What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920s-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is _algebraic_ in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only (...) indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity: matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities---indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity. The Putnam-Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th-21st century space-time philosophy in the light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the 'universal force' influencing the causal structure. Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space-time theory that would have blocked Moritz Schlick's supposed refutation of synthetic _a priori_ knowledge, and how Einstein's false analogy between the Neumann-Seeliger-Einstein modification of Newtonian gravity and the cosmological constant \Lambda generated lasting confusion that obscured massive gravity as a conceptual possibility. (shrink)

This article reflects on the received view of the rupture which constitutes the beginning of a critical, ethical, political and legal opening, the understanding of which inhabits the cry of, and response to, injustice. It takes the very critique that feeds into, and is distorted by, practical reasoning, as its point of departure. Grasping this rupture as the complementary relation between deconstruction and radical alterity, would entail unreflectively accepting a certain kind of truthfulness—truthfulness as [in]correctness, manifesting in a relationship that (...) involves rootless and controlling movement of making and unmaking of world. In closely reading Wittgenstein and Heidegger on the level of seeing, showing and saying, truthfulness is shown to contain an essential tension between, on the one hand, the Socratic, metaphysically-bound notion of beingness, correctness and meaning-steering and, on the other hand, the pre-Socratic notion of unconcealment (a-lethia), which, pointing even earlier than pre-Socratics into aboriginality, involves attentive letting of gliding in the inexpressible saying of language. While steering is about generating new possibilities of expressibility, gliding is about poetic dwelling, or enduring inexpressibility as a constitutive part of saying. Although aletheia is taken to be the key influence on rootless post-foundational thinking, it is argued that unconcealment involves letting and enduring the presencing inexpressibility of place and home-coming, that is, worlding-rootedness; thus showing Heidegger’s originary politics as the district of the uncanny to be about worlding that attentively lets the presencing inexpressibility of earth be as place. In reading Heidegger’s views on humanism, beginning and language, the argument links inexpressibility—essentially and historically—to the grasping of the belongingness together of world, earth and place, viewing this belongingness as key to both the saying of art and of mortals dwelling together temporally, spatially, materially in a manner always strange to, and nearer than, the steering/controlling of beingness, time, space and place that the very gesture and emergence of critique is captive of and is not capable of attuning to and capturing. Art always estranges the metaphysical cycle of correctness which preserves pain and suffering—a cycle that inhabits a double bind of responding to violence and injustice generated by the violence of metaphysics with metaphysical violence and justice. In showing essential strife within truthfulness itself, Heidegger points to even greater and earlier problematic than the pre-Socratics—to the painful core of inexpressibility between the ontology of steering time, spaces and material—steering places—and the gliding temporality, spatiality and materiality of ontology of place. (shrink)

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself (...) increases in entropy, and that (iii) the Second Law of thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse. (shrink)

It is here argued that Halley's comet had a more pivotal role than has hitherto been believed in triggering Newton's acceptance of the law of gravity, dispelling his belief in Descartes' theory of vortices. It is found that historians have been unduly prone to credit Newton with dynamical insights at an earlier date than is warranted by the historical documents. A more convincing account of the transition from the period of Newton's alchemical researches of the 1670s to that of (...) his dynamical insights in the 1680s thereby becomes feasible. Acceptance of a principle of rectilinear inertia was a precondition for formulating the law. (shrink)

Euler’s interpretation of Newton’s gravity (NG) as Archimedes’ thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler’s, is recalled and compared with the latter. None of these two ‘‘gravitational ethers’’ can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a (...) compressible ether leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newton’s second law. The observational status for the theory with the older version of the correspondence is summarized. (shrink)

All of us had fallen from 100 stories.Falling is rarely a good thing. It is something to avoid for safety, and such avoidance, for those of us fortunate enough to be in good health, has been burned into the unconscious memory of our muscles and bones. Unless we find ourselves in high places, or on some kind of precipice, falling tends not to be on the mind. It is, most of the time, a surprise.But it is also always a possibility, (...) in part because of one of those characteristics that define the human—our upright posture. Without this trait that. (shrink)

This paper is a study of the consequences that follow from modeling a nonlinear and nonrelativistic quantum theory for gravitating particles. At present there exists no relativistic generalizations that do not sacrifice certain assumptions which are standard in covariant field theories.

A closer examination of scientific practice has cast doubt recently on the thesis that observation necessarily fails to determine theory. In some cases scientists derive fundamental hypotheses from phenomena and general background knowledge by means of demonstrative induction. This note argues that it is wrong to interpret such an argument as providing inductive support for the conclusion, e.g. by eliminating rival hypotheses. The examination of the deduction of the inverse square law of gravitation due to J. Bertrand, and R. Fowler's (...) deduction of the quantization of the linear harmonic oscillator's energy spectrum from Planck's radiation law illustrates this point. It is suggested that demonstrative induction is a computational step in fitting a theoretical model and a set of phenomena, with little direct confirmational impact. The thesis of underdetermination, whatever one may think of it, is not threatened by demonstrative induction. (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)

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)

The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a quantum theory of space-time and therefore focus on loop quantum gravity. We conceive atoms of space, represented in terms of nodes linked by edges in a graph, as the primitive ontology of the theory and show how a non-local law (...) in which a universal and stationary wave-function figures can provide an order of configurations of such atoms of space such that the classical space-time of general relativity is approximated. Although there is as yet no fully worked out physical theory of quantum gravity, we regard the Bohmian approach as setting up a standard that proposals for a serious ontology in this field should meet and as opening up a route for fruitful physical and mathematical investigations. (shrink)

Comparativism—the view that mass ratios are not grounded in absolute masses—faces a challenge by Baker which suggests that absolute masses are empirically meaningful. Regularity comparativism uses a liberalized version of the Mill-Ramsey-Lewis Best Systems Account to have both the laws of Newtonian gravity and the absolute mass scale supervene on a comparativist Humean mosaic as a package deal. I discuss three objections to this view and conclude that it is untenable. The most severe problem is that once we have (...) reduced away the absolute masses, there is nothing that stops us from also reducing the mass ratios. (shrink)

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second-order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's law of gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted (but actually still open to question) assumptions which go into the formulation (...) of the standard second-order Einstein theory in the first place. In particular, we show that while the familiar second-order Poisson gravitational equation (and accordingly its second-order covariant Einstein generalization) may be sufficient to yield Newton's law of gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth-order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved nonluminous or dark matter. (shrink)

It can seem obvious that we live in a world governed by laws of nature, yet it was not until the seventeenth century that the concept of a law came to the fore. Ever since, it has been attended by controversy: what does it mean to say that Boyle's law governs the expansion of a gas, or that the planets obey the law of gravity? Laws are rules that permit calculations and predictions. What does the universe have to be (...) like, if it is to play by them? This book sorts the most prominent answers into three families. Laws first arose in a theological context; they govern events only because God enforces them. Those wishing to reverse the order of explanation, and argue that the powers of objects fix the laws, struggled to claim for themselves the results of new science. The stand-off between these two families bred a third which rejects any kind of enforcer for the laws. On this view, laws summarize events; they do not govern anything. This book traces the fortunes of the three families, from their origins to the present day. It uses objections - and the revisions needed to answer them - to produce the best representative of each. Along the way, it tries to settle the rules of this game, the debate over laws of nature. What should we expect from an account of laws? The book aims to help readers develop their own desiderata and judge the merits of the competing positions. (shrink)

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the law (...) of motion of test particles. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity in some sense relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a (...) space-time coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the “multiverse” picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order (...) to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the “observer dependence” of horizons/spacetime—these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincaré transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics—it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time coordinate (...) system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

'Holographic' relations between theories have become a main theme in quantum gravity research. These relations entail that a theory without gravity is equivalent to a gravitational theory with an extra spatial dimension. The idea of holography was first proposed in 1993 by Gerard 't Hooft on the basis of his studies of evaporating black holes. Soon afterwards the holographic 'AdS/CFT' duality was introduced, which since has been heavily studied in the string theory community and beyond. Recently, Erik Verlinde (...) has proposed that even Newton's law of gravitation can be related holographically to the thermodynamics of information on screens. We discuss inter-theoretical relations in these scenarios: what is the status of the holographic relation in them and in what sense is gravity, or spacetime, emergent? (shrink)

It has been argued within some philosophy of quantum gravity circles that endorsing Lewisian modal metaphysics is incompatible with endorsing the fundamental physical ontology of any quantum gravity theory. Speaking concisely, the unsolvable tension would be between Lewis' metaphysical commitment to the fundamentality of space and time, and the physical lesson of quantum gravity about the disappearance of space and time from the fundamental structure of the world. In this essay I argue against the idea that the (...) tension is unsolvable. The analysis does not apply to quantum gravity in general, but only to the specific perspective delivered by quantum string theory. In the first two sections I describe what I think is the general formal payoff of Lewisian possible worlds semantics, and more importantly the general metaphysical payoff generated by some Lewisian metaphysical applications of that formal framework. Lewisian possible worlds semantics is not among the topics of this essay, still a concise presentation of its basic features is required for a more accurate description of the type of modal metaphysics Lewis delivers by applying that formal machinery. The moral of the story in the first two sections is that an attempt of preserving crucial features of Lewisian modal metaphysics, although endorsing the quantum string theory lesson on spacetime non fundamentality, would be not only possible, but also philosophically worthy in a general sense. Then, section three is divided in three parts. In the first part I summarize some formal tools of the methodology used elsewhere - (Vistarini, Routledge, 2019, chapter 6)- to argue for string theory background independence. More precisely, I briefly re-describe some crucial features of a topological-vector bundle structure there defined on a "space" associated to the theory. Such structure is there shown to carry physical and dynamical information about quantum strings systems supporting the thesis of background independence of quantum strings laws (string theory background independence is not a topic of this essay, and the construction of the full formal structure as well as the full argumentative line can be found in the work cited above). The rationale behind the choice of including these formal tools is explained in the second and third parts of section three: that very same topological-fiber bundle structure associated to string theory, if read differently, is shown to also carry structural properties of the Lewisian metaphysical scheme. More precisely, in the second part of section three I attempt to show that such topological-fiber bundle structure owns a topology which qualifies as a plausible accessibility structure extending the Lewisian similarity accessibility. To avoid confusion, I will denote the extended similarity order with S*, or S*-similarity. The latter has some interesting properties. It is quantitatively describable, and even more interestingly its spectrum of variation is a countable one. Then, insofar Lewisian similarity order can be regained from the S*-similarity, one might say that the latter is a metaphysical accessibility relation underlying the former because "more fundamental". As we will see, the explanation of what "more fundamental" means in this metaphysical context mainly involves the idea that the formal nature of S*-similarity, in particular its property of having a countable spectrum of variation, calibrates a metaphysical similarity that reflects the discreteness of the fundamental quantum nature of reality. The extended modal metaphysics with accessibility structure S*-similarity is informed by quantum string physics. Within the extended scheme, the Lewisian claim "things could have been different in countless ways" (Lewis 1973) is an approximate one because only permitted by ordinary language. As soon as one refines the accessibility structure by using the formal language of quantum string theory, it appears things could have been different in countable ways. But the Lewisian variety of alternative states of affairs can be regained from the underlying countable variety via a specific interpretation of the Humean supervenience thesis, one that changes the metaphysical status of the thesis' content and restricts the thesis' domain of application. Finally, in the third part of section three I attempt to show that the same topological-fiber bundle structure used to extend Lewisian similarity has a bundle component producing the formal scheme for a tentative extension of Lewisian nomological accessibility through the lens of string dualities. This will prove to be a non trivial task, and the Lewisian accessibility structure will be regained from the extended one only partially. Finally, the essay contains two short appendices summarizing two argumentative lines outside the main topic of the essay. They briefly describe different ways in which the non fundamentality of spatiotemporal structures can be found in quantum string theory. These sections can be skipped. Nevertheless, they might contribute to understand more robustly the general view endorsed by this essay, i.e. that there isn't any unsolvable tension between Lewis' commitment to the fundamentality of spatiotemporal relations and quantum gravity's lesson about their non fundamentality. -/- . (shrink)

A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as (...) the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined. (shrink)

An analysis of the concept of law, its source and connection with human positive law. The article begins by noting that “law” relates not only to prescriptions governing the behavior of human individuals. The term has a far wider sense. It can also refer to a standard or rule that binds things or events. This sense of the term covers the laws of the physical as well as the moral sciences. There is a distinction to be drawn between scientific laws (...) of nature and moral laws. Regularities in natural occurrences are often regarded as laws of nature even though what we ordinarily think of as laws are those rules that govern human behavior. We speak, for example, of the “law” of gravity and of Newton's, Einstein's, and Kepler's laws. In so doing we emphasize the regularity and binding nature implicit in each of their formulas. The thought that there are laws of the natural sciences as well as moral laws has traditionally been seen as implying a creator and regulator of all things, and an eternal source of these laws. Equally it raises the disputed question of the place of miracles, or those suspensions of regularities, in the natural scheme of things. In the same way, sacred scripture speaks of Divine Wisdom as directing all actions and movements. This article considers the physical and moral laws more generally and considers human law and its connection with the natural law. (shrink)

Quantum gravity’s suggestion that spacetime may be emergent and so only exist contingently would force a radical reconception of extant analyses of laws of nature. Humeanism presupposes a spatiotemporal mosaic of particular matters of fact on which laws supervene; primitivism and dispositionalism conceive of the action of primitive laws or of dispositions as a process of ‘nomic production’ unfolding over time. We show how the Humean supervenience basis of non-modal facts and primitivist or dispositionalist accounts of nomic production can (...) be reconceived, avoiding a reliance on fundamental spacetime. However, it is unclear that naturalistic forms of Humeanism can maintain their commitment to there being no necessary connections among distinct entities. Furthermore, non-temporal conceptions of production render this central concept more elusive than before. In fact, the challenges run so deep that the survival of the investigated analyses into the era of quantum gravity is questionable. (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)

We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7’ of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar’s radio wave is equivalent to comparison of the relativistic laws of the (...) Lorentz transformation for gravity and light. Because, according to Einstein, the Lorentz transformation of gravity field variables must depend on a fundamental speed c, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. In particular, the v/c term beyond of the standard Einstein’s deflection, which we measured to 20% accuracy, is associated with the aberration of the null direction of the gravity force (“aberration of gravity”) caused by the Lorentz transformation of the Christoffel symbols from the static frame of Jupiter to the moving frame of observer. General relativistic formulation of the experiment identifies the aberration of gravity with the retardation of gravity because the speed of gravitational waves in Einstein’s theory is equal to the speed of propagation of the gravity force. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual–Sánchez, and Carlip and show that their “speed of light” interpretations confuse the Lorentz transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar. For this reason, the “speed of light” interpretations are not entirely consistent with a retarded Liénard–Wiechert solution of the Einstein equations, and do not properly incorporate how the phase of the radio waves from the quasar is perturbed by the retarded gravitational field of Jupiter. Although all of the formulations predict the same deflection to the order of v/c, our formulation shows that the underlying cause of this deflection term is associated with the aberration of gravity and not of light, and that the interpretations predict different deflections at higher orders of v/c beyond the Shapiro delay, thus, making their measurement highly desirable for deeper testing of general relativity in future astrometric experiments like Gaia, SIM, and SKA. (shrink)

This article investigates the relationship between Hume’s causal philosophy and Newton ’s philosophy of nature. I claim that Newton ’s experimentalist methodology in gravity research is an important background for understanding Hume’s conception of causality: Hume sees the relation of cause and effect as not being founded on a priori reasoning, similar to the way that Newton criticized non - empirical hypotheses about the properties of gravity. However, according to Hume’s criteria of causal inference, the law of universal (...) gravitation is not a complete causal law, since it does not include a reference either to contiguity or to temporal priority. It is still argued that because of the empirical success of Newton ’s theory—the law is a statement of an exceptionless repetition—Hume gives his support to it in interpreting gravity force instrumentally as if it bore a causal relation to motion. (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)

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)

The domains of quantum theory and general relativity overlap in situations where quantum mechanical effects cannot be ignored. In order to deal with this overlap of theoretical domains, there has been a tendency to apply the rules of quantum field theory to the classical gravitational field equations and without much regard for the implications of the whole enterprise. The gravitational version of the asymmetric ageing of identical biological specimens shows that curved spacetime is not dispensable. This result is used to (...) conclude that the particle-based interpretations of quantum gravity are not acceptable. (shrink)

Newton’s argument for universal gravitation in the Principia eventually rested on the third “Rule of Philosophizing,” which warrants the generalization of “qualities of bodies.” An analysis of the rule and the history of its development indicate that the term ‘quality’ should be taken to include both inherent properties of bodies and relations among systems of bodies, generalized into `laws'. By incorporating law‐induction into the rule, Newton could legitimately rebuff objections to his theory by claiming that universal gravitation was justified by (...) his method even if he could not specify the cause of gravity . †To contact the author, please write to: Department of Philosophy, Duke University, 201 West Duke Building, Box 90743, Durham, NC 27708; e‐mail: [email protected]. (shrink)

Science is at a cross-roads. For several decades, the Standard Model of particle physics has managed to fit vast amounts of particle scattering data remarkably well, but many questions remain. During those decades, some sophisticated theoretical hypotheses such as string theory, quantum gravity, and quantum cosmology have been proposed and studied intensively, in an effort to break the log-jam of the Standard Model. None of those hypotheses have succeeded to date. Of greater concern is the increasing tendency by some (...) practitioners in those fields to downplay the empirical principles of science. In response, this book is a restatement of those principles, covering numerous aspects of observation. A particular focus is on contextuality versus realism, the two fundamentally contrasting ideologies that underpin modern physics. (shrink)

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a (...) time machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently "potent" to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident "yes" has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

We investigate the evolution of linear density contrasts obtained with respect to a homogeneous spatially flat Friedman-Lemaître–Robertson–Walker background by solving the density contrast equations governed by Newtonian and MONDian force laws using symmetry-based approach. We find eight-parameter Lie group symmetries for the linear order density perturbation equation for the Newtonian case whereas the density contrast equation follows only one parameter Lie group symmetry in MONDian case. We use Lie symmetries to find the group invariant solutions from invariant curve condition. The (...) physical features of the evolution for various mode of density contrast with respect to the global cosmic background density in homogeneous isotropic cosmological models have been investigated using analytical group invariant solutions along with their numerical solutions. An account for cosmological density contrast and mass fluctuation also have been provided. We also have shown that the MONDian force law generates higher amplitudes in the density fluctuation, results in a more rapid structure formation that cannot be possible under the Newtonian force law. (shrink)

The central problem of the article is the paradox in the history of Newton’s mechanics: prominent researchers of the genesis of the Principia did not believe Newton’s words about the origin of the idea of universal gravity. They did not believe that he could have come up with this idea as early as 1666, considering circular orbits, and believed that Newton invented the story of the falling apple. The article proposes a “subjunctive” scenario leading to the law of universal (...) gravity and feasible at the level of Galileo’s knowledge and skills in 1611. The basis for such a scenario is the description of a thought experiment in Newton’s manuscript “The System of the World”, preceding the creation of Principia. The proposed reconstruction helps to consider and clarify the concept of “modern physics”, the birth of which was the main event of the Scientific Revolution of the XVI–XVII centuries. The traditional understanding reduces the essence of modern physics to a reliance on experience and on the language of mathematics. Such a definition, however, is not sufficient. The geometry of Euclid and the physics of Archimedes were mathematically perfect, and their axioms were based on objective experience. Despite the importance of the tools of mathematics and experiment, the key innovation of modern physics has become the belief in the hidden fundamental laws of the Universe and in the right of the researcher to invent invisible, “illogical”, “absurd” concepts and postulates, experimentally verifiable only together with the theory based on them. This postulate of fundamental cognitive optimism combines bold ingenuity with a humble need for empirical verification. (shrink)

We provide a suitable theoretical foundation for the notion of the quantum coherent state which describes the electrostatic field due to a static external macroscopic charge distribution introduced by the author in 1998 and use it to rederive the formulae obtained in 1998 for the inner product of a pair of such states. (We also correct an incorrect factor of 4π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\pi$$\end{document} in some of those formulae.) Contrary to what one might expect, (...) this inner product is usually non-zero whenever the total charges of the two charge distributions are equal, even if the charge distributions themselves are different. We actually display two different frameworks that lead to the same inner-product formulae, in the second of which Gauss’s law only holds in expectation value. We propose an experiment capable of ruling out the latter framework. We then address the problem of finding a product picture for QED—i.e. a reformulation in which it has a total Hamiltonian, arising as a sum of a free electromagnetic Hamiltonian, a free charged-matter Hamiltonian and an interaction term, acting on a Hilbert space which is a subspace (the physical subspace) of the full tensor product of a charged-matter Hilbert space and an electromagnetic-field Hilbert space. (The traditional Coulomb gauge formulation of QED isn’t a product picture in this sense because, in it, the longitudinal part of the electric field is a function of the charged matter operators.) Motivated by the first framework for our coherent-state construction, we find such a product picture and exhibit its equivalence with Coulomb gauge QED both for a charged Dirac field and also for a system of non-relativistic charged balls. For each of these systems, in all states in the physical subspace (including the vacuum in the case of the Dirac field) the charged matter is entangled with longitudinal photons and Gauss’s law holds as an operator equation; albeit the electric field operator (and therefore also the full Hamiltonian) while self-adjoint on the physical subspace, fails to be self-adjoint on the full tensor-product Hilbert space. The inner products of our electrostatic coherent states and the product picture for QED are relevant as analogues to quantities that play a rôle in the author’s matter-gravity entanglement hypothesis. Also, the product picture provides a temporal gauge quantization of QED which appears to be free from the difficulties which plagued previous approaches to temporal-gauge quantization. (shrink)

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...) machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

The second law results in the growth of the entropy – in superficial interpretation this principle presumes that the sufficient energy inevitably turns into the substandard energy. Order turns into chaos over time; however, chaos also turns into order under certain circumstances. The first research objective is to establish the possible prescientific ideas about the phenomenon – some philosophical intuitions that have preceded the scientific discovery of the second law and have conformed to it in a certain sense. It is (...) essential because there are always certain bonds and continuity in the history of philosophy and science – the correct interpretation of the phenomenon becomes difficult, if not impossible, without the establishment of such bonds.Moreover, the main task is to understand what the second law is and which significance its principal corollaries have. We need to give the second law a correct interpretation that will allow making assumptions about its connection with time in the context of the initial state problem and about the possible new ways of modern physics development – in particular, the creation of the quantum theory of gravity. Two solutions to the entropy and initial state connection problem are proposed in the context of the time arrow discussion (G. Calender’s approach to solving the problem is disputed). (shrink)

We review studies on catching that reveal internalization of physics for action control. In catching free-falling balls, an internal model of gravity is used by the brain to time anticipatory muscle activation, modulation of reflex responses, and tuning of limb impedance. An internal model of the expected momentum of the ball at impact is used to scale the amplitude of anticipatory muscle activity. [Barlow; Hecht; Shepard].

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work (...) relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical properties even (...) for a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier. (shrink)

In the ten years following the publication of Galileo Galilei's Discorsi e dimostrazioni matematiche intorno a due nuove scienze , the new science of motion was intensely debated in Italy, France and northern Europe. Although Galileo's theories were interpreted and reworked in a variety of ways, it is possible to identify some crucial issues on which the attention of natural philosophers converged, namely the possibility of complementing Galileo's theory of natural acceleration with a physical explanation of gravity; the legitimacy (...) of Galileo's methods of proof and of his theory of the composition of continuous magnitudes; and the adequacy of the experimental evidence in favor of his theory.Through his published works and his correspondence, Marin Mersenne contributed in a significant way to each of these discussions. In the following, I shall provide a sketch of Mersenne's multiple engagement with the new science of motion, while trying to account for his growing skepticism concerning Galileo's law of free fall. Whereas in the 1630s, Mersenne still firmly believed in the validity of this law and tried to devise experimental and mathematical proofs in its favor, in the 1640s he developed serious doubts regarding the possibility of constructing an exact science of motion. As we shall see, Mersenne's evolving attitude sheds an interesting light on his views concerning the relation between physics and mathematics.---------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ----------------------------------------------------. (shrink)

The following is the second part of our Archaeology of the Inverse Square Law. Together these papers examine the transformation of the inverse square ratio from its origins in a metaphysical image of medieval thought in Grosseteste and the perspectivist tradition, through a playful magical practice in the Renaissance with Cusanus and Dee, and into a mathematical tool, applicable to the physical world. This last transformation allowed Newton to condense the geometrical image into a celebrated algebraic equation for universal (...) class='Hi'>gravity, but it proved particularly confusing for the people who wrought it, Kepler and Hooke. (shrink)