Local Position Invariance Research Articles

Cosmological test of local position invariance from the asymmetric galaxy clustering

ABSTRACT The local position invariance (LPI) is one of the three major pillars of Einstein equivalence principle, ensuring the space–time independence on the outcomes of local experiments. The LPI has been tested by measuring the gravitational redshift effect in various depths of gravitational potentials. We propose a new cosmological test of the LPI by observing the asymmetry in the cross-correlation function between different types of galaxies, which predominantly arises from the gravitational redshift effect induced by the gravitational potential of haloes at which the galaxies reside. We show that the ongoing/upcoming galaxy surveys give a fruitful constraint on the LPI-violating parameter, α, in the distant universe (redshift z ∼ 0.1–1.8) over the cosmological scales (separation s ∼ 5–$10\, {\rm \mathit{ h}^{ -1}\,Mpc}$) that have not yet been explored, finding that the expected upper limit on α can reach 0.03.

Similarity matching of medical question based on Siamese network

BackgroundWith the rapid development of the medical industry and the gradual increase in people’s awareness of their health, the use of the Internet for medical question and answer, to obtain more accurate medical answers. It is necessary to first calculate the similarity of the questions asked by users, which further matches professional medical answers. Improving the efficiency of online medical question and answer sessions will not only reduce the burden on doctors, but also enhance the patient’s experience of online medical diagnosis.MethodThis paper focuses on building a bidirectional gated recurrent unit(BiGRU) deep learning model based on Siamese network for medical interrogative similarity matching, using Word2Vec word embedding tool for word vector processing of ethnic-medical corpus, and introducing an attention mechanism and convolutional neural network. Bidirectional gated recurrent unit extracts contextual semantic information and long-distance dependency features of interrogative sentences; Similar ethnic medicine interrogatives vary in length and structure, and the key information in the interrogative is crucial to similarity identification. By introducing an attention mechanism higher weight can be given to the keywords in the question, further improving the recognition of similar words in the question. Convolutional neural network takes into account the local information of interrogative sentences and can capture local position invariance, allowing feature extraction for words of different granularity through convolutional operations; By comparing the Euclidean distance, cosine distance and Manhattan distance to calculate the spatial distance of medical interrogatives, the Manhattan distance produced the best similarity result.ResultBased on the ethnic medical question dataset constructed in this paper, the accuracy and F1-score reached 97.24% and 97.98%, which is a significant improvement compared to several other models.ConclusionBy comparing with other models, the model proposed in this paper has better performance and achieve accurate matching of similar semantic question data of ethnic medicine.

Testing the gravitational redshift with an inner Solar System probe: The VERITAS case

The NASA Discovery-class mission VERITAS, selected in June 2021, will be launched toward Venus after 2027. In addition to the science instrumentation that will build global foundational geophysical datasets, VERITAS proposed to conduct a technology demonstration for the Deep Space Atomic Clock (DSAC-2). A first DSAC successfully operated in low-Earth orbit for more than two years, demonstrated the trapped ion atomic clock technology, and established a new level of performance for clocks in space. DSAC-2 would have further improvements in size, power, and performance. It would host a $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ grade USO to produce a frequency output with short-term stability of less than $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$ (where $\ensuremath{\tau}$ is the averaging time). However, due to funding shortfalls, DSAC-2, had to be canceled. The initially foreseen presence of an atomic clock on board the probe, however, raised the question whether this kind of instrumentation could be useful not only for navigation and time transfer but also for fundamental physics tests. In this work, we consider the DSAC-2 atomic clock and VERITAS mission as a specific example to measure possible discrepancies in the redshift predicted by general relativity by using an atomic clock onboard an interplanetary spacecraft. In particular we investigate the possibility of measuring possible violations of the local Lorentz invariance and local position invariance principles. We perform accurate simulations of the experiment during the VERITAS cruise phase. We consider different parametrizations of the possible violations of the general relativity, different operational conditions, and several different assumptions on the expected measurement performance. We show that DSAC-2 onboard VERITAS would provide new and improved constraints with respect to the current knowledge. Our analysis shows the scientific value of atomic clocks like DSAC-2 hosted onboard interplanetary spacecraft.

Universality-of-clock-rates test using atom interferometry with T3 scaling

Metric descriptions of gravitation, among them general relativity as today's established theory, are founded on assumptions summarized by the Einstein equivalence principle (EEP). Its violation would hint at unknown physics and could be a leverage for the development of quantum gravity. Atomic clocks are excellent systems to probe aspects of EEP connected to (proper) time and have evolved into a working horse for tests of local position invariance (LPI). Even though the operational definition of time requires localized and idealized clocks, quantum systems like atoms allow for spatial superpositions that are inherently delocalized. While quantum experiments have tested other aspects of EEP, no competitive test of LPI has been performed or proposed allowing for an intrinsic delocalization. We extend the concepts for tests of the universality of clock rates (one facet of LPI) to atom interferometry generating delocalized quantum clocks. The proposed test depends on proper time with a favorable scaling and is, in contrast to fountain clocks, robust against initial conditions and recoil effects. It enables optical frequencies so that the projected sensitivity exceeds the one of state-of-the-art localized clocks. These results extend our notion of time, detached from classical and localized philosophies.

Time keeping and searching for new physics using metastable states of Cu, Ag, and Au

We study the prospects of using the electric quadrupole transitions from the ground states of Cu, Ag and Au to the metastable state $^2{\rm D}_{5/2}$ as clock transitions in optical lattice clocks. We calculate lifetimes, transition rates, systematic shifts, and demonstrate that the fractional uncertainty of the clocks can be similar to what is achieved in the best current optical clocks. The use of these proposed clocks for the search of new physics, such as time variation of the fine structure constant, search for low-mass scalar dark matter, violation of Local Position Invariance and violation of Lorenz Invariance is discussed.

Improved Limits for Violations of Local Position Invariance from Atomic Clock Comparisons.

We compare two optical clocks based on the ^{2}S_{1/2}(F=0)→^{2}D_{3/2}(F=2) electric quadrupole (E2) and the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition of ^{171}Yb^{+} and measure the frequency ratio ν_{E3}/ν_{E2}=0.932829404530965376(32), improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ν_{E3}=642121496772645.10(8) Hz, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant α to 1.0(1.1)×10^{-18}/yr and of the proton-to-electron mass ratio μ to -8(36)×10^{-18}/yr. Using the annual variation of the Sun's gravitational potential at Earth Φ, we improve limits for a potential coupling of both constants to gravity, (c^{2}/α)(dα/dΦ)=14(11)×10^{-9} and (c^{2}/μ)(dμ/dΦ)=7(45)×10^{-8}.

Test of the Einstein Equivalence Principle near the Galactic Center Supermassive Black Hole.

During its orbit around the four million solar mass black hole Sagittarius A* the star S2 experiences significant changes in gravitational potential. We use this change of potential to test one part of the Einstein equivalence principle: the local position invariance (LPI). We study the dependency of different atomic transitions on the gravitational potential to give an upper limit on violations of the LPI. This is done by separately measuring the redshift from hydrogen and helium absorption lines in the stellar spectrum during its closest approach to the black hole. For this measurement we use radial velocity data from 2015 to 2018 and combine it with the gravitational potential at the position of S2, which is calculated from the precisely known orbit of S2 around the black hole. This results in a limit on a violation of the LPI of |β_{He}-β_{H}|=(2.4±5.1)×10^{-2}. The variation in potential that we probe with this measurement is six magnitudes larger than possible for measurements on Earth, and a factor of 10 larger than in experiments using white dwarfs. We are therefore testing the LPI in a regime where it has not been tested before.

Gravitational Redshift Test Using Eccentric Galileo Satellites.

We report on a new test of the gravitational redshift and thus of local position invariance, an integral part of the Einstein equivalence principle, which is the foundation of general relativity and all metric theories of gravitation. We use data spanning 1008days from two satellites of Galileo, Europe's global satellite navigation system, which were launched in 2014, but accidentally delivered on elliptic rather than circular orbits. The resulting modulation of the gravitational redshift of the onboard atomic clocks allows the redshift determination with high accuracy. Additionally, specific laser ranging campaigns to the two satellites have enabled a good estimation of systematic effects related to orbit uncertainties. Together with a careful conservative modeling and control of other systematic effects we measure the fractional deviation of the gravitational redshift from the prediction by general relativity to be (0.19±2.48)×10^{-5} at 1 sigma, improving the best previous test by a factor 5.6. To our knowledge, this represents the first reported improvement on one of the longest standing results in experimental gravitation, the Gravity Probe A hydrogen maser rocket experiment back in 1976.

A null test of general relativity based on a long-term comparison of atomic transition frequencies

The local position invariance principle of general relativity stipulates that non-gravitational experiments should give outcomes that are independent of the position and orientation of the reference frames in which they have been performed. Here, we study the change in the rates of clocks on Earth with the spatial change of the solar potential, constraining the variation of a non-gravitational interaction—the hyperfine splitting in hydrogen and caesium atoms—to β = (2.2 ± 2.5) × 10−7, a factor of two improvement over previous estimates. Our result is based on the comparison between the long-term fractional frequency variation of four hydrogen masers that are part of an ensemble of clocks comprising the National Institute of Standards and Technology, Boulder, and the fractional frequencies of primary frequency standards operated by leading metrology laboratories in the United States, France, Germany, Italy and the United Kingdom over a period of more than 14 years. Using our results together with the previous best estimates of β, we impose strict limits on the variation of fundamental constants, resulting in a test of general relativity with an unprecedented level of precision.

General relativity tests with space clocks in highly elliptic orbits

The test of the Einstein Equivalence Principle (EEP) is of crucial importance as a deviation from it could hint to quantum effects in gravity or to unification with the other fundamental forces. One aspect of EEP is the local position invariance (LPI), which can be tested by measuring the gravitational red-shift. As an example of a possible space mission which could test the EEP, we will discuss a recently proposed satellite experiment, Einstein Gravitational RedShift Probe (E-GRIP), with the aim to test LPI using an hydrogen maser atomic clock on a highly elliptic orbit around Earth and compare the on-board clock to clocks located on Earth via a microwave link.

Resonator with Ultrahigh Length Stability as a Probe for Equivalence-Principle-Violating Physics.

In order to investigate the long-term dimensional stability of matter, we have operated an optical resonator fabricated from crystalline silicon at 1.5K continuously for over one year and repeatedly compared its resonance frequency f_{res} with the frequency of a GPS-monitored hydrogen maser. After allowing for an initial settling time, over a 163-day interval we found a mean fractional drift magnitude |f_{res}^{-1}df_{res}/dt|<1.4×10^{-20}/s. The resonator frequency is determined by the physical length and the speed of light and we measure it with respect to the atomic unit of time. Thus the bound rules out, to first order, a hypothetical differential effect of the Universe's expansion on rulers and atomic clocks. We also constrain a hypothetical violation of the principle of local position invariance for resonator-based clocks and derive bounds for the strength of space-time fluctuations.

Tests of gravitational symmetries with radio pulsars

Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.

Some progress of the weak equivalence principle test

The Weak Equivalence Principle (WEP) together with Local Position Invariance (LPI) and Local Lorentz Invariance (LLI) forms the Einstein Equivalence Principle (EEP), which is one of the basic assumptions of Einsteins General Relativity. However, most of the theories trying to unify the gravitation with the quantum world, which is mostly described by the Standard Model, indicate some violation of the WEP. So the discovery of violation of the WEP would have a very important scientific significance. Testing the WEP with the highest possible precision is always a frontier issue in the world. This paper introduces almost all the ways of testing the WEP all over the world, including using the simple pendulum, torsion balance, free fall and lunar laser ranging. Whats more, a lot of space missions have been proposed to test the WEP with a higher precision by many groups and institutions. The latest progress of these tests will also be described here.

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.

Spacecraft Doppler tracking with possible violations of LLI and LPI: upper bounds from one-way measurements on MEX

We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express (MEX) spacecraft to test possible violations of local Lorentz invariance (LLI) and local position invariance (LPI). These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China. These downlink signals were sent by MEX for telemetry at X-band. Because we are not able to decode the data in the form of telemetry and separate them from the carrier frequency, this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s−1. Even so, the residuals can still impose upper bounds on LLI and LPI at 10−1, which is consistent with the prediction based on our analysis of the detectability. Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work, one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.

Testing the local position invariance of Planck's constant in general relativity

Testing the local position invariance of Planck's constant in general relativity

The stability of fundamental constants

Abstract The tests of the constancy of fundamental constants are tests of the local position invariance and thus of the equivalence principle, at the heart of general relativity. After summarising the links between fundamental constants, gravity, cosmology and metrology, a brief overview of the observational and experimental constraints on their variation is proposed.

Spacecraft Doppler tracking with possible violations of LLI and LPI: preliminary bounds on LLI from Mars Express

Three-way spacecraft Doppler tracking is currently widely used and it plays an important role in the control and navigation of deep space missions. Using the theory of three-way Doppler tracking, including possible violations of the local Lorentz invariance (LLI) and the local position invariance (LPI), we analyze the post-fit residuals of three-way Doppler tracking data of Mars Express. These Doppler observations were carried out from August 7th to 8th in 2009, with an uplink station administered by the European Space Agency at New Norcia in Australia and three downlink stations at Shanghai, Kunming and Urumqi in China. We find that, although these observations impose preliminary bounds on LLI at the level of 10−2, they are not suitable for testing LPI because of the configuration of these stations and the accuracy of the observations. To our knowledge, this is one of the first attempts in China to apply radio science to the field of fundamental physics.

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.

Spacecraft Doppler tracking with possible violations of LLI and LPI: a theoretical modeling

Currently two-way and three-way spacecraft Doppler tracking techniques are widely used and play important roles in control and navigation of deep space missions. Starting from a one-way Doppler model, we extend the theory to two-way and three-way Doppler models by making them include possible violations of the local Lorentz invariance (LLI) and the local position invariance (LPI) in order to test the Einstein equivalence principle, which is the cornerstone of general relativity and all other metric theories of gravity. After taking the finite speed of light into account, which is the so-called light time solution (LTS), we make these models depend on the time of reception of the signal only for practical convenience. We find that possible violations of LLI and LPI cannot affect two-way Doppler tracking under a linear approximation of LTS, although this approximation is sufficiently good for most cases in the solar system. We also show that, in three-way Doppler tracking, possible violations of LLI and LPI are only associated with two stations, which suggests that it is better to set the stations at places with significant differences in velocities and gravitational potentials to obtain a high level of sensitivity for the tests.