21 pages, no figures; submitted to a "focus issue" of Classical and Quantum Gravity on Tests of the Weak Equivalence Principle, organized by Clive Speake and Clifford Will
We review several theoretical aspects of the Equivalence Principle (EP). We emphasize the unsatisfactory fact that the EP maintains the absolute character of the coupling constants of physics while General Relativity, and its generalizations (Kaluza-Klein,..., String Theory), suggest that all absolute structures should be replaced by dynamical entities. We discuss the EP-violation phenomenology of dilaton-like models, which is likely to be dominated by the linear superposition of two effects: a signal proportional to the nuclear Coulomb energy, related to the variation of the fine-structure constant, and a signal proportional to the surface nuclear binding energy, related to the variation of the light quark masses. We recall the various theoretical arguments (including a recently proposed anthropic argument) suggesting that the EP be violated at a small, but not unmeasurably small level. This motivates the need for improved tests of the EP. These tests are probing new territories in physics that are related to deep, and mysterious, issues in fundamental physics.
We give a general overview of various flavors of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We also discuss its generalisation to a theory of quantum gravity. Our analysis suggests that only the strong equivalence principle can be considered fundamental enough to be generalised to a quantum gravity context, since all other flavors of equivalence principle hold only approximately already at the classical level.
We review the possible violation of the Equivalence Principle at finite temperature T in the framework of curvature based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at non-vanishing T. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quanti…
Humboldt-Universität zu Berlin（柏林洪堡大学）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Universidad Complutense de Madrid（马德里康普顿斯大学）；Dublin Institute for Advanced Studies（都柏林高等研究院）；Charles University（查理大学）
In this essay I point out that, in the context of semi-classical gravity, the equivalence principle can mitigate the cosmological constant problem. On a Minkowski space-time background with the usual $\mathbb{R}^4$ topology, the vacuum self-energy is removed by normal ordering; this is allowed because it is not observable; I argue that, in a freely-falling frame of reference, the same must hold true, up to contributions from modes whose wavelength is of the order of the background radius of curvature. Thus, the equivalence principle implies that ultra-violet modes do not contribute to the effe…
We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances. Specifically, we observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched. To obtain the above result, spinor and scalar fields are separately analyzed by considering the non-relativist…
The symmetry of the theory of relativity under diffeomorphisms strongly depends on the equivalence principle. Violation of Equivalence Principle (VEP) can be tested by looking for deviations from the standard framework of neutrino oscillations. In recent works, it has been shown that strong constraints on the VEP parameter space can be placed by means of the atmospheric neutrinos observed by the IceCube neutrino telescope. In this paper, we focus on the KM3NeT neutrino telescope and perform a forecast analysis to assess its capacity to probe VEP. Most importantly, we examine the crucial role p…
We analyze possible violations of the Equivalence Principle in scalar-tensor gravity at finite temperature $T.$ Before we present an approach where the Equivalence Principle violation is achieved within the framework of Quantum Field Theory. After, we rely on an alternative approach first proposed by Gasperini, which leads to the same outcome obtained in the framework of Quantum Field Theory (one-loop corrections) at finite $T$. Finally, we exhibit the application of the above formalism both to a generic diagonal metric, cast in spherical coordinates, and to the Brans-Dicke theory. In the last…
The Einstein equivalence principle is based on the equality of gravitational mass and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities. Here, we will provide a simple protocol based on creating large spatial superposition states in a laboratory to test the fully qua…
Einstein's Equivalence Principle and the Gravitational Red Shift II
早在1916年广义相对论最终形成之前，完全基于爱因斯坦等效原理的论点就预言了众所周知的引力红移现象。今天，同样的论点被广泛用于推导同样的现象。因此，经常有人声称，观测到的引力红移是对等效原理的验证，而不是对广义相对论完整理论的验证。在这里，我们表明，与这些要求相反，基于等价原则的论点是错误的，\it{only the full theory of general relativity can correctly and unambiguously predict the gravitational red shift}。
The Einstein-Hilbert action of general theory of relativity (GR) is the integral of the scalar curvature $R$. It is a theory that is drawn from the Equivalence principle, and has predictions that come out as a consequence of the principle, in observables. Testing such observables to find confirmation/infirmation of the principle have formed a significant chunk of tests of GR itself. It is expected that quantum corrections to GR may add additional higher powers of $R$ to the Einstein-Hilbert action, or more generally, modifying the action into a generic class of functions of the Ricci scalar. T…
