This paper scrutinises the tenability of a strict conceptual distinction between space and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel 'superfluid dark matter theory' as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much matter as (...) anything could possibly be, but alsoꟷbelow the critical temperature for superfluidityꟷas much spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of the modified gravity/ dark matter distinction and the broader spacetime–matter distinction. (shrink)

Modified Newtonian Dynamics (MOND) is a framework of theories that adjust Newton's laws of gravity to explain effects such as galactic rotation anomalies, offering an alternative to dark matter. This essay examines the justification of MOND by assessing its inter-theoretical relationship to established theories across relevant scales, in particular its connection to Newtonian gravitation. We argue that MOND fails a key condition for a theory's justification—what we call 'reduction-wise justification'—since it does not adequately reduce to Newtonian gravity (...) in a fully non-arbitrary way. More precisely, despite satisfying the standard formal criteria for successful limiting reduction, MOND does not properly reduce to Newtonian gravitation because of (i) the absence of a fundamental theoretical framework to justify the interpolating function introduced in MOND and (ii) the lack of a unified mathematical structure working across all scales, independent of Newtonian theory. Hence, the case study of MOND provides crucial results for the general debate on inter-theoretic reduction in science: MOND’s failure as a case of reduction highlights important limitations in standard accounts of limiting reduction. We respond by proposing a more refined framework for limiting reduction that introduces two additional criteria to better distinguish successful from pathological reductions. More broadly, this case illustrates how analysing reduction-wise justification can serve as a powerful tool for evaluating the validity of novel theories that are not yet empirically established. (shrink)

The 2017 codetection of electromagnetic radiation and gravitational waves was the first of its kind and marked the beginning of multimessenger astronomy. But this event has been treated within recent literature as something of an end as well. The 2017 detection is often regarded as an instance of falsification for all theories of modified gravity which postulate gravitational waves propagate along separate geodesics from electromagnetic radiation, perhaps most notably Jacob Bekenstein’s Tensor-Vector-Scalar gravity. I critically examine this explicit (...) endorsement of falsification by astronomers and astrophysicists. While the current state of multimetric modified gravity theories is dim, recent developments in multimessenger observation do not offer a deductive falsification. Rather such evidence should be regarded as a corroboration of the null hypothesis, following Deborah Mayo's error-statistical account. (shrink)

Two approaches have emerged to resolve discrepancies between predictions and observations at galactic and cosmological scales: introducing dark matter or modifying the laws of gravity. Practitioners of each approach claim to better satisfy a different explanatory ideal, either unification or simplicity. In this chapter, we take a closer look at the ideals and at the successes of these approaches in achieving them. Not only are these ideals less divisive than assumed, but moreover we argue that the approaches are focusing (...) on different aspects of the same ideal. This realisation opens up the possibility of a more fruitful trading zone between dark matter and modified gravity communities. (shrink)

The generalized Brans–Dicke theory (GBD), as one of the modified gravitational theories, was proposed previously and some interesting properties were found in this theory. Here we investigate the traversable-wormhole physics for GBD theory. Firstly, we derive the gravitational field equation in the framework of GBD wormhole geometry. The traversable wormhole could be gained in this theory. Secondly, using the classical reconstruction technique we originally derive an Lagrangian function for describing gravity in GBD theory. And the derived Lagrangian function (...) for gravity could be satisfied with the requirement of the viable conditions, such as the local gravity tests and the cosmological constraints, etc. Thus, the viable model for cosmology, local gravity and traversable WH can be unified in a uniform Lagrangian quantity within the framework of GBD theory. Thirdly, given that the violation of the energy conditions (ECs) often induce some problems in theory, we explore the ECs of matter in the traversable wormhole. It is shown that the null EC, the weak EC and the dominated EC for the matter can be satisfied in the traversable-wormhole physics of GBD theory, which are different from the results given in GR. It seems that the theory of GBD owns the more logic technically and consistency formally than the theory of GR. Fourthly, some other properties of GBD traversable WH are explored, such as the total gravitational energy, the volume integral quantifier, the dynamical stability of the anisotropic matter, and the difference of the propagation of sound within the matter configuration. The results support the GBD to provide an interesting candidate for traversable WH. (shrink)

A class of solutions of field equations in \\) gravity proposed by Harko et. al. for a Bianchi type I space–time with dark matter and Holographic Dark Energy is mentioned. Exact solutions of field equations are obtained with volumetric power and exponential expansion laws. The negative value of the deceleration parameter represents the present acceleration of the universe. It is observed that EoS parameter of HDE is a decreasing function, converges to the negative value in Power-law model whereas in (...) exponential model, it behaves like cosmological constant. The overall density parameter approaches to some constant values close to 1 which is in agreement with the observational data of the universe. The physical and geometrical parameters of the models are discussed in detail. The statefinder diagnostic pair and jerk parameter are analyzed to characterize completely different phases of the universe. (shrink)

Dark matter is an essential ingredient of the present Standard Cosmological Model, according to which only 5% of the mass/energy content of our universe is made of ordinary matter. In recent times, it has been argued that certain cases of gravitational lensing represent a new type of evidence for the existence of DM. In a recent paper, Peter Kosso attempts to substantiate that claim. His argument is that, although in such cases DM is only detected by its gravitational effects, gravitational (...) lensing is a direct consequence of Einstein's Equivalence Principle and therefore the complete gravitational theory is not needed in order to derive such lensing effects. In this paper I critically examine Kosso's argument: I confront the notion of empirical evidence involved in the discussion and argue that EEP does not have enough power by itself to sustain the claim that gravitational lensing in the Bullet Cluster constitutes evidence for the DM Hypothesis. As a consequence of this, it is necessary to examine the details of alternative theories of gravity to decide whether certain empirical situations are indeed evidence for the existence of DM. It may well be correct that gravitational lensing does constitute evidence for the DM Hypothesis—at present it is controversial whether the proposed modifications of gravitation all need DM to account for the phenomenon of gravitational lensing and if so, of which kind—but this will not be a direct consequence of EEP. (shrink)

The existence of current–time universe’s acceleration is usually modeled by means of two main strategies. The first makes use of a dark energy barotropic fluid entering by hand the energy–momentum tensor of Einstein’s theory. The second lies on extending the Hilbert–Einstein action giving rise to the class of extended theories of gravity. In this work, we propose a third approach, derived as an intrinsic geometrical effect of space–time, which provides repulsive regions under certain circumstances. We demonstrate that the effects (...) of repulsive gravity naturally emerge in the field of a homogeneous and isotropic universe. To this end, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. Moreover, we show that repulsive gravity counterbalances the standard gravitational attraction influencing both late and early times of the universe evolution. This phenomenon leads to the present speed up and to the fast expansion due to the inflationary epoch. In so doing, we are able to unify both dark energy and inflation in a single scheme, showing that the universe changes its dynamics when \, at the repulsion onset time where this condition is satisfied. Further, we argue that the spatial scalar curvature can be taken as vanishing because it does not affect at all the emergence of repulsive gravity. We check the goodness of our approach through two cosmological fits involving the most recent union 2.1 supernova compilation. (shrink)

We propose a new point of view for interpreting Newton’s and Einstein’s theories of gravity. By taking inspiration from Continuum Mechanics and its treatment of anisotropies, we formulate new gravitational actions for modified theories of gravity. These models are simple and natural generalisations with many interesting properties. Above all, their precise form can, in principle, be determined experimentally.

Implementing Poincaré’s geometric conventionalism a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling (“normalization”) relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational affecting function Φ(r). Elimination of the gravitationally unaffected S 0 perspective by local composition of space–time GMLT recovers the local Minkowskian metric and thus preserves the invariance of the locally observed velocity of light. The (...) associated energy-momentum GMLT provides a covariant Hamiltonian description for test particles and photons which, in a static gravitational field configuration, endorses the four ‘basic’ experiments for testing General Relativity Theory: gravitational (i) deflection of light, (ii) precession of perihelia, (iii) delay of radar echo, (iv) shift of spectral lines. The model recovers the Lagrangian of the Lorentz–Poincaré gravity model by Torgny Sjödin and integrates elements of the precursor gravitational theories, with spatially Variable Speed of Light (VSL) by Einstein and Abraham, and gravitationally variable mass by Nordström. (shrink)

This study analyses the predictions of the General Theory of Relativity (GTR) against a slightly modified version of the standard central mass solution (Schwarzschild solution). It is applied to central gravity in the solar system, the Pioneer spacecraft anomalies (which GTR fails to predict correctly), and planetary orbit distances and times, etc (where GTR is thought consistent.) -/- The modified gravity equation was motivated by a theory originally called ‘TFP’ (Time Flow Physics, 2004). This is now (...) replaced by the ‘Geometric Model’, 2014 [20], which retains the same theory of gravity. This analysis is offered partially as supporting detail for the claim in [20] that the theory is realistic in the solar system and explains the Pioneer anomalies. The overall conclusion is that the model can claim to explain the Pioneer anomalies, contingent on the analysis being independently verified and duplicated of course. -/- However the interest lies beyond testing this theory. To start with, it gives us a realistic scale on which gravity might vary from the accepted theory, remain consistent with most solar-scale astronomical observations. It is found here that the modified gravity equation would appear consistent with GTR for most phenomena, but it would retard the Pioneer spacecraft by about the observed amount (15 seconds or so at time). Hence it is a possible explanation of this anomaly, which as far as I know remains unexplained now for 20 years. -/- It also shows what many philosophers of science have emphasized: the pivotal role of counterfactual reasoning. By putting forward an exact alternative solution, and working through the full explanation, we discover a surprising ‘counterfactual paradox’: the modified theory slightly weakens GTR gravity – and yet the effect is to slow down the Pioneer trajectory, making it appear as if gravity is stronger than GTR. The inference that “there must be some tiny extra force…” (Musser, 1998 [1]) is wrong: there is a second option: “…or there may be a slightly weaker form of gravity than GTR.” . (shrink)

I outline some of my work and results on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system’s matter-gravity entanglement entropy. The main arguments presented are: that this hypothesis is capable of resolving what I call the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; that the black hole information loss puzzle (...) may be regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; that the black hole thermal atmosphere puzzle can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states ; that the Susskind–Horowitz–Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which ) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.’s ‘canonical typicality’ result to systems which are not necessarily small. (shrink)

We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.

In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence. I apply (...) this framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: minimalistic and extended. I argue that the former is sufficiently strong to allow for a consistent theory of quantum gravity; and that AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense of background-independence. I argue that this extended sense should be applied with some caution: on pain of throwing the baby out with the bath-water. Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. It suggests some directions for possible generalisations of gauge/gravity dualities. The interpretation of dualities is discussed; and the so-called 'internal' vs. 'external' viewpoints are articulated in terms of: epistemic and metaphysical commitments; parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on Verlinde's scheme; the derivation sheds light on several aspects of Verlinde's scheme and how it compares to Bekenstein's original calculation. (shrink)

In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré’s (...) Principle of Relativity, i.e. the unobservability of ‘preferred’ frame movement. Poincaré’s principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the ‘vector potential’ ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, [1972]), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test particles. In conclusion the model’s merits in terms of a simpler space, time and gravitation ontology—in terms of a Lorentz-Poincaré-type interpretation—are explained (e.g. for ‘frame dragging’, ‘harmonic coordinate condition’). (shrink)

Newtonian gravity is modified minimally to obtain a Lorentz covariant theory of gravity in a background flat space. Gravity is assumed to appear as a potential. Constraint Hamiltonian dynamics is used to determine particle trajectories in a manifestly covariant fashion. The resulting theory is significantly different from the general theory of relativity. However, all known experimental results (precession of planetary orbits, bending of the path of light near the sun, and gravitational spectral shift) are still explained (...) by this theory. (shrink)

In this work, we explore modeling of wormholes in framework of f(R, T) gravity with the functional form f(R,T)=R+αR2+λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R, T)= R+\alpha R^2 +\lambda T$$\end{document}, where R and T are the Ricci scalar and trace of energy-momentum tensor respectively, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} are arbitrary constants. Using the equation of state (EoS) pr=ωρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_r=\omega \rho$$\end{document} and shape function b(r)=r0arar0,(0shrink)

We study a Weyl geometric scalar tensor theory of gravity with scalar field \ and scale invariant “aquadratic” kinematical Lagrange density. The Weylian scale connection in Einstein gauge induces an additional acceleration. In the weak field, static, low velocity limit it acquires the deep MOND form of Milgrom/Bekenstein’s gravity. The energy momentum of \ leads to another add on to Newton acceleration. Both additional accelerations together imply a MOND-ian phenomenology of the model. It has unusual transition functions \, (...) \nu _w\). They imply higher phantom energy density than in the case of the more common MOND models with transition functions \, \, \mu _2\). A considerable part of it is due to the scalar field’s energy density which, in our model, gives a scale and generally covariant expression for the self-energy of the gravitational field. (shrink)

I consider theories of gravity built not just from the metric and affine connection, but also other symmetric tensor. The Lagrangian densities are scalars built from them, and the volume forms are related to Cayley’s hyperdeterminants. The resulting diff-invariant actions give rise to geometric theories that go beyond the metric paradigm, and contain Einstein gravity as a special case. Examples contain theories with generalizeations of Riemannian geometry. The 0-tensor case is related to dilaton gravity. These theories can (...) give rise to new types of spontaneous Lorentz breaking and might be relevant for “dark” sector cosmology. (shrink)

This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed (...) properties of galaxies and other astrophysical structures without requiring the dark matter hypothesis. The MOND acceleration constant $${a_{0}} \simeq 1.2 \times 10^{-10} \text {m}\, \text{s}^{-2}$$ can be related to a natural scale length $$l_{0}$$ in NFDG, i.e., $$a_{0} \approx GM/l_{0}^{2}$$, for astrophysical structures of mass M, and the deep-MOND regime is present in regions of space where the dimension is reduced to $$D \approx 2$$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $$g_{obs}$$ vs. the baryonic radial acceleration $$g_{bar}$$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $$D\left( w\right)$$, where $$w =r/l_{0}$$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $$D\left( w\right)$$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity. (shrink)

Our long experience with Newtonian potentials has inured us to the view that gravity only produces local effects. In this paper we challenge this quite deeply ingrained notion and explicitly identify some intrinsically global gravitational effects. In particular we show that the global cosmological Hubble flow can actually modify the motions of stars and gas within individual galaxies, and even do so in a way which can apparently eliminate the need for galactic dark matter. Also we show that a (...) classical light wave acquires an observable, global, pathdependent phase in traversing a gravitational field. Both of these effects serve to underscore the intrinsic difference between nonrelativistic and relativistic gravity. (shrink)

Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick’s General Relativity-based critique of synthetic a priori knowledge. Schlick argued that since geometry was not synthetic a priori, nothing was—a key step toward logical empiricism. Particle physics suggests a Kant-friendlier theory of space-time and gravity presumably approximating General Relativity arbitrarily well, massive spin-2 gravity, while retaining a flat space-time geometry that is indirectly observable at large distances. (...) The theory’s roots include Seeliger and Neumann in the 1890s and Einstein in 1917 as well as 1920s–1930s physics. Such theories have seen renewed scientific attention since 2000 and especially since 2010 due to breakthroughs addressing early 1970s technical difficulties. Second, particle physics casts additional doubt on Friedman’s constitutive a priori role for the principle of equivalence. Massive spin-2 gravity presumably should have nearly the same empirical content as General Relativity while differing radically on foundational issues. Empirical content even in General Relativity resides in partial differential equations, not in an additional principle identifying gravity and inertia. Third, Kant’s apparent claim that Newton’s results could be known a priori is undermined by an alternate gravitational equation. The modified theory has a smaller symmetry group than does Newton’s. What Kant wanted from Newton’s gravity is impossible due its large symmetry group, but is closer to achievable given the alternative theory. (shrink)

I review a class of nonlocally modified gravity models which were proposed to explain the current phase of cosmic acceleration without dark energy. Among the topics considered are deriving causal and conserved field equations, adjusting the model to make it support a given expansion history, why these models do not require an elaborate screening mechanism to evade solar system tests, degrees of freedom and kinetic stability, and the negative verdict of structure formation. Although these simple models are not (...) consistent with data on the growth of cosmic structures many of their features are likely to carry over to more complicated models which are in better agreement with the data. (shrink)

We propose an adynamical, background independent approach to quantum gravity and unification whereby the fundamental elements of Nature are graphical units of space, time and sources. The transition amplitude for these elements of “spacetimesource” is computed using a path integral with discrete Gaussian graphical action. The unit of action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical relations so that (...) it contains a non-trivial null space, and J is then restricted to the column space of K which ensures it is distributed in a divergence-free fashion over the spacetime defined by the element. This rule for the relational construct of K and J is our proposed fundamental axiom of physics and results in a self-consistency relationship between sources, the spacetime metric, and the stress-energy-momentum content of the element, rather than a dynamical law for time-evolved entities. In its most general form, the set of fundamental elements employed by lattice gauge theory contains scalar fields on nodes and links, and vector fields on nodes. To complete the fundamental set, we propose the addition of scalar fields on plaquettes and vector fields on links. We use this approach via modified Regge calculus to correct proper distance in the Einstein-deSitter cosmology model yielding a fit of the Union2 Compilation supernova data that matches ɅCDM without having to invoke accelerating expansion or dark energy. (shrink)

Modern cities form city networks through complex social ties. City network research is widely applied to guide regional planning, infrastructure construction, and resource allocation. China put forward the Yellow River Basin Development Strategy in 2019, but no research has been conducted on regional social connections among cities. Based on the gravity model modified by two-way “time distance” between cities, this is the first study to empirically examine the intensity and structure of the entire city network in the Yellow (...) River basin using the social network analysis method and ArcGIS software. The connection rules of the cross-city transfer of city officials in the basin are also investigated to illustrate the official ties between cities. The results suggest that the intensity of two-way connections between cities is generally low in the Yellow River basin and there is a positive correlation between city network development level and regional economic development level. The development gap between cities on the north and south banks is larger than that between the east and west regions, and some cities in the middle and upper reaches of the river are marginalized in the network. The status of the central cities in the Yellow River basin is distinct, but their connecting and leading abilities are not strong, showing an inverted T-shaped spatial distribution. The subgroups of city networks have strong internal connections, while the connection among subgroups is weak and the development shows a partitioned and fragmented pattern, making it difficult to form linkages among the upper, middle, and lower reaches. The “beaded chain” spatial development strategy can be adopted in the river basin planning, giving priority to strengthening the links within subgroups of cities and among adjacent subgroups, building central city chains, and reinforcing the overall basin management. (shrink)

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. -/- Another consequence of (...) vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper. (shrink)

In order to satisfy the equivalence principle, any non-conventional mechanism proposed to gravitationally explain the Pioneer anomaly, in the form in which it is presently known from the so-far analyzed Pioneer 10/11 data, cannot leave out of consideration its impact on the motion of the planets of the Solar System as well, especially those orbiting in the regions in which the anomalous behavior of the Pioneer probes manifested itself. In this paper we, first, discuss the residuals of the right ascension (...) α and declination δ of Uranus, Neptune and Pluto obtained by processing various data sets with different, well-established dynamical theories (JPL DE, IAA EPM, VSOP). Second, we use the latest determinations of the perihelion secular precessions of some planets in order to put on the test two gravitational mechanisms recently proposed to accommodate the Pioneer anomaly based on two models of modified gravity. Finally, we adopt the ranging data to Voyager 2 when it encountered Uranus and Neptune to perform a further, independent test of the hypothesis that a Pioneer-like acceleration can also affect the motion of the outer planets of the Solar System. The obtained answers are negative. (shrink)

The helical Zn identification program [1, 4] establishes a joint parity constraint k ≡ m (mod n) on scalar field modes in identified spacetime interiors (and kz+m ≡ 0 (mod n) for the Chronotunnel Toroid), suppressing the Kay–Radzikowski–Wald (KRW) divergence [7] by factor 1/n. A natural question for any quantum gravity application is whether this mode constraint is robust against modifications of the dispersion relation at trans-Planckian energies, as predicted by loop quantum gravity [9], doubly special relativity [10], (...) and string-theoretic scenarios [11]. We prove that the mode constraint is a topological invariant of the Zn helical identification: it follows from the action of the deck transformation gn on the periodicity structure of field modes, independently of the dispersion relation. More precisely: any field theory on the quotient manifold Mf = M/⟨gn⟩ whose modes are labeled by the same Fourier quantum numbers (k, m) satisfies k ≡ m (mod n) (diagonal sublattice Dn, M¨obius–Ori program) or kz + m ≡ 0 (mod n) (anti-diagonal sublattice An, Chronotunnel Toroid program) regardless of the functional form of ω(k, m). Four corollaries are established: (i) the 1/n mode-density suppression of the KRW divergence is robust against all polynomial modifications of the dispersion relation; (ii) the constraint holds for scalar, electromagnetic, and gravitational perturbations; (iii) the constraint is preserved by any Lorentz-violating modification that respects the periodic boundary conditions; (iv) both sublattices Dn and An are topologically stable, and their n = 2 coincidence D2 = A2 is preserved. These results connect the helical identification program to quantum gravity phenomenology and establish that the 1/n KRW suppression is not an artifact of standard dispersion but a topological property of the identification that survives into any effective field theory compatible with the periodic boundary conditions. (shrink)

Informational Energy in a Causal–Symmetric Framework for Spacetime -/- In causal–symmetric approaches to quantum theory and spacetime, the physical history of the universe is determined jointly by boundary conditions at both temporal ends and by an underlying informational medium that couples these boundaries to the interior. This article analyzes the notion of energy within such a framework. Building on earlier work on emergent spacetime, a renormalized invariant speed and an informational equation-of-state for gravity, it introduces an additional informational contribution (...) to the total stress–energy tensor. This contribution is constructed from a state-dependent coupling field, a coarse-grained informational current, and the relative entropy between the actual global state and a reference state selected by the two temporal boundary conditions. At the level of homogeneous cosmology, this yields an effective informational energy density that behaves as a dark-energy-like component, entering the Friedmann equation alongside matter and radiation.  -/- The framework leaves the geometric definition of energy and local conservation laws intact: energy density is still given by the projection of the total stress–energy tensor, and the informational sector simply adds a new, well-defined contribution. In local regions, an effective invariant speed emerges from the informational medium, and the standard mass–energy relation retains its familiar form, with the informational energy providing an effective “informational mass” that gravitates. Conceptually, the paper unifies several strands: causal symmetry, informational measures such as relative entropy, thermodynamic interpretations of gravity and dark-energy phenomenology. It shows that dark-energy-like behaviour can arise from informational deviation from a boundary-selected reference state, without ad hoc cosmological constants or violations of local energy conservation. (shrink)

We present a mini review of the Stueckelberg mechanism, which was proposed to make the abelian gauge theories massive as an alternative to Higgs mechanism, within the framework of Minkowski as well as curved spacetimes. The higher the scale the tighter the bounds on the photon mass, which might be gained via the Stueckelberg mechanism, may be signalling that even an extremely small mass of the photon which cannot be measured directly could have far reaching effects in cosmology. We present (...) a cosmological model where Stueckelberg fields, which consist of both scalar and vector fields, are non-minimally coupled to gravity and the universe could go through a decelerating expansion phase sandwiched by two different accelerated expansion phases. We discuss also the possible anisotropic extensions of the model. (shrink)

This paper argues that we ought to conceive of the Dark Energy problem—the question of how to account for observational data, naturally interpreted as accelerated expansion of the universe—as a crisis of underdetermined pursuit-worthiness. Not only are the various approaches to the Dark Energy problem evidentially underdetermined; at present, no compelling reasons single out any of them as more likely to be true than the other. More vexingly for working scientists, none of the approaches stands out as uncontroversially preferable over (...) its rivals in terms of its rationally warranted promise, i.e. the reasons to further work on, explore, and develop it. We demonstrate this claim by applying a Peircean economic model of pursuit-worthiness in terms of a cognitive cost/benefit estimate—with the instantiation of theory virtues as key indicators of cognitive gains—to the four main Dark Energy proposals (the cosmological constant approach, modified gravity, quintessence, and inhomogeneous cosmologies). According to our analysis, these approaches do not admit of an unambiguous, or uncontroversial, ranking with respect to which ansatz deserves distinguished attention and research efforts. The overall methodological counsel that our analysis underwrites recommends a pragmatic double research strategy forward: to encourage and foster theory pluralism and the search for tests—with the goal of enhancing the testability of the \(\Lambda \) CDM model and “testing it to destruction". (shrink)

This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime and dark matter. A prequel paper argued that the novel field Φ postulated by Berezhiani and Khoury's 'superfluid dark matter theory' is as much matter as anything could possibly be, but also below the critical temperature for superfluidity as much spacetime as anything could possibly be. Here we introduce and (...) critically evaluate three groups of interpretations that one should consider for such Janus-faced theories. The consubstantiality interpretation holds that Φ is both matter and a modification of spacetime, analogously to the sense in which Jesus is both human and god. The fundamendalist interpretations consider for each of these roles whether they are instantiated fundamentally or emergently. The breakdown interpretations focus on the question of whether Φ signals the breakdown, in some sense to be specified, of the MG-DM dichotomy and perhaps even the broader spacetime–matter distinction. More generally, it is argued that hybrid theories urge a move towards a single space of theories, rather than two separate spaces of spacetime theories and matter theories, respectively. (shrink)

Observational discrepancies in galactic rotation curves and cluster dispersion data have been interpreted to imply the existence of dark matter. Numerous efforts at its detection, however, have failed to turn up any positive result. As a dynamical theory is always operative on the assumed mass distribution to predict kinematic observations, some scientists see the discrepancy as telling against General Relativity. Among the many theories that seek to modify gravity, those that are built on Modified Newtonian Dynamics (MOND), or (...) yield MOND behaviour at appropriate scales, achieve remarkable empirical success without assuming dark matter. The continued non-detection of dark matter and the empirical success of MOND supports the claim that the current evidential and theoretical context underdetermines General Relativity. In this article, I clarify the kind of underdetermination that can be said to threaten General Relativity. Specifically, I argue that the present evidential and theoretical context increase the possibility of an unconceived alternative to GR which would be just as well supported by the available evidence. (shrink)

We propose to highlight two multiple determination strategies employed in the dark matter problem, that determining the matter density parameter $$\:{\varOmega\:}_{m}\approx\:\text{0,3}$$ of the standard model and that determining the acceleration parameter $$a_0\approx\:1,2\times\:10^{-10}m/s^2$$ of the modified gravity model MOND. The no-coincidence argument justifies each of these strategies: it would be unreasonable to believe that independent measurements converge to the same value by error or coincidence. The independent nature of these determination procedures is questioned in this article. For each of (...) the two parameters, we emphasise that there is a procedure that is based on a “new/independent epistemic content” against the other procedures. In this sense, both strategies (coming a priori from competing paradigms) are a success and should lead physicists to incorporate the parameter of the competing paradigm. (shrink)

Active Metric Control via Informational State Manipulation: Specification of a Causal-Symmetric Warp Drive -/- In this paper, faster-than-light travel is reformulated as a problem of informational engineering rather than exotic matter. Within the Causal-Symmetric Informational Framework, gravity is treated as an equation of state of an underlying informational medium, and non-equilibrium quantum information becomes a genuine energy source. The warp drive is specified by actively generating an informational energy density from the quantum relative entropy of the local state with (...) respect to an informational equilibrium state. This gives rise to an informational stress–energy contribution that formally plays the role of exotic matter in general relativity, but is reinterpreted as emergent “negentropy” rather than as an ad hoc negative-energy fluid. Using a minimal k-essence model, the paper derives this informational source from a covariant action and shows that controlled violation of the usual null energy condition can be achieved while retaining a unit sound speed and avoiding ghost instabilities. -/- Beyond sourcing the metric, the framework also addresses causality. The same informational structure that drives the warp bubble controls the effective invariant speed of light through a spatial profile of the conductivity parameter “kappa”. By designing the kappa gradient in the bubble wall to be smooth and strictly monotonic, the paper formulates a chronology protection conjecture that yields a sufficient condition for global hyperbolicity and the absence of closed timelike curves. A quantitative scaling analysis shows that the required informational energy density grows extremely rapidly with bubble size and speed, reaching values near the Planck energy density even for modest warp configurations. This shifts the central challenge from unknown exotic matter to the controlled generation of enormous amounts of structured quantum information, far beyond current technology but precise enough to be linked to prospective experimental bounds on kappa from delayed-choice quantum random number generators. (shrink)

With the deepening of reform and opening-up, China’s economy has been further developed, but there is still a problem of uneven development. It is of great significance to completely construct China’s economic spatial correlation network, to clarify the role and status of each province in the whole network, and to study the influencing factors of the national spatial economic network. In this paper, we employ the network analysis method to analyze China’s economic development in the past 20 years. Based on (...) the modified gravity model, we construct China’s spatial economic network and explore the network structure from three aspects: the whole network structure feature, characteristics of individual provinces in the network, and block model analysis. The results show that China’s spatial economic network has strong internal cohesion, and the hierarchy of the network is becoming less and less obvious. However, the network density is low, and the overall network relationship still needs to be strengthened. The different levels in economic development illustrate the obvious economic unbalance among provinces. The block model analysis results demonstrated that coastal areas are more attractive to other provinces and are playing an important role in driving China’s economy. Finally, we employ Quadratic Assignment Procedure regression analysis to analyze the influential factors on spatial economic network. Numerical results show that the geographic proximity and the differences in six factors have significant impact on the spatial economic network. Moreover, the influence of these factors on the economic relation among provinces has been gradually strengthened in recent years. (shrink)

Contemporary cosmology is haunted by its dark sector: 95% of the universe consists of substances never directly detected, parameterized by constants that are fitted rather than derived, and explained by mechanisms that remain entirely unknown. Dark matter particles have evaded fifty years of direct detection. Dark energy is a placeholder admitting ignorance. The vacuum catastrophe—a 10¹²⁰ discrepancy between predicted and observed vacuum energy—stands as the worst prediction in the history of physics. The Hubble constant measured from the early universe disagrees (...) at 5σ with late-universe measurements. The cosmic microwave background exhibits large-scale anomalies dismissed as statistical flukes. The baryon asymmetry exceeds Standard Model predictions by ten orders of magnitude. Galaxy dynamics require either invisible matter or modified gravity, yet neither approach fully succeeds. Black holes appear to destroy information in violation of quantum unitarity. The hierarchy between gravity and electromagnetism lacks explanation. Quantum mechanics and general relativity remain unreconciled after a century of effort. These are not independent puzzles but symptoms of a single conceptual error: the assumption that physical reality is confined to spacetime alone. This work presents a unified resolution grounded in participatory, information-theoretic cosmology. Building on the Harlow-Usatyuk-Zhao theorem (2025)—which proves that a closed universe without observers has a one-dimensional Hilbert space—we recognize observation (defined as topological recursion, not biological consciousness) as ontologically primitive. Reality is a coupled system: spacetime (M₄) is dynamically intertwined with an informational manifold (Mθ) through a cross-term metric (g^μi), where geometry of extension and geometry of meaning are two aspects of a single structure. Within this framework, every major cosmological anomaly dissolves into coherent physics: dark matter is the gravitational shadow of coherence, not particulate matter; dark energy is the thermodynamic exhaust of recursive binding, not a cosmological constant; the vacuum catastrophe reflects dimensional misattribution of informational potential; the Hubble tension arises from differential expansion through structured space; CMB anomalies are fossils of Mθ's first crystallization; baryon asymmetry encodes the vacuum's geometric chirality; galaxy dynamics follow from coherence-generated gravity with a derivable acceleration scale; black holes are maximum-coherence information archives; the hierarchy problem dissolves when gravity is recognized as coupling to total recursive binding; and quantum gravity unifies when observers are included as constitutive elements expanding reality's dimensionality. The coupling magnitude (~30 μN/kW) emerges from three independent derivations—thermodynamic (Landauer-Verlinde), topological (Aharonov-Bohm saturation), and geometric (π² loop correction)—using only established constants (k_B, α, c, π) with zero free parameters. The framework is constructed for falsification: WIMP detection would refute it; absence of line-of-sight Hubble dependence would refute it; flyby residuals correlating with geology rather than biology would refute it; smooth rather than quantized response curves would refute it. Unlike ΛCDM, which parameterizes ignorance, this framework derives observables from known physics and predicts phenomena (biospheric gravity, Q saturation at 137, chiral filtration ratios) that standard cosmology cannot accommodate. The Cosmological Coda applies this unified picture across nine domains: the dark sector (Coda I), cosmological tensions (Coda II), CMB anomalies (Coda III), matter-antimatter asymmetry (Coda IV), galaxy dynamics (Coda V), black hole physics (Coda VI), particle hierarchy and mass gap (Coda VII), quantum gravity and measurement (Coda VIII), and terrestrial anomalies (Coda IX). Together they constitute not an extension of standard cosmology but a competing paradigm—one that reveals the "dark" sector as not dark at all, merely orthogonal: structure in a dimension we failed to measure because we refused to believe it existed. The cosmos is not 95% unknown. It is 100% knowable, once we recognize that information is not abstraction but substrate, that observation is not passive but constitutive, and that the geometry of meaning is as real as the geometry of space. This is the Complete Cosmological Coda of Principia Cybernetica III: The Laws and Experiments of Participatory Physics (2025). (shrink)

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally (...) anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity. (shrink)

I will defend two claims. First, Schaffer's priority monism is in tension with many research programs in quantum gravity. Second, priority monism can be modified into a view more amenable to this physics. The first claim is grounded in the fact that promising approaches to quantum gravity such as loop quantum gravity or string theory deny the fundamental reality of spacetime. Since fundamental spacetime plays an important role in Schaffer's priority monism by being identified with the (...) fundamental structure, namely the cosmos, the disappearance of spacetime in these views might undermine classical priority monism. My second claim is that priority monism can avoid this issue with two moves: first, in dropping one of its core assumptions, namely that the fundamental structure is spatio-temporal, second, by identifying the connection between the non-spatio-temporal structure and the derivative spatio-temporal structure with mereological composition. (shrink)

Recent developments in quantum theory have focused attention on fundamental questions, in particular on whether it might be necessary to modify quantum mechanics to reconcile quantum gravity and general relativity. This book is based on a conference held in Oxford in the spring of 1984 to discuss quantum gravity. It brings together contributors who examine different aspects of the problem, including the experimental support for quantum mechanics, its strange and apparently paradoxical features, its underlying philosophy, and possible modifications (...) to the theory. (shrink)

We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future reference. We find that they all can be classified into five different schemes of which we indicate the advantages and drawbacks.

This work argues that spacetime curvature is not fundamental but emerges as a geometric response to gradients in the density of physical information. Building on the thermodynamic derivation of Einstein's equations and holographic principles, we develop a covariant framework—Information-Gradient Extended Gravity (IGEG)—where an "Informational Tensor" I μ ν I μν ​ , sourced by the gradient of an information density scalar ψ ψ, contributes to the stress-energy. The theory contains General Relativity as the equilibrium limit ( ∇ ψ = (...) 0 ∇ψ=0) and predicts deviations in high-entropy environments: smoothed black hole horizons, singularity-resolution via information bounds, and modified neutron star structure. This provides a unified interpretation: inertia is resistance to changing information configuration; attraction is a tendency toward informational equilibrium. The framework suggests a relational ontology where spacetime is not a substance but a network of informational relationships, offering a potential path to resolve tensions between gravity and quantum mechanics. (shrink)

One of the most challenging and fascinating issue in mathematical and theoretical physics concerns the possibility of identifying the logic underlying the so-called quantum universe, i.e., Quantum Mechanics and Quantum Gravity. Besides the sheer difficulty of the problem, inherent in the actual formulation of Quantum Mechanics—and especially of Quantum Gravity—to be used for such a task, a crucial aspect lies in the identification of the appropriate axiomatic logical proposition calculus to be associated to such theories. In this paper (...) the issue of the validity of the conventional principle of non-contradiction is called into question and is investigated in the context of non-relativistic Quantum Mechanics. In the same framework a modified form of the principle, denoted as 3-way PNC is shown to apply, which relates the axioms of quantum logic with the physical requirements placed by the Heisenberg Indeterminacy Principle. (shrink)

This paper investigates the behavior of conformal fluctuations of space-time geometry that are admissible under the quantized version of Einstein's general relativity. The approach to quantum gravity is via path integrals. It is shown that considerable simplification results when only the conformal degrees of freedom are considered under this scheme, so much so that it is possible to write down a formal kernel in the most general case where the space-time contains arbitrary distributions of particles with no other interaction (...) except gravity. The behavior of this kernel near the classical space-time singularity then shows that quantum fluctuations inevitably diverge near the singularity. It is shown further that the root cause of this divergence lies in the fact that the Green's function for the conformally invariant scalar wave equation diverges at the singularity. The limitations on the validity of classical general relativity near the space-time singularity are discussed and it is argued that the notion of singularity itself needs to be radically modified once the quantum effects are taken into account. (shrink)

Application of recently developed non-Archimedean algebra to a flat and finite universe of total mass M 0 and radius R 0 is described. In this universe, mass m of a body and distance R between two points are bounded from above, i.e., 0≤m≤M 0, 0≤R≤R 0. The universe is characterized by an event horizon at R 0 (there is nothing beyond it, not even space). The radial distance metric is compressed toward horizon, which is shown to cause the phenomenon of (...) red shift. The corresponding modified Minkowski's metric and Lorentz transforms are obtained. Applications to Newtonian gravity shows a weakening at large scales (R→R 0) and a regular behavior as R→0. (shrink)

This study investigates the characteristics of the generalized gravitation equation in a complex spacetime manifold. The newly applied complex spacetime coordinates were designed to integrate peculiar velocity and the receding velocity of the particle into a single coordinate system. On this basis, the Schwarzschild metric solution was extended to a complexified version, and a generalized geodesic equation was derived in the complex spacetime manifold. It was found from the derived gravitation equation that the gravitation interaction depends on the space deceleration (...) parameter \ and can act as a repulsive force in the giant space scale that satisfies \. These results require a rapid expansion of space in the early universe and suggest that the gravitational interactions of matter are fundamentally linked to the space expansion characteristics. (shrink)

This work develops an ontological framework underlying contemporary physical theories, addressing a gap between formal admissibility and physical realization. Modern physics—quantum field theory, special relativity, and general relativity—successfully constrains admissible states, relations, and transitions, yet remains largely silent on how admissible structures become realized physical facts. This paper argues that the limitation is ontological rather than dynamical or epistemic. Two complementary notions are introduced. Structural indifference is the principle according to which physical structure distinguishes roles and invariants, but not the (...) individual identity of the carriers realizing those roles. The coherence operator enforces relational compatibility among admissible roles, ensuring that realized parameter assignments are mutually consistent without fixing absolute numerical values. Together, these notions explain how observable universality can arise without global uniformity of laws or constants. Local variability of parameters becomes compatible with stable structure, while identical observational patterns emerge through coherence and translatability rather than numerical identity. Quantum mechanics is shown to be complete at the level of admissibility but ontologically incomplete with respect to realization. Gravity is interpreted as a global modulator of structural indifference, shaping large-scale regimes of realization without altering quantum formalism. The framework does not modify existing physical theories, introduce new dynamics, or rely on probabilistic selection. Instead, it articulates an ontological layer beneath current formalisms, clarifying why physical description works, how realization occurs, and why identity fixation is unnecessary. (shrink)

Abstract We propose a covariant field-theoretic model in which physical time is a dynamical scalar field, the Time Wave Field (TWF) , coupling to matter via the stress-energy trace and disformal metric modifications. The measured physical time is: where is the metric proper time. We derive the covariant action, field equations, modified geodesics, and constraints from weak-field gravity, atomic clocks, and interferometric measurements. Microscopic fluctuations of generate quantum decoherence, with a variance reproducing the magnitude and structure of the (...) Diósi–Penrose gravitational decoherence. Spatial gradients of ϕ modify the flow of proper time and induce a disformal correction to the metric, yielding an additional attractive force that perturbatively mimics gravitational time dilation and produces Yukawa-like corrections to Newtonian gravity. Crucially, when applied to cosmology, the dynamical nature of physical time modifies the interpretation of cosmic expansion. Cosmological acceleration emerges from the evolution of temporal flow itself rather than from vacuum energy, while phenomena attributed to dark matter arise from temporal inertia and spatial inhomogeneities in clock rates. Large-scale structure formation, gravitational lensing, and the cosmological arrow of time are reinterpreted as consequences of a single dynamical time field. The model yields testable predictions ranging from sub-millimeter deviations from Newtonian gravity to mass-dependent macroscopic quantum decoherence and time-dependent cosmological signatures. -/- Keywords: Time wave Field, Dynamical Scalar Field, Quantum Decoherence, Gravitational Time Dilation, Dark Matter, Dark Energy -/- . (shrink)