Purpose. To examine the existential anthropology of G. Marcel and E. Minkowski, in order to demonstrate the necessity of distinguishing the universal-spiritual, as human in human being, apart from the individual-existential in him, and to reveal the hierarchical correlation of biosocial, existential and spiritual spheres in personality. Theoretical basis. Within existential philosophy the author differentiates two separate traditions and proceeds from the insufficiency of the distinction of existential sphere, proposed by phenomenological tradition, showing the necessity of its correlation with (...) the spiritual sphere as a sphere of humanity, proposed by non-phenomenological tradition of G. Marcel and E. Minkowski. Originality. The author presents the anthropological conception of G. Marcel and E. Minkowski, in which human personality is understood as unity of individual-existential and universal-spiritual, which requires a special trans-empirical field of culture, which contains senses, images and symbols of humanity. Also, the author presents the recent developments of existential thinkers in distinguishing existential and spiritual dimensions, both not reducible to the physical and social dimensions. Conclusions. In both existential traditions, the specifically human was founded as a trans-biological and trans-social phenomenon, which appears as indefinable and non-predetermined. But in first tradition, humanity is understood as an existence, as a unique individuality, "project", variant of humanity, equivalent to other variants, and universal is understood as a community of human condition in the world. While in the second tradition, the universal is understood as spiritual. Thus, horizontal level of our private existence, as the process of movement from birth to death, is supplemented by vertical of human, universal ideals and images. Humanity appears as a task, on the way to which human being transcends beyond the limits of his individual "self" to the "super-individual", through inclusion into spiritual community, into universal culture. (shrink)

This paper clarifies the notion of "contact with reality" by investigating one way in which lack of such contact can be expressed: the interrogative attitude. The case of a socially withdrawn, seventeen-year-old schoolboy is examined. Paul C. had long been overly logical and precise in his style of thinking. An acute disturbance began with mental fatigue along with apparent obsessive symptoms (e.g., extreme monitoring of his own actions) to the point that simple, everyday actions became very time-consuming; he also developed (...) a tendency to ask endless questions even about trivial phenomena. However, unlike those of the true obsessive, Paul's monitoring, doubting, and querying seemed to lack any emotional or personal element; he was not anxious but, rather, apathetic. Also, Paul lacked real curiosity: To him, everything had the same level of importance, and his attention was not directed by any precise or personal goal. This paper argues that Paul's interrogative attitude was actually a form of autistic-schizophrenic thinking characterized by "pragmatic weakening" and a loss of vital contact with reality, which are consequences of a weakening of the "élan vital" with its "vital propulsion toward the future." Such patients retain their intellectual powers but do not use these powers in accord with the requirements of reality. The interrogative attitude can be seen as a compensation mechanism—a way to maintain some minimal contact with the world. The paper ends with psychotherapeutic recommendations. (Abstract written by special issue editor: L.A.S.). (shrink)

It is hypothesized that de Broglie’s ‘matter waves’ provide a dynamical basis for Minkowski spacetime in an antisubstantivalist or relational account. The relativity of simultaneity is seen as an effect of the de Broglie oscillation together with a basic relativity postulate, while the dispersion relation from finite rest mass gives rise to the differentiation of spatial and temporal axes. Thus spacetime is seen as not fundamental, but rather as emergent from the quantum level. A result by Solov’ev which demonstrates (...) that time is not an applicable concept at the quantum level is adduced in support of this claim. Finally, it is noted that de Broglie waves can be seen as the “bridge of becoming” discussed by ( 2005 ). (shrink)

This book of readings would make a superb ancillary text for an advanced or even graduate course in "existential phenomenology." Twelve of the twenty-two selections have been translated for the first time into English. This includes Sartre's defense of the major theses of Being and Nothingness before the Société française de philosophie and Ric£ur's similar defense of La Philosophie de la Volonté, I before the same body. As with Merleau-Ponty's similar defense, "The Primacy of Perception," also included in this volume, (...) the discussion which followed these defenses is presented. Integral texts in the form of articles rather than extracts from books are presented in most cases, including the first appearance of an essay by Marcel entitled "Desire and Hope." Where this is not done, as is partly the case for Strasser and wholly the case for Scheler, Dufrenne, Wild, and Ingarden, lengthy and context-faithful excerpts are given. There are four sections in the book: I. Existence in the Modalities of Consciousness, II. Existence as Embodied, III. Existence and Value, and IV. Existence and the Human Sciences. Each of these sections is skillfully laid out and effectively introduced. In addition to the philosophers mentioned, work by Buytendijk, May, Schutz, Van Kaam, Berger, Bollnow, Minkowski, Straus, and de Waelhens is included. Husserl is missing, as is Heidegger, but these gaps can be supplemented easily enough.—E. A. R. (shrink)

This paper places Julian Schwinger's development of the Euclidean Green's function formalism for quantum field theory in historical context. It traces the techniques employed in the formalism back to Schwinger's work on waveguides during World War II, and his subsequent formulation of the Minkowski space Green's function formalism for quantum field theory in 1951. Particular attention is dedicated to understanding Schwinger's physical motivation for pursuing the Euclidean extension of this formalism in 1958.

Galilean space-time plays the same role in nonrelativistic physics that Minkowski space-time does in relativistic physics. In this paper, the fundamental concepts (velocity, momentum, kinetic energy, etc.) and principles (laws of motion and conservation laws) of classical physics are formulated in the language of Galilean space-time. Much of the development closely parallels the development of similar concepts and principles in the theory of special relativity.

The purpose of this paper is twofold: a) to explore the compatibility of Minkowski’s space-time representation of the Special theory of relativity with a dynamic conception of space-time; b) to locate its roots in invariant features - like entropic relations - of the propagation of signals in space-time. From its very beginning Minkowski’s four-dimensional space-time was associated with a static view of reality, e.g. a block universe. Einstein added his influential voice to this conception when he wrote: ‘From (...) a “happening” in three-dimensional space, physics becomes (…) an “existence” in the four-dimensional “world”.’ (Einstein, Relativity 1920, 122) Yet it is by no means clear that Minkowski himself was a believer in the block universe. In his 1908 Cologne lecture on ‘Space and Time’ he speaks of a four-dimensional physics but concedes that a ‘necessary’ time order can be established at every world point. Although the conception of the block universe has gained much currency, an alternative view has been in circulation since the 1910s according to which the trajectories of particles constitute histories in space-time. (Robb 1914, Cunningham 1915, Carathéodorys 1924, Schlick 1917, Reichenbach 1924). (shrink)

Mach's principle is discussed as a fundamental statement on kinematics, and an apparent contradiction is identified in the Lorentz-Minkowski form of the inertial metric. To resolve the incompatibility, length is redefined so that the speed of light is a field-dependent variable, although still constant for all inertial observers at a point in space-time. Gravitational theories with variableG are considered, and it is shown that a redefinition of length and time results in constantG and variablec.

Penrose’s Spin Geometry Theorem is extended further, from SU(2) and E(3) (Euclidean) to E(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of E(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of E(1, 3)-invariant basic observables, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for E(1, 3)-invariant elementary quantum (...) mechanical systems in terms of the basic quantum observables in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the metric structure of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems. (shrink)

In this paper, we introduce the concept of N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. This is the first of a series of papers devoted to the investigation of the Killing symmetries of generalized Minkowski spaces. In particular, we discuss here the infinitesimal-algebraic structure of the space-time rotations in such spaces. It is shown that the maximal Killing group of these spaces is the (...) direct product of a generalized Lorentz group and a generalized translation group. We derive the explicit form of the generators of the generalized Lorentz group in the self-representation and their related, generalized Lorentz algebra. The results obtained are specialized to the case of a 4-dimensional, “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\widetilde M}$$ \end{document}4, i.e., a pseudoeuclidean space with metric coefficients depending on energy. (shrink)

In this paper, we continue the study of the Killing symmetries of an N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space–time rotations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space M_4, for which we derive the explicit general form (...) of the finite rotations and boosts in different parametric bases. (shrink)

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\widetilde M_4 $$ \end{document}.

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can be (...) generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the invariance (...) to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

Se è nel tempo e attraverso il movimento che partecipiamo alla vita, la morte ci nega per sempre questa possibilità. Nei sistemi viventi il tempo funge da organizzatore della situazione vitale dell’organismo. Il metabolismo e le funzioni vitali si compiono infatti attraverso lo scandire preciso e incalzante di ritmi biologici. Con la morte si verifica il disgregamento della nozione di tempo. Non si tratta più del tempo della vita che unisce, che coordina, che costruisce, che organizza. Il tempo della morte (...) è un tempo che distrugge, che disgrega, che disorienta, che sfilaccia l’unità della nostra esistenza nei frammenti non più ricomponibili di un puzzle. Ma la morte non è un fatto solo individuale, osserva lo psichiatra Eugène Minkowski in Le temps vécu. La morte, infatti, pone anche fine a tutte le relazioni di affetto, parentela e amicizia che ci hanno accompagnato durante la vita. Nell’articolo mostro come, a partire dalla riflessione di Minkowski, si possa parlare della morte da una duplice prospettiva di tempo vissuto: la morte come evento che impone una riflessione sulla finitudine umana, e come esperienza del vissuto individuale, oppure della morte patologica, la quale implica la morte del vissuto, ossia del contatto vitale costitutivo dell`esistenza umana. (shrink)

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, e.g., (...) the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)

Émile Meyerson (1859-1933), philosophe français, juif d'origine polonaise, chimiste formé en Allemagne, a élaboré une œuvre de philosophie des sciences considérable, forte de plusieurs volumes, qui embrasse les conceptions de la science classique comme les principes de la thermodynamique, la théorie de la relativité et la mécanique quantique. L'œuvre de Meyerson a longtemps été négligée dans la tradition épistémologique française, alors qu'elle avait rallié à elle nombre des physiciens aussi éminents qu'Einstein et de Broglie ou des psychiatres comme Minkowski (...) et le jeune Lacan. La " philosophie de l'intellect " de Meyerson fait de la recherche d'invariants dans la nature le principe fondamental de la raison et le ressort inaperçu de l'histoire des sciences. Elle a su aussi bien s'expliquer avec la pensée idéaliste allemande qu'interroger le fonctionnement du sens commun. Elle a entretenu des relations complexes avec certaines théories majeures de son temps, celles de Brunschvicg et de Bachelard, ou celles de Frege et de Schlick. Par son analyse des paradigmes scientifiques du passé, Meyerson annonce Koyré et Kuhn, qui se sont d'ailleurs réclamés de lui. Il ouvre ainsi des perspectives plus que jamais d'actualité dans les débats contemporains en philosophie des sciences. (shrink)

A partire da testi profondamente diversi come il Canzoniere petrarchesco e una raccolta di scritti autobiografici di pazienti oncologiche, l'autore compie un'indagine sul concetto di speranza, in particolare sulla sua dimensione temporale e sulla sua connessione con l'attivazione del pensiero. Con riferimenti teorici eterogenei che vanno da Bloch a Borgna, da Minkowski a Marcel, da Demetrio a Bénasayag e Schmit, dalla psicoanalisi alla teologia biblica e alla sociologia, si indagano gli aspetti regressivi e quelli evolutivi della speranza considerata come (...) proiezione del futuro nel presente che influisce sull'elaborzione del proprio passato personale. Infine si osserva come il tempo della contemporaneitÀ sia impermeabile alla speranza, che sopravvive solo in ambiti quali la scrittura, la creativitÀ, la lentezza, il silenzio nei quali ci si puň ancora prendere cura di sé. (shrink)

L'avènement des théories modernes de la physique au XXe siècle a suscité des discussions acharnées autour de la causalité dans la nature. Les ruptures avec les conceptions classiques de la physique du me siècle, alors rendues nécessaires, et les nouvelles synthèses opérées, attestent du caractère problématique de cette notion telle que l'appréhende la science physique. Le présent travail analyse de près les conceptions de la causalité qui se dégagent de deux théories majeures, la théorie de la relativité (sous ses deux (...) formes) et la théorie quantique, en se centrant sur les écrits de leurs principaux fondateurs : Albert Einstein et Hermann Minkowski d'une part, Niels Bohr, Werner Heisenberg et Erwin Schrödinger, de l'autre. Ceci sans négliger les aperçus indispensables donnés par les versions plus récentes de ces théories. Son but philosophique est de déterminer quelles sont les conceptions et les formes de la causalité qui sont engagées dans ces théories, quelle fonction exacte leur est conférée, et enfin jusqu'à quel point ces théorisations de la causalité se montrent capables de mettre à jour l'intelligibilité du monde. Il en ressort que le caractère idéal des catégorisations de la science physique empêche d'en faire une lecture directement réaliste. Ce qui invite à continuer d'interroger le discours scientifique afin de déterminer quelle connaissance effective il nous donne du monde."--Page 4 of cover. (shrink)

The article deals with the development of E.Minkowski’s concept of «morbid rationalism», as a cause of the alienation of consciousness from lived experience, by his followers R.D. Laing and J.Gabel. R.D. Laing considers the existential alienation as the alienation of the «false» or «outer self» from the «true,» or «inner self.» According to Laing, «false self» forms in the process of socialization as a socially acceptable image of thyself, which gradually suppresses and supersedes the true image. According to J.Gabel, (...) the concept of the «morbid rationalism» should be extended to the «normal» state of a person, who doesn’t live, but leads an alienated reified existence as a thing, instrument, and social function. Both Laing and Gabel agree, that the «norm» is only a socially legalized form of alienation, while psychopathology is all, that differs from the first one. But if Laing considers schizophrenia to be the way to freedom from social masks, to return to the true self, for Minkowski schizophrenia, as a rebellion of existence against the violence of reason, is not a solution. So, the way out is not in the destruction of the subject, but in overcoming the alienation of one's consciousness from the world and people, in transcending one's partial «ego». Marcel and Minkowski overcome the dichotomy of consciousness-vs-the-world (and-vs-body), seeking to bother the person with his consciousness. They return consciousness to the body, treating man not simply as embodied consciousness, but as the oneness of body-existence-consciousness-spirit. And in this way, the absolutization of freedom is an obstacle. A person involved in the world (bodily, sensual), and in humanity (existentially, spiritually) - inevitably depends on them. (shrink)

In this paper, I aim to show the importance of transferring metaphors from our aesthetic experiences to social praxis. I will therefore focus on reverberation, a phenomenon in the perceptual field of sound, to argue that it offers a deep understanding of social experiences. Reverberation is a secondary concept in Paul Ricœur's hermeneutic phenomenology, but it plays a crucial role in his analysis of imagination. Firstly, I will examine Ricœur's analysis of the phenomenon of reverberation within the framework of his (...) phenomenology of imagination. Secondly, I will read Ricœur's reference to G. Bachelard, considering the reverberation in the poetic image. Thirdly, I will study his reference to E. Minkowski, who thinks about reverberation within a cosmological scope. Finally, based on these analyses, I will outline the transfer of the phenomenon of reverberation to the field of social praxis. (shrink)

Editorial: the second phenomenology, by A. T. Tymieniecka.--Roman Ingarden, critique de Bergson, par J. M. Fataud.--Some remarks on the ego in the phenomenology of Husserl, by C. van Peursen.--The empirical and transcendental ego, by M. Natanson.--Rencontre et dialogue, par E. Minkowski.--Quelques thèmes d'une phénoménologie de rêve, par J. Héring.--Man and his life-world, by J. Wild.--Die Verwirklichung des Wesens in der Sprache der Dichtung: Gustave Flaubert, von F. Kaufmann.--Le langage de la poésie, par J. F. Mora.--L'analyse de l'idée et la (...) participation, par A. T. Tymieniecka. (shrink)

STRAUS'S Vom Sinn der Sinne was published in 1935, Kurt Goldstein's Der Aufbau des Organismus had been published the previous year, E. Minkowski's Le Temps Vécu in 1933, Helmuth Plessner's Die Stufen des Organischen und der Mensch in 1928. In the European literature of philosophical anthropology and, more broadly, of philosophical biology, all these works have exerted a profound influence. In particular, when one reads this literature, the phrase "das schöne Buch von E. Straus" becomes almost a fixed epithet (...) like "swift-foot Achilles" or "the incomparable Mr. Newton." Even Buytendijk, who takes issue with Straus's theory of sensing, pays tribute to—and borrows a great deal from—particular Strausian themes. (shrink)

Editorial: the second phenomenology, by A. T. Tymieniecka.--Roman Ingarden, critique de Bergson, par J. M. Fataud.--Some remarks on the ego in the phenomenology of Husserl, by C. van Peursen.--The empirical and transcendental ego, by M. Natanson.--Rencontre et dialogue, par E. Minkowski.--Quelques thèmes d'une phénoménologie de rêve, par J. Héring.--Man and his life-world, by J. Wild.--Die Verwirklichung des Wesens in der Sprache der Dichtung: Gustave Flaubert, von F. Kaufmann.--Le langage de la poésie, par J. F. Mora.--L'analyse de l'idée et la (...) participation, par A. T. Tymieniecka. (shrink)

Compactified Minkowski spacetime is suggested by conformal covariance of Maxwell equations, while E. Cartan's definition of simple spinors leads to the idea of compactified momentum space. Assuming both diffeomorphic to (S 3 × S 1 )/Z 2 , one may obtain in the conformally flat stereographic projection field theories both infrared and ultraviolet regularized. On the compact manifold themselves instead, Fourier integrals of wave-field oscillations would have to be replaced by Fourier series summed over indices of spherical eigenfunctions: n, (...) l, m, m′. Tentatively identifying those wave structures with spacetime itself (in the frame of Big-Bang) and/or with matter and radiation distribution, some large-scale (hydrogenic) and small-scale (lattice) space structures are conjectured. (shrink)

This article presents an introductory overview of the interpretations of schizophrenia offered by three phenomenological psychiatrists: Eugene Minkowski (1885-1972), Wolfgang Blankenburg (b. 1928), and Kimura Bin (b. 1931). Minkowski views schizophrenia as characterized by a diminished sense of dynamic and vital connection to the world ("loss of vital contact"), often accompanied by a hypertrophy of intellectual and static tendencies ("morbid rationalism," "morbid geometrism"). Blankenburg emphasizes the patient's loss of the normal sense of obviousness or "natural self-evidence"—a loss of (...) the usual common-sense background that enables normal persons to cope easily with the social and practical world. Kimura focuses on certain distortions of self-experience: a distinctive splitting of the subjective self, alienated awareness of one's own ongoing consciousness, and profound uncertainty about the "I-ness" of the self. In addition to a summary, this article offers a comparison and critique of these three approaches. The three approaches are also considered in light of a more recent, phenomenological formulation of schizophrenia as a disorder of self-experience (an ipseity disturbance) involving hyperreflexivity and diminished self-affection (i.e., heightened awareness of aspects of experience that would normally remain tacit or presupposed and decline in the feeling of existing as a subject of awareness). (shrink)

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a (...) particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field. (shrink)

In this paper we study the emergence of Minkowski space–time from a discrete causal network representing a classical information flow. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity—including space–time—be defined through precise measurement procedures. Topological homogeneity is a requirement for having space–time metric emergent from the pure topology of causal connections, whereas physically homogeneity (...) corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock. The illustrated simple classical construction can be extended to space dimension greater than one, with the price of anisotropy of the maximal speed, due to the Weyl-tiling problem. This issue is cured if the causal network is quantum, as e.g. in a quantum cellular automaton, and isotropy is recovered by quantum coherence via superposition of causal paths. We thus argue that in a causal network description of space–time, the quantum nature of the network is crucial. (shrink)

Hardly any other problem has been discussed more than that of the status of time in modem physics. This is only natural since there are not many other more important problems in philosophy of science and in philosophy in general. There are also few other areas where controversies as well as confusion were more frequent. This is true not only of popular and semi-popular expositions of the Minkowski concept of space-time but also of a number of its philosophical interpretations. (...) Generally we do not find anything of this kind in the writings of physicists, at least as long as they confine themselves to strictly mathematical and physical expositions; but when they sometimes venture beyond a strictly mathematical approach, they often do not escape certain unconscious or semi-conscious prejudices which are contrary not only to the spirit but sometimes even to the letter of relativity. The true significance of the relativistic fusion of space and time can be understood only when we contrast it with its classical counterpart, i.e., with what may be called the Newtonian space-time. Only on such a contrasting background will the revolutionary meaning of the new concept clearly stand out. (shrink)

A rigorous ab initio derivation of the (square of) Dirac’s equation for a particle with spin is presented. The Lagrangian of the classical relativistic spherical top is modified so to render it invariant with respect conformal changes of the metric of the top configuration space. The conformal invariance is achieved by replacing the particle mass in the Lagrangian with the conformal Weyl scalar curvature. The Hamilton-Jacobi equation for the particle is found to be linearized, exactly and in closed form, by (...) an ansatz solution that can be straightforwardly interpreted as the “quantum wave function” of the 4-spinor solution of Dirac’s equation. All quantum features arise from the subtle interplay between the conformal curvature acting on the particle as a potential and the particle motion which affects the geometric “pre-potential” associated to the conformal curvature itself. The theory, carried out here by assuming a Minkowski metric, can be easily extended to arbitrary space-time Riemann metric, e.g. the one adopted in the context of General Relativity. This novel theoretical scenario appears to be of general application and is expected to open a promising perspective in the modern endeavor aimed at the unification of the natural forces with gravitation. (shrink)

Zeeman argued that the Euclidean (i. e. manifold) topology of Minkowski space-time should be replaced by a strictly finer topology that was to have a closer connection with the indefinite metric. This proposal was extended in 1976 by Rudiger Göbel and Hawking, King and McCarthy to the space-times of General Relativity. It is the purpose of this paper to argue that these suggestions for replacement misrepresent the significance of the manifold topology and overstate the necessity for a finer topology. (...) The motivation behind such arguments is a realist view of space-time topology as against (what can be construed to be) the instrumentalist position underlying some of the suggestions for replacement. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Relativistic quantum field theories (RQFTs) are invariant under the action of the Poincaré group, the symmetry group of Minkowski spacetime. Non-relativistic quantum field theories (NQFTs) are invariant under the action of the symmetry group of a classical spacetime; i.e., a spacetime that minimally admits absolute spatial and temporal metrics. This essay is concerned with cashing out two implications of this basic difference. First, under a Received View, RQFTs do not admit particle interpretations. I will argue that the concept of (...) particle that informs this view is motivated by nonrelativistic intuitions associated with the structure of classical spacetimes, and hence should be abandoned. Second, the relations between RQFTs and NQFTs also suggest that routes to quantum gravity are more varied than is typically acknowledged. The second half of this essay is concerned with mapping out some of this conceptual space. (shrink)

Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects $E_{\rm B}$ (related to the Planck scale) and the much higher scale $E_{\rm L}$ signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: $E_{\rm L}$ is the energy scale below which a special relativistic spacetime emerges, (...) $E_{\rm B}$ is the scale below which this spacetime geometry becomes curved. This implies that the first ‘quantum’ gravitational effect around $E_{\rm B}$ could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of $E_{\rm L}$ . This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 8.4 (2001) 295-298 [Access article in PDF] A Dialectical Conception of Autism Giovanni Stanghellini Some Reasons for the Philosophical Turn in the Psychopathology of Schizophrenia There are many ways to become a schizphrenic. Each individual has her own schizophrenia, coherent with her life history, her problems and alternatives deriving from them (Binswanger 1960). What clinical psychiatry calls "schizophrenia" is not a unitary illness but a (...) common final state—a "syndrome" in the etymological sense, that is, a condition to which different psychopathological pathways may lead. Schizophrenic symptoms, like Schneiderian first-rank symptoms (delusions, hallucinations, experiences of passivity), are nothing but a rather uniform type of reaction. First-rank Schneiderian symptoms may be interpreted as attempts to explain disturbing basic experiences of change in self, body, and world perception (Klosterkoetter 1988) or as the epiphenomena of complex interactions between sensory disorders (aberrations in the perception of self, body, and world), conceptualisation disorders (impairments in the constitution of meanings and intentions), and attitudinal disorders (eccentric structure of values and beliefs) (Stanghellini 2000a). Since the schizophrenic syndrome, as defined by current diagnostic manuals, lacks any authentic core phenomena, and so-called schizophrenic symptoms are not specific (Berner and Kufferle 1982), the clinical diagnosis of schizophrenia finally becomes a diagnosis by exclusion (Maj 1998). This conceptual weakness is obviously unacceptable (not only for old dissenters from operational diagnostic criteria) and is kindling a velvet revolution in nosological studies and a renaissance of philosophically oriented psychopathological research (Parnas and Zahavi 2000). Autism: The Loss of Vital Contact with Reality Eugène Minkowski was a forerunner in the field of philosophical psychopathology: "The psychiatrist and the metaphysician become one in their common research concerning what is human and human experience" (Minkowski 1947). Indeed, his doctoral thesis on autism (Minkowski 1926) was dedicated to his teachers, the psychiatrist E. Bleuler and the philosopher H. Bergson, and his conceptualisation of autism is an ideal example of the link between philosophical perspectives and psychopathological research. The term "autism" was introduced by Bleuler (1911) to describe detachment from outer reality and immersion in inner life. Bleuler's concept of autism relied on Freud's (1905) notion of autoerotism and on associationistic psychology. According to Bleuler, autism was a consequence of the [End Page 295] splitting of psychic functions: a defense mechanism serving to avoid conflicts between desires and reality testing, promoting the shift to inner fantasy life and entailing social withdrawal, emotional indifference, inappropriate behaviors, and idiosyncratic values and beliefs.Minkowski, who was influenced by Bergson and phenomenology, departed from Bleuler's conceptualisation and defined autism as "loss of vital contact with reality" (Minkowski 1926, 1927). For Minkowski, autism is not a symptom, but a global phenomenon investing the whole person. Autism is a way of being whose essential feature is a pragmatic deficit: Autistic activity consists in the reduced capacity to interact with the external world. Autistic thought is characterized by its lack of communicative action. The pragmatic deviance of autistic language is a good example: The autistic person is not interested in communicating her inner world to the others; language is not a means of communication which serves mutual understanding, a cooperative process whose aim is interlacing one's own world with that of others. The autistic person's use of language is much like a soliloquy, the monologue of the solitary thinker more focused on ex-pression—the outward portrayal of immanent contents of consciousness—than on dialogue—the exchange of meanings between speaker and listener. Moreover, each meaning is presented in its manifold profiles or adumbrations and the task of selecting the context-relevant meaning is left to the listener.The pragmatic weakening of the autistic person, according to Minkowski, is not simply a social or occupational dysfunction (APA 1994), that is, a renunciation or refusal to act according to social expectations and standards. It involves the loss of vital contact with reality. The meaning Minkowski attributes to the term "vital" is essential for understanding his philosophical approach to defining the schizophrenic condition. Minkowski assumes that contact with reality is vital when it is established through action (and language... (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of (...) choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim (...) \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$. (shrink)

In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian density turns out to be of the Yang-Mills type (with an auto-interaction plus gauge-fixing terms). We give a brief comparison (...) of our theory with other field theories of the gravitational field in the flat Minkowski spacetime. (shrink)

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner–Fronsdal local isometric embedding of the corresponding black hole geometry. Allowing for globally non-trivial embeddings, living in Kaluza–Klein-like M 5 × S 1 (rather than in standard Minkowski M 6 ) and parametrized by some wave number k, extensibility can be achieved for apparently “forbidden” frequencies ω in the range ω 1 (k) ≤ ω ≤ ω 2 (k). As k → (...) 0, ω 1, 2 (0) → ωH (e.g., ωH = 1/4M in the Schwarzschild case) such that the Hawking–Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza–Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding gauge field. (shrink)

In this paper, we use the differential forms of three-dimensional Euclidean space to realize a Clifford algebra which is isomorphic to the algebra of the Pauli matrices or the complex quaternions. This is an associative vector-antisymmetric tensor algebra with division: We provide the algebraic inverse of an eight-component spinor field which is the sum of a scalar + vector + pseudovector + pseudoscalar. A surface of singularities is defined naturally by the inverse of an eight-component spinor and corresponds to a (...) generalized Minkowski “double” light cone in the parameter space. A general description of finite spatial rotations, which utilizes the Baker-Campbell-Hausdorff formula, generalizes the usual infinitesimal treatments of the rotation group. We derive an explicit expression for the angle corresponding to two successive finite rotations in any direction. We also discuss Lorentz transformations and duality rotations of the electromagnetic field and exhibit a relationship between the algebraic inverse and a duality rotated field. Using a combined transformation, one can always transform an arbitrary electromagnetic field (E≠0) into a pure electric field, but never into a pure magnetic field. (shrink)

Growing concern has been expressed that we have entered a “post-truth” era in which each of us willfully believes whatever we choose, aided and abetted by alternative and social media that spin alternative realities for boutique consumption. A prime example of the belief in alternative realities is said to be acceptance of “conspiracy theories”—a term that is often used as a pejorative to indict claims of conspiracy that are so obviously absurd that only the unhinged could believe them. The epistemological (...) standard often involved in this indictment, however—the standard of “obvious” falsity—invites subjectivity in its application, because what is obviously false to one person can be common sense to another. This is not just a truism; considerable research suggests that people’s political beliefs, in general, and their acceptance or rejection of conspiracy theories in particular, tends in large part to be determined by partisan, ideological, and other priors. (shrink)

A simplified definition of point local clocks and the relationship between an inertial reference frame and a class of such clocks, at rest with respect to each other, are used for an algebraic determination of the geometry of Minkowski's space-time on the set of point events. The group of all automorphisms that preserve the time ordering induced by the set of all equivalent local clocks is shown to be generated by the inhomogeneous orthochronous Lorentz group and dilatations, consistently with (...) a well-known result of E. C. Zeeman. The existence of a universal limit velocity and of an invariant clock cone through any event is among the implications of our proof, thus effectively exploiting a suggestion due to F. Severi. (shrink)