We develop a geometro-dynamical approach to the cosmological constant problem (CCP) by invoking a geometry induced by the energy-momentum tensor of vacuum, matter and radiation. The construction, which utilizes the dual role of the metric tensor that it structures both the spacetime manifold and energy-momentum tensor of the vacuum, gives rise to a framework in which the vacuum energy induced by matter and radiation, instead of gravitating, facilitates the generation of the gravitational constant. The non-vacuum sources comprising (...) matter and radiation gravitate normally. At the level of classical gravitation, the mechanism deadens the CCP yet quantum gravitational effects, if strong, can keep it existent. (shrink)

The Weyl-Dirac theory of gravitation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe. One is led to a natural gauge giving ${{\dot G} \mathord{\left/ {\vphantom {{\dot G} G}} \right. \kern-0em} G} = - 5.5 \times 10^{ - 12} y^{ - 1} $ . This is smaller by about a factor of ten than the value obtained on the basis of Dirac's large number hypothesis.

The fine structure constant α ≡ e2/ c ≈ 1/137 is one of the fundamental parameters of the standard model of particle physics. There is a long history of attempts to derive the measured value of α from an underlying theory, or exhibit it in the form of a compact mathematical expression [2–4, 6, 8, 14–16]. The most significant advance in this endeavour was made by Dirac, who showed that if magnetic monopoles exist, with magnetic charge μ, then..

Physics presents us with a symphony of natural constants: G, h, c, etc. Up to this point, constants have received comparatively little philosophical attention. In this paper I provide an account of dimensionful constants, in particular the gravitational constant. I propose that they represent inter-quantity structure in the form of relations between quantities with different dimensions. I use this account of G to settle a debate over whether mass scalings are symmetries of Newtonian Gravitation. I argue that they (...) are not, but only if we interpret mass anti-quidditistically. This is analogous to anti-haecceitism in the presence of spacetime symmetries. (shrink)

It is pointed out that the Higgs field may be supplanted by an ordinary Klein-Gordon field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theories. In the theory (...) presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature. (shrink)

The field equations of the quadratic action principle of relativity are solved, assuming a weak perturbation of the basic structure, which is a highly agitated Riemannian lattice field of a very small lattice constant. A field emerges which can be interpreted as the weak gravitational field of an apparently Minkowskian space. This field does not coincide with Einstein's theory of weak gravitational fields. Whereas the redshift remains unchanged, the light deflection becomes reduced by11.1% of the value predicted (...) by Einstein. (shrink)

Two problems have long been confused with each other: the gravitational redshift as discussed by the equivalence principle; and the Doppler shift observed by a detector which moves with constant proper acceleration away from a stationary source. We here distinguish these two problems and give for the first time a solution of the former which is ‘exact’ within the context of the equivalence principle in a sense discussed in the paper. The equivalence principle leads to transformations between flat (...) spacetimes. These are analyzed, and a generalized Lorentz transformation is proposed which covers transformations from inertial to uniformly accelerated frames of reference. (shrink)

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

The question is discussed whether the description of the gravitational Doppler effect as a simple energy effect is consistent with its general-relativistic description as a metric-time effect. The difference between a local description and a global one is stressed. In the local description one is permitted to ignore metric effects. The global description yields a position-dependent rate of proper time in a gravitational field, and the energy, or the frequency, of a “freely falling” photon is described as a (...) constant of motion. An experiment of nonlocal character measuring, simultaneously, the gravitational Doppler effect and the position-dependent rate of proper time may be performed by the use of a geostationary satellite. A simple general-relativistic treatment of the satellite experiment is obtained by transforming the Schwarzschild metric to a rotating frame, and describing the motion of free particles and the rates of standard clocks in the resulting metric. (shrink)

A variant of the Rosen bimetric general relativity with the Lobachevski background space metric is considered. An exact static external solution for the gravitational field of a concentrated electrically charged mass is found when the space is spherically symmetric. When the Lobachevski constant k → ∞, the solution turns into the Nordström-Reissner solution in general relativity, expressed via the harmonic coordinates. The results are also valid for the Chernikov theory with two connections and one metric.

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)

We study the possible interpretation of the "universal constants" by the classification of J.-M. Lévy-Leblond. The Planck constant and the speed of light in vacuum are the most common examples of constants of this type. Using Fock’s principle of the relativity w.r.t. observation means, we show that these two constants can be viewed as manifestations of certain relativity. We also show that there is a possibility to interpret the Boltzmann constant in a similar way, and make some comments (...) about the relativistic interpretation of the constant spacetime curvature and gravitational constant G. (shrink)

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary (...) charge), the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge. (shrink)

The paper sheds light from philosophical and methodological points of view on limitations, imposed on the building of the ontological basis of the theory of quantum gravitation by the quantum field theory: 1. this basis necessarily has to be a constantly fluctuating global dynamic field; 2. the field has to be locally excited and of quantum character, i.e, with local excitations subordinated to the principle of indeterminacy and the principle of canonic relationship between commutativeness and noncommutativeness; 3. sufficient theoretical grounds (...) are needed so that quantum theory of gravitation could justify the basic concepts of the structure of the quantum field theory. The analysis of these limitations should show which fundamental concepts and categories of the quantum field theory could in their transformed forms become a part of the ontological basis of the theory of quantum gravitation. (shrink)

A gravitational model is proposed that relates the terrestrially measured value of the gravitational constantG directly to the density and angular velocity of the galaxy. The model indicates a constant scalar value forG within most regions of our galaxy, but predicts thatG will be different in other galaxies and zero in intergalactic space. The model offers explanations for galactic cluster stability, discrepancies in terrestrial measurements ofG, and atomic particle stability. The model also provides a causal relationship between (...) strong, electromagnetic, weak, and gravitational interactions. The two postulates required for the proposed model reduce to two assumptions made in GRT in regions whereG is constant; these postulates are consistent with the existence of a 2.7 K blackbody background radiation. (shrink)

In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (...) (2) one with a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained. (shrink)

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and other alternative cosmologies, such (...) as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)

This article seeks to provide a historically well-informed analysis of an important post-Newtonian area of research in experimental physics between 1798 and 1898, namely the determination of the mean density of the earth and, by the end of the nineteenth century, the gravitational constant. Traditionally, research on these matters is seen as a case of “puzzle solving.” In this article, the author shows that such focus does not do justice to the evidential significance of eighteenth- and nineteenth-century experimental (...) research on the mean density of the earth and the gravitational constant. As Newton’s theory of universal gravitation was mainly based on astronomical observation, it remained to be shown that Newton’s law of universal gravitation did not break down at terrestrial distances. In this context, Cavendish’ experiment and related nineteenth-century experiments played a decisive role, for they provided converging and increasingly stronger evidence for the universality of Newton’s theory of gravitation. More precisely, the author shall argue that, as the accuracy and precision of the experimental apparatuses and the procedures to eliminate external disturbances involved increasingly improved, the empirical support for the universality of Newton’s theory of gravitation improved correspondingly. (shrink)

The questions of what represents space-time in GR, the status of gravitational energy, the substantivalist-relationalist issue, and the exceptional status of gravity are interrelated. If space-time has energy-momentum, then space-time is substantival. Two extant ways to avoid the substantivalist conclusion deny that the energy-bearing metric is part of space-time or deny that gravitational energy exists. Feynman linked doubts about gravitational energy to GR-exceptionalism, as do Curiel and Duerr; particle physics egalitarianism encourages realism about gravitational energy. In (...) that spirit, this essay proposes a third possible view about space-time, one involving a particle physics-inspired non-perturbative split that characterizes space-time with a constant background _matrix_, a sort of vacuum value, thus avoiding the inference from gravitational _energy to substantivalism. On this proposal, space-time is, where eta=diag is a spatio-temporally constant numerical signature matrix, a matrix already used in GR with spinors. The gravitational potential, to which any gravitational energy can be ascribed, is g_{\mu\nu}- eta, an _affine_ geometric object with a tensorial Lie derivative and a vanishing covariant derivative. This non-perturbative split permits strong fields, arbitrary coordinates, and arbitrary topology, and hence is pure GR by almost any standard. This razor-thin background, unlike more familiar backgrounds, involves no extra gauge freedom and so lacks their obscurities and carpet lump-moving. After a discussion of Curiel's GR exceptionalist denial of the localizability of gravitational energy and his rejection of energy conservation, the two traditional objections to pseudotensors, coordinate dependence and nonuniqueness, are explored. Both objections are inconclusive and getting weaker. A literal interpretation involving infinitely many energies corresponding by Noether's first theorem to the infinite symmetries of the _action_ largely answers Schroedinger's false-negative coordinate dependence problem. Bauer's false-positive objection has multiple answers. Non-uniqueness might be handled by Nester et al.'s finding physical meaning in multiplicity in relation to boundary conditions, by an optimal candidate, or by Bergmann's identifying the non-uniqueness and coordinate dependence ambiguities as one. (shrink)

An information-theoretic approach is shown to derive both the classical weak-field equations and the quantum phenomenon of metric fluctuation within the Planck length. A key result is that the weak-field metric $\bar h_{\mu \nu } $ is proportional to a probability amplitude φuv, on quantum fluctuations in four-position. Also derived is the correct form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the concept of the Fisher information I acquired (...) in a measurement of the weak-field metric. An associated physical information K is defined as K=I−J, where J is the information that is intrinsic to the physics (stress-energy tensor Tμv) of the measurement scenario. A posited conservation of information change δI=ΔJ implies a variational principle δK=0. The solution is the weak-field equations in the metric $\bar h_{\mu \nu } $ and associated equations in the probability amplitudes φuv. The gauge condition φ v uv =0 (Lorentz condition) and conservation of energy and momentum Tv μv=0 are used. A well-known “bootstrapping” argument allows the weak-field assumption to be lifted, resulting in the usual Einstein field equations. A special solution of these is well known to be the geodesic equations of motion of a particle. Thus, the information approach derives the classical field equations and equations of motion, as well as the quantum nature of the probability amplitudes φuv. (shrink)

In the traditional frame of classical electrodynamics, a hydrogen atom would emit electromagnetic waves and thus constantly lose energy, resulting in the fall of the electron on the proton over a finite period of time. The corresponding results were derived under the assumption of the instantaneous interaction between the proton and the electron. In 2004, Raju published a paper where he removed the assumption of the instantaneous interaction and studied the role of a time delay in the classical hydrogen atom. (...) He introduced a model of this effect that can be solved analytically. He calculated the radius rsel of a selected orbit, for which this effect and the radiation reaction force would cancel each other with respect to the tangential acceleration. It turned out that rsel is by an order of magnitude smaller than the Bohr radius. In the present paper we use Raju’s model for the corresponding gravitational situation. In frames of Newton’s gravity, we calculate analytically the radius and the energy Esel of a selected orbit, for which the retardation effect and the radiation reaction force would cancel each other out with respect to the tangential acceleration. Then we compare our outcome with some results of Kaplan’s solution for the two-body gravitational problem based on the Schwarzschild’s field. We show that Esel is very close to the minimum energy of bound states obtained by Kaplan in Einstein’s gravity. We emphasize that the selected orbit from the present paper represents the second only physical situation where the radiation reaction force is zero, but the radiation-caused energy loss is not zero. (shrink)

I try to revive, and possibly reconcile, a debate started a few years ago, about the relative roles of a bare cosmological constant and of a vacuum energy, by taking the attitude to try to get the most from the physics now available as established. I notice that the bare cosmological constant of the Einstein equations, which is there ever since GR emerged, is actually constrained (if not measured) indirectly combining the effective cosmological constant observed now, as (...) given by ΛCDM Precision Cosmology, with the cumulative vacuum contribution of the particles of the Standard Model, SM. This comes out when the vacuum energy is regularized, as given by many Authors, still within well established Quantum Field Theory, QFT, but without violating Lorentz invariance. The fine tuning, implied by the compensation to a small positive value of the two large contributions, could be seen as offered by Nature, which provides one more fundamental constant, the bare Lambda. The possibility is then discussed of constraining (measuring) directly such a bare cosmological constant by the features of primordial gravitational wave signals coming from epoch’s precedent to the creation of particles. I comment on possibilities that would be lethal, that is if the vacuum does not gravitate. This last issue is often raised, and I discuss the current situation about. Finally a hint is briefly discussed for a possible “bare Lambda inflation” process. (shrink)

We show that in 1929 Cartan and Einstein almost produced a theory in which the electromagnetic (EM) field constitutes the time-like 2-form part of the torsion of Finslerian teleparallel connections on pseudo-Riemannian metrics. The primitive state of the theory of these connections would not, and did not, permit Cartan and Einstein to realize how their torsion field equations contained the Maxwell system and how the Finslerian torsion contains the EM field. Cartan and Einstein discussed curvature field equations, though failing to (...) focus on the fact that teleparallelism automatically implies gravitational field equations with torsion terms as source, both in first and second order. We further show that the first-order contribution of the EM field to the source of the gravitational field may play havoc with the remeasurement of Newton's gravitational constant, even if the experiment is electrically grounded. These results are also used as support for the thesis that there is an alternative to the present way of dealing with the great theoretical questions of physics. On the practical side, the inconveniences faced in measuring G may be greatly compensated by the possibility of manipulating spacetime with electric fields at the first-order level. (shrink)

The equivalence principle as well as the spin-two character of the weak gravitational field lead to difficulties in the measurability analysis of this field which are not encountered in Bohr and Rosenfeld's corresponding inquiry into the electromagnetic field. To meet these difficulties, atomic elastic structures are proposed as gravitational field detectors whose parameters (masses, total volumes, lattice and elastic constants) are adjustable. The limitations imposed by the uncertainty principle and by the radiation reaction of the detectors on the (...) determination of the amplitude, frequency, and direction of the field are then exhibited. Finally, the relevance of the present work to the investigation of DeWitt and to Einstein's full theory of gravitation is briefly considered. (shrink)

The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of (...) the curvature of the 8D cotangent space and based on the (torsionless) Levi-Civita connection is provided that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in $\mathit{momentum}$ space is very large, namely the small size of P is of the order of $( 1/R_{\mathit{Hubble}})$ . Finally we develop a Born’s reciprocal complex gravitational theory as a local gauge theory in 8D of the $\mathit{deformed}$ Quaplectic group that is given by the semi-direct product of U(1,3) with the $\mathit{deformed}$ (noncommutative) Weyl-Heisenberg group involving four $\mathit{noncommutative}$ coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented. (shrink)

I offer a novel argument for spacetime substantivalism: We should take the spacetime of general relativity to be a substance because of its active role in gravitational causation. As a clear example of this causal behavior I offer the cosmological constant, a term in the most general form of the Einstein field equations which causes free floating objects to accelerate apart. This acceleration cannot, I claim, be causally explained except by reference to spacetime itself.

Based on formal arguments from Zermelo–Fraenkel set theory we develop the environment for explaining and resolving certain fundamental problems in physics. By these formal tools we show that any quantum system defined by an infinite dimensional Hilbert space of states interferes with the spacetime structure M. M and the quantum system both gain additional degrees of freedom, given by models of Zermelo–Fraenkel set theory. In particular, M develops the ground state where classical gravity vanishes. Quantum mechanics distinguishes set-theoretic random forcing (...) such that M and gravitational degrees of freedom are parameterized by extended real line. The large scale smooth geometry compatible with the forcing extensions is one of exotic smoothness structures of \. The amoeba forcing makes the old real line to have Lebesgue measure zero in the extended one. We apply the entire procedure to the cosmological constant problem, especially to discard the zero-modes contributions to the gravitational vacuum density. Moreover, there exists certain exotic smooth \ from which one determines the realistic, agreeing with observation, small value of the vacuum energy density. (shrink)

We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of QM, Bell’s model (...) implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck. (shrink)

It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.

The Schuster-Blackett (S-B) conjecture, which supposes the relationshipM/J=βG 1/2 /2c between the magnetic dipole moments (M) of celestial objects and their angular momenta (J), where G is the Newtonian constant of gravitation, c the speed of light, and β a dimensionless constant of order unity, is examined in the context of the evolution of pulsar gyromagnetic ratios. It is demonstrated that the evolution of pulsar gyromagnetic ratios is not consistent with the strong form of the S-B conjecture where (...) β is taken to be a constant. The pulsar evidence, which shows evolution withM/J constant for individual short-period pulsars, however, does admit the validity of a weaker form of the S-B conjecture, where β is allowed to take on a range of values. It is also shown that the only conventional explanation of the origin of pulsar magnetic fields that produces evolution where the gyromagnetic ratio remains constant for individual pulsars which generates magnetic fields of sufficient strength, the thermally driven Hall-field-limited battery effect, may not convincingly account for the observed behavior of pulsars. A few of the implications of the S-B conjecture and the pulsar evidence are explored. (shrink)

In order to resolve the cosmological constant problem, the notion of reference frame is re-examined at the quantum level. By using a quantum non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame is proposed. The underlying mathematical structure is a new geometry endowed with intrinsic second central moment (variance) or even higher moments of its coordinates, which generalizes the classical Riemannian geometry based on only first moment (mean) of its coordinates. The second central moment of the coordinates (...) directly modifies the quadratic form distance which is the foundation of the Riemannian geometry. At semi-classical level, the second central moment introduces a flow which continuously deforms the Riemannian geometry driven by its classical Ricci curvature, which is known as the Ricci flow. A generalized equivalence principle of quantum version is also proposed to interpret the new geometry endowed with at least second moment. As a consequence, the spacetime is stabilized against quantum fluctuation, and the cosmological constant problem is resolved within the framework. With an isotropic positive curvature initial condition, the long flow time solution of the Ricci flow exists, the accelerating expansion universe at cosmic scale is an observable effect of the spacetime deformation of the normalized Ricci flow. A deceleration parameter − 0.67 consistent with measurement is obtained by using the reduced volume method introduced by Perelman. Effective theory of gravity within the framework is also discussed. (shrink)

The renormalization group is used to analyze the behavior of certain gravitationally significant renormalized coupling constants under a scaling of the spacetime curvature. After discussing a simple example, the results are summarized for a class of grand unified theories.

It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the (...) choice of time, and in almost all time gauges, is a non-linear function of the cosmological constant. This non-linear relation is a calculation for the vacuum energy density given some arbitrary value of the cosmological constant. Hence, in this non-perturbative framework, certain conventional aspects of the cosmological constant problem do not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: “Does vacuum gravitate?”. (shrink)

Unitary field theories and “SUPER-GUT” theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian (1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, (4,5) and Heisenberg (6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against “all transformations” and which “depend on nothings” (Planck (9–11) ). A satisfactory unitary theory has to involve these constants like (...) the mathematical numbers. Today, Planck's conception of the three elementary constants ħ, c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory (12–16) of induction, such unitary theories are “universal explaining theories.” The fundamental constants involve the complementarity between the universal statements in unitary theory and the “basic statements” in the language of classical observables. (shrink)

In evolutionary biology, niche construction is sometimes described as a genuine evolutionary process whereby organisms, through their activities and regulatory mechanisms, modify their environment such as to steer their own evolutionary trajectory, and that of other species. There is ongoing debate, however, on the extent to which niche construction ought to be considered a bona fide evolutionary force, on a par with natural selection. Recent formulations of the variational free-energy principle as applied to the life sciences describe the properties of (...) living systems, and their selection in evolution, in terms of variational inference. We argue that niche construction can be described using a variational approach. We propose new arguments to support the niche construction perspective, and to extend the variational approach to niche construction to current perspectives in various scientific fields. (shrink)

In this paper, I am going to cast doubt on an idea that is shared, explicitly or implicitly, by most contemporary pragmatic theories: that the inferential interpretation procedure described by Grice, neo-Griceans, or post-Griceans applies only to the interpretation of ostensive stimuli. For this special issue, I will concentrate on the relevance theory (RT) version of this idea. I will proceed by putting forward a dilemma for RT and argue that the best way out of it is to accept that (...) the relevance-theoretic comprehension procedure ap- plies to certain non-ostensive stimuli, contrary to what is generally claimed within RT. In particular, I will argue that relevance theorists should accept that (ceteris paribus) non- ostensive emotional expressions in interactions guarantee a presumption of relevance such that they are interpreted through the relevance-theoretic comprehension procedure. This leads me to propose what I call 'the expressive principle of relevance'. (shrink)

In this chapter, we start by spelling out three important features that distinguish expressives—utterances that express emotions and other affects—from descriptives, including those that describe emotions (Section 1). Drawing on recent insights from the philosophy of emotion and value (2), we show how these three features derive from the nature of affects, concentrating on emotions (3). We then spell out how theories of non-natural meaning and communication in the philosophy of language allow claims that expressives inherit their meaning from specificities (...) of emotions—namely, from being felt, evaluative attitudes toward propositional or non-propositional contents (4). (shrink)

Cognitive niche construction is the process whereby organisms create and maintain cause–effect models of their niche as guides for fitness influencing behavior. Extended mind theory claims that cognitive processes extend beyond the brain to include predictable states of the world. Active inference and predictive processing in cognitive science assume that organisms embody predictive (i.e., generative) models of the world optimized by standard cognitive functions (e.g., perception, action, learning). This paper presents an active inference formulation that views cognitive niche construction as (...) a cognitive function aimed at optimizing organisms' generative models. We call that process of optimization extended active inference. (shrink)

The first English translation of the major political works of Benjamin Constant (1767-1830), one of the most important of the French political figures in the aftermath of the revolution of 1789, and a leading member of the liberal opposition to Napoleon and later to the restored Bourbon monarchy. The texts included in this volume are widely regarded as one of the classic formulations of modern liberal doctrine.

Together, the code and inferential models of communication are often thought to range over all cases of communication. However, their prevailing versions seem unable to fully explain what I call underdeterminacy without ostension. The latter is constituted by communication where stimuli that are not (nor appear to be) produced with communicative or informative intentions nevertheless communicate information underdetermined by the relevant codes. Though the prevailing accounts of communication cannot fully explain how communication works in such cases, I suggest that some (...) version of the inferential model can—if we allow it to extend to non‐ostensive, non‐intentional behaviors. (shrink)

Over the last 30 years, representationalist and dynamicist positions in the philosophy of cognitive science have argued over whether neurocognitive processes should be viewed as representational or not. Major scientific and technological developments over the years have furnished both parties with ever more sophisticated conceptual weaponry. In recent years, an enactive generalization of predictive processing – known as active inference – has been proposed as a unifying theory of brain functions. Since then, active inference has fueled both representationalist and dynamicist (...) campaigns. However, we believe that when diving into the formal details of active inference, one should be able to find a solution to the war; if not a peace treaty, surely an armistice of a sort. Based on an analysis of these formal details, this paper shows how both representationalist and dynamicist sensibilities can peacefully coexist within the new territory of active inference. (shrink)

Dans cette entrée, après une introduction qui servira de cadre à notre discussion (section 1.), nous allons présenter et analyser des définitions du concept « Art ». Nous discuterons brièvement les définitions classiques les plus influentes puis nous nous concentrerons sur les principales définitions contemporaines. -/- Nous verrons pourquoi les définitions classiques sont aujourd’hui considérées comme insatisfaisantes (2.a.), et comment les philosophes, à partir de la seconde moitié du XXème siècle ont tenté de pallier leurs défauts. Dans les grandes lignes, (...) le problème principal soulevé à l’encontre des théories classiques est qu’elles cherchent toutes l’essence de l’art dans un trait caractéristique qui serait reconnaissable dans les œuvres elles-mêmes. Les théories contemporaines répondent à ce problème principalement de quatre façons, comme on le verra dans les sections 2.b à 2.d. Les théories sceptiques (2.b.) défendent qu’il est dès lors impossible de définir l’art – qu’on peut au mieux en donner certains caractères typiques, des airs de famille. Les théories relationnalistes (2.c.) défendent que ce qui fait qu’une chose est de l’art est à trouver en dehors de celle-ci, notamment dans les relations qu’elle entretient avec son contexte de création ou de présentation. Les théories néo-classiques (2.d.) continuent à chercher l’essence de l’art dans un trait caractéristique reconnaissable dans les œuvres elles-mêmes tout en prenant en compte les réactions sceptiques ou relationnalistes. Enfin, la théorie du ‘renvoi de la balle’ (2.e.) défend que l’on ne peut pas définir l’art mais seulement des sous-catégories comme la musique, la sculpture, les installations, les performances, etc. -/- Nous présenterons les avantages et les inconvénients principaux des théories contemporaines. Nous verrons qu’aucune n’est dénuée de problèmes, expliquant pourquoi il n’existe pas de consensus sur une définition de l’art aujourd’hui. Nous verrons également que – à l’exception d’un certain scepticisme qui jette, semble-t-il, trop vite l’éponge – chacune de ces théories amène, par son originalité, à une compréhension nouvelle et plus profonde de cette notion extrêmement complexe qu’est le concept « Art ». (shrink)

Autism Spectrum Condition presents a challenge to social and relational accounts of the self, precisely because it is broadly seen as a disorder impacting social relationships. Many influential theories argue that social deficits and impairments of the self are the core problems in ASC. Predictive processing approaches address these based on general purpose neurocognitive mechanisms that are expressed atypically. Here we use the High, Inflexible Precision of Prediction Errors in Autism approach in the context of cultural niche construction to explain (...) atypicalities of the relational self, specifically its minimal, extended, and intersubjective aspects. We contend that the social self in ASC should not be seen as impaired, but rather as an outcome of atypical niche construction. We unpack the scientific, ethical, and practical consequences of this view, and discuss implications for how the challenges that autistic persons face should be approached. (shrink)

When we see or hear a spontaneous emotional expression, we usually immediately, effortlessly, and often correctly interpret it to mean happiness, sadness, or some other emotion as well as what this emotion is about. How do we do that? In this article, I evaluate how useful the concepts of natural meaning and probabilistic meaning are when it comes to explaining how we and other animals interpret emotional signs displayed without communicative intentions. I argue that Grice’s notion of natural meaning, because (...) it is a factive relation, is too restrictive for this purpose. I then present the notion of probabilistic meaning. The latter seems adequate for analyzing our ability to interpret non-communicative emotional signs, but it faces several difficulties when it comes to analyzing how we and other animals interpret emotional _signals_, i.e. signs that have the function to communicate emotional information. I present three of these difficulties. En passant, I suggest that a teleosemantic notion may be better suited for these challenges. (shrink)

Bayesian approaches to legal reasoning propose causal models of the relation between evidence, the credibility of evidence, and ultimate hypotheses, or verdicts. They assume that legal reasoning is the process whereby one infers the posterior probability of a verdict based on observed evidence, or facts. In practice, legal reasoning does not operate quite that way. Legal reasoning is also an attempt at inferring applicable rules derived from legal precedents or statutes based on the facts at hand. To make such an (...) inference, legal reasoning follows syllogistic logic and first order transitivity. This paper proposes a Bayesian model of legal syllogistic reasoning that complements existing Bayesian models of legal reasoning using a Bayesian network whose variables correspond to legal precedents, statutes, and facts. We suggest that legal reasoning should be modelled as a process of finding the posterior probability of precedents and statutes based on available facts. (shrink)