On the parity of general mechanics and general relativity, and misconceptions of Einstein’s theory

About a century ago, Albert Einstein realized how the Theory of Newton's Universal Gravitation was inadequate to describe nature and needed to be revised in order to be neatly incorporated into the relativistic scheme with its undesirable instantaneous force shortcomings. Since then we have come to adopt the relativistic high energy tensor theory of General Relativity, which saw its inception into mainstream physics in the year 1916. General Relativity has stood firm against varied tests, such as: gravitational lensing, perihelion of mercury, gravitational time dilation, PSR1913+16 etc, but with the steady advancement of Quantum Mechanics, and its overwhelming experimental success, we are yet again faced with the same problem that was faced a century ago, but this time, the problem is much worse, and the elephant in the room is General Relativity. The fact that General relativity and Quantum mechanics, share different views in the description of space and time or space-time, with quantum mechanics in favor of the latter and general relativity of the former; does not allow one to have a smooth transition from one representation to the other. This automatically implies that for scenarios where both quantum mechanics and gravity / general relativity are required, then that scenario is unsolvable with our current model of physics (hence either General Relativity or Quantum Mechanics is flawed). It becomes clear from the microscopic realm of quantum mechanics and the cosmological problems associated with General Relativity, such as dark energy, dark matter, the inflation force... perhaps a bit closer to home for general relativity being the singularities inherent in its own equations, and the very nature of General Relativity, allowing mostly approximate solutions (reason why most physicist, even today still cling to Newtonian dynamics), because of this and more a new theory of gravity is required – the much anticipated “Quantum Gravity” – just as it was required those many years ago. In the theory that I propose, we will see how from the most basic concepts of quantum mechanics, a theory of gravity can emerge that has the power to not only be mathematically simpler than General Relativity, explain dark energy, dark matter and inflation without any ad-hoc mechanisms, but also have the power to unify all the forces of nature into a single unified theory of everything.

A new relativistic theory of gravity is presented. This theory agrees with all experiments to date. It is a metric theory; it is Lagrangian-based; and it possesses a preferred frame with conformally flat space slices. With an appropriate choice of certain adjustable functions and parameters and of the cosmological model, this theory possesses precisely the same post-Newtonian limit as general relativity.

Quantum Fields on Noncommutative Spacetimes

The Mie‐de Broglie theory of quantum gravity, derived in a previous paper by the author, had a restricted value because it seemed rather disconnected from main stream modern physics, due to the circumstance that both Mie’s and de Broglie’s theories have become “losing” or forgotten theories in the history of physics. But the Mie‐de Broglie QG, incorporating a unification at the level of electrons, atoms and nuclei, is less isolated than it seems. With the use of von Laue’s relativistic tensor dynamics I will connect the Mie‐de Broglie QG to modern physics. A relation derived by Yarman will prove to be a key ingredient. As a result, we claim that one of the basic axioms of General Theory of Relativity, the principle of equivalence, is incompatible with the existence of de Broglie’s wave‐lengths in Quantum Mechanics. So GTR and QM, as based on the wavelength postulate, are non‐unifiable. If we choose de Broglie’s phase harmony as fundamental, a new theory of gravity is needed. The Mie‐Yarman theory of gravity seems to qualify as such.

With the goal of giving evidence for the theoretical consistency of the Hořava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Hořava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant λ. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of λ deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model. There have been a lot of interest about Hořava’s proposal of a new theory of gravity which in principle has a renormalizable quantum version [1] (an important part of the conceptual and technical basis was previously developed in Ref. [2]). To build such a theory, Hořava has proposed to abandon the principle of space-time relativity as a fundamental symmetry of nature, reducing the freedom to perform coordinate transformations to those transformations that preserve some preferred universal time-like foliation. The advantage of this scheme is that one can include higher spatial-derivative terms in the Lagrangian that render the theory renormalizable. According to Hořava’s point of view, jorgebellorin@usb.ve arestu@usb.ve

An exciting time for gravitational wave astronomy

After recalling the coceptual foundations and the vasic sturcture of general relativity, we review some of its main modern developments (apart from cosmology): ( i ) the post-Newtonian limit and weak-field tests in the solar system, (ii) strong gravitationl feelds and black holes, (iii) strong-field and radiative tests in binary pulsar observations, (iv) gravitational waves, (v) general relativity and quantum theory.KeywordsBlack HoleString TheoryNeutron StarGravitational WaveOpen StringThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The post-Newtonian approximation is developed for a new theory of gravity based on a Hermitian metric gμν. The approximation gives Newtonian theory in lowest order, but differs from general relativity in post-Newtonian order. The equations of motion, energy–momentum conservation, and perihelion precession are investigated. The equations of motion are derivable from the conservation laws of the energy–momentum tensor. A multipole expansion of the metric is formulated, and the PPN parameters α, β, and γ are found all to be unity. Several new parameters occur, most notably I, which is related to the number density of fermions of a system.

The wave equation for a scalar field ψ is solved in the background metric of a new theory of gravity, based on a non-Riemannian field structure with a nonsymmetric Hermitian gμν. In contrast to the solution of the problem in a Schwarzschild background metric, in which only orbits close to r ~ 3M yield significant gravitational radiation, the new metric leads to an effective potential with stable orbits for a substantial range of r. The solution yields ψ = (1 − ℓ4/r4)−1/2ψGR where ℓ is a new integration constant. The null surface r = ℓ determines an astrophysical object called a "deflectar", which for ℓ > 2M conceals the Schwarzschild black-hole event horizon at r = 2M. As r → ℓ the gravitational synchrotron radiation increases to infinity. The actual power output of gravitational radiation for physically allowed stable orbits closest to r = ℓ is estimated, demonstrating that a deflectar is a potentially strong source of gravitational radiation.

Einstein’s theory of general relativity has passed all precision tests to date. At some length scale, however, general relativity (GR) must break down and be reconciled with quantum mechanics in a quantum theory of gravity (a beyond-GR theory). Binary black hole mergers probe the non-linear, highly dynamical regime of gravity, and gravitational waves from these systems may contain signatures of such a theory. In this thesis, we seek to make gravitational wave predictions for binary black hole mergers in a beyond-GR theory. These predictions can then be used to perform model-dependent tests of GR with gravitational wave detections. We make predictions using numerical relativity, the practice of precisely numerically solving the equations governing spacetime. This allows us to probe the behavior of a binary black hole system through full inspiral, merger, and ringdown. We choose to work in dynamical Chern-Simons gravity (dCS), a higher-curvature beyond-GR effective field theory that couples spacetime curvature to a scalar field, and has motivations in string theory and loop quantum gravity. In order to obtain a well-posed initial value formalism, we perturb this theory around GR. We compute the leading-order behavior of the dCS scalar field in a binary black hole merger, as well as the leading-order dCS correction to the spacetime metric and hence gravitational radiation. We produce the first numerical relativity beyond-GR waveforms in a higher-curvature theory of gravity. This thesis contains additional results, all of which harness the power of numerical relativity to test GR. We compute black hole shadows in dCS gravity, numerically prove the leading-order stability of rotating black holes in dCS gravity, and lay out a formalism for determining the start time of binary black hole ringdown using information from the strong-field region of a binary black hole simulation.

Shape Dynamics is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity. The most important feature of this theory is the replacement of relativity of simultaneity with a more tractable gauge symmetry, namely invariance under spatial conformal transformations. This book contains both a quick introduction for readers curious about Shape Dynamics and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and an in-depth description of its present status. The book is sufficiently self-contained for an undergrad student with some basic background in General Relativity and Lagrangian/Hamiltonian mechanics. It is intended both as a reference text for students approaching the subject and as a review for researchers interested in the theory.

The 1998 discovery that the universe is accelerating set off an enormous amount of activity, both theoretical and observational. The original result, from two groups observing the Hubble diagram of Type Ia supernovae, has since been verified by a variety of independent types of observations. It seems clear that our universe really is accelerating; what remains a mystery is why.The most straightforward explanation for the universe's acceleration is the presence of a dark energy component comprising 70% of the universe. In order to fit the data, dark energy must have two features: it should be smoothly distributed, so as not to show up in dynamical studies of galaxies and clusters, and its density should be nearly constant as the universe expands, to provide the persistent impulse necessary to make the universe accelerate.The simplest candidate for dark energy is vacuum energy, equivalent to Einstein's cosmological constant. Simple estimates from quantum field theory indicate that vacuum energy should exist – indeed, in an amount larger than what we observe by a factor of 10120. This discrepancy, the 'cosmological constant problem', led to a widespread assumption that some mysterious mechanism worked to set the vacuum energy precisely to zero. If the dark energy really is a cosmological constant, we must find a mechanism to suppress its natural value without driving it all the way to vanishing.Alternatively, the dark energy could be a dynamical field, albeit one that changes very gradually with time. Such a case is observationally distinguishable, at least in principle, from that of a truly constant vacuum energy. Constraints on the evolution of the dark-energy density come from a variety of measurements, and improving the precision of these techniques is a major goal of the next decade in cosmology.Most dramatically, there might not be any dark energy at all, even if the universe is accelerating – a possibility that is well-explored in this focus issue of New Journal of Physics. Two possibilities present themselves. On the one hand, general relativity could break down on cosmological scales, forcing us to a new theory of gravity. In that case, we may use other observed phenomena to put limits on the way in which gravity could deviate from Einstein's theory. On the other hand, general relativity could be correct, but differ in its true predictions from the simple approximations we are used to applying. Such a possibility is both dramatically different from more conventional approaches, and yet radically conservative, attempting to explain all of the accumulated observations with nothing more than matter particles and ordinary general relativity. Only a great deal of additional theoretical investigation and observational progress will be able to distinguish which of these possibilities explains the behaviour of our universe on large scales.The articles below represent the first contributions and further additions will appear.Focus on Dark Energy ContentsCosmic clocks, cosmic variance and cosmic averages David L WiltshireDark energy, a cosmological constant, and type Ia supernovae Lawrence M Krauss, Katherine Jones-Smith and Dragan HutererCosmological dark energy: prospects for a dynamical theory Ignatios Antoniadis, Pawel O Mazur and Emil MottolaPredictive power of strong coupling in theories with large distance modified gravity G Dvali Constraints on dynamical dark energy: an update Alessandro Melchiorri, Barbara Paciello, Paolo Serra and Anze Slosar Scaling solutions to 6D gauged chiral supergravity Andrew Tolley, C P Burgess, Claudia de Rham and D Hoover Modified-source gravity and cosmological structure formation Sean Carroll, I Sawicki, A Silvestri and M Trodden On cosmic acceleration without dark energy E W Kolb, Sabino Matarrese and A Riotto Sean Carroll, California Institute of Technology, Pasadena, USA

The scalar–tensor–vector–gravity (STVG), a prototype of modified gravity developed by Moffat, can correctly explain galaxy rotation curves, cluster dynamics, Bullet Cluster phenomena and cosmological data without invoking the observationally elusive general relativistic (GR) dark matter. Further, recent observations of neutron star masses are shown to defy some GR predictions, whereas STVG turns out to be more consistent with those observations. These successes indicate that STVG could be a potential candidate for a new theory of gravity. However, an important question concerns the possible range of values of the STVG dimensionless parameter [Formula: see text] imposed by various physical scenarios. In the literature, the range [Formula: see text] corresponding to different central source masses has been suggested. We show here that the [Formula: see text] can be considerably constrained into the range [Formula: see text] assuming that the updated GPS fluctuation does not exceed the [Formula: see text]-dependent correction to the terrestrial Sagnac delay.

The combination of Brans and Dicke's idea of a variable gravitational constant with the Higgs-field mechanism of elementary particle physics results in a new theory of gravity. Einstein's theory is realized after symmetry breaking in the neighborhood of the Higgs-fleld ground state.

In this paper we discuss Internal Relativity, a recent program to address the problem of quantum gravity. In our approach we change the relationship between spacetime and matter. Currently we view matter as propagating on spacetime. Einstein’s equations encode how spacetime curves due to the presence of matter and how spacetime, in turn, tells matter how to propagate. In internal realtivity matter and spacetime cease to exist as distinct entities, rather, they arise simultaneously from an underlying quantum system. It is through the emergent matter degrees of freedom that geometry is inferred. We have termed our program Internal Relativity to stress the importance of looking at the system from the point of view of an internal observer. We argue that special relativity is then a natural consequence of this viewpoint. The most important new aspect of Internal Relativity involves how gravity appears. It is not just a new quantum theory of gravity but a new theory of gravity. We also argue that the presence of a massive object implies curvature. In particular we show that Newtonian gravity arises in the appropriate limit. Our argument implies that there is no propagation without gravitation.