A Possible Modification of Einstein's Theory of General Relativity

This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to introduce the Einstein's tensor. In order to satisfy automatically the geodesic postulate, an additional coordinate condition is needed.For the spherically symmetric static field, it leads us to quite different conclusions from those of Einstein's general relativity in the interior region of the surface of infinite redshift. Accurate to the first order of GM/r, it obtains the same results about the four experimental tests of general relativity.     

An Analytical Treatment of the Clock Paradox in the Framework of the Special and General Theories of Relativity

No Heading In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear (in space). No inertial motion steps are considered. The rest clock is denoted as (1), the to and fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: (1) What is the effect of the finite force acting on (2) on the proper time interval ⁽²⁾ measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The special theory of relativity is used in order to describe the hyperbolic (in spacetime) motion of (2) in the frame I. (II) Is this effect an absolute one, i.e., does the accelerated observer A comoving with (2) obtain the same results as that obtained by the observer in I, both qualitatively and quantitatively, as it is expected? We use the general theory of relativity in order to answer this question. It turns out that _I = _A for both the clocks, ⁽²⁾ does depend on g = F/m, and = ⁽²⁾/⁽¹⁾ = (1 – ²atanhj)/ < 1. In it ; = V/c and V is the velocity acquired by (2) when the force is inverted.     

The End Results of General Relativity Theory Via Just Energy Conservation and Quantum Mechanics

Herein we present a whole new approach that leads to the end results of the general theory of relativity via just the law of conservation of energy (broadened to embody the mass and energy equivalence of the special theory of relativity) and quantum mechanics. We start with the following postulate. Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-á-vis the gravitational field of concern.     

相对性原理对普遍定律和非普遍定律参考系变换性质的不同要求——关于协变性疑难的进一步讨论

提出普遍定律和非普遍定律以及“协变”与“可导出”的明确定义，证明狭义相对性原理（及其伽利略近似）要求在惯性系变换下，自然界普遍定律是协变的，非普遍定律不协变但是“可导出”的，一切定律都服从相对性原理，从而进一步解答了由爱因斯坦，朗道关于狭义相对性原理的一种错误表述所引起的“协变性疑难”，还将有关结论推广到广义相对性原理情况。     

From De Sitter Special Relativity and Snyder's Model to Complete Yang Model

The de Sitter special relativity on the Beltrami-de Sitter-spacetime and Snyder's model in the momentum space can be combined together with an IR-UV duality to get the complete Yang model at both classical and quantum levels, which are related by the proposed Killing quantization. It is actually a special relativity based on the principle of relativity of three universal constants (c,l_P,R).     

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics: not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero-dimensional) serves as the base for the holographic image of the universe. In this way our theory is connected with p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of the Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans–Dicke theory. We found a surprising informational interrelation between the fundamental constants, h, c, G, and their DH analogues, h(D), c(D), G(D). DH theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhances the role of the Bohm potential.     

用洛伦兹磁场力挑战狭义相对论首文的论点简

实验论证表明：基于欧式空间的伽利略相对运动,①当磁铁静止而线圈运动时,其感应电流是经典洛伦兹磁力F1的作用结果;②当线圈静止而磁铁运动时,其感应电流是广义洛伦兹磁力F2的作用结果。这就否定了狭义相对论的论点,也质疑了麦克斯韦电动力学。     

The Principle of Covariance and the Hamiltonian Formulation of General Relativity

The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out.     

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.     

The Principle of Equivalence and the Twin Paradox

No Heading The canonical twin paradox is explained by making a correct use of the principle of equivalence. The role of the principle of equivalence is to provide a physical agent i.e gravity which can supply the required extra aging to the rocket-bound sibling during its acceleration phase through a gravitational time-offset effect. We follow an approach where a novel variation on the twin paradox is used to connect gravity with the desynchronization in the clocks of two spatially distant, identically accelerated observers. It is shown that this approach removes certain drawbacks of an earlier effort which claims to exploit the equivalence principle in explaining the differential aging in the paradox. * Author to whom all correspondences should be made.     

A Theory of Evolving Natural Constants Based on the Unification of General Theory of Relativity and Dirac's Large Number Hypothesis

Taking Dirac's large number hypothesis as true, we have shown [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory of general relativity with fixed gravitation constant G to cosmology, and a modified theory for varying G is found, which reduces to Einstein's theory outside the gravitating body for phenomena of short duration in small distances, thereby agrees with all the crucial tests formerly supporting Einstein's theory. The modified theory, when applied to the usual homogeneous cosmological model, gives rise to a variable cosmological tensor term determined by the derivatives of G, in place of the cosmological constant term usually introduced ad hoc. Without any free parameter the theoretical Hubble's relation obtained from the modified theory seems not in contradiction to observations, as Dr. Wang's preliminary analysis of the recent data indicates [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004) 703 we shall study in this paper the modification of electromagnetism due to Dirac's large number hypothesis in more detail to show that the approximation of geometric optics still leads to null geodesics for the path of light, and that the general relation between the luminosity distance and the proper geometric distance is still valid in our theory as in Einstein's theory, and give the equations for homogeneous cosmological model involving matter plus electromagnetic radiation. Finally we consider the impact of the modification to quantum mechanics and statistical mechanics, and arrive at a systematic theory of evolving natural constants including Planck's ħ as well as Boltzmann's k_B by finding out their cosmologically combined counterparts with factors of appropriate powers of G that may remain truly constant to cosmologically long time.     

Einstein's ‘Zürich Notebook’ and his journey to general relativity

On the basis of his ‘Zürich Notebook’ I shall describe a particularly fruitful phase in Einstein's struggle on the way to general relativity. These research notes are an extremely illuminating source for understanding Einstein's main physical arguments and conceptual difficulties that delayed his discovery of general relativity by about three years. Together with the ‘Entwurf’ theory in collaboration with Marcel Grossmann, these notes also show that the final theory was missed late in 1912 within a hair's breadth. The Einstein‐Grossmann theory, published almost exactly hundred years ago, contains, however, virtually all essential elements of Einstein's definite gravitation theory.     

Quirino Majorana’s Experiments on the Speed of Light and Gravitational Absorption

Quirino Majorana (1871–1957) was an outstanding Italian experimental physicist who investigated a wide range of phenomena during his long career in Rome,Turin, and Bologna. We focus on his experiments in Turin during 1916–1921 and in Bologna during 1921–1934 to test the validity of Albert Einstein’s postulate on the constancy of the speed of light and to detect gravitational absorption. These experiments required extraordinary skill, patience, and dedication, and all of them confirmed Einstein’s postulate and Isaac Newton’s law of universal gravitation to high precision. Had they not done so, Majorana’s fame among historians and physicists no doubt would be much greater than it is today. Giorgio Dragoni is Professor of History of Physics at the University of Bologna. Giulio Maltese is a Roman member of the Italian Society for the History of Physics and Astronomy. Luisa Atti is a Bolognese member of the Association for the Teaching of Physics.     

Derivation of the Evans Wave Equation from the Lagrangian and <Emphasis Type="Italic">Action</Emphasis>: Origin of the Planck Constant in General Relativity

No Heading The Evans wave equation is derived from the appropriate Lagrangian and action, identifying the origin of the Planck constant in general relativity. The classical Fermat principle of least time, and the classical Hamilton principle of least action, are expressed in terms of a tetrad multiplied by a phase factor exp(iS/), where S is the action in general relativity. Wave (or quantum) mechanics emerges from these classical principles of general relativity for all matter and radiation fields, giving a unified theory of quantum mechanics based on differential geometry and general relativity. The phase factor exp(iS/) is an eigenfunction of the Evans wave equation and is the origin in general relativity and geometry of topological phase effects in physics, including the Aharonov-Bohm class of effects, the Berry phase, the Sagnac effect, related interferometric effects, and all physical optical effects through the Evans spin field B⁽³⁾ and the Stokes theorem in differential geometry. The Planck constant is thus identified as the least amount possible of action or angular momentum or spin in the universe. This is also the origin of the fundamental Evans spin field B⁽³⁾, which is always observed in any physical optical effect. It originates in torsion, spin and the second (or spin) Casimir invariant of the Einstein group. Mass originates in the first Casimir invariant of the Einstein group. These two invariants define any particle.     

Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.