A fundamental tenet of general relativity is geodesic motion of point particles. For extended objects, however, tidal forces make the trajectories deviate from geodesic form. In fact Mathisson, Papapetrou, and others have found that even in the limit of very small size there exists a residual curvature-spin force. Another important physical case is that of field theory. Here the ray (WKB) approximation may be used to obtain the equation of motion. In this article I consider an alternative procedure, the proper (...) time translation operator formalism, to obtain the covariant Heisenberg equations for the quantum velocity, momentum, and angular momentum operators for the case of spinor fields. I review the flat spacetime results for Dirac particles in Yang-Mills fields, where we recover the Lorentz force. For curved spacetime I find that the geodesic equation is modified by an additional term involving the spin tensor, and the parallel transport equation for the momentum is modified by an additional term involving the curvature tensor. This curvature term is the “Lorentz force” of the gravitational field. The main result of this article is that these equations are exactly the (symmetrized) Mathisson-Papapetrou equations for the quantum operators. Extension of these results to the case of spin-one fields may be possible by use of the KDP formalism. (shrink)

The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0)within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic (...) equation with a free parameter h′ with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h′>0. The exact solutions for which h′<h are called sub-Heisenberg states. These nonperturbative solutions appear in the form of Gaussian, non-Heisenberg states for which the initial classical uncertainty relation takes the form 〈(δx 2)〉〈(δp) 2 〉=(h′/2) 2,which includes the limit of zero indeterminacy (h → 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy hΩ 0 /2 and 〈(δx) 2 〉〈(δp) 2 〉=h 2 /4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states. (shrink)

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at mH=1.35×10-69\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}=1.35 \times 10^{-69}$$\end{document} kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to mH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}$$\end{document} is, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, (...) is equated to the luminosity distance dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} which corresponds to a red shift zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. When using the Concordance-Model parameters, we get dH=8.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H} = 8.4$$\end{document} Gpc and zH=1.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}=1.3$$\end{document}. Remarkably, dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. Finally, in terms of quantum quantities, the expansion constant H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0$$\end{document} reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant. (shrink)

The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency Ω 0)within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic (...) equation with a free parameter h′ with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h′>0. The exact solutions for which h′Heisenberg states. These nonperturbative solutions appear in the form of Gaussian, non-Heisenberg states for which the initial classical uncertainty relation takes the form 〈(δx 2)〉〈(δp) 2 〉=(h′/2) 2,which includes the limit of zero indeterminacy (h → 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy hΩ 0 /2 and 〈(δx) 2 〉〈(δp) 2 〉=h 2 /4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states. (shrink)

This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac’s work, which, in particular Dirac’s derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg’s earlier work leading him to the discovery (...) of quantum mechanics, which inspired Dirac’s work. I argue that Heisenberg’s and Dirac’s work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D’Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac’s equations from these principles alone, without using the principles of relativity. (shrink)

In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of n point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by (...) using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions. (shrink)

G. Breit's original paper of 1929 postulates the Breit equation as a correction to an earlier defective equation due to Eddington and Gaunt, containing a form of interaction suggested by Heisenberg and Pauli. We observe that manifestly covariant electromagnetic Two-Body Dirac equations previously obtained by us in the framework of Relativistic Constraint Mechanics reproduce the spectral results of the Breit equation but through an interaction structure that contains that of Eddington and Gaunt. By repeating for our equation the (...) analysis that Breit used to demonstrate the superiority of his equation to that of Eddington and Gaunt, we show that the historically unfamiliar interaction structures of Two-Body Dirac equations (in Breit-like form) are just what is needed to correct the covariant Eddington Gaunt equation without resorting to Breit's version of retardation. (shrink)

It is shown that in every gauge the potential of the electromagnetic field in the presence of sources is resolved by an extension of the Helmholtz theorem into a solenoidal component and an irrotational component irrelevant for description of the field. Only irrotational components are affected by gauge transformations; in Coulomb gauge the irrotational component vanishes: the potential is solenoidal. The method of solution of the wave equation by use of positive- and negative-frequency parts is extended to solutions of D'Alembert's (...) equation, and applied to equations satisfied by the potential in Coulomb gauge and the electric and magnetic vectors. Fourier transforms of potentials specifying destruction/creation operators become time dependent in the presence of sources. Our central equation states this time dependence. Frequency parts of Maxwell's equations are obtained. When the retarded potential in Coulomb gauge is resolved into kinetic and dissipative components, the latter is shown to be in radiation gauge. Correspondingly, the energy/stress tensor is resolved into three components; the power/force density, into two: a kinetic and a dissipative component. Work done by the latter component is negative: energy and momentum are dissipated from matter to radiation. Boson quantization conditions are satisfied by the kinetic component of the retarded potential, but commutators of the dissipative component are determined by the current sources. The energy/stress tensor and Hamiltonian of the field in the presence of sources are derived from the classical Lagrangian density. The relation between the Hamiltonian and the energy is shown to agree with the time dependence of the destruction/creation operators in Heisenberg picture. (shrink)

We discuss the main results of Linear Stochastic Electrodynamics, starting from a reformulation of its basic assumptions. This theory shares with Stochastic Electrodynamics the core assumption that quantization comes about from the permanent interaction between matter and the vacuum radiation field, but it departs from it when it comes to considering the effect that this interaction has on the statistical properties of the nearby field. In the transition to the quantum regime, correlations between field modes of well-defined characteristic frequencies arise, (...) which coincide with the transition frequencies of quantum mechanics and are therefore directly related with the energy quantization. The Heisenberg equations of motion of (non-relativistic) quantum electrodynamics are thus obtained. After a detailed consideration of the significance of the approximations made, we present a discussion on some of the most delicate or controversial features of quantum mechanics from the perspective provided by the present theory. (shrink)

A theory is presented in which a field depends not only on spacetime coordinates xμ, but also on a Lorentz-invariant parameter τ. Such a theory is conceptually and technically simple and manifestly covariant at every step. The generator of evolution and the generator of spacetime translations and Lorentz transformations are obtained in a straightforward way. In the quantized theory the Heisenberg equation of motion is written in a covariant form and is equivalent to the field equation. The equal τ (...) commutator between the field and its canonically conjugate momentum is just proportional to the spacetime δ function. Finally comparison with the conventional field theory is done, and it is found that the expectation value of the momentum operator in the on shell states is the same. (shrink)

Principles of Laser Spectroscopy and Quantum Optics is an essential textbook for graduate students studying the interaction of optical fields with atoms. It also serves as an ideal reference text for researchers working in the fields of laser spectroscopy and quantum optics. The book provides a rigorous introduction to the prototypical problems of radiation fields interacting with two- and three-level atomic systems. It examines the interaction of radiation with both atomic vapors and condensed matter systems, the density matrix and the (...) Bloch vector, and applications involving linear absorption and saturation spectroscopy. Other topics include hole burning, dark states, slow light, and coherent transient spectroscopy, as well as atom optics and atom interferometry. In the second half of the text, the authors consider applications in which the radiation field is quantized. Topics include spontaneous decay, optical pumping, sub-Doppler laser cooling, the Heisenberg equations of motion for atomic and field operators, and light scattering by atoms in both weak and strong external fields. The concluding chapter offers methods for creating entangled and spin-squeezed states of matter. Instructors can create a one-semester course based on this book by combining the introductory chapters with a selection of the more advanced material. A solutions manual is available to teachers. Rigorous introduction to the interaction of optical fields with atoms Applications include linear and nonlinear spectroscopy, dark states, and slow light Extensive chapter on atom optics and atom interferometry Conclusion explores entangled and spin-squeezed states of matter Solutions manual. (shrink)

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow due to an expansion of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due (...) to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the “force” accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum. (shrink)

An analysis is briefly presented of the possible causes of the failure of stochastic electrodynamics (SED) when applied to systems with nonlinear forces, on the basis that the main principles of the theory are correct. In light of this analysis, an alternative approach to the theory is discussed, whose postulates allow to establish contact with quantum mechanics in a natural way. The ensuing theory, linear SED, confirms the essential role of the vacuum–particle interaction as the source of quantum phenomena.

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are (...) the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed. (shrink)

It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be (...) of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science. (shrink)

The validity of the confinement limit obtain by Unanyan et al. (Phys Rev A 79:044101, 2009) is extended by including non-symmetric vector and scalar potentials. It shows that the confinement limit of one-dimensional Dirac particles in vector and scalar potentials is \(\lambda _C/\sqrt{2}\) , with \(\lambda _C\) being the Compton wavelength.

Some problems relating to the probabilistic description of a free particle and of a charged particle moving in an electromagnetic field are discussed. A critical analysis of the Klein-Gordon equation and of the Dirac equation is given. It is also shown that there is no connection between commutativity of operators for physical quantities and the existence of their joint probability. It is demonstrated that the Heisenberg uncertainty relation is not universal and explained why this is so. A universal uncertainty (...) relation for canonically conjugate coordinates and momenta is suggested. (shrink)

The article analyzes the effectiveness of quantum theories of mental experience in relation to two ontological problems - the problem of the existence of consciousness in the material world and the problem of the interaction of consciousness and body. A critical analysis of the quantum theories of consciousness by Penrose-Hameroff, M. Tegmark, G. Stapp, M. Fischer and M.B. Mensky shows that they fail to fully explain how complex physical systems generate mental experience without violating the principle of causal closure of (...) the physical world and the principle of epistemological completeness of physics. Quantum mechanics provides specific processes that are the physical basis of the psyche, but do not explain the phenomenal aspect of subjective reality. Nevertheless, the Heisenberg uncertainty principle gives an understanding of how the interaction of consciousness and body within the scientific picture of the world can be carried out without violating the law of energy conservation. It is shown that the quantum theories of consciousness currently being developed have a predominantly panprotopsychic character, which faces a problem due to the fact that the protomental property of physical systems must be expressed quantitatively and correspond to the value included in the physical equations. As a result, it is concluded that in order to develop quantum theories of consciousness more effectively, it is necessary to give an emergent character, not jumping from the quantum level to the psychic, but explaining the mechanism of the emergence of systemic properties during the sequential transition between different ontological regions of existence, including physical, chemical, biological, neurophysiological and psychic. (shrink)

Quantum probability is used to provide a new organization of basic quantum theory in a logical, axiomatic way. The principal thesis is that there is one fundamental time evolution equation in quantum theory, and this is given by a new version of Born’s Rule, which now includes both consecutive and conditional probability as it must, since science is based on correlations. A major modification of one of the standard axioms of quantum theory allows the implementation of various mathematically distinct models (...) (commonly called ‘pictures’) of them. A natural definition of isomorphism of models is presented next. For a given Hamiltonian the standard ‘pictures’ of quantum theory (e.g., Schrödinger, Heisenberg, interaction) are isomorphic models, whose probabilities are nonetheless model independent. The Schrödinger equation remains valid in one model of the axioms, even though it is no longer the fundamental equation of time evolution. All the usual calculations of standard, textbook quantum theory remain valid, but they are put in a new light. For example, the ‘collapse’ of the state is now viewed in the Schrödinger model as _one_ step in a _two_ step algorithm for calculating _one_ conditional probability. In the isomorphic Heisenberg model, where states are constant in time, one has the same conditional probability given by the same formula. Also, entanglement is defined in a new, more general model independent way as an aspect of quantum probability without using ‘collapse’ or tensor products. (shrink)

I argue that a particle ontology naturally emerges from the basic dynamical equations of non-relativistic quantum mechanics, when the quantum continuity equation is realistically interpreted. This was recognized by J.J. Sakurai in his famous textbook “Modern Quantum Mechanics”, and then dismissed on the basis of the Heisenberg position–momentum uncertainty principle. In this paper, I show that the reasons of this rejection are based on a misunderstanding of the physical import of the uncertainty principle. As a consequence, a particle (...) ontology can be derived from the quantum formalism without the need of additional ad hoc assumptions, and therefore it cannot be regarded as “extra-structure”. (shrink)

continent. 1.1 (2011): 60-67. At the beginning of Martin Heidegger’s lecture “Time and Being,” presented to the University of Freiburg in 1962, he cautions against, it would seem, the requirement that philosophy make sense, or be necessarily responsible (Stambaugh, 1972). At that time Heidegger's project focused on thinking as thinking and in order to elucidate his ideas he drew comparisons between his project and two paintings by Paul Klee as well with a poem by Georg Trakl. In front of Klee's (...) Saints from the Window and Death of Fire —though we wouldn’t absolutely understand what we were seeing—he writes, “we should want to stand…a long while.” In a similar manner, of Trakl’s poem “Septet of Death”—although it is likely we are unsure in what we hear—Heidegger states that, “we should want to hear…[it] often.” Heidegger further states that in appreciating these, “we “should abandon any claim that [they] be immediately intelligible” (1). So also we must we approach, Heidegger continues, the realm of theoretical physics, in which the difficult work of Werner Heisenberg, be listened to “without protest” and without “any claim that he be immediately understood.” These works, like his own project, merit the time they take to be originally (mis)understood. But this is not necessarily true for philosophy, Heidegger advises, because, “That thinking is supposed to offer ‘worldly wisdom’ and perhaps even a ‘way to a blessed life’” (1). Philosophy is in the unique position of being both abstract (what do we talk about when we talk?) and at the same moment, useful. There are demands that it make sense, that it be, grounded, immediate, and most importantly, rational. Heidegger draws these comparisons between the works of Klee and Trakl and Heisenberg not to claim that philosophy is totally irresponsible. He does not claim that the poet, the painter, nor the physicist have acted irresponsibly. Rather, he would say, they are rising to the highest levels of intelligibility, though it is perhaps an intelligibility that is commonly unavailable to us. In Trakl’s case, as we shall see, mastery is the end result of difficult words. Instead, Heidegger seems be making pleas: for a period of uninterrupted unintelligibility (pure unintelligibility); and that there is a time (that time is now) when, “thinking is…placed in a position which demands of it reflections that are far removed from any useful, practical wisdom” (1-2). Heidegger argues that philosophy requires a period of time in which, instead of focusing on the practical—or even on the worldly—the discipline draw its “determination” instead from the place of painting and poetry and physics. In doing so, “we should have to abandon any claims to immediate intelligibility” (2). But Heidegger doesn’t offer this as a way out. We still have to turn up, we “still have to listen, because we must think what is inevitable, but preliminary” (2). The point for Heidegger, is not to listen to a series of propositions, but instead to “follow the movement of showing” (2). I. … Maybe we're here only to say: house, bridge, well, gate, jug, olive tree, window— at most: pillar, tower … but to say them, remember, oh, to say them in a way that the things themselves never dreamed of existing so intensely.… Rainer Maria Rilke, “The Ninth Elegy” There is little more fundamental, preliminary, in the world than language. We use language, in the form of speech, constantly, whether we are saying anything or not. “Man speaks,” Heidegger writes, and goes on to describe in his essay “Language” (2001) the constant speaking that we do. “We are always speaking, even when we do not utter a single word aloud, but merely listen or read, and even when we are not particularly speaking or listening but are attending to some work or taking a rest” (187). Speaking is expression, an utterance of something internal. It is a recognition of a world. It is a way of communicating thought and it is an activity that we all do, inevitably. Speaking separates the human from the animal world, and despite advances in primatology that seek to give ‘voice’ to primates and other non-human animals, it can safely be said that our form of communication—what we call speech and know as language—is the most advanced, the most complicated. We use it to present and represent the world around us; through actual utterances (vocalization) or through the written word or through ‘unvoiced thoughts’ and dreams. We use language, but more specifically speech—naming—to transmit moods, thoughts, desires, aversions, and feelings. These expressions, mere utterances, nearly always find a source in words, whether spoken or not. Heidegger writes that this common view of language means “that only speech enables man to be the living being he is as man. It is as the one who speaks that man is—man” (187). Speaking then—utterance—surrounds us constantly, whether in the form of careful thought—in the form of an academic paper, say—or in the half mutterings and forgotten thoughts of a nearly remembered dream. Like scaffolding, the apparatus of speech sustains and explains the world, making, in a sense, the world rational, making it apparent. When we speak, we describe, and in doing so, name the world. We use words, through this process of naming, to interpret and sustain the world we see, and the world we imagine. Like Rilke’s naming of jug, and bridge, and window, and stream, we describe—and inscribe upon—the world through an activity of naming. Are we here, perhaps, to name? Is it possible not to name? Is it possible to regard and to view and to look around without naming what we see? Is it possible to feel—to experience—world without giving utterance to that feeling, that process? Sadness, grief, joy, ecstasy, hunger, thirst. Desk, light, room, pen, book, world. White, black, tomorrow, today. Each of these words is a name given to a thing I see in front of me, or a concept that I imagine (in the case of tomorrow or world). What arises in my mind has already existed. If I imagine it, it is named. The word for ‘tomorrow’ and ‘desk’ and ‘light’ precedes me, and precedes my concept of it. The idea of it is already pre-informed, and I must, in a certain sense, bend my ideas to it. When I imagine a table, I imagine my own table (or I imagine an idea of table) but that imagining must follow certain general rules; while, perhaps, it might not always require four legs and a horizontal surface, it must, at least not be, say, a pool of water, or a pile of excrement. It must have some tableness to it to be a table. It must, with Heidegger, table. Otherwise, speech is reduced to gibberish. For Heidegger however, the discussion of language points to something deeper than its “scientific and analytic” study as a communicative device. Indeed, Heidegger seeks to understand language not in reference to man or woman, not as an utterance of humanity, but in reference to itself. In doing so he abandons the conversation—that is, he casts away the traditional arguments surrounding philosophy of language; that it is a means of expression; that it is a human activity; and that it is somehow a representation of something that is—in order to seek to understand language as language, on its own terms. Heidegger is not a philosopher of language, but a philosopher of world, of being. Despite these “correct ideas” holding sway “over the whole field of the varied scientific perspectives on language…they ignore completely the oldest natural cast of language” (191). What is this “oldest natural cast of language? It is the act of language itself. Language is language and language speaks. “Most often,” Heidegger writes, “and too often, we encounter what is spoken only as the residue of a speaking long past” (195). Speech, as we normally encounter it, is like Echo herself calling out to Narcissus, doomed to repeat what has already been said, a mere remnant of what was once language, a trace left behind in the gathering silence of becoming. In both the essay “Language” and in his three lecture course “The Nature of Language” (1982), Heidegger attempts to unpack the seeming tautology of language as language. In each, he focuses on poetry as a way out, or into, a true discussion of the oldest natural cast of language. Poetry is pure speech. In poetry, language is brought to language and language speaks ( Die Sprach spricht ). In the act of poetry, the act of pure speech, the poet names (on the surface not different from how I name this table, this computer) but in the poet naming, the naming does not “hand out titles,” “apply terms,” but rather the naming is a call, a calling forth of entities that bring them into their own, allow them to take their place purely, without compromise. This calling, Heidegger (2001) states, “here calls into a nearness. But even so the call does not wrest what it calls away from the remoteness, in which it is kept by the calling there. The calling calls into itself and therefor always here and there—here into presence, there into absence” (196). II. Window with falling snow is arrayed, Long tolls the vesper bell, The house is provided well, The table is for many laid. Wandering ones, more than a few, Come to the door on darksome courses. Golden blooms the tree of graces Drawing up the earth’s cool dew. Wanderer quietly steps within; Pain has turned the threshold to stone. There lie, in limpid brightness shown, Upon the table bread and wine. Georg Trakl “A Winter Evening” Heidegger is often given short shrift as an abysmally difficult writer, as one that makes no sense and is needlessly difficult. In doing this though, we forget sometimes his eloquence, his simple beauty in writing. Of the above opening stanza, “Window with falling snow is arrayed/ Long tolls the vesper bell.” he writes (2001), This speaking names the snow that soundlessly strikes the window late in the waning day, while the vesper bell rings. In such a snowfall, everything lasts longer. Therefore the vesper bell, which daily rings for a strictly fixed time, tolls long. The speaking names the winter evening time (197). The speaking names the winter evening time. It is almost impossible to comment on that one line by Heidegger. It is as though it must exist on its own completely, without elucidation—as though in front of it we must stand as we do in front of a painting by Klee, that is, we must abandon any claim . Silent and devoted. The speaking of the poem here is not clearly different from common speech ( rede ) yet there is, via Heidegger, an invitation to experience that auracular quality of light and stillness that a gentle, dusk tinged snowfall gives; words evoking a quality so clear, so poignant that, in a sense, Heidegger’s work, at this moment, has been done. But what does this naming accomplish? What does the call call? Remember, it is not the poet that calls, but the naming which calls. The poet has only brought the words forward; it is now the words— snow, vesper bell, window— that take new life in the pure language of the poem. Entities are called forth into presence, like the speaking that names the winter evening time. Not to be present amongst us now, however; naming ‘table’ in the poem does not place it in front of us in this room. Rather, the naming places entities into a gathering which is also a sheltering. The naming brings them to be. In an act of appropriation, things come to be purely as their own, unimpeded by a predetermined expectation. They are called to themselves into an arrival. In Being and Time (1962), Heidegger famously describes the movement between present-at-hand and ready-to-hand in his analysis of the hammer, and of equipment in general. This analysis is already known, if not always clear, to most readers of Heidegger. Briefly, a hammer is ordinarily zuhanden or ready-to-hand; it is part of the background of the world, equipment used and never thought about, like this desk, this sheet of paper, this room. Our interaction with it is temporary and it is historically different for each entity and each relation. We need a hammer, we use a hammer. If all goes according to plan, the hammer remains ready-to-hand; it remains, in a sense, undisclosed and certainly unobtrusive. Our world is undisturbed by the hammer. Only when the hammer or the car or the computer is broken (or sometimes unused or unrecognized or missing) does it intrude into our world, become conspicuous as an object present-at-hand, or vorhanden . In this case, we reach for the hammer, it is broken and we suddenly notice it’s being, broken though it is. The thing which was always ready to hand—handy—is suddenly abstract, something to be examined, if only in its absence or disfunction. This can be exhibited for all entities, and it is important to note that in this analysis the zuhanden / vorhanden split is not restricted to a specific form of constructed material; zuhanden does not refer to the car, and vorhanden the sunset. No entity is ever exclusively ready-to-hand or present-at-hand; they are instead, interpenetrated with each others mode of being, one informing the other in a way that both brings things forth into the world—discloses is the word Heidegger chooses—and at the same time conceals them. As one mode is coming to be so another mode is withdrawing. This flux and movement between modes is precisely what brings the world forward, and what makes it manifest. It exists beyond where we tread and before man took dubious control of the world. We go to find a book or turn on the computer and it is missing or broken and we become aware of the object, as though for the first time. We walk to the water to glimpse the sunset and miss it, or it is less than stellar; in the sunset’s grayness, we become aware of it’s being sunset. The thing is disclosed in its withdrawal. Echoing Heraclitus, we can say that as something is coming to be, it is already becoming something other. Of similar importance to the fact that things are never all of one, or all of the other, they are also never alone. The hammer is never a single object, but is in relation always to the whole. Heidegger (1962) states, Equipment—in accordance with its equipmentality—always is in terms of its belonging to other equipment: ink-stand, pen, ink, paper, blotting pad, table, lamp, furniture, windows, doors, room. These ‘Things’ never show themselves proximally as they are for themselves…What we encounter as closest to us…is the room; and we encounter it not as something ‘between four walls’ in a geometrical, spatial sense, but as equipment for residing…it is in this that any ‘individual’ item of equipment shows itself. Before its does so, a totality of equipment has already been discovered (97). Equipment resides—dwells—in its relations, in its proximal being to other beings. Within the structure of totality, a series of relations is always occurring. The hammer is on the workbench in the carpenter’s hand in the workshop in the village under the sky and under the sun. It doesn’t stop there. Equipment surrounds us and the focus is not on what it does, or what one does with it—the carpenter with the hammer, the writer with laptop—but with the fact that it is. Equipment occurs in relation and is always occurring around us overhead, underfoot, by the stream and in the city. There is a constant exchange of relations happening, and as this occurs, so the world occurs, so the world both discloses and withdraws, into and out of itself. In a very real sense, language is also equipment. It is the thing that we use most often without thought, it is ready-to-hand (except when it’s not.) As we re- cognize the world around us, as we offer names for things and make lists, we are using language much like we might use a hammer, that is, bluntly. Most of the time it is invisible and we draw on it without wondering how we are going to say something. When language does intrude, it does so in an awkward moment, that moment when we can’t remember the right word, when we forget a phrase. At that second, it “speaks itself as language,” it reveals itself as malfunctioning equipment, and we “undergo” an experience with language, in Heidegger’s famous formulation. Language is not a tool anymore that we use to bludgeon an object, but something instead that we submit to, that we experience. In “The Nature of Language,” Heidegger (1982) writes, But when does language speak to us as language? Curiously enough, when we cannot find the right word for something that concerns us, carries us away, oppresses or encourages us. Then we leave unspoken what we have in mind and, without rightly giving it a thought, undergo moments in which language itself has distantly and fleetingly touched us with its essential being (59). The poet’s words become themselves, become appropriate, only when they no longer function in the prosaic world; they instead intrude as they come to be. Language itself brings itself to language. Names, like the entities they indicate, are always becoming something else. As noted above, language, through the poet, has brought forth entities from words previously “known.” I thought that I knew snow, but through Trakl’s re- presentation of the word, language calls forth a new image of snow, indeed calls forth snow itself. The vesper bell tolls longer, the table is for many laid. In bringing forth things , language has brought the world to presence. In everyday naming, word occludes world, preventing, in its everydayness, its coming forth, its disclosing. But what is this world that word has been brought forth into? In the same way that language speaks, world worlds. World, left alone, un-interfered with, comes into itself. It worlds. Again, this sounds like a tautology, but it is essential to Heidegger’s thought (and in my mind is more of a “god killer” than Nietzsche.) One of the most overlooked (and under-appreciated) aspects of Heidegger is his later examination and enthusiasm for the “fourfold,” or the system through which things come to be, through which things thing in a world worlding. The fourfold is the interaction of earth and sky, mortals and gods. Things come to be in the interstices and gathering of the fourfold. The fourfold provides both a place of being, and a sheltering, a place to dwell. Heidegger writes that “the things that were named, thus called, gather to themselves sky and earth, mortals and divinities. The four are united primally in being toward one another, a fourfold.” The poet has called, through the act of pure naming, things to come forth. In the purity of the fourfold—that is, when that is all that there is, when there are no other distractions, definitions, things—entities themselves can come to be. It is important to note that Heidegger is not saying that there are four formal things in the world, autonomous entities unto themselves. He is not evoking a pre-Socratic formula as to what makes up the world; instead, the four mirror each other constantly. (Heidegger calls this the ‘mirror-play.’) They interpenetrate in the same way that the modes of being of things interpenetrate themselves. There is no discrete exclusivity in being or the fourfold. What makes up things is not a precise recipe of the four main components; what makes up things is the action of the fourfold coming together, the movement of the fourfold which is a becoming. Heidegger (2001) writes that “this gathering, assembling, letting stay is the thinging of things.” And he later adds that “thinging, things are things. Thinging, they gesture—gestate—world” (197). Language brings the world to be. It works not again as a recipe added to things, but instead it is a bridge, or more precisely, a relation. Language relates world to thing, brings world to thing. In a sense, it does not say anything; rather it allows, or calls in its movement. Heidegger (2001) writes that, The intimacy of world and thing is not a fusion. Intimacy obtains only where the intimate—world and thing—divides itself cleanly and remains separated. In the midst of the two, in the between of world and thing, in their inter, division prevails: a dif-ference (199). It is in this inter that language prevails. Language is difference, it is the differential aspect between world and thing that brings world to thing. In the final stanza of Trakl’s poem “The Winter Evening,” Trakl evokes this difference in the second line when he writes, “Pain has turned the threshold to stone.” Christopher Fynsk, in his essay “Noise at the Threshold,” draws attention to this point when he writes “it is the figure of the threshold that is language itself, inasmuch as language is defined as the articulation of difference by which difference comes about” (25). Language, as used in the pure language of the poem, draws together world and thing, bridging relation between entity and world. The calling of language calls world to thing, world to being. Heidegger (2001) describes this difference as unique; “of itself, it holds apart the middle in and through which world and things are at one with each other” (200). III. Neither reading nor writing, nor speaking—and yet it is by those paths that we escape what has been said already, and knowledge, and reciprocity, and enter the unknown space, the space of distress where what is given is perhaps not received by anyone (99). Maurice Blanchot The Writing of Disaster So far, we have allowed Heidegger to put forward what language does, how it functions as a relation and how it operates as a threshold, as a bridge. What interests me is what happens beyond language, beyond the relation. What happens to the thing without the naming, without the poet, or even without the everyday chatter—Fynsk calls this ‘noise’—intruding on being? If language allows things to become by bringing thing to world, what happens when we remove this bringing, this threshold turned to pain? In “The Nature of Language,” Heidegger examines the work of the poet Stefan George, specifically “The Word”: Wonder or dream from distant land I carried to my county’s strand And waited till the twilight norn Had found the name within her bourn— Then I could grasp it close and strong It blooms and shines now the front along… Once I returned from happy sail, I had a prize so rich and frail, She sought for long and tidings told: “No like of these depths unfold.” And straight it vanished from my hand, The treasure never graced my land… So I renounced and sadly see: Where word breaks off no thing may be. That final line, “Where word breaks off no thing may be” is evoked on nearly every page of Heidegger’s essay. It is the line to which he returns over and over and bears repeating. Where word breaks off no thing may be. Where naming ends, no thing. We can interpret this in two ways (at least.) Where word—naming—breaks off, then there is nothing . Or, as I choose to read it, where word breaks off no thing may be. In this I see a hint forward, a marker left behind by Heidegger. What could this look like? What does no thing look like? Like a zen koan ( there is no mirror ) it is as thrilling and horrifying as contemplating what preceded the Big Bang. Because language as naming wasn’t always here; we weren’t always here. One or maybe two aspects of the fourfold (depending on your view of gods) were not always here, and there is no guarantee that we will always be around. What then? Heidegger (1982) describes the landscape that the poet finds, “It names the realm into which the renunciation must enter: it names the call to enter into that relation between thing and word which has now been experienced” (65). The poet, in renouncing, allows for the “may be” of “where word breaks off no thing may be.” This “may be” becomes “a kind of imperative, a command which the poet follows, to keep it from then on.” No thing is lacking. Where word breaks off, there may be, a totality, a completion. If we place the emphasis on may be , we make it affirmative, make it positive. One allows it. No thing is where the word, that is the name, is lacking. If we remove then (if we can remove) the word, the name, than that is where no thing is, that is where no thing may blossom, enrich, belong, become. What is no thing? Heidegger writes that “thing is anything that in any way is.” And just after this he writes that the “world alone gives being to the thing.” But what happens if there is no word? Word, in this formulation can be seen as an enframing, a challenging of language. By naming, by drawing a perimeter around an object, we hold it, by its definition (that is a brick) to an ordered future. If we borrow from Heidegger’s essay “The Question Concerning Technology” (1993) the idea of this standing-reserve of an ordered future, we see that “everywhere everything is ordered to stand by, to be immediately on hand, indeed to stand there just so that it may be on call for a further ordering” (322). What happens if there is no naming of the thing? Silence perhaps. Stillness. We can name—and do name—that which we know. We equate knowledge with knowing the name of something. A brick is a brick, a hammer is a hammer, the universe is the universe. By naming a thing, we create, and draw its parameters, the parameters of the thing, not as thing thinging in the fourfold, but as blunt object apparent. In the four dimensions relatively available to us, we observe (and name) that the brick takes up possibly six by four by two inches and is, in the sense that it currently occupies this time slot. It fulfills its destiny, its being, its brickness, it bricks . But what happens when we remove the name for this brick. We no longer know what to call this no-thing (if indeed we can even arrive at the point of uncalled calling.) In fact the it (this brick) is no longer a thing in the sense that by not naming—by removing the name—it still occupies the same dimension but is indiscernible from the world. It simply is , un-reliant, un- needed by me. By removing the subject (me) from it (the brick) do I not then also remove the object—or at least the duality objectifying it? Why is this important? Why does this matter? I have not really removed anything. I have not changed any thing , per se . The brick still occupies the same space in geographic and temporal dimensions. I have literally not even touched the brick sitting on my desk. But what I have done is removed the name, removed the word (the bridge, according to Heidegger) and in this (again, if this is even possible) there is something vertiginously liberating, not only for me (and my way of thinking) but also for the brick itself. Like the poet who calls the thing forward, by refusing to name, by avoiding any thing that demands me to name it, I release the thing into the fourfold. I am no longer challenging the thing to be there for me ; I do not en frame it through language. Rather I, in an act of extreme responsibility, am refusing the challenge. By refusing the name (refusing to name) one allows, (or no one allows no thing) the brick to be all things , to manifest its manifold being, to incorporate all things into its thinging . It becomes, quite literally, every thing . Because, in its infinite manifestness, it incorporates everything; the mud that gave it its current being, the water that formed the mud, the sun, the stars, the universe and it also allows it to become mud again, to become landfill, to become again, water and sun and stars and universe in an endless, infinite cycle of coming to be some thing (else). Perhaps this is what Heidegger is suggesting when he talks about the stillness at the end of his essay, “Language” (2001): The dif-ference stills particularly in two ways: it stills the things in thinging and the world in worlding. Thus stilled, thing and world never escape from the dif-ference. Rather, they rescue it in the stilling, where the dif-ference is itself the stillness (206). It is in this stillness that I can imagine a gellasenheit (here I mean both “releasement in the Heideggarean sense, as well as Meister Eckhart’s use of the term meaning “letting the world go and giving oneself to God”) of thing and world, a releasing into the stillness and silence of no thing beyond where word breaks off. It is here where I may no longer be, and yet no thing is, but may be. (shrink)

The generally covariant Lagrangian densityG = ℛ + 2K ℒmatter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg ikand φ of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form Γ kl i = kl i for the coefficients г kl i of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of φ, gik, and the (...) coefficients г kl i . Then the г kl i are determined by the Palatini equations. From these equations and from the symmetry г kl i = г lk i for all matter fields with δℒ/δΓ=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, δℒ/δΓ becomes dependent on the Dirac current, essentially with a coupling factor ∼Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10−81erg cm3. (shrink)

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to (...) construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell's inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications. (shrink)

We give picture-covariant formulations of the equations of motion for observables and states such that the Hamiltonian operator is transformed asH-0304;=U(t)HU † (t) under a time-dependent unitary transformationU(t). Next, we consider the explicit and implicit covariance of Heisenberg's equations of motion for observables with respect to general transformations of coordinate operators. Most of our representation is spread out over a number of textbooks and articles, where the subject has been considered with greater or lesser clarity from different (...) points of view. (shrink)

Breaking Bad, hailed by Stephen King, Chuck Klosterman, and many others as the best of all TV dramas, tells the story of a man whose life changes because of the medical death sentence of an advanced cancer diagnosis. The show depicts his metamorphosis from inoffensive chemistry teacher to feared drug lord and remorseless killer. Driven at first by the desire to save his family from destitution, he risks losing his family altogether because of his new life of crime. In defiance (...) of the tradition that viewers demand a TV character who never changes, Breaking Bad is all about the process of change, with each scene carrying forward the morphing of Walter White into the terrible Heisenberg. Can a person be transformed as the result of a few key life choices? Does everyone have the potential to be a ruthless criminal? How will we respond to the knowledge that we will be dead in six months? Is human life subject to laws as remorseless as chemical equations? When does injustice validate brutal retaliation? Why are drug addicts unsuitable for operating the illegal drug business? How can TV viewers remain loyal to a series where the hero becomes the villain? Does Heisenberg's Principle of Uncertainty rule our destinies? In Breaking Bad and Philosophy, a hand-picked squad of professional thinkers investigate the crimes of Walter White, showing how this story relates to the major themes of philosophy and the major life decisions facing all of us. (shrink)

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a “particle wave,” which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle (...) can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity. (shrink)

Many physicists view the most sublime task of physics in presenting some day a world formula or a simple Theory of Everything that accounts for all major physical theories and from which everything follows by pure deduction.1 This striving for universality can look back on a long history, which contains the failed attempts to incorporate electrodynamics into universal mechanics, Einstein’s einheitliche Feldtheorie and Heisenberg’s explicit proposal of an Urgleichung. Those attempts were encouraged by the success of general relativity, which (...) embraced classical mechanics and Newtonian gravity as well defined limits. A decade later quantum mechanics was given its final shape, which allowed the explanation of all atomic phenomena known up to then and contained classical mechanics as its macroscopic limit at least in the stochastic interpretation, i.e. comparing both as theories of measurement. After the success of gauge theories in elementary particle physics, the search for a fundamental simple equation was replaced by the search for a basic symmetry group that described all fundamental interactions apart from gravity. It resulted in the famous gauge group of the Standard Model SU × SU L × U , which comprises the strong, the weak and the electromagnetic interaction. But the fact that the Standard Model contains 18 parameters, which have to be introduced from outside, inspired the search for a larger unifying gauge group. These Grand Unified Theories tried to derive some of the parameters of the Standard Model from more fundamental gauge symmetries. With the rise of string theory, which intends to include gravity as well, a new term popped up to express the old claims: Theory of Everything. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical (...) equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

The traditional standard quantum mechanics theory is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle”. A complete and straightforward solution of the spin–statistics problem is presented on the basis of the “conformal quantum geometrodynamics” theory. This theory provides a Weyl-gauge invariant formulation of the standard quantum mechanics and reproduces successfully all relevant quantum processes including the formulation of Dirac’s or Schrödinger’s equation, of Heisenberg’s uncertainty relations and of the nonlocal EPR correlations. When (...) the conformal quantum geometrodynamics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the “intrinsic helicity”. This property, not considered in the Standard Quantum Mechanics, determines the correct spin–statistics connection observed in Nature. (shrink)

I attempt to develop further the statistical interpretation of quantum mechanics proposed by Einstein and developed by Popper, Ballentine, etc. Two ideas are proposed in the present paper. One is to interpret momentum as a property of an ensemble of similarly prepared systems which is not satisfied by any one member of the ensemble of systems. Momentum is regarded as a statistical parameter like temperature in statistical mechanics. The other is the holistic assumption that a probability distribution is determined as (...) a whole as most likely to be realized. This is the same as the chief assumption in statistical mechanics, and maximum likelihood in classical statistics. These ideas enable us to understand statistically (1) the formalism of quantum mechanics, (2) Heisenberg's uncertainty relations, and (3) the origin of quantum equations. They also explain violation of Bell's inequality and the interference of probabilities. (shrink)

In the context of a parametric theory (with the time being a dynamical variable) we consider here the coupling between the quantum vacuum and the background gravitation that pervades the universe (unavoidable because of the universality and long range of gravity). We show that this coupling, combined with the fourth Heisenberg relation, would break the parametric invariance of the gravitational equations, introducing thus a difference between the marches of the atomic and the astronomical clocks. More precisely, they would (...) be progressively and adiabatically desynchronized with respect to one another in such a way that the latter would lag behind the former. This would produce a discrepancy between gravitational theory and observations, which use astronomical and atomic time respectively. It turns out that this result, surprising at it might be, is fully compatible with current physics, since it does not conflict with any known physical law or principle. We argue that this phenomenon must be studied, since it could have cosmological consequences. (shrink)

A great effort has been devoted to formulating a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in connecting classical and quantum theories rests in finding a parameter that plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneering works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut (...) and Zanghi. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level, we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. (shrink)

The effect of short disturbances on nonrelativistic motion is formulated in terms of operators. Analogies with quantum mechanics are developed and some disparities noted. For the one-dimensional particle we obtain analogues of the de Broglie wave commonly associated with particle motion, Heisenberg's commutation relation, Schrödinger's equation, and the statistical interpretation. Whether these results have any bearing on quantum mechanics itself is left an open question.

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 discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a “quantization of geometry.” However, classical and quantum gravitation have the same physical (...) meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies. (shrink)

In November of 1925 Born, Heisenberg and Jordan wrote an article together in which they demonstrated that Einstein's energy fluctuation formula could be derived from quantum mechanics. They remark that the equations are subject to reinterpretation. Specifically, the states of radiation oscillators can be reinterpreted as numbers of quanta of radiation. They also connected this latter idea up with Bose-Einstein statistics. Heisenberg wrote to Pauli that it was Jordan who contributed the idea of reinterpreting the terms. This (...) was the first step toward quantum field theory. In August of the following year Dirac derived Einstein's A and B coefficients for induced transitions between states but on the assumption that the electromagnetic field could be treated classically (Dirac 1927). In 1927 Dirac lay the mathematical foundations for quantum electrodynamics. Early that year he combined quantum mechanics, special relativity, and radiation theory in treating the electromagnetic field as if it were an infinite collection of oscillators. (shrink)

Presents German physicist Werner Heisenberg's 1958 text in which he discusses the philosophical implications and social consequences of quantum mechanics and other physical theories.

The seminal work by one of the most important thinkers of the twentieth century, Physics and Philosophy is Werner Heisenberg's concise and accessible narrative of the revolution in modern physics, in which he played a towering role. The outgrowth of a celebrated lecture series, this book remains as relevant, provocative, and fascinating as when it was first published in 1958. A brilliant scientist whose ideas altered our perception of the universe, Heisenberg is considered the father of quantum physics; (...) he is most famous for the Uncertainty Principle, which states that quantum particles do not occupy a fixed, measurable position. His contributions remain a cornerstone of contemporary physics theory and application. Book jacket. (shrink)

The contributions of few contemporary scientists have been as far reaching in their effects as those of Nobel Laureate Werner Heisenberg.

Available here for the first time in English, "Reality and Its Order" is a remarkable philosophical text by Werner Heisenberg, the father of quantum mechanics and one of the leading scientists of the 20th century. Written during the wartime years and initially distributed only to his family and trusted friends, the essay describes Heisenberg’s philosophical view of how we understand the natural world and our role within it. In this volume, the essay is introduced by the physicist Helmut (...) Rechenberg and annotated by the science historian Ernst Peter Fischer. The content, particularly within its historical context, will be of great interest to many physicists, philosophers and historians of science. (shrink)

Werner Heisenberg: Der Teil und das Ganze.

In nine essays and lectures composed in the last years of his life, Werner Heisenberg offers a bold appraisal of the scientific method in the twentieth century--and relates its philosophical impact on contemporary society and science to the particulars of molecular biology, astrophysics, and related disciplines. Are the problems we define and pursue freely chosen according to our conscious interests? Or does the historical process itself determine which phenomena merit examination at any one time? Heisenberg discusses these issues (...) in the most far-ranging philosophical terms, while illustrating them with specific examples. (shrink)

The seminal work by one of the most important thinkers of the twentieth century, Physics and Philosophy is Werner Heisenberg's concise and accessible narrative of the revolution in modern physics, in which he played a towering role. The outgrowth of a celebrated lecture series, this book remains as relevant, provocative, and fascinating as when it was first published in 1958. A brilliant scientist whose ideas altered our perception of the universe, Heisenberg is considered the father of quantum physics; (...) he is most famous for the Uncertainty Principle, which states that quantum particles do not occupy a fixed, measurable position. His contributions remain a cornerstone of contemporary physics theory and application. (shrink)

In this paper, I argue that Kant’s philosophy of history underwent a significant change be- tween his 1784 Idea for a Universal History and his 1790 Third Critique. My proposal is that in between these two texts Kant decisively revised his conception of the sources of historical, i. e. cultural and political, progress: In 1784, he conceived of historical progress as primarily accomplished through social antagonism among human beings, whereas beginning in 1790, he elevates ethical cooperation into a second, significant (...) source of progress. Between 1784 and the 1790s, in other words, Kant re-conceived the collaboration between moral agents as a driving force of history and of the progressing cultivation of humankind. In this paper I offer evidence for this change and suggest reasons why it might have occurred. (shrink)