Quantum Equivalence Principle Research Articles

Earthquake Quantization

In this homage to Einstein's 144th birthday we propose a novel quantization prescription, where the paths of a path-integral are not random, but rather solutions of a geodesic equation in a random background. We show that this change of perspective can be made mathematically equivalent to the usual formulations of non-relativistic quantum mechanics. To conclude, we comment on conceptual issues, such as quantum gravity coupled to matter and the quantum equivalence principle.

Decoherence of a composite particle induced by a weak quantized gravitational field

Even though we have some proposals for the quantum theory of gravity like string theory or loop quantum gravity, we do not have any experimental evidence supporting any of these theories. Actually, we do not have empirical evidence pointing in the direction that we really need a quantum description of the gravitational field. In this scenario, several proposals for experimentally investigating quantum gravitational effects far from the Planck scale have recently appeared in literature, like gravitationally induced entanglement, for instance. An important issue of these approaches is the decoherence introduced by the quantum nature not only of the system under consideration but also from the gravitational field itself. Here, by means of the Feynman–Vernon influence functional, we study the decoherence of a quantum system induced by the quantized gravitational field—in the linearized gravity regime—and also by its own quantum nature. Our results may be significant in better understanding many phenomena like the decoherence induced by the gravitational time-dilation, the quantum reference frames, and the quantum equivalence principle.

General formalism of the quantum equivalence principle

A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass operators, and for non-relativistic particles in a weak gravitational field. In this work, we propose a generalization to a fully relativistic formalism of the quantum equivalence principle, valid for all background space-times, as well as for massive bosons and fermions. The principle is trivially satisfied for massless particles. We show that if the equivalence principle is broken at the quantum level, it implies the modification of the standard Lorentz transformations in flat space-time and a corresponding modification of the metric in curved space-time by the different mass ratios. In other words, the observed geometry would effectively depend on the properties of the test particle. Testable predictions of potential violations of the quantum equivalence principle are proposed.

Precise and robust optical beam steering for space optical instrumentation

We present a novel optical beam steering technique for fiber to free-space to fiber-coupling schemes on optical breadboards, which is based on a glass plate and a pair of glass wedges. Our approach permits much finer adjustments of the beam direction and position when compared to conventional beam steering techniques that use adjusting elements of the same mechanical precision. This results in a much increased precision, accuracy, and stability. Furthermore, the presence of a beam steering element in proximity to the fiber coupler allows a great simplification of the design of this element which is typically considered as the most complex and sensitive element on an optical fiber breadboard. Overall, a beam steering precision of better than $$5\,\upmu $$rad and $$5\,\upmu $$m is demonstrated, resulting in a resolution in coupling efficiency of 0.1%. Likewise, we demonstrate a fiber-to-fiber-coupling efficiency of more than 89.8%, with a stability of 0.2% in a stable temperature environment and 2% fluctuations over a temperature range from 10 to 40 °C over a measurement time of 14 h. Finally, we observe no non-reversible change in the coupling efficiency after performing a series of tests over large temperature variations ($$\varDelta T > 30$$ K). This technique can find direct application in proposed missions for quantum experiments in space (Bongs et al. in STE-QUEST space–time explorer and quantum equivalence principle space test, Technical report STE-QUEST, European Space Agency, 2013; Kaltenbaek et al. in EPJ Quantum Technol 3(1):5, 2016; Carraz et al. in Microgravity Sci Technol 26:139, 2014), e.g., in space-based quantum sensing, where precisely controlled laser light is used to cool and manipulate atoms, or in inter-satellite quantum key distribution.

On the observer dependence of the Hilbert space near the horizon of black holes

One of the pronounced characteristics of gravity, distinct from other interactions, is that there are no local observables which are independent of the choice of the spacetime coordinates. This property acquires crucial importance in the quantum domain in that the structure of the Hilbert space pertinent to different observers can be drastically different. Such intriguing phenomena as the Hawking radiation and the Unruh effect are all rooted in this feature. As in these examples, the quantum effect due to such observer-dependence is most conspicuous in the presence of an event horizon and there are still many questions to be clarified in such a situation. In this paper, we perform a comprehensive and explicit study of the observer dependence of the quantum Hilbert space of a massless scalar field in the vicinity of the horizon of the Schwarzschild black holes in four dimensions, both in the eternal (two-sided) case and in the physical (one-sided) case created by collapsing matter. Specifically, we compare and relate the Hilbert spaces of the three types of observers, namely (i) the freely falling observer, (ii) the observer who stays at a fixed proper distance outside of the horizon and (iii) the natural observer inside of the horizon analytically continued from outside. The concrete results we obtain have a number of important implications on black hole complementarity pertinent to the quantum equivalence principle and the related firewall phenomenon, on the number of degrees of freedom seen by each type of observer, and on the "thermal-type" spectrum of particles realized in a pure state.

Thermodynamics of quantum spacetime histories

We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez and Bianchi. This allows us to apply a recent argument of Jacobson to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.

A test of the equivalence principle(s) for quantum superpositions

We propose an experimental test of the quantum equivalence principle introduced by Zych and Brukner (arXiv:1502.00971), which generalises the Einstein equivalence principle to superpositions of internal energy states. We consider a harmonically trapped atom in the presence of both gravity and an external magnetic field and show that when the external magnetic field is suddenly switched off, various violations of the equivalence principle would manifest as otherwise forbidden transitions. Performing such an experiment would put bounds on the various phenomenological violating parameters. We further demonstrate that the classical weak equivalence principle can be tested by suddenly putting the apparatus into free fall, effectively ‘switching off’ gravity.

Analysis of Sun/Moon gravitational redshift tests with the STE-QUEST space mission

The Space-Time Explorer and Quantum Equivalence principle Space Test (STE-QUEST) space mission will perform tests of the gravitational redshift in the field of the Sun and the Moon to high precision by frequency comparisons of clocks attached to the ground and separated by intercontinental distances. In the absence of Einstein equivalence principle (EP) violation, the redshift is zero up to small tidal corrections, as the Earth is freely falling in the field of the Sun and Moon. Such tests are thus null tests, allowing us to bound possible violations of the EP. Here we analyze the Sun/Moon redshift tests using a generic EP-violating theoretical framework, with clocks minimally modelled as two-level atoms. We present a complete derivation of the redshift (including both general relativity (GR) and non-GR terms) in a realistic experiment such as the one envisaged for STE-QUEST. We point out and correct an error in previous formalisms linked to the atom’s recoil not being properly taken into account.

QED trace anomaly, non-local Lagrangians and quantum equivalence principle violations

We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light.

A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1 × 10(-15.).

We present a compact and robust transportable ultra-stable laser system with minimum fractional frequency instability of 1 × 10(-15) at integration times between 1 and 10 s. The system was conceived as a prototype of a subsystem of a microwave-optical local oscillator to be used on the satellite mission Space-Time Explorer and QUantum Equivalence Principle Space Test (STE-QUEST) (http://sci.esa.int/ste-quest/). It was therefore designed to be compact, to sustain accelerations occurring during rocket launch, to exhibit low vibration sensitivity, and to reach a low frequency instability. Overall dimensions of the optical system are 40 cm × 20 cm × 30 cm. The acceleration sensitivities of the optical frequency in the three directions were measured to be 1.7 × 10(-11)/g, 8.0 × 10(-11)/g, and 3.9 × 10(-10)/g, and the absolute frequency instability was determined via a three-cornered hat measurement. Two additional cavity-stabilized lasers were used for this purpose, one of which had an instability σy < 4 × 10(-16) at 1 s integration time. The design is also appropriate and useful for terrestrial applications.

Atom interferometry in space: thermal management and magnetic shielding.

Atom interferometry is an exciting tool to probe fundamental physics. It is considered especially apt to test the universality of free fall by using two different sorts of atoms. The increasing sensitivity required for this kind of experiment sets severe requirements on its environments, instrument control, and systematic effects. This can partially be mitigated by going to space as was proposed, for example, in the Spacetime Explorer and Quantum Equivalence Principle Space Test (STE-QUEST) mission. However, the requirements on the instrument are still very challenging. For example, the specifications of the STE-QUEST mission imply that the Feshbach coils of the atom interferometer are allowed to change their radius only by about 260 nm or 2.6 × 10(-4) % due to thermal expansion although they consume an average power of 22 W. Also Earth's magnetic field has to be suppressed by a factor of 10(5). We show in this article that with the right design such thermal and magnetic requirements can indeed be met and that these are not an impediment for the exciting physics possible with atom interferometers in space.

STE-QUEST—test of the universality of free fall using cold atom interferometry

The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The spacetime explorer and quantum equivalence principle space test satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the universality of free fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose–Einstein condensates of 85Rb and 87Rb. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the Eötvös parameter of at least 2 × 10−15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources.

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. It is surprising that the consistency between such an important principle and quantum mechanics depends crucially on the imposition of a non-fundamental restriction. The objective of this work is show that, contrary to what the standard account holds, the compatibility between the principle of equivalence and quantum mechanics does not depend on the introduction of such a superselection rule. For this purpose, we consider the extended Galileo group, in which mass is treated as an operator, and show that within this scheme superpositions of different masses behave as they should in order to obey the equivalence principle.

Probing the flyby anomaly with the future STE-QUEST mission

In this study, we demonstrate that the flyby anomaly, an unexpected acceleration detected in some of the gravitational assists of the Galileo, NEAR, Cassini and Rosetta spacecraft, could be probed by accurate orbital tracking available in the proposed Space–Time Explorer and Quantum Equivalence Principle Space Test (STE-QUEST); following a recent work, we focus on the similarity between a hyperbolic flyby and the perigee passage in a highly elliptic orbit of the latter, as well as its Global Navigation Satellite System precise orbital determination capabilities.

Quantum equivalence principle violations in scalar-tensor theories

We study the equivalence principle and its violations by quantum effects in scalar-tensor theories that admit a conformal frame in which matter only couples to the spacetime metric. These theories possess Ward identities that guarantee the validity of the weak equivalence principle to all orders in the matter coupling constants. These Ward identities originate from a broken Weyl symmetry under which the scalar field transforms by a shift, and from the symmetry required to couple a massless spin two particle to matter (diffeomorphism invariance). But the same identities also predict violations of the weak equivalence principle relatively suppressed by at least two powers of the gravitational couplings, and imply that quantum corrections do not preserve the structure of the action of these theories. We illustrate our analysis with a set of specific examples for spin zero and spin half matter fields that show why matter couplings do respect the equivalence principle, and how the couplings to the gravitational scalar lead to the weak equivalence principle violations predicted by the Ward identities.

Minimal length in quantum gravity, equivalence principle and holographic entropy bound

A possible discrepancy has been found between the results of a neutron interferometry experiment and quantum mechanics. This experiment suggests that the weak equivalence principle is violated at small length scales, which quantum mechanics cannot explain. In this paper, we investigated whether the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, can explain the violation of the weak equivalence principle at small length scales. We also investigated the consequences of the GUP on the Liouville theorem in statistical mechanics. We have found a new form of invariant phase space in the presence of GUP. This result should modify the density states and affect the calculation of the entropy bound of local quantum field theory, the cosmological constant, black body radiation, etc. Furthermore, such modification may have observable consequences at length scales much larger than the Planck scale. This modification leads to a -type correction to the bound of the maximal entropy of a bosonic field which would definitely shed some light on the holographic theory.

EMERGENT GEOMETRY AND QUANTUM GRAVITY

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant [Formula: see text] whose physical dimension is of (length)2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L P . The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ω in terms of electromagnetic fields F = dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.

Quantum mechanics versus equivalence principle

We consider the scattering of a photon by a weak gravitational field, treated as an external field, up to second order of the perturbation expansion. The resulting cross section is energy dependent which indicates a violation of Galileo's equivalence principle (universality of free fall) and, consequently, of the classical equivalence principle. The deflection angle $\ensuremath{\theta}$ for a photon passing by the sun is evaluated afterward and the likelihood of detecting $\frac{\ensuremath{\Delta}\ensuremath{\theta}}{{\ensuremath{\theta}}_{E}}\ensuremath{\equiv}\frac{\ensuremath{\theta}\ensuremath{-}{\ensuremath{\theta}}_{E}}{{\ensuremath{\theta}}_{E}}$ (where ${\ensuremath{\theta}}_{E}$ is the value predicted by Einstein's geometrical theory for the light bending) in the foreseeable future, is discussed.

WHY THERE IS SOMETHING SO CLOSE TO NOTHING: TOWARDS A FUNDAMENTAL THEORY OF THE COSMOLOGICAL CONSTANT

The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle which demands a consistent gauging of the geometric structure of canonical quantum theory. We argue that string theory can be formulated to accommodate such a principle, and that in such a theory the observed cosmological constant is a fluctuation about a zero value. This fluctuation arises from an uncertainty relation involving the cosmological constant and the effective volume of space–time. The measured, small vacuum energy is dynamically tied to the large "size" of the universe, thus violating naive decoupling between small and large scales. The numerical value is related to the scale of cosmological supersymmetry breaking, supersymmetry being needed for a nonperturbative stability of local Minkowski space–time regions in the classical regime.

The acoustical equivalence principle for ray tracing

While the acoustical wave functions for various acoustical problems can be mapped into each other by a coordinate transformation (the acoustical equivalence principle), the corresponding ray tracings cannot be so mapped. Applying the acoustical equivalence principle [A. E. Faraggi and M. Matone, Int. J. Mod. Phys. A 15, 1869–2017 (2000) for the analogous quantum equivalence principle] to the underlying acoustical Hamilton–Jacobi equation for ray tracing renders a modified acoustical Hamilton–Jacobi equation which does obey the quantum equivalence principle. Solutions of the modified acoustical Hamilton-Jacobi equation, which are either acoustical Hamilton’s principal function or the acoustical reduced action (acoustical Hamilton’s characteristic function), are the generators of motion for rigorous ray tracing.