Matter

Interpretations of Einstein’s equation differ primarily concerning whether E = mc2 entails that mass and energy are the same property of physical systems, and hence whether there is any sense in which mass is ever ‘converted’ into energy. In this paper, I examine six interpretations of Einstein’s equation and argue that all but one fail to satisfy a minimal set of conditions that all interpretations of physical theories ought to satisfy. I argue that we should prefer the interpretation of Einstein’s (...) equation that holds that mass and energy are distinct properties of physical systems. This interpretation also carries along the view that while most cases of ‘conversion’ are not genuine examples of mass being ‘converted’ into energy, it is possible that the there are such ‘conversions’ in the sense that a certain amount of energy ‘appears’ and an equivalent of mass ‘disappears’. Finally, I suggest that the interpretation I defend is the only one that does not blur the distinction between what Einstein called ‘principle’ and ‘constructive’ theories. This is philosophically significant because it emphasizes that explanations of Einstein’s equation and the ‘conversion’ of mass and energy must be top‐down explanations. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...) former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

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

Aritsotle's hyle is contrasted with Plato's chora and Aquinas's prima materia. It is argued that Plato and Aristotle developed their concepts in response to very different needs, and that Aquinas's theory reflects a conflation of their views by Neoplatonic commentators. Hyle is shown to be an active potential to a determinate form in contrast to Aquinas's prima materia, which is a purely indeterminate passive potential. This gives a point of attachment in Aristotle's philosophy of nature for the later notion of (...) universal laws of nature. (shrink)

تجلت المعالجة الفيزيائية المعاصرة لموضوع الاتصال في نظريتين كبريتين تقاسمتا البحث في الظواهر الطبيعية منذ بداية القرن العشرين: إحداهما نظريــة النسبية (الخاصـة والعامـة)، والأخرى نظرية الكم. وبينما تُعيد النسبية الخاصة صياغة القوانين الأساسية للحركة على نحو أدق مما قدمه نيوتن، تتجه النسبية العامة إلى تعليل خواص المادة على النطاق الواسع، أي على مستوى الكون الأكبر، حيث النجوم والكواكب وحركاتها التجاذبية. أما نظرية الكمّ فتًعلل خواص المادة على النطاق الضيق جدًا، أي على مستوى الكون الذري. وليس هناك فيما يبدو أية رابطة (...) بين النسبية العامة والكم، اللهم إلا في أساسهما المشترك وهو النسبية الخاصة. ومن ناحية أخرى، بينما تنجح النسبية في تحطيم الأطر المطلقة التي افترض نيوتن أن قوانين الطبيعة تعمل بمقتضاها، وهي الزمان والمكان، تُحرز نظرية الكمَّ نجاحًا مماثلاً في تفتيت عالم الذرة الذي ظنه نيوتن مصمتًا لا داخل له. والحق أنها لمهمة شاقة أن نعرض في بحثٍ واحد لنظريتين أثارتا من المشكلات الفلسفية أكثر مما اضطلعتا بحله. ولكننا مع ذلك سنحاول تتبع الخطوط الرئيسة لكلتيهما، تدفعنا رغبة مُلحة في الحصول على إجابة شافية عما إذا كان الاتصال قائمًا في الطبيعة أم لا. (shrink)

The concept of mass is one of the most fundamental notions in physics, comparable in importance only to those of space and time. But in contrast to the latter, which are the subject of innumerable physical and philosophical studies, the concept of mass has been but rarely investigated. Here Max Jammer, a leading philosopher and historian of physics, provides a concise but comprehensive, coherent, and self-contained study of the concept of mass as it is defined, interpreted, and applied in contemporary (...) physics and as it is critically examined in the modern philosophy of science. With its focus on theories proposed after the mid-1950s, the book is the first of its kind, covering the most recent experimental and theoretical investigations into the nature of mass and its role in modern physics, from the realm of elementary particles to the cosmology of galaxies.The book begins with an analysis of the persistent difficulties of defining inertial mass in a noncircular manner and discusses the related question of whether mass is an observational or a theoretical concept. It then studies the notion of mass in special relativity and the delicate problem of whether the relativistic rest mass is the only legitimate notion of mass and whether it is identical with the classical mass. This is followed by a critical analysis of the different derivations of the famous mass-energy relationship E = mc2 and its conflicting interpretations. Jammer then devotes a chapter to the distinction between inertial and gravitational mass and to the various versions of the so-called equivalence principle with which Newton initiated his Principia but which also became the starting point of Einstein's general relativity, which supersedes Newtonian physics. The book concludes with a presentation of recently proposed global and local dynamical theories of the origin and nature of mass.Destined to become a much-consulted reference for philosophers and physicists, this book is also written for the nonprofessional general reader interested in the foundations of physics. (shrink)

In the second part of this essay, I aim to show that Leibniz, in asserting that bodies are aggregates of substances, wants to affirm something about bodies insofar as they exist a parte rei or in reality: in reality a body is not a being, but a multitude of beings or substances. And this, on my view, is precisely what leads Leibniz to assert that bodies are phenomena: since a body is not in reality a being, but many beings, it (...) follows that a body, conceived as a being, is something that exists only objectively in the soul. That is, a body, conceived as a single thing, is not something real, but an imaginary being, a creature of the mind, a phenomenon. (shrink)

We set out a fundamental ontology of atomism in terms of matter points. While being most parsimonious, this ontology is able to match both classical and quantum mechanics, and it remains a viable option for any future theory of cosmology that goes beyond current quantum physics. The matter points are structurally individuated: all there is to them are the spatial relations in which they stand; neither a commitment to intrinsic properties nor to an absolute space is required. The spatial relations (...) change. All that is needed to capture change is a dynamical structure, namely dynamical relations as expressed in terms of the dynamical parameters of a physical theory. (shrink)

In Kant's Metaphysical Foundations of Natural Science are found a dynamist reduction of matter and an account of the communication of motion by impact. One would expect to find an analysis of the causal mechanism involved in the communication of motion between bodies given in terms of the fundamental dynamical nature of bodies. However, Kant's analysis, as given in the discussion of his third law of mechanics (an action-reaction law) is purely kinematical, invoking no causal mechanisms at all, let alone (...) dynamist mechanisms, in the explanation. It is argued that the reason for the non-incorporation of Kant's theory of matter in the account of impact is his overriding desire to provide a mathematical framework to explain the communication of motion, a provision which Kant felt to be impossible in the context of a metaphysical dynamism. (shrink)

This book reconstructs the kalām theories of matter, space, and void in the tenth and eleventh centuries A.D., using texts that have only recently become available.

Unifying physics by describing a variety of interactions – or even all interactions – within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian. Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called (...) solitons), and he clarified the use of variational principles in the context of special relativity. The following brief introduction to Mie’s work has three main objectives. The first is to explain how Mie’s project fit into the contemporary development of the electromagnetic world view. Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie’s criticisms of Einstein, in particular, bring out the subtlety and novelty of the ideas that Einstein used to guide his development of general relativity. (shrink)

In the standard model of cosmology, λCDM, were introduced to explain the anomalies of the orbital velocities of galaxies in clusters highest according estimated by General Relativity the dark matter and the accelerated expansion of the universe the dark energy. The model λCDM is based in the equations of the General Relativity that of the total mass-energy of the universe assigns 4.9% to matter (including only baryonic matter), 26.8%, to dark matter and 68.3% to dark energy adjusted according observed in (...) Planck mission, therefore, excluding bosonic matter (quantum vacuum). However, the composition of dark matter and dark energy are unknown. Due to that it lacks of a correct physical theory of gravity since General Relativity is only their powerful equations, which in their applications, their results are interpreted arbitrarily. Properties as curvature, viscous fluid, dragging frame and gravity action are attributed mistakenly to the spacetime by the materialist substantivalism, the most credible philosophical interpretation that complements the General Relativity, caused by its absence of physical definition of spacetime and static gravitational field as immaterial, but which violates, the conception of gravity as an effect of coordinates of the generalization of the inertial motion to the accelerated motion and, in particular, the description of the metric tensor of gravity as a geometric field. These properties are really of the quantum vacuum, the main existence form of the matter. In this paper we propose that the quantum vacuum is the source of dark matter and dark energy, therefore, the components of the quantum vacuum are of them. Both are opposite effects of the quantum vacuum that when gravitationally interacts with the cosmic structures, the vacuum it curves and when such interaction tends to cease by declination of the formation of these structures, occurring since near five milliard of years ago, vacuum it maintains quasi plane, since it interacts gravitationally very weakly with itself, accelerating expansion of the universe. (shrink)

Western science claims to provide unique, objective information about the world. This is supported by the observation that peoples across cultures will agree upon a common description of the physical world. Further, the use of scientific instruments and mathematics is claimed to enable the objectification of science. In this work, carried out by reviewing the scientific literature, the above claims are disputed systematically by evaluating the definition of physical reality and the scientific method, showing that empiricism relies ultimately upon the (...) human senses for the evaluation of scientific theories and that measuring instruments cannot replace the human sensory system. Nativist and constructivist theories of human sensory development are reviewed, and it is shown that nativist claims of core conceptual knowledge cannot be supported by the findings in the literature, which shows that perception does not simply arise from a process of maturation. Instead, sensory function requires a long process of learning through interactions with the environment. To more rigorously define physical reality and systematically evaluate the stability of perception, and thus the basis of empiricism, the development of the method of dimension analysis is reviewed. It is shown that this methodology, relied upon for the mathematical analysis of physical quantities, is itself based upon empiricism, and that all of physical reality can be described in terms of the three fundamental dimensions of mass, length and time. Hereafter the sensory modalities that inform us about these three dimensions are systematically evaluated. The following careful analysis of neuronal plasticity in these modalities shows that all the relevant senses acquire from the environment the capacity to apprehend physical reality. It is concluded that physical reality is acquired rather than given innately, and leads to the position that science cannot provide unique results. Rather, those it can provide are sufficient for a particular environmental setting. (shrink)

This paper attempts to resolve the puzzle associated with the non-spatiality of monads by investigating the possibility that Leibniz employed a version of the extension of power doctrine, a Scholastic concept that explains the relationship between immaterial and material beings. As will be demonstrated, not only does the extension of power doctrine lead to a better understanding of Leibniz’ reasons for claiming that monads are non-spatial, but it also supports those interpretations of Leibniz’ metaphysics that accepts the real extension of (...) bodies. (shrink)

In the Principles of Philosophy, Descartes attempts to explicate the well-known phenomena of varying bodily size through an appeal to the concept of "solidity," a notion that roughly corresponds to our present-day concept of density. Descartes' interest in these issues can be partially traced to the need to define clearly the role of matter in his natural laws, a problem particularly acute for the application of his conservation principle. Specifically, since Descartes insists that a body's "quantity of motion," defined as (...) the product of its "size" and speed, is conserved in all material interactions, it is imperative that he explain how solidity influences the magnitude of this force. As a means of resolving this problem, Descartes postulated an idealized condition of "perfect solidity" which correlates a body's "agitation" force (a forerunner of Newton's concept of non-accelerating, or "inertial" motion) with the interplay of its volume, surface area, and composition of minute particles. This essay explores this often misunderstood aspect of Descartes' physics, as well as the special function of idealized conditions in his collision rules. Contrary to those commentators who regard "perfect solidity" as a stipulation on bodily impact, this notion, it will be argued, is primarily concerned with the internal composition of macroscopic bodies, and only indirectly with their collision characteristics. Along the way, many of Descartes' hypotheses will be shown to display a level of sophistication and intricacy that, despite their essential incompatibility, belie several of the common misconceptions of Cartesian science. (shrink)

This essay examines Hobbes’ philosophy of space, with emphasis placed on the variety of interpretations that his concept of imaginary space has elicited from commentators. The process by which the idea of space is acquired from experience, as well as the role of nominalism, will be offered as important factors in tracking down the elusive content of Hobbes’ conception of imaginary space.

This chapter looks at Euler’s relation to Newton, and at his role in the rise of ‘Newtonian’ mechanics. It aims to give a sense of Newton’s complicated legacy for Enlightenment science, and to raise awareness that some key ‘Newtonian’ results really come from Euler.

Quantum theory’s irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be consistent with it. It must make it possible to identify a system of observables that have measurement-independent values.What makes this possible is the incompleteness of the spatiotemporal differentiation of the physical world. This is shown by applying a novel interpretive principle to interfering (...) alternatives involving distinctions between regions of space. Applying the same interpretive principle to alternatives involving distinctions between things makes it safe to claim that the macroworld comes into being through a progressive differentiation of a single, intrinsically undifferentiated entity. By entering into reflexive spatial relations, this entity gives rise to (1) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (2) what looks like a substantial expanse if the spatial quality of the relations is reified. The necessary distinction between two domains (classical and quantum, or macro and micro) and their mutual dependence is best understood as a distinction between the manifested world and its manifestation. [Paper presented at BergeFest, a conference celebrating the 60th birthday of Berge Englert, held at the Centre for Quantum Technologies, National University of Singapore, 22–25 April 2014]. (shrink)

In recent years, the philosophy of Ludwig Boltzmann has become a point of interest within the field of history of philosophy of science. Attention has centred around Boltzmann’s philosophical considerations connected to his defense of atomism in physics. In analysing these considerations, several scholars have attributed a pragmatist stance to Boltzmann. In this paper, I want to argue that, whatever pragmatist traits may be found in Boltzmann’s diverse writings, his defense of atomism in physics can not be analysed this way. (...) In other words, I wish to show that he did not defend atomism as “preferable for its practical virtues”, as has been alleged.1 On the contrary, Boltzmann considered the atomist picture to be indispensable — more precisely, an indispensable prerequisite for making the application of continuous differential equations an understandable enterprise. (shrink)

The debate concerning the relations between matter and motion has the same age as philosophy itself. In modern times this problem was transformed into the one concerning the relations between mass and energy. Newton identified mass with matter. Classical thermodynamics brought this conception to its logical conclusion, establishing an ontic dichotomy between mass-matter and energy. On the basis of this pre-relativistic conception, Einstein's famous equation has been interpreted as a relation of equivalence between mass-matter and energy. Nevertheless, if we reject (...) this epistemologically illegitimate identification, it is possible to elaborate a unitary conception of matter, which at the same time is an argument for the unity between matter and motion. In particular, the classical antithesis between matter and field becomes obsolete in the frame of the proposed interpretation. (shrink)

The prediction of general relativity on the gravitational collapse of matter ending in a point is viewed as an absurdity of the kind to be expected in any consistent physical theory due to ultimate conflicts of the axioms of geometry with the properties of physical objects. The necessity to introduce a probability interpretation for the solution of partial differential equations in space time for quantum theory points to similar roots. It is pointed out that quantum theory in the very small (...) is not going to eliminate the problem, but macroscopic quantum effects in the large, modifying the properties of the horizon, may achieve it. Solutions such as wormholes allow as much empirical evidence as any science fiction. The present approach considers successive modifications of the field equations and equations of motion of gravitational theory by admixture of terms with higher derivatives. The rigorous application of a gauge principle combines Einstein's equations with the tensor analog of Maxwell's equations which are of third order for the metric. It is speculated that the natural presence of torsion in such a gauge theory is related to matter sources. (shrink)

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a charged particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc2/ħ. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper frame (...) of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schrödinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis appled to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation.Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schrödinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated waveand the ensemble of particles. (shrink)

It is suggested that the dark matter of the universe is due to the presence of a scalar field described by the gauge function introduced by Dirac in his modification of the Weyl geometry. The behavior of such dark matter is investigated.

Two revolutionary concepts of the twentieth century—continental drift and the existence of superdense stars and black holes—had extended histories which ran in curious parallel for five decades. Between the wars each encountered a fierce and emotionally charged resistance which may have had a common psychological root. Each threatened man's instinctive faith in the permanence of matter.

The concept of waves associated with any material particle has been a considerable boost to theoretical physics, and it appears to be in accordance with many experimental results. Some relativistic properties of these assumed waves are studied in comparison to other physical waves. It turns out that matter waves may nor be considered as objectively real, and that any physics resting on such a concept can only be subjective.

Relativistic mean field theory with mesons σ, ω, π and ρ mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is a composite (...) object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear σ-model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions. (shrink)

This paper considers the issue of Bose–Einstein condensation in a weakly interacting Bose gas with a fixed total number of particles. We use an old current algebra formulation of non-relativistic many body systems due to Dashen and Sharp to show that, at sufficiently low temperatures, a gas of weakly interacting Bosons displays Off-diagonal Long Range Order in the sense introduced by Penrose and Onsager. Even though this formulation is somewhat cumbersome it may demystify many of the standard results in the (...) field for those uncomfortable with the conventional broken symmetry based approaches. All the physics presented here is well understood but as far as we know this perspective, although dating from the 60's and 70's, has not appeared in the literature. We have attempted to make the presentation as self-contained as possible in the hope that it will be accessible to the many students interested in the field. (shrink)

We give a derivation of exclusion principles for the elementary particles of the standard model, using simple mathematical principles arising from a set theory of identical particles. We apply the theory of permutation group actions, stating some theorems which are proven elsewhere, and interpreting the results as a heuristic derivation of Pauli's Exclusion Principle (PEP) which dictates the formation of elements in the periodic table and the stability of matter, and also a derivation of quark confinement. We arrive at these (...) properties by using a symmetry property of collections of the particles themselves as compared for example to the symmetry property of their wave function under interchange of two particles. (shrink)

We discuss the nature of reality in the ontological context of Penrose’s math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math. Non-physicists should be wary of any claim that modern physics leads us to any particular resolution of this circularity, since even the sample of three theoretical physicists writing this paper hold three divergent views. Some physicists (...) believe that current physics has already found the basic framework for a complete description of reality, and only has to fill in the details. Others suspect that no single framework, from physics or other sources, will ever capture reality. Yet others guess that reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks. We will designate these three approaches as the fundamentalist, secular and mystic views of the world, as seen by practicing physicists. We present and contrast each of these views, which arguably form broad categories capturing most if not all interpretations of physics. We argue that this diversity in the physics community is more useful than an ontological monoculture, since it motivates physicists to tackle unsolved problems with a wide variety of approaches. (shrink)

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ3). This space allows a simple physical interpretation as a phase space of a lattice of cells.We find the SM SU(3) c ×SU(2) L ×U(1) Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ3) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic (...) structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations.The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ2-valued (spin) field theory.A metric theory of gravity compatible with this model is presented too. (shrink)

The late 19th century debate among German-speaking physicists about theoretical entities is often regarded as foreshadowing the scientific realism debate. This paper brings out differences between them by concentrating on the part of the earlier debate that was concerned with the conceptual consistency of the competing conceptions of matter—mainly, but not exclusively, of atomism. Philosophical antinomies of atomism were taken up by Emil Du Bois-Reymond in an influential lecture in 1872. Such challenges to the consistency of atomism had repercussions within (...) the physics community, as can be shown for the examples of Heinrich Hertz and Ludwig Boltzmann. The latter developed a series of counter-arguments, culminating in an ingenious attempt to turn the tables on the critics of atomism and prove the inconsistency of non-atomistic conceptions of nature. Underlying this controversy is a disagreement over specific goals of physical research which was considered crucially relevant to the further course of physical inquiry. It thereby exemplifies an attitude towards the realism issue that can be contrasted with a different, more neutral attitude of construing the realism issue as merely philosophical and indifferent with respect to concrete research programs in physics, which one also occasionally finds expressed in the 19th century controversy and which may be seen as the prevailing attitude of the 20th century debate. (shrink)

A Hamiltonian which is bounded from below by a multiple of the number of particles is called stable. We discuss which interactions are stable and which are not. Furthermore we show how this stability is related to other notions of stability.

Proposals of quantizing matter without also quantizing fields are assessed. In one of these the principle of superposition is given up and an estimate of its violation is suggested. Another proposal, which retains the principle of superposition, is shown to be inconsistent with the equations of motion.

The Bose-Einstein condensation of free relativistic particles [ε=(M 2 c 4 +c 2 p 2 ) 1/2 −Mc 2 ] is studied rigorously. For massless bosons (ε=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T 2 (T 3 ) law below the condensation temperature Tc [k B Tc=(2πħ 2 c 2 n/1.645) 1/2 [(π 2 ħ 3 c 3 n/1.202) 1/3 ], reaches4.38 (10.8) R at T=Tc, and approaches the (...) high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature Tc always smaller than that of the corresponding nonrelativistic bosons [ε=(2M) −1 p 2 ]. If the mass M is reduced to zero, the condensation temperature Tc grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of Tc is therefore distinct from the case of nonrelativistic bosons, where Tc grows to infinity as M →0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons). (shrink)

The foundations of a theory of nonminimal coupling of matter and the gravitational field in the framework of Riemannian (or Riemann-Cartan) geometry are presented. In the absence of matter, the Einstein vacuum field equations hold. In order to allow for a Newtonian limit, the theory contains a new parameter l0 of dimension length. For systems with finite total mass, l0 is set equal to the Schwarzschild radius.

The Lorentz transformation is derived without assuming that the velocity of light is a constant. This suggests that the constantc which appears in the transformation has a deeper significance than heretofore commonly assumed. It is hypothesized that there exists, in all of physical reality, velocities of only one magnitude. The magnitude isc, the speed of light in vacuum. This hypothesis forces us to view a fundamental particle as an extended object and matter in general as a field ρ(t, r, θ), (...) which we give the generic name “stuff.” An important feature of the ρ field is that at each spacetime point(t, r) stuff travels in all directions θ with speedc. In order to elucidate the nature of ρ(t, r, θ), the equations determining ρ for a one-dimensional world are derived and solved. Fundamental particles are shown to exist and their structure is obtained. (shrink)

Matter is pictured as a primitive fluid substratum having the fundamental property of fluctuating at a constant frequency. From this are derived the discrete properties of space and time, and it follows that, at the microlevel, talk of pure space and pure time involves us in ambiguities. A new interpretation of Planck's constant emerges according to which it is a quantum of matter-time combination. Thus, a quantum of matter-space combination should exist. On pursuing further the hydrodynamic model, such a constant (...) is in fact discovered as the drag-quantum of the quantum fluid. A fourth-degree differential equation is considered which, with the help of this new constant, generates spectra of frequency, mass, and fine structure constants. The theory seems to answer some important fundamental questions. (shrink)

An attempt is made to give a methodological and physical characterization to the concept of the structure of matter. The methodological status of theories describing the structure of hadrons is discussed. A parallelism is drawn between the quark model as a theory of the mathematical composite structure of hadrons and Plato's theory of matter. The merger of the bootstrap idea with a quark substructure of hadrons is discussed. A third approach to the structure of hadron matter is presented. It resembles (...) the Aristotelian conception of primary matter on which form is imprinted potentially. (shrink)

The equation for the fundamental field quantity ϱ is obtained. It is Div $\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } $ ,where h is an arbitrary function oft andr, and [,]− is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ϱ.(2) Relativistic covariance of the equations governing ϱ.(3) Principle of continguous action.(4) Conservation of total amount (...) of ϱ. The equation appears to be unique. It is suggested that the physical world corresponds to ϱ being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential Aμ is identified with ε ρμ dΩ. Conservation laws on various measures of ϱ are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ϱ to the metric is made via Einstein's gravitational equation Gμυ =KTμυ. (shrink)