Mach argued for a relational rather than an absolute notion of space, insisting that centrifugal forces inside a rotating object such as a bucket can be reproduced by keeping the bucket fixed and rotating the universe. In response to a paper of ours denying the validity of Mach's views, Bhadra and Das elaborate on Mach's position. We address several of their arguments and show that Mach's relational notion of space is wrong-headed. Special and general relativity distinguish between a bucket (i.e. any system) rotating in a fixed universe and a bucket fixed in a rotating universe and between a non-rotating bucket in a non-rotating universe and a co-rotating bucket in a rotating universe, distinctions that go against Mach's relational theory of space. Even when taken on its own terms, Mach's theory can apply only to single point-like buckets rotating at infinitesimal angular velocities.
Starting from the Lovelock action and its supplementation by the relevant Gibbons-Hawking-York boundary term, the curvature action corresponding to second-order General Relativity is stated in accordance to the topological properties of the space-time manifold $\mathcal{M}$ with metric solutions being interpreted as topological solitons. Furthermore, this is shown to arise naturally from a topological interpretation of Mach's principle, with the appropriate manifestation of general covariance. Mach's principle is again invoked to suggest formulations of the curvature action in alternative elli…
Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the case for a `physics first' approach to introducing general relativity to undergraduate physics majors.
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This review presents a comprehensive survey of the various versions of the first law and second law of black hole mechanics in general relativity and beyond. The emphasis is to understand how these laws can constrain the physics beyond general relativity.
We define a new parameter `cumulative drag index' for a particle in circular orbit in a stationary, axisymmetric gravitational field and study its behaviour in the two well known solutions of general relativity {\it viz.}, the Kerr spacetime and the Gödel spacetime, wherein the inertial frame dragging has an important role. As it shows similar behaviour for both co and counter rotating particles, it may indeed be an indication of the influence of the faraway universe on local physics and thus Machian.
This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@physics.umd.edu .
The evolution of black-hole binaries in vacuum spacetimes constitutes the two-body problem in general relativity. The solution of this problem in the framework of the Einstein field equations is a substantially more complex exercise than that of the dynamics of two point masses in Newtonian gravity, but it also presents us with a wealth of new exciting physics. Numerical methods are likely the only method to compute the dynamics of black-hole systems in the fully non-linear regime and have been pursued since the 1960s, culminating in dramatic breakthroughs in 2005. Here we review the methodolo…
Mach's Principle is usually taken to mean that the mass of a particle as measured locally is determined in some way by the other matter in the universe. This is difficult to formalize in 4D,but is feasible in 5D if the scalar potential of non-compactified Kaluza-Klein theory is interpreted as an inertial field. We therefore review 5D space-time-matter theory, but take the local particle mass to be defined by the integral of a global scalar field. This approach smoothly embeds general relativity, and leads to several new effects which can be tested.
Mach's principle is surely one of those tantalizingly beautiful concepts in physics which remain elusive. Though General Relativity (GR) was conceived in the spirit of realizing it, the theory failed to fulfill this expectation. Here a study on the implications of imposing Mach's principle on GR with an insight that spacetime has no independent existence without a material background, is presented. This inclusion of the principle in GR turns out to be unexpectedly rewarding. The resulting theory solves many mysteries and averts lingering problems of the conventional forms of GR and cosmology.
Frank Wilczek's essay "Total Relativity: Mach 2004" (PHYSICS TODAY April, 2004, p. 10) cogently updates the status of the intuitively compelling, but partly unrealized, theory of Mach's Principle. I think, however, that an important consequence of the Principle has been skipped: that is, the possibility of linear deformations of the internal structure of elementary particles from the Minkowski structure imposed by the local gravitational (metric) field. [Note: This Comment is similar to one submitted to, but not published by, PHYSICS TODAY as a Letter to the Editor.]
Mach Principle presents the absolute universe. For example, when Einstein stood on the ground and relaxed, his arms fell down naturally. However, if he rotated his body then his arms were lifted up as the rotation was faster and faster. Mach principle is that the matter of the whole universe can affect local dynamic systems. That is, the matter of the whole universe sets up the local absolute reference frames. However, Einstein's general theory of relativity is against the absolute reference frames of Mach Principle.
We argue that space-time geometry is not absolute with respect to the frame of reference being used. The space-time metric differential form $ds$ in noninertial frames of reference (NIFR) is caused by the properties of the used frames in accordance with the Berkley - Leibnitz - Mach - Poincaré ideas about relativity of space and time . It is shown that the Sagnac effect and the existence of inertial forces in NIFR can be considered from this point of view. An experimental test is proposed.
In their recent "Mach's principle and higher-dimensional dynamics", Mashhoon and Wesson argue that Mach's principle is not properly incorporated into general relativity and that in Einstein's theory "the origin of inertia remains essentially the same as in Newtonian physics." While it is true that the motion of a single test particle in a Newtonian inertial frame of reference appears essentially the same as in an Einsteinian local inertial frame, this misses the point. The issue is not what motion looks like in an inertial frame of reference but what is the origin of the inertial frame. Unlike…
Machs principle and the principle of relativity have been discussed by H. I. Hartman and C. Nissim-Sabat in this journal. Several phenomena were said to violate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenon of inertial dragging been invoked, and no calculation have been offered by either side to substantiate their claims. Here I discuss the possible validity of the principle of relativity for rotating motion within the context of the general theory of relativit…
Mach's principle fits into the wider "relational principle", advocating that not only inertia, but also space and time emerge from the interaction of matter. Concepts of a Machian/relational theory are proposed, where inertia and energy are defined as mutual properties between pairs of objects. Due to Berkeley, only radial motion represents kinetic energy between (point) masses, which is the basis of anisotropic inertia, which in turn underlies the relational principle. The Newtonian definition of potential energy is considered a model for Machian inertia, leading to a frame independent defini…
General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints. These constraints can be thought of as a way of imposing temporal and spatial relationalism. The same type of constraints can be used in non-relativistic particle models to produce relational theories that suffer from the same Problem of Time as that encountered in General Relativity. As a result, these simple toy models are well suited for studying the Problem of Time in quantum gravity. In this paper, a version of these particle models is…
We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass …
Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine learning has not been given much awareness to. This work is a hybrid of physics and machine learning where concepts of physics are used in machine learning. We propose the supervised Gravitational Dimensionality Reduction (GDR) algorithm where the data points of every class are moved to each other for reduction of intra-class variances and better separation of classes. For every data point, the other points are cons…
A study of kinematics of a 2-body system is used to show that the Mach principle, previously rejected by general relativity, can still serve as an alternative to the concept of absolute space, if one takes into account that the background of distant stars (galaxies) determines {\it both} the inertial and the gravitational masses of a body.
Observations of an apparent acceleration in the expansion rate of the universe, derived from measurements of high-redshift supernovae, have been used to support the hypothesis that the universe is permeated by some form of dark energy. We show that an alternative cosmological model, based on a linearly expanding universe with Omega=1, can fully account for these observations. This model is also able to resolve the other problems associated with the standard Big Bang model. A scale-invariant form of the field equations of General Relativity is postulated, based on the replacement of the Newtoni…
A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational terms. A new formulation of the relativity principle based on Poincare's analysis of the problem of absolute and relative motion (Mach's principle) is given. The enire dynamics is based on shape and nothing else. It leads to much stronger predictions than standard Newtonian theory. For the dynamics of Riemannian 3-geometries on which matter fields also evolve,…
Barbour's response to our recent paper on "Mach's principle and higher-dimensional dynamics" describes an approach to Mach's principle in which the universe as a whole is involved in the definition of inertial frames of reference. Moreover, Barbour's theoretical procedure is in agreement with general relativity for a finite universe that is spatially closed. However, we prefer an operational approach that relies ultimately on observational data.
We consider the fact that noticing on the operational meaning of the physical concepts played an impetus role in the appearance of general relativity (GR). Thus, we have paid more attention to the operational definition of the gravitational coupling constant in this theory as a dimensional constant which is gained through an experiment. However, as all available experiments just provide the value of this constant locally, this coupling constant can operationally be meaningful only in a local area. Regarding this point, to obtain an extension of GR for the large scale, we replace it by a confor…
In this paper we develop a formalism which models all massive particles as travelling at the speed of light(c). This is done by completing the 3-velocity v of a test particle to the speed of light by adding an auxiliary 3-velocity component z for the particle. According to the observations and laws of physics defined in our spacetime these vectors are generalized to domains and then two methods are developed to define c domain in terms of our spacetime(v domain). By using these methods the formalism is applied on relativistic quantum theory and general theory of relativity. From these, the rel…
Hartman and Nissim-Sabat have argued that Mach's idea of the relativity of rotational motion suffers from internal inconsistencies and leads to a contradiction that there cannot be a stationary bucket in a rotating universe. They also claimed that non-inertial electromagnetic and stellar aberration observations can distinguish between a rotating and a stationary universe, whereas according to Mach there cannot be any observable way to distinguish these two cases. We contest these objections.
The main aim of this paper is to extend the early approach to quantum cosmogenesis provided by Fomin. His approach was developed independently to the well-known Tryon description of the creation of the closed universe as a process of quantum fluctuation of vacuum. We apply the Fomin concept to derive the cosmological observables. We argue that Fomin's idea from his 1973 work, in contrast to Tryon's one has impact on the current Universe models and the proposed extension of his theory now can be tested by distant supernovae SNIa. Fomin's idea of the creation of the Universe is based on the inte…
The equivalence principle is the conceptual basis for general relativity. In contrast Mach's principle, although said to have been influential on Einstein in his formulation of general relativity, has not been shown to be central to the structure of general relativity. In this essay we suggest that the quantum effects of Hawking and Unruh radiation are a manifestation of a {\it thermal} Mach's principle, where the local thermodynamic properties of the system are determined by the non-local structure of the quantum fields which determine the vacuum of a given spacetime. By comparing Hawking and…
Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from experimental space gravitation to atomic and particle physics. After a reformulation of special relativistic physics in a form taking into account the non-dynamical chrono-geometrical structure of Minkowski space-time (parametrized Minkowski theories and rest-frame instant form) and in particular the conventionality of simultaneity (re-phrased as a gauge freedom), a …
The analyses of high precision astrometric surveys, such as Gaia, implicitly assume a modern version of Mach's Principle: the local inertial frame of our Solar System should be non-rotating in the frame of distant quasars. On the contrary, Einstein's General Relativity allows a rotating universe. Thus, relaxing the assumption of Mach's Principle will allow placing a constraint on a class of rotating cosmologies by comparing high precision astrometry of quasars with well-measured solar system orbits. Constraining global rotation will test General Relativity, inflation, and the isotropy of cosmo…
We use a particular machine learning approach, called the genetic algorithms (GA), in order to place constraints on deviations from general relativity (GR) via a possible evolution of Newton's constant $μ\equiv G_\mathrm{eff}/G_\mathrm{N}$ and of the dark energy anisotropic stress $η$, both defined to be equal to one in GR. Specifically, we use a plethora of background and linear-order perturbations data, such as type Ia supernovae, baryon acoustic oscillations, cosmic chronometers, redshift space distortions and $E_g$ data. We find that although the GA is affected by the lower quality of the …
Einstein regarded as one of the triumphs of his 1915 theory of gravity --- the general theory of relativity --- that it vindicated the action--reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the w…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational interaction on local physics. A reanalysis of the situation suggests that all relativistic effects that are presently attributed to kinematics of relative motion in flat space-time are in fact gravitational effects of the nearly homogeneous and isotropic Universe. The correct theory of relativity is the one with a preferred cosmic rest frame. Yet, the theory pre…
We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a coordinate system or induced by the curvature of spacetime, and (ii) computer visualizations which bring out the alien features of the Goedel Universe. In order to keep the paper self-contained, we summarize in several appendices crucial ingredients of the mathematical tools used in general relativity. In this way, our lecture notes should be accessible to re…
The basic principles of General Theory of Relativity historically have been tested in gedanken experiments in rotating frame of references. One of the key issues, which still evokes a lot of controversy, is the centrifugal acceleration. Machabeli & Rogava (1994) argued that centrifugal acceleration reverse direction for particles moving radially with relativistic velocities within a "bead on a wire" approximation. We show that this result is frame-dependent and reflects a special relativistic dilution of time (as correctly argued by de Felice (1995)) and is analogous to freezing of motion on t…
Binary neutron star mergers with SPHINCS_BSSN: temperature-dependent equations of state and damping of constraint violations
Hamburger Sternwarte（汉堡天文台）；The Oskar Klein Centre, Department of Astronomy, Stockholm University（斯德哥尔摩大学奥斯卡·克莱因中心天文学系）；Center for Computation & Technology, Louisiana State University（路易斯安那州立大学计算与技术中心）；Department of Physics & Astronomy, Louisiana State University（路易斯安那州立大学物理与天文学系）
