Kinematics in matrix gravity

We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a new kind of geometry, which is equivalent to a collection of Finsler geometries with several Finsler metrics depending both on the position and on the velocity. As a result the Riemannian geodesic flow is replaced by a collection of Finsler flows. This naturally leads to a model in which a particle is described by several mass parameters. If these mass parameters are different then the equivalence principle is violated. In the non-relativistic limit this also leads to corrections to the Newton’s gravitational potential. We find the first and second order corrections to the usual Riemannian geodesic flow and evaluate the anomalous nongeodesic acceleration in a particular case of static spherically symmetric background.     

Operational definition of (brane-induced) space–time and constraints on the fundamental parameters

First we contemplate the operational definition of space–time in four dimensions in light of basic principles of quantum mechanics and general relativity and consider some of its phenomenological consequences. The quantum gravitational fluctuations of the background metric that comes through the operational definition of space–time are controlled by the Planck scale and are therefore strongly suppressed. Then we extend our analysis to the braneworld setup with low fundamental scale of gravity. It is observed that in this case the quantum gravitational fluctuations on the brane may become unacceptably large. The magnification of fluctuations is not linked directly to the low quantum gravity scale but rather to the higher-dimensional modification of Newton's inverse square law at relatively large distances. For models with compact extra dimensions the shape modulus of extra space can be used as a most natural and safe stabilization mechanism against these fluctuations.     

The eastward displacement of a freely falling body on the rotating Earth: Newton and Hooke's debate of 1679

In this article I would like to tell the story of the beginning of modern theoretical physics, freed from all kinds of questionable anecdotes which have entered the scientific literature over the centuries. It all began in the seventeenth century when the mathematical theory of astronomy began to take shape. A major step in the history of modern science was taken when a few members of The Royal Society in London realized that the laws ruling the motions of heavenly bodies as manifested in Kepler's three laws are also effective in the dynamics of Earth‐bound particle motion. Everything started, not with I. Newton, but with R. Hooke. Not Newton's falling apple (Voltaire's invention), but a far‐reaching response by R. Hooke to a letter by I. Newton, dated November 28, 1679, ignited Newton's interest in gravity. That letter contained the famous spiral which a falling body would follow when released from a certain height above the surface of the Earth. Hooke's answer, based on Keplerian orbits, expressed the opinion that the body's trajectory would rather follow an elliptical path. In his spiral sketch Newton, however, predicted correctly that the falling body would be found to suffer an eastward deviation from the vertical in consequence of the Earth's rotation. In the course of time, many a researcher, including Hooke himself, was able to verify this conjecture. But it took until 1803 for the first satisfactory calculation of the eastward displacement of a freely falling body to be performed, and was provided by C.F. Gauss.     

Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space–time dimension

A profound quantum-gravitational effect of space–time dimension running with respect to the size of space–time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this Letter is twofold. First, we find that box-counting dimension in face of finite resolution of space–time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.     

Beyond the speed of light on Finsler spacetimes

As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman–Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.     

Newtons Wissenschaftslehre als Basis der Quantenphysik

Newton's Epistemology as Basic Concept of Quantum Physics It is correct to say that quantum physics cannot be derived from classical physics, which is founded on Newton's principles. However, it is also correct that Newton's epistemology, a more developed Platonian one, can be considered as basic for quantum physics. That is previously shown. Here, we remember Newton's epistemology more thoroughly, and consider particularly the difference to the Cartesian epistemology, a difference often veiled in the Newton tradition. Finally, we apply the result on some phenomena of quantum optics.     

A Spherical Symmetrical Spacetime Solution in Finsler Gravity

Several physical principles of Finsler gravity are proposed in this paper, and I apply the principles to construct a Finsler gravity action, which satisfy the condition that the action can be reduced to the General Relativity action once the metric is independent from the tangent vector. I also get a spacetime solution in Finsler spacetime with the tangent vector y _φ , moreover the solution indicates that the metric relies on the property of test particle in Finsler spacetime.     

Newtons Theorie der Schallgeschwindigkeit

Newton's Theory of the Velocity of Sound Newton's theory of the velocity of sound is faithfully, critically explained in a modern style of reasoning.     

Contemporary electrostatics—I: Physical background and applications

This article contains a brief introduction to Newton's early life to put into context the subsequent events in this narrative. It is followed by a summary of accounts of Newton's famous story of his discovery of universal gravitation which was occasioned by the fall of an apple in the year 1665/6. Evidence of Newton's friendship with a prosperous Yorkshire family who planted an apple tree arbour in the early years of the eighteenth century to celebrate his discovery is presented. A considerable amount of new and unpublished pictorial and documentary material is included relating to a particular apple tree which grew in the garden of Woolsthorpe Manor (Newton's birthplace) and which blew down in a storm before the year 1816. Evidence is then presented which describes how this tree was chosen to be the focus of Newton's account. Details of the propagation of the apple tree growing in the garden at Woolsthorpe in the early part of the last century are then discussed, and the results of a dendrochronological study of two of these trees is presented. It is then pointed out that there is considerable evidence to show that the apple tree presently growing at Woolsthorpe and known as 'Newton's apple tree' is in fact the same specimen which was identified in the middle of the eighteenth century and which may now be 350 years old. In conclusion early results from a radiocarbon dating study being carried out at the University of Oxford on core samples from the Woolsthorpe tree lend support to the contention that the present tree is one and the same as that identified as Newton's apple tree more than 200 years ago. Very recently genetic fingerprinting techniques have been used in an attempt to identify from which sources the various 'Newton apple trees' planted throughout the world originate. The tentative result of this work suggests that there are two separate varieties of apple tree in existence which have been accepted as 'the tree'. One may conclude that at least some of the current Newton apple trees have no connection with the original tree at Woolsthorpe Manor.     

Critical remarks on Finsler modifications of gravity and cosmology by Zhe Chang and Xin Li

I do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in [Zhe Chang, Xin Li, Phys. Lett. B 668 (2008) 453] and [Zhe Chang, Xin Li, Phys. Lett. B 676 (2009) 173], respectively). They consider that “In Finsler manifold, there exists a unique linear connection – the Chern connection … It is torsion freeness and metric compatibility …”. There are well-known results (for example, presented in monographs by H. Rund and R. Miron and M. Anastasiei) that in Finsler geometry there exist an infinite number of linear connections defined by the same metric structure and that the Chern and Berwald connections are not metric compatible. For instance, the Chern's one (being with zero torsion and “weak” compatibility on the base manifold of tangent bundle) is not generally compatible with the metric structure on total space. This results in a number of additional difficulties and sophistication in definition of Finsler spinors and Dirac operators and in additional problems with further generalizations for quantum gravity and noncommutative/string/brane/gauge theories. I conclude that standard physics theories can be generalized naturally by gravitational and matter field equations for the Cartan and/or any other Finsler metric compatible connections. This allows us to construct more realistic models of Finsler spacetimes, anisotropic field interactions and cosmology.     

Newtons lex prima in der Quantenmechanik

Newton's lex prima in Quantum Mechanics The probability for detecting a free massless particle in a region in which it was localized initially, does not decrease monotonically with time. This seems to contradict Newton's lex prima.     

Newtons „Principia Mathematica Philosophia”︁ und Plancks Elementarkonstanten

Newton's “Principia Mathematica Philosophia” and Planck's Elementary Constants Together with Planck's elementary constants Newton's principles prove a guaranteed basis of physics and “exact” sciences of all directions. The conceptions in physics are competent at all physical problems as well as technology too. Classical physics was founded in such a way to reach far beyond the physics of macroscopic bodies.     

Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

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

Complex Dynamics of Glass-forming Liquids: A Mode-coupling Theory,by Wolfgang Götze

Newton's life and work are briefly summarized and it is reasoned that we are in a better position today than a century ago for evaluating his accomplishment. The Principia is then presented and discussed in some detail. Stress is laid especially on the difference between the first two books, where Newton put together into one coherent ‘general mechanics’ his own and his predecessors' discoveries, and the third, where the theorems are applied for explaining the Solar System, the motions of planets and comets, and the tides. There follows an explanation of how Newton's ideas were propagated, even though the Principia, unlike the Opticks, was understood by only a few scientists. Through the work of D. Bernoulli and L. Euler, especially, Newton's mechanics was transformed and expanded into an endeavour of endless application. It is shown that the theory of relativity, although marking a limit to the validity of Newton's mechanics, has made clear how much better than most of his critics Newton understood the problems behind his work.     

Vakuum-Lichtgeschwindigkeit und differentielle Aberration

Vacuum Light Velocity and Differential Abberation In the frame work of Newton's theories of gravity and of light Laplace (1796) has deduced that the effective velocity c* of light is dependent on the gravitational potential of its source: Laplace, Olbers, a. o. have demonstrated that this effect implies differential aberrations of the light of different cosmisc sources. - But, Einstein's principles of relativity imply the independence of the velocity of light on its sources. This assertion is the fundamental principle of the Einsteinian theories of relativity. However, there seems to be no direct experimental facts disproving Laplace's formula, till today.     

Modified dispersion relations in Hořava–Lifshitz gravity and Finsler brane models

We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein–Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Hořava–Lifshitz, HL, and/or Einstein’s general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Hořava–Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.     

Scalar–tensor representation of f(R) gravity and Birkhoff's theorem

Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar–tensor representation. Modified gravity has become very popular in recent times as it is able to reproduce the unification of inflation and late‐time acceleration with no need of a dark energy component or an inflation field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to general relativity, the well‐known Brans–Dicke theory. As a novelty, here both theories are studied using a conformal transformation and writing the actions in the Einstein frame, where spherically symmetric solutions are studied using perturbation techniques. The differences between both theories are analyzed as well as the validity of the theorem within the Jordan and Einstein frames, where interesting results are obtained.     

Zu Newtons Erde-Mond-Test von 1665/66

On Newton's Earth-Moon-Test of 1665/66 Newton's proof on the earth-moon-system — whether the gravitation of the earth which gives freely falling bodies near the earth's surface an acceleration of g ≈ 982 cm/sec² and decreasing proportional to the inverse square of the distance from the earth's centre fully compensates the centrifugal force of the moon orbiting around the earth — is reexamined using new observational values for g, the earth's dimensions and the constants of the moon's motion. A first order calculation of the disturbances in the moon's orbit caused by the gravitation of the sun shows that the mass of the moon in relation to the mass of the earth must be near to 1:81 if the moons average distance from the earth's center is assumed to be 384 400 km.     

Confronting Finsler space–time with experiment

Within all approaches to quantum gravity small violations of the Einstein Equivalence Principle are expected. This includes violations of Lorentz invariance. While usually violations of Lorentz invariance are introduced through the coupling to additional tensor fields, here a Finslerian approach is employed where violations of Lorentz invariance are incorporated as an integral part of the space–time metrics. Within such a Finslerian framework a modified dispersion relation is derived which is confronted with current high precision experiments. As a result, Finsler type deviations from the Minkowskian metric are excluded with an accuracy of 10⁻¹⁶.