Universality Of Free Fall Research Articles

Free‐Fall Non‐Universality in Quantum Theory

AbstractThe author shows by embodying the Einstein equivalence principle—local Poincaré invariance—and general covariance in quantum theory that wave‐function spreading rules out the universality of free fall, that is, the free‐fall trajectory of a quantum (test) particle depends on its internal properties. The author provides a quantitative estimate of the free‐fall non‐universality in terms of the Eötvös parameter, which turns out to be measurable in atom interferometry.

Exploring the foundations of the physical universe with space tests of the equivalence principle

We present the scientific motivation for future space tests of the equivalence principle, and in particular the universality of free fall, at the 10− 17 level or better. Two possible mission scenarios, one based on quantum technologies, the other on electrostatic accelerometers, that could reach that goal are briefly discussed. This publication is a White Paper written in the context of the Voyage 2050 ESA Call for White Papers.

Resolution of the colocation problem in satellite quantum tests of the universality of free fall

A major challenge common to all Galilean drop tests of the Universality of Free Fall (UFF) is the required control over the initial kinematics of the two test masses upon release due to coupling to gravity gradients and rotations. In this work, we present a two-fold mitigation strategy to significantly alleviate the source preparation requirements in space-borne quantum tests of the UFF, using a compensation mechanism together with signal demodulation. To this end, we propose a scheme to reduce the gravity-gradient-induced uncertainties in an atom-interferometric experiment in a dedicated satellite mission and assess the experimental feasibility. We find that with moderate parameters, the requirements on the initial kinematics of the two masses can be relaxed by five orders of magnitude. This does not only imply a significantly reduced mission time but also allows to reduce the differential acceleration uncertainty caused by co-location imperfections below the $10^{-18}$ level.

Space test of the equivalence principle: first results of the MICROSCOPE mission

The weak equivalence principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of general relativity. The MICROSCOPE mission aims to test its validity to a precision of 10−15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE’s first results show no hint for such a difference, expressed in terms of Eötvös parameter (both 1 uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1 uncertainties leads to a current limit on of about .

Axionic instabilities and new black hole solutions

The coupling between scalar and vector fields has a long and interesting history. Axions are one key possibility to solve the strong CP problem and axion-like particles could be one solution to the dark matter puzzle. Given the nature of the coupling, and the universality of free fall, nontrivial important effects are expected in regions where gravity is strong. Here, we show that i. A background EM field induces an axionic instability in flat space, for large enough electric fields. Conversely, a homogeneous harmonic axion field induces an instability in the Maxwell sector. When carried over to curved spacetime, this phenomena translates into generic instabilities of charged black holes (BHs). ii. In the presence of charge, BH uniqueness results are lost. We find solutions which are small deformations of the Kerr-Newman geometry and hairy stationary solutions without angular momentum, which are `dragged' by the axion. Axion fields must exist around spinning BHs if these are immersed in external magnetic fields. The axion profile can be obtained perturbatively from the electro-vacuum solution derived by Wald. iii. Ultralight axions trigger superradiant instabilities of spinning BHs and form an axionic cloud in the exterior geometry. The superradiant growth can be interrupted or suppressed through axionic or scalar couplings to EM. These couplings lead to periodic bursts of light, which occur throughout the history of energy extraction from the BH. We provide numerical and simple analytical estimates for the rates of these processes. iv. Finally, we discuss how plasma effects can affect the evolution of superradiant instabilities.

Tests of gravitational symmetries with pulsar binary J1713+0747

Symmetries play an important role in modern theories of gravity. The strong equivalence principle (SEP) constitutes a collection of gravitational symmetries which are all implemented by general relativity. Alternative theories, however, are generally expected to violate some aspects of SEP. We test three aspects of SEP using observed change rates in the orbital period and eccentricity of binary pulsar J1713+0747: 1. the gravitational constant's constancy as part of locational invariance of gravitation; 2. the post-Newtonian parameter $\hat{\alpha}_3$ in gravitational Lorentz invariance; 3. the universality of free fall (UFF) for strongly self-gravitating bodies. Based on the pulsar timing result of the combined dataset from the North American Nanohertz Gravitational Observatory (NANOGrav) and the European Pulsar Timing Array (EPTA), we find $\dot{G}/G = (-0.1 \pm 0.9) \times 10^{-12}\,{\rm yr}^{-1}$, which is weaker than Solar system limits, but applies for strongly self-gravitating objects. Furthermore, we obtain the constraints $|\Delta|< 0.002$ for the UFF test and $-3\times10^{-20} < \hat{\alpha}_3 < 4\times10^{-20}$ at 95% confidence. These are the first direct UFF and $\hat{\alpha}_3$ tests based on pulsar binaries, and they overcome various limitations of previous tests.

Universality of free fall from the orbital motion of a pulsar in a stellar triple system

Einstein's theory of gravity-the general theory of relativity1-is based on the universality of free fall, which specifies that all objects accelerate identically in an external gravitational field. In contrast to almost all alternative theories of gravity2, the strong equivalence principle of general relativity requires universality of free fall to apply even to bodies with strong self-gravity. Direct tests of this principle using Solar System bodies3,4 are limited by the weak self-gravity of the bodies, and tests using pulsar-white-dwarf binaries5,6 have been limited by the weak gravitational pull of the Milky Way. PSRJ0337+1715 is a hierarchical system of three stars (a stellar triple system) in which a binary consisting of a millisecond radio pulsar and a white dwarf in a 1.6-day orbit is itself in a 327-day orbit with another white dwarf. This system permits a test that compares how the gravitational pull of the outer white dwarf affects the pulsar, which has strong self-gravity, and the inner white dwarf. Here we report that the accelerations of the pulsar and its nearby white-dwarf companion differ fractionally by no more than 2.6×10-6. For a rough comparison, our limit on the strong-field Nordtvedt parameter, which measures violation of the universality of free fall, is a factor of ten smaller than that obtained from (weak-field) Solar System tests3,4 and a factor of almost a thousand smaller than that obtained from other strong-field tests5,6.

Higher-order gravity and the classical equivalence principle

As is well known, the deflection of any particle by a gravitational field within the context of Einstein’s general relativity — which is a geometrical theory — is, of course, nondispersive. Nevertheless, as we shall show in this paper, the mentioned result will change totally if the bending is analyzed — at the tree level — in the framework of higher-order gravity. Indeed, to first order, the deflection angle corresponding to the scattering of different quantum particles by the gravitational field mentioned above is not only spin dependent, it is also dispersive (energy-dependent). Consequently, it violates the classical equivalence principle (universality of free fall, or equality of inertial and gravitational masses) which is a nonlocal principle. However, contrary to popular belief, it is in agreement with the weak equivalence principle which is nothing but a statement about purely local effects. It is worthy of note that the weak equivalence principle encompasses the classical equivalence principle locally. We also show that the claim that there exists an incompatibility between quantum mechanics and the weak equivalence principle, is incorrect.

Does universality of free-fall apply to the motion of quantum probes?

Can quantum-mechanical particles propagating on a fixed spacetime background be approximated as test bodies satisfying the weak equivalence principle? We ultimately answer the question in the negative but find that, when universality of free-fall is assessed locally, a nontrivial agreement between quantum mechanics and the weak equivalence principle exists. Implications for mass sensing by quantum probes are discussed in some details.

A nonmetric theory of gravity

A nonmetric theory of gravity is presented, which agrees with all experiments to date. It possesses a Lagrangian-based nonmetric (i.e. nonminimum) coupling between electromagnetism and gravity which has complete continuous-coordinate-transformation symmetry but violates parity and time-reversal-invariance. The theory predicts the universality of free fall for test bodies, i.e. it obeys the Weak Equivalence Principle (WEP). But due to the nonmetrical coupling between electromagnetism and gravity, it violates the Einstein Equivalence Principle (EEP). Hence, this theory disproves the conjecture due to Schiff which states that any gravitation theory that obeys the WEP must also, unavoidably, obey the EEP. Further examination of the empirical status implications of the EEP is therefore urged.

A quantum test of free fall

Physics![Figure][1] The Leaning Tower of Pisa, Italy PHOTO: © STEFANO POLITI MARKOVINA/ALAMY STOCK PHOTO Galileo Galilei is purported to have dropped objects of different mass from the Leaning Tower of Pisa to demonstrate that they fall at the same rate. In formulating his general theory of relativity, Einstein described this as the universality of free fall—that all objects, irrespective of their mass, will behave identically when subject to the same gravitational field. Taking this into the quantum regime, Duan et al. performed Galileo's drop experiment with rubidium atoms of different quantum mechanical spins. With a sensitive atom-interferometer setup, they showed that the atoms fall at the same rate to within one part in 10 million, upholding Einstein's universality proposition for now. While we await a theory that can unify relativity and the principles of quantum mechanics, such precision-based experimental tests should help place bounds on any proposed theories of quantum gravity. Phys. Rev. Lett. 117 , 023001 (2016). [1]: pending:yes

Test of the Universality of Free Fall with Atoms in Different Spin Orientations.

We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6} m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.

Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6

The Einstein Equivalence Principle (EEP) is one of the foundations of the theory of General Relativity and several alternative theories of gravitation predict violations of the EEP. Experimental constraints on this fundamental principle of nature are therefore of paramount importance. The EEP can be split into three sub-principles: the universality of free fall (UFF), the local Lorentz invariance (LLI) and the local position invariance (LPI). In this paper we propose to use stable clocks in eccentric orbits to perform a test of the gravitational redshift, a consequence of the LPI. The best test to date was performed with the Gravity Probe A (GP-A) experiment in 1976 with an uncertainty of Our proposal considers the opportunity of using Galileo satellites 5 and 6 to improve on the GP-A test uncertainty. We show that considering realistic noise and systematic effects, and thanks to a highly eccentric orbit, it is possible to improve on the GP-A limit to an uncertainty around after one year of integration of Galileo 5 and 6 data.

Gravitational mass of relativistic matter and antimatter

The universality of free fall, the weak equivalence principle (WEP), is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial, m, and gravitational, mg, masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no confirmation for the matter and antimatter at high energies. For the antimatter the situation is even less clear – current direct observations of trapped antihydrogen suggest the limits −65<mg/m<110 not excluding the so-called antigravity phenomenon, i.e. repulsion of the antimatter by Earth. Here we demonstrate an indirect bound 0.96<mg/m<1.04 on the gravitational mass of relativistic electrons and positrons coming from the absence of the vacuum Cherenkov radiation at the Large Electron–Positron Collider (LEP) and stability of photons at the Tevatron collider in presence of the annual variations of the solar gravitational potential. Our result clearly rules out the speculated antigravity. By considering the absolute potential of the Local Supercluster (LS), we also predict the bounds 1−4×10−7<mg/m<1+2×10−7 for an electron and positron. Finally, we comment on a possibility of performing complementary tests at the future International Linear Collider (ILC) and Compact Linear Collider (CLIC).

Finsler-type modification of the Coulomb law

Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest a modified dispersion relation which could be phrased in terms of Finsler geometry. On a Finslerian space-time, the universality of free fall is still satisfied but local Lorentz invariance is violated in a way not covered by standard Lorentz invariance violation schemes. In this paper we consider a Finslerian modification of Maxwell's equations. The corrections to the Coulomb potential and to the hydrogen energy levels are computed. We find that the Finsler metric corrections yield a splitting of the energy levels. Experimental data provide bounds for the Finsler parameters.

Some remarks on an old problem of radiation and gravity

The assumed universality of the equivalence principle suggests that a particle in a gravitational field has identical physics to one in an accelerated frame. Yet, energy considerations prohibit radiation from a static particle in a gravitational field while the accelerating counterpart emits. Solutions to the fundamental problems of radiation from charges in a gravitational field and consequences to the equivalence principle usually contrast the far-field and global nature of radiation with the local validity of the equivalence principle. Here, we suggest reliable physical solutions that recognizes the essential need for motional currents and the magnetic component for radiation to occur. Our discussion reiterates the need for a fresh careful look at universality of free fall (UFF) for charged particles in a gravitational field.

Measuring the gravitational free-fall of antihydrogen

Antihydrogen holds the promise to test, for the first time, the universality of free-fall with a system composed entirely of antiparticles. The AEgIS experiment at CERN’s antiproton decelerator aims to measure the gravitational interaction between matter and antimatter by measuring the deflection of a beam of antihydrogen in the Earths gravitational field (\(\overline {\textrm {g}}\)). The principle of the experiment is as follows: cold antihydrogen atoms are synthesized in a Penning-Malberg trap and are Stark accelerated towards a moire deflectometer, the classical counterpart of an atom interferometer, and annihilate on a position sensitive detector. Crucial to the success of the experiment is the spatial precision of the position sensitive detector. We propose a novel free-fall detector based on a hybrid of two technologies: emulsion detectors, which have an intrinsic spatial resolution of 50 nm but no temporal information, and a silicon strip / scintillating fiber tracker to provide timing and positional information. In 2012 we tested emulsion films in vacuum with antiprotons from CERN’s antiproton decelerator. The annihilation vertices could be observed directly on the emulsion surface using the microscope facility available at the University of Bern. The annihilation vertices were successfully reconstructed with a resolution of 1–2 μmon the impact parameter. If such a precision can be realized in the final detector, Monte Carlo simulations suggest of order 500 antihydrogen annihilations will be sufficient to determine \(\overline {\textrm {g}}\)with a 1 % accuracy. This paper presents current research towards the development of this technology for use in the AEgIS apparatus and prospects for the realization of the final detector.

Summary of session C9: experimental gravitation

General relativity (GR) is based on the Universality of Free Fall, the Universality of the Gravitational Redshift, and Local Lorentz Invariance, alltogether called the Einstein Equivalence principle. This implies that gravity has to be described by a metrical theory. Such theories in general give rise to the standard effects like perihelion shift, light deflection, gravitational time delay, Lense-Thirring effect, and the Schiff effect. Only if the underlying theory is Einstein’s GR we have certain values for these effects. GR in turn predicts the existence, certain properties, and a particular dynamics of gravitational waves, black holes, binary systems, etc. which are also subject to experimental/observational proof. This includes practical applications in clock synchronization, positioning, navigation and geodesy.

Rydberg atom in gravity

The local position invariance of a physical system is examined using a Rydberg atom and the universality of free fall is found to be invalid for a quantum system. A Rydberg atom is analysed in Newtonian gravity and curved space. The energy is found to vary as n2 for very large values of the principal quantum number n. The change in energy is calculated using this formalism and compared to a similar calculation by Chiao. The value that we have got from our calculation is found to be 6 orders higher in magnitude than Chiao's value. These results can be of significance in gravitational redshift experiements proposed by Muller et al and Wolf et al.

Was Newton right? A search for non-Newtonian behavior of weak-field gravity

Empirical tests of Einstein's metric theory of gravitation, even in the non- relativistic, weak-field limit, could play an important role in judging theory-driven extensions of the current Standard Model of fundamental interactions. Guided by Galileo's work and his own experiments, Newton formulated a theory of gravity in which the force of attraction between two bodies is independent of composition and proportional to the inertia of each, thereby transparently satisfying Galileo's empirically informed conjecture regarding the Universality of Free Fall. Similarly, Einstein honored the manifest success of Newton's theory by assuring that the linearized equations of GTR matched the Newtonian formalism under classical conditions. Each of these steps, however, was explicitly an approximation raised to the status of principle. Perhaps, at some level, Newtonian gravity does not accurately describe the physical interaction between uncharged, unmagnetized, macroscopic bits of ordinary matter. What if Newton were wrong? Detecting any significant deviation from Newtonian behavior, no matter how small, could provide new insights and possibly reveal new physics. In the context of physics as an empirical science, for us this yet unanswered question constitutes sufficient motivation to attempt precision measurements of the kind described here. In this paper we report the current status of a project to search for violation of the Newtonian inverse square law of gravity.