Quantum equivalence principle without mass superselection

The standard argument for the validity of Einstein?s equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. The objective of this work is to show that, contrary to widespread opinion, the compatibility between the equivalence principle and quantum mechanics does not depend on the introduction of such a restriction. For this purpose, we develop a formalism based on the extended Galileo group, which allows for a consistent handling of superpositions of different masses, and show that, within such scheme, mass superpositions behave as they should in order to obey the equivalence principle.     

Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration can equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle.     

Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics.     

The equivalence principle

The experimental basis of the equivalence principle is reviewed, and the implications for the gravitational interactions of elementary particles are studied within a special relativistic framework. The gravitational red shift is treated in detail and is used to show that antiparticles also obey the equivalence principle. The profound consequences of a violation of the equivalence principle are discussed.     

VariableG and the strong equivalence principle

A possible time variability ofG, implying a violation of the strong equivalence principle, was first proposed by P. A. M. Dirac in 1937. Since such a feature cannot be accommodated within either Newton’s or Einstein’s theories, a new theoretical framework is needed. In this paper we review one such possible scheme, the scale covariant theory, within which the consequences of a variableG on geophysics, astrophysics, and cosmology can be treated consistently. The global verdict is thatG may have varied by as much as a factor of 25 since the time of nucleosynthesis, without any disagreement emerging in any case. In spite of this result, we are not entitled to conclude from our analysis that a variableG has been shown to exist or that it is needed, but only that its variation iscompatible with known data. The proof thatG varies can in fact only come from direct observations. However, since the previous analyses had concluded that aG(t) would entail severe discrepancies with known data, the reversal of the verdict is believed to be significant, since it may hopefully spur new observational interest in this basic problem. Presented at the Dirac Symposium, Loyola University, New Orleans, May 1981.     

ADM electrons and the equivalence principle

Noting that the general relativistic ADM equation for the mass of a sphere of charged dust (with no angular momentum) reveals that the masses of point-like particles are determined solely by their electrical charge, electron models based on extended spheres of such purely electrical dust are examined. It is shown that for all realistic electron models of this type (where the observed electron mass is positive and many orders of magnitude smaller than either the Planck or ADM mass) the electron's bare active gravitational mass must be taken to be negative. Because of the negativity of the bare active gravitational mass, one of the two realistic models leads to a violation of the weak equivalence principle, but the other does not. A means of testing whether negative mass obeys the equivalence principle is mentioned.     

Energy conservation and the principle of equivalence

If the equivalence principle is violated, then observers performing local experiments can detect effects due to their position in an external gravitational environment (preferred-location effects) or can detect effects due to their velocity through some preferred frame (preferred-frame effects). We show that the principle of energy conservation implies a quantitative connection between such effects and structure-dependence of the gravitational acceleration of test bodies (violation of the Weak Equivalence Principle). We analyze this connection within a general theoretical framework that encompasses both non-gravitational local experiments and test bodies as well as gravitational experiments and test bodies, and we use it to discuss specific experimental tests of the equivalence principle, including non-gravitational tests such as gravitational redshift experiments, Eötvös experiments, the Hughes-Drever experiment, and the Turner-Hill experiment, and gravitational tests such as the lunar-laser-ranging “Eötvös” experiment, and measurements of anisotropies and variations in the gravitational constant. This framework is illustrated by analyses within two theoretical formalisms for studying gravitational theories: the PPN formalism, which deals with the motion of gravitating bodies within metric theories of gravity, and the TH?μ formalism that deals with the motion of charged particles within all metric theories and a broad class of non-metric theories of gravity.     

Scalar-tensor theories and the principle of equivalence

We investigate the restrictions on scalar-tensor theories of gravitation implied by the assumptions: (i) the field equations are derivable from an action principle, (ii) units of mass length and time are defined by atomic standards, and (iii) the principle of equivalence holds whenever gravitational self-energy can be neglected. We show that in all these theories the presence of gravitational energy in a system leads to violations of the principle of equivalence.     

Test of the equivalence principle in space

Summary Any violation of the equivalence principle (EP) between test masses in the near-Earth orbit is about 500 times bigger than on the ground, which makes the case for a space experiment very strong. Indeed, ESA and NASA (the European Space Agency and the American National Aeronautics and Space Administration) are currently studying at Phase A level the space mission STEP, whose main goal is to test the universality of free fall to 1 part in 10¹⁷ by means of a combination of very advanced technologies (drag free with proportional thrusters, superfluid-He temperature, SQUID sensors). We discuss the key features of STEP as well as some novel ideas about the possibility of testing the equivalence principle at room temperature in a non-drag-free satellite. Paper presented at the 6th Cosmic Physics National Conference, Palermo, 3–7 November 1992.     

Physics with and without the equivalence principle

A differential manifold (d-manifold, for short) can be defined as a pair (M, C), where M is any set and C is a family of real functions on M which is (i) closed with respect to localization and (ii) closed with respect to superposition with smooth Euclidean functions; one also assumes that (iii) M is locally diffeomorphic to Rⁿ. These axioms have a straightforward physical interpretation. Axioms (i) and (ii) formalize certain compatibility conditions which usually are supposed to be assumed tacitly by physicists. Axiom (iii) may be though of as a (nonmetric) version of Einstein's equivalence principle. By dropping axiom (iii), one obtains a more general structure called a differential space (d-space). Every subset of Rⁿ turns out to be a d-space. Nevertheless it is mathematically a workable structure. It might be expected that somewhere in the neighborhood of the Big Bang there is a domain in which space-time is not a d-manifold but still continues to be a d-space. In such a domain we would have a physics without the (usual form of the) equivalence principle. Simple examples of d-spaces which are not d-manifolds elucidate the principal characteristics the resulting physics would manifest.on leave of absence from the Institute of Nuclear Physics, Department of Theoretical Physics, ul. Radzikowskiego 152, 31–342 Cracow, Poland.     

Neutrino oscillations in non-inertial frames and the violation of the equivalence principle Neutrino mixing induced by the equivalence principle violation

Neutrino oscillations are analyzed in an accelerating and rotating reference frame, assuming that the gravitational coupling of neutrinos is flavor dependent, which implies a violation of the equivalence principle. Unlike the usual studies in which a constant gravitational field is considered, such frames could represent a more suitable framework for testing if a breakdown of the equivalence principle occurs, due to the possibility to modulate the (simulated) gravitational field. The violation of the equivalence principle implies, for the case of a maximal gravitational mixing angle, the presence of an off-diagonal term in the mass matrix. The consequences on the evolution of flavor (mass) eigenstates of such a term are analyzed for solar (oscillations in the vacuum) and atmospheric neutrinos. We calculate the flavor oscillation probability in the non-inertial frame, which does depend on its angular velocity and linear acceleration, as well as on the energy of neutrinos, the mass-squared difference between two mass eigenstates, and on the measure of the degree of violation of the equivalence principle (). In particular, we find that the energy dependence disappears for vanishing mass-squared difference, unlike the result obtained by Gasperini, Halprin, Leung, and other physical mechanisms proposed as a viable explanation of neutrino oscillations. Estimations on the upper values of are inferred for a rotating observer (with vanishing linear acceleration) comoving with the earth, hence rad/sec, and all other alternative mechanisms generating the oscillation phenomena have been neglected. In this case we find that the constraints on are given by for solar neutrinos and for atmospheric neutrinos. Received: 14 December 2000 / Published online: 15 March 2001     

Can the equivalence principle survive quantization?

It is well known that Einstein gravity is non-renormalizable; however a generalized approach is proposed that leads to Einstein gravity after renormalization. This then implies that at least one candidate for quantum gravity treats all matter on an equal footing with regard to the gravitational behaviour. Harsh constraints are also placed on any anti-matter gravity theory if one does not wish to violate the conservation of energy. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the equivalence principle in quantum theory

The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.     

弱等效原理的实验检验

惯性质量与引力质量相等是广义相对论基本理论假设之一，这个假设称为等效原理。本文介绍等效原理的检验实验的框架以及检验实验的历史、现状和未来。     

Derivation of the principle of equivalence for antimatter

In view of the announcement of some experiments testing the principle of equivalence for antimatter, we give here stringent arguments, based on elementary and well-established physical principles, that these experiments will turn out negative. The question is important because disproving the principle of equivalence (equality of inertial and gravitating mass) would entail a breakdown of general relativity. (There is only one type of geodesics and there are no antigeodesics for antimatter).     

A new test of the weak equivalence principle

The Eötvös, Dicke, and Braginski experiments do not rule out the recent suggestion that the weak equivalence principle (WEP) might be violated at intermediate ranges (10^–1 m r 10⁴ m). I briefly discuss the problems inherent in Eötvös-type apparatus in searches for WEP-violating forces (hyperforces) between laboratory masses and suggest an alternative detector free of such problems. The proposed detector is driven by a hyperforce torque at the rotational frequency. If the detector is tuned to this frequency, the signal, enhanced by resonance, may be detected synchronously. I derive the response equations for the detector and discuss how spurious responses due to gravity torques may be suppressed.This essay received the third award from the Gravity Research Foundation for the year 1986-Ed.