - Detectarea neutronilor - - Detectoare moderne - - - Detector ermetic - - Instrumente de protecție împotriva radiațiilor - - - Instrumente instalate - - - Instrumente portabile - - Detectoare de particule în cercetare - Transmutarea elementelor (Transmutarea nucleară) - - Istorie - - - Alchimie - - - Fizica modernă - - Transmutarea naturală (Transmutarea în univers) - - Transmutarea artificială (Transmutarea deșeurilor nucleare) - - - Tipurile de reactoare - - - Tipuri de combustibil - - - Motivația din spatele transmutării - - - Produse de fisiune cu durată lungă de viață - Izotopi radioactivi (Radionuclizi) - - Origine - - - Natural - - - Fisiunea nucleară - - - Sintetic - - Utilizări - Datarea radiometrică - - Bazele datării radiometrice - - - Dezintegrarea radioactivă - - - Precizia datării radiometrice - - - Temperatura de închidere - - - Ecuația vârstei - - Datarea cu carbon - - - Detaliile fizice și chimice - - - Principii - - - Considerații privind datarea - - Datarea cu uraniu - - - Metoda de datare cu uraniu-plumb - - - Metoda de datare cu uraniu-toriu - Efectele radiațiilor asupra oamenilor - - Efectele asupra sănătății - - Expunerea la radiații - - - Expunerea profesională - - - Expunerea publica - - - Zborul în spațiu - - - Transportul aerian - - - Semne de avertizare privind pericolele de radiație - - Dozarea radiațiilor - - - Măsurare Fizica particulelor - Istoria - Modelul Standard - Fizica particulelor experimentală - Obiecții - Politici publice - Particule elementare - - Particule elementare - - - Fermioni - - - - Cuarci - - - Cuarci - - - - Leptoni - - - Leptoni - - - Bosoni - - - Particule ipotetice - - Particule compuse - - - Hadroni - - - Barioni - - - Mezoni - - - Nuclee atomice - - - Atomi - - - Molecule - - Substanțe condensate - - Alte particule - - Extensii ale Modelului Standard - - - Marea unificare - - - Supersimetria - - - Teoria corzilor - - - Teoria preonilor - Protoni - Neutroni - - Istoric - - - Evoluția actuală - Electron - - Clasificare - - Proprietăți fundamentale - Cuarci - Fotoni - Gluoni - Bosoni W și Z - - Bosonul Higgs - Neutrino - - Neutrino, noul sistem de comunicații - - Telefonul – particulă - - Comunicații cu submarinele - - Mesaje pentru călătoria în timp - Fizica acceleratorilor - - Accelerarea și interacțiunea particulelor cu structuri RF - - Dinamica fluxului - - Coduri de modelare - - Diagnosticările fluxului - - Toleranțele mașinii Fisiunea și fuziunea nucleară - Istorie - - Descoperirea nucleului - - Descoperirea neutronului - - Câmpul bozonic - - Mezoni - Fisiunea nucleară - - Mecanismul - - Reactoare de fisiune nucleară - - - Mecanism - - - - Fisiunea - - - - Generarea de căldură - - - - Răcirea - - - - Controlul reactivității - - - - Generarea de energie electrică - - Reactoare nucleare cu apă grea presurizată - CANDU - - - Scopul utilizării apei grele - - - Avantaje și dezavantaje - - - Emisiile de tritiu - - - Reactorul CANDU - - - Centrala Nucleară de la Cernavodă - - - - Reactoarele - - - - Incidente - - Plutoniu - - - Proprietăți fizice - - Reactoare nucleare reproducătoare - - - Eficiența combustibilului și tipurile de deșeuri nucleare - - - Raportul de conversie, pragul de rentabilitatea, raportul de reproducere, timpul de dublare și arderea - - - Tipuri de reactoare reproducătoare - - Energia de fisiune - - - Centrale nucleare - - - Probleme de mediu - - - Energia nucleară în România - - Echivalența masă-energie în reacțiile nucleare - - - Istorie - - - Exemplu practic - - - Eficiența - Fuziunea nucleară - - Procesul - - Controlul fuziunii (Energia de fuziune) - - - Descriere - - - - Mecanism - - - - Secțiunea transversală - - - - Criteriul Lawson - - - - Produs triplu: densitate, temperatură, timp - - - - Comportamentul plasmei - - - - Captarea energiei Probleme nerezolvate - Fizica nucleară - Fizica particulelor / Fizica energiilor înalte Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing . 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What is the meaning of the wave-function? After almost 100 years since the inception of quantum mechanics, is it still possible to say something new on what the wave-function is supposed to be? Yes, it is. And Shan Gao managed to do so with his newest book. Here we learn what contemporary physicists and philosophers think about the wave-function; we learn about the de Broglie-Bohm theory, the GRW collapse theory, the gravity-induced collapse theory by Roger Penrose, and the famous PBR (...) theorem; we learn about Schrödinger's original idea that the wave-function represents charge densities; we learn about the notorious measurement problem and its consequences; we learn about the challenges to find a consistent relativistic quantum theory; and we learn, of course, Gao's own suggestion for the status of the wave-function. Above all, Gao shows us the significance of protective measurements for our search of the ontology of quantum mechanics. Still not widely recognized among physicists and philosophers, protective measurements let us look deeper into quantum mechanics. For Gao this is the main tool to settle the issue on the ontological status of the wave-function: the wave-function is real because one can measure it. (shrink)

This essay introduces the transcription and translation of Paul Feyerabend's "Der Begriff der Verständlichkeit in der modernen Physik" [The concept of intelligibility in modern physics] (1948), which is an early essay written by Paul Feyerabend in 1948 on the topic of intelligibility (Verständlichkeit) and visualizability (Anschaulichkeit) of physical theories. The existence of such essay was likely. It is listed in his bibliography as his first publication. Yet the content of the essay was unknown, as no original or copy is extant (...) in Feyerabend's Nachlass and no known published version was available to the community—until now. The essay has both historical and philosophical interest: it is, as far as our current knowledge goes, Feyerabend's earliest extant publication. It documents Feyerabend's philosophical interest as a physicist-to-be, in what he himself called his “positivist” phase; and it gives a rare if fragmentary insight into the early discussions of the ‘Third Vienna Circle’ and, more generally, the philosophical culture of discussion in Vienna. (shrink)

Carnap’s ‘Empiricism, Semantics, and Ontology’ (Carnap (1950a), ESO hereafter) is certainly a classic of twentieth century analytic philosophy. For decades now, most undergraduates are expected to read it at some point in their studies. Lately, it is being seen as the inspiration for a host of positions in the field of metaontology. Despite the widespread agreement on the importance of the paper, there is a lack of agreement on what Carnap attempts to do in the paper. My main aim in (...) this chapter is to defend an interpretation of ESO by displaying its relation to Carnap’s earlier works. My secondary goal will be to draw a lesson from this discussion for Carnap’s later work on unobservable entities in science. (shrink)

With the help of syncretiсs as a new philosophical logic, the philosophy of carriers, the theory of similarity and the theory of Infinite Hierarchical Nesting of Matter, the problems of modern physics are analyzed. We consider the classical and relativistic mechanics, the special and general theories of relativity, the theory of electromagnetic and gravitational fields, of weak and strong interactions. The goal is axiomatization of these theories, building models of elementary particles and of their interactions with each other. The main (...) obtained results are: description of the electrokinetic theory of the origin of magnetic fields in cosmic bodies; calculation of metric in the uniformly accelerated reference frame; the axiomatic construction of electrodynamics, Lorentz invariant (LITG) and covariant theories of gravitation (CTG); comparing CTG with the general theory of relativity and with the results of gravitational experiments. Among other results – the analysis of the properties of ether as the medium responsible for transfer of electromagnetic and gravitational waves, and derivation of the formula for entropy in a tensor form. For students and researchers, as well as for those interested in physical and philosophical problems. (shrink)

Besides the presentation and conclusions, the chapter is divided into two equally important sections. The first one describes the modern development of atomic and molecular structure, emphasising some of the philosophical problems that have been taken, and those that have to be faced in its understanding. The second discusses the alternative conceptions and difficulties of students of different educational levels and also the different approaches to its historical or philosophical teaching. Finally, we recognise the necessity for science teachers to assume (...) a specific historical-philosophical position. (shrink)

To be, or not to be, that is the question…In his wonderful Facts and Mysteries, Martinus Veltman terminates a section with an anecdote: “When quarks were not immediately discovered after the introduction by Gell-Mann he took to calling them symbolic, saying they were indices. In the early seventies I met him at CERN and he again said something in that spirit. I then jumped up, coming down with some impact that made the floor tremble, and asked him: Do I look (...) like a heap of indices? This visibly rattled him, and indeed after that he no more advocated this vision, at least not as far as I know” (see page 240 in Veltman 2003). Although it is probable that Murray Gell-Mann, the inventor of quarks, has changed his mind regarding the reality of his symbols after this tough conversation, even later in the start of eighties the reality of quarks, as basic constituents of protons and neutrons, was a matter of disputes and exchanges (Shrader-Frechette 1982a, b; Albright 1982; Gruender 1982). A g. (shrink)

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass (...) ratios suggest some further foundational interpretations of quantum electrodynamics. (shrink)

This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that these new (...) versions accommodate Maddy’s history of the atomic theory. Counter-examples are provided regarding the role of the mathematical continuum and mathematical infinity in science. (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.

Scale is central to understanding nanotechnologies. These technologies are usually described as the understanding and control of matter at the nanoscale, with one nanometer being 10^-9 meter. At this scale, some materials gain new properties that can be used in the creation of new products. These properties may contribute to economic growth and social welfare but, conversely, they may also create negative effects, such as new risks to human health and the environment. As an emerging field whose consequences are still (...) uncertain, the meanings of nanotechnologies are hotly contested. (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)

Within the context of Born-Infeld (BI) nonlinear electrodynamics (NED) we revisit the non-relativistic, spinless H-atom. The pair potential computed from the Born-Infeld equations is approximated by the Morse type potential with remarkable fit over the critical region where the convergence of both the short and long distance expansions slows down dramatically. The Morse potential is employed to determine both the ground state energy of the electron and the BI parameter.

The prolongation of lifetimes for an excited atom due to the presence of nearby atoms in the ground state is shown to follow simply from unitarity of the time evolution. We also discuss possible approaches to the detection and the overcoming of various technical obstacles.

Ich thematisiere die beiden Konzeptionen als Varianten der wissenschaftlichen Weltsicht. Der Reiz des Vergleichs liegt aber weniger in den Gemeinsamkeiten als vielmehr in den Differenzen und den dabei hervortretenden Desideraten der beiden Konzeptionen. Heisenberg versteht sein Schichtenmodell nicht wie Hartmann als Fortsetzung und Zusammenfassung vorangehender philosophischer Bemühungen, sondern als einen Bruch mit den Hauptströmungen der philosophischen Tradition. In der geschichtlichen Entwicklung der Versuche um eine Bestimmung der Weltstruktur sieht er statt einer Generaltendenz, die langfristig auf eine Annäherung an die Wahrheit (...) hinausläuft, tiefgreifende Diskontinuitäten zwischen den aufeinanderfolgenden epochalen Thematisierungsmöglichkeiten. Heisenbergs Motivation für die Suche nach einer Weltordnung ist den Intentionen von Hartmann damit geradezu entgegengesetzt. Er fragt nicht nach einer epochenübergreifenden Orientierung, sondern nach einer epochenspezifischen Charakterisierung der Welt, deren zukünftig möglicher Geltungsverlust zum Maßstab neuer historischer Umbruchsphasen wird. -/- Die Desiderate der beiden Schichtenkonzeptionen gehen teils auf die nachfolgende Entwicklung der einzelwissenschaftlichen Erkenntnis, teils auf den seitherigen Wandel der auch alltagspraktisch wirksamen kulturellen Selbstverständlichkeiten zurück. Einige Schwächen könnten durch Anpassung an veränderte Wissensbedingungen behoben werden. In diesem Zusammenhang schlage ich die Einführung zweier neuer Schichten vor: Die subatomare Schicht der Quantenobjekte und die Schicht der in kosmischen Dimensionen wirksamen Materie- und Energieformen. Es lassen sich aber auch grundlegende Bedenken formulieren, die in Richtung einer Ordnung der Wirklichkeit weisen, die keiner Schichtenauffassung mehr folgt. (shrink)

A criticism of a recent article published in this journal, claiming to have reached a classical description of the Stern-Gerlach phenomenon, is presented here. The author of the article, among other mistakes, wrongly writes the total energy of each silver atom and, moreover, presents a nonsensical equation, from which his results and the conclusion of his article are derived.

The issue of shifting scales between the microscopic and the macroscopic dimensions is a recurrent one in the history of science, and in particular the history of microscopy. But it took on new dimensions in the context of early twentieth-century microscophysics, with the progressive realisation that the physical laws governing the macroscopic world were not always adequate for describing the sub-microscopic one. The paper focuses on the researches of Jean Perrin in the 1900s, in particular his use of Brownian motion (...) to produce evidence of the existence of atoms and in favour of the kinetic theory. His results were described by many contemporaries, and subsequently by historians, as the first direct proof of atomic and molecular reality. The paper examines the different strategies developed by Perrin for bridging the macro and sub-microphysical realms and making the latter accessible to the senses; even though neither atoms nor molecules were ever actually seen, and in fact very few visual representations were shown and published in connection with these experiments. This case provides a good example of how visualizing, representing and convincing could be interwoven in the production of evidence about the sub-microphysical realm circa 1900.Keywords: Jean Perrin; Brownian motion; Ultramicroscope; Evidence; Atom; Atomism. (shrink)

Many structures in nature are invariant under the transformation pair, (p,r)→(b r,−p/b), where b is some scale factor. Born’s reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale b≡mΩ. We find that an Ω∼1.5×10−15 s−1 has essentially no effect on atomic physics but might (...) possibly offer an explanation for galactic rotation, without invoking dark matter. (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)

Gregor Schiemann führt allgemeinverständlich in das Denken dieses Physikers ein. Thema sind die Erfahrungen und Überlegungen, die Heisenberg zu seinen theoretischen Erkenntnissen geführt haben, die wesentlichen Inhalte dieser Erkenntnisse sowie die Konsequenzen, die er daraus für die Geschichte der Physik und das wissenschaftliche Weltbild gezogen hat. Heisenbergs Vorstellungswelt durchzieht durch ein Spannungsverhältnis, das heute noch das Denken vieler Wissenschaftlerinnen und Wissenschaftler bewegt. Er ist um ein umfassendes Verständnis der Naturprozesse bemüht, zugleich aber von der Berechenbarkeit und Beherrschbarkeit von Phänomenen auch (...) dann schon fasziniert, wenn die zugrunde liegenden Prozesse erst teilweise verstanden sind. Aus der Geschichte der Physik zieht er die wirkungsreiche Lehre, daß sich die naturwissenschaftliche Erkenntnis nicht kontinuierlich, sondern sprunghaft in Form von Revolutionen entwickelt. Die Reichweite des physikalischen Wissens begrenzt er in einer Schichtentheorie der Welt, nach der die komplexen Phänomene des Lebens nicht allein durch die Wechselwirkungen zwischen ihren Bestandteilen erklärt werden können. Der zunehmenden Technisierung der Welt steht Heisenberg kritisch gegenüber. Seiner Zeit weit voraus, glaubt er, daß die Technisierung der Welt eine epochal neue Stufe erreicht habe, in der der Mensch „nur noch sich selbst“ gegenüberstehe. (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)

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.

It is shown that the Kapitza-Dirac effect with atoms, which has been considered to be evidence for their wavelike character, can be interpreted as a scattering of pointlike objects by the periodic laser field.

In the centennial of Ettore Majorana’s birth (1906–1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi’s solution of the celebrated Thomas–Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical nuclear physics. In all his (...) papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed. (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.

Pierre Gassendi was a major factor in the revival of Epicureanism in early modern philosophy, not only through his contribution to the restoration and criticism of Epicurean texts, but also by his adaptation of Epicurean ideas in his own philosophy, which was itself influential on such important figures of early modern philosophy as Hobbes, Locke, Newton, and Boyle (to name just a few). Despite his vigorous defense of certain Epicurean ideas and ancient atomism, Gassendi goes to great lengths to differentiate (...) his philosophy from Epicureanism on certain key points. In this paper I argue that those key points on which Gassendi rejects and and criticizes the Epicurean view, such as the immortality of the soul and divine creation of the cosmos, are central not only to Epicureanism, but also to Gassendi's own philosophy. In order to see Gassendi's philosophy for what it is, and understand its role in the history of natural theology, we need accept and understand better why he rejected the central theses of Epicureanism. (shrink)

Using the time-dependent wave function we have studied the properties of the atomic transverse motion in an interferometer, and the cause of the non-classical behavior of atoms reported by Kurtsiefer, Pfau, and Mlynek [Nature 386, 150 (1997)]. The transverse wave function is derived from the solution of the two-dimensional Schrödinger's equation, written in the form of the Fresnel–Kirchhoff diffraction integral. It is assumed that the longitudinal motion is classical. Comparing data of the space distribution and of the transverse momentum distribution (...) in interferometers with one and two open slits, it follows that the atomic motion is influenced by the atomic matter wave and violates the laws of classical mechanics. However, the negative values of Wigner's function should not be taken as evidence that the atoms in an interferometer violate the classical statistical law of the addition of positive probabilities. This inference follows from the comparison of properties of Wigner's function and of the de Broglian probability density in phase space. (shrink)