The Principle of Equivalence,electrodynamics and General Relativity

It is shown that the customary covariant formulation of electrodynamics in General Relativity is incompatible with the Einstein Principle of Equivalence. This is demonstrated for the case of a resistanceless current-carrying wire in a static spherically symmetric gravitational field—where the Einstein Principle of Equivalence implies the existence, in the vicinity of the wire, of a non-zero component of the electric field parallel to the wire, whereas the covariant form of Maxwell's equations does not. An experiment, involving a superconducting current-carrying wire segment placed in the Earth's gravitational field, is suggested. Whether or not a component of electric field parallel to the wire, at a point in the wire's vicinity, would be detected would resolve the issue.     

Point-like sources and the scale of quantum gravity

We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of neutral matter which has vanishing total energy in the small-volume limit. We then show that, by assuming a Generalised Uncertainty Principle, which implies the existence of a minimum length of the order of the Planck scale, the total energy instead remains finite and equal to the shell's proper mass both for very heavy and very light particles. This suggests that the quantum structure of space–time might be related to the classical Equivalence Principle and possible implications for the late stage of evaporating black holes are briefly mentioned.     

The Equivalence Principle as a Symmetry

It is shown that the extra coordinate of 5D induced-matter and membrane theory is related in certain gauges to the inertial rest mass of a test particle. This implies that the Weak Equivalence Principle is a geometric symmetry, valid only in the limit in which the test mass is negligible compared to the source mass. Exact solutions illustrate this, and show the way to possible resolutions of the cosmological-constant and hierarchy problems.     

The Equivalence Principle Revisited

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.     

Über das Äquivalenzprinzip in der Wellenmechanik

On the Principle of Equivalence in Wave-mechanics We verify the meaning of Galilei's and Einstein's principles of equivalence in wavemechanics by new discussions of Einstein's “Gedanken-Experimente”.     

Testing the Equivalence Principle in the Quantum Regime

We consider possible tests of the Einstein Equivalence Principle for physical systems in which quantum-mechanical vacuum energies cannot be neglected. Specific tests include a search for the manifestation of non-metric effects in Lamb-shift transitions of hydrogenic atoms and in anomalous magnetic moments of massive leptons. We discuss how current experiments already set bounds on the violation of the equivalence principle in this sector and how new (high-precision) measurements of these quantities could provide further information to this end.     

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.     

The Abell cluster A586 and the detection of violation of the equivalence principle

We discuss the current bounds on the Equivalence Principle (EP), in particular from structure formation and, reexamine in this context, the recent claim on the evidence of the interaction between dark matter and dark energy in the Abell Cluster A586 and the ensued violation of the EP.     

A Lorentz-Poincaré Type Interpretation of the Weak Equivalence Principle

The validity of the Weak Equivalence Principle relative to a local inertial frame is detailed in a scalar-vector gravitation model with Lorentz-Poincaré type interpretation. Given the previously established first Post-Newtonian concordance of dynamics with General Relativity, the principle is to this order compatible with GRT. The gravitationally modified Lorentz transformations, on which the observations in physical coordinates depend, are shown to provide a physical interpretation of parallel transport. A development of ‘geodesic’ deviation in terms of the present model is given as well. PACS subject classifications. 04.20.-q, 04.50.+h     

Almost complex structures that model nonlinear geometries

This article studies a class of connections defined on a symplectic manifold with a Lagrangian foliation that model certain aspects of local differential geometry. This construction is of interest because it provides a more satisfactory treatment of the Equivalence Principle in General Relativity, and it offers a new approach to the study of geometric structures. Homogeneous direction-dependent metrics are studied using these techniques. Conditions are given that guarantee the existence of horizontal distributions that generalize the Levi-Civita and Cartan connections.     

ISLAND, revisited

This paper is in answer to the comment on the GRG paper: Lockerbie N.A. Gen. Rel. Grav. 36, 593 (2004), made by A.V. Sanders, G.T. Gillies (ibid.). N. A. Lockerbie is a member of the STEP (Satellite Test of the Equivalence Principle) Science Study Team, and an Associate of the Institute for Gravitational Research at the University of Glasgow, Scotland, UK.     

String theory and gravity

It is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data. Under a certain assumption of universality of the dilaton coupling functions, the cosmological evolution drives the dilaton towards values where it decouples from matter. At the present cosmological epoch, the coupling to matter of the dilaton should be very small, but non zero. This provides a new motivation for improving the experimental tests of Einstein's Equivalence Principle.This essay received the first award from the Gravity Research Foundation, 1994-Ed.     

Can gluon spin contribute to that of nucleon?

The transformation of angular momentum to its Belinfante form requires the smooth behaviour of classical fields at infinity which for the case of quantum operators transforms to the smooth behaviour of matrix elements at small momentum transfers. For the case of quarks this provides the kinematical counterpart of U _A (1) problem while for gluons there is a contradiction between kinematics and dynamics governed by Kogut-Susskind pole. This may result in the violation of Equivalence Principle for nucleons or in the stringent constraints to the strange quark polarization in nucleons, while the most likely outcome would be the impossibility to separate gluon angular momentum to spin and orbital parts in the meaningful way.     

‘Faster than light’ photons in gravitational fields — Causality,anomalies and horizons

A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions induced by vacuum polarisation in QED in curved spacetime. Two general theorems are presented: first, a polarisation sum rule which relates the polarisation averaged velocity shift to the matter energy-momentum tensor and second, a ‘horizon theorem’ which ensures that the geometric event horizon for black hole spacetimes remains a true horizon for real photon propagation. These results are consequences of an effective action which in QED is valid only for low frequency photons. Their relevance to signal propagation and causality, which are controlled by high frequency propagation, is dependent on the dispersive properties of the modified propagation. This will be discussed elsewhere. A comparison is made with the equivalent results for electromagnetic birefringence and possible connections between superluminal photon propagation, causality and the conformal anomaly are exposed.     

Spherical harmonic representation of the gravitational coupling between a truncated sector of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

The gravitational interaction between grooves machined in a hollow cylindrical mass of uniform density, and an external point mass, is derived in terms of the Associated Legendre functions, and the parametric form of the coupling coefficients is presented. The cross-sections of the grooves, which are regularly spaced in azimuth, are in the form of truncated sectors of the cylinder's end-faces. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, for which four grooves have been assumed, and an expression for the axialforce is derived which is more than 10⁴ times faster to compute than a Monte-Carlo integration of similar accuracy. Following this analysis it is suggested that the STEP test-masses should carry at least 6 grooves. This theory has wider application to gravitational problems involving general sectored cylindrical bodies.     

Gravity: the inside story

It is well known that one could determine the kinematics of gravity by using the Principle of Equivalence and local inertial frames. I describe how the dynamics of gravity can be similarly understood by suitable thought experiments in a local Rindler frame. This approach puts in proper context several unexplained features of gravity and describes the dynamics of spacetime in a broader setting than in Einstein’s theory. First Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Equivalence Principle and the Principle of Local Lorentz Invariance

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.     

Torsion balance experiments: A low-energy frontier of particle physics

We review recent mechanical experiments that test some of the most basic principles of physics including the weak and strong forms of the Equivalence Principle, the gravitational inverse-square law, and Lorentz invariance. The very high sensitivity of these tests allows one to place interesting constraints on string-theory inspired conjectures about new Yukawa forces from the exchange of very light scalar, pseudoscalar or vector particles, large extra dimensions, the chameleon mechanism, non-commutative spacetime geometry, and Planck-scale Lorentz violation.     

高功率微波照射下半空间上方天线罩耦合特性

利用两次傅里叶变换得到半空间界面的反射波后,将直接入射波和界面反射波两个时域脉冲源通过等效原理引入到包含目标的时域有限差分(FDTD)的计算域中。计算了高功率微波入射情形下,改变入射面、极化方式时天线罩内部观察点的能流密度的变化,并总结其规律。数值算例表明,对于贴近地面的目标来讲,半空间的反射波会给目标内部带来新的能量冲击。该方法可以用于计算目标内部耦合近场及功率密度。