Probing the Nature of Gravity: Confronting Theory and Experiment in Space (Space Sciences Series of ISSI, 34)

Observing our Universe and its evolution with ever increasing sensitivity from ground-based or space-borne telescopes is posing great challenges to Fundamental Physics and Astronomy. The remnant cosmic microwave background, as beautifully measured by successive space missions COBE, WMAP, and now PLANCK, provides a unique probe of the very early stages of our Universe. The red-shift of atomic lines in distant galaxies, the dynamics of pulsars, the large scale structure of galaxies, and black holes are a few manifestations of the theory of General Relativity. Yet, today, we understand only 4% of the mass of our Universe, the rest being called dark energy and dark matter, both of unknown origin! A second family of space missions is currently emerging; rather than designing ever more re nedobservationalinstruments,physicistsandengineersseekalsotousethespaceenvironment to perform high-precision tests of the fundamental laws of physics. The technology required for such tests has become available only over the course of the last decades. Clocks of high accuracy are an example. They are based on advances in atomic and laser physics, such as cold atoms, enabling a new generation of highly sensitive quantum sensors for ground and space experiments. Two experiments in space have now tested Einstein’s relativity theory: • Several decades ago, Gravity Probe A con rmed the accuracy of the gravitational red-shift ?5 according to general relativity to a level of 7× 10 [R. F. C. Vessot et al. , Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser, Phys. Rev. Lett. 45, 2081–2084 (1980)]. Contents Preface Foreword Introduction The Confrontation Between General Relativity and Experiment Introduction The Einstein Equivalence Principle and Metric Theories of Gravity Solar-System Tests of Weak-Field Gravity Binary Pulsars Gravitational-Wave Tests of Gravitation Theory Tests of Gravity in the Strong-Field Regime Conclusions Acknowledgements References From Classical Theory to Quantum Gravity Introduction How to Break General Relativity Low-energy Effects of Quantum Gravity Models Involving Extra Dimensions Alternative Approaches Dark Energy Where to Look for Broken General Relativity Conclusions Open Access References Wolfgang Pauli and Modern Physics Introduction A Brief Biography Discovery of the Exclusion Principle Some Side Remarks Exclusion Principle and the New Quantum Mechanics Pauli's Discovery of the Relation between Matrix Mechanics and Wave Mechanics (Letter to P. Jordan) Supplementary Remarks. On Pauli's Invention of non-Abelian Kaluza-Klein Theory in 1953 The Pauli Letters to Pais Acknowledgements References Gravitomagnetism in Physics and Astrophysics Introduction Spinning Objects in Flat Spacetime Curvilinear Coordinates in Flat Spacetime The Coriolis Field Einstein Gravity Particle Dynamics in Curved Spacetime Classical Spin and Gravity Clock Effect and Gravitomagnetism Phase Shift and Gravitomagnetism The Gravitomagnetic Field of Rotating Objects Precession Effects in Gravitating Many-Body Systems Lense-Thirring Effect Schiff Effect de Sitter Effect Effects in the Field of Rotating Black Holes Higher Order Dynamics of Gravitating Spinning Binaries Acknowledgement References Gravity Probe B Data Analysis The NASA-Stanford Gravity Probe B Mission (GP-B) The Actual vs. the Ideal Gravity Probe B Issue 1: Changing Polhode Period Issues 2 & 3: The Two Forms of Newtonian Torque The Evolving Data Analysis Process Trapped Flux Mapping (TFM) TFM and the Resonance Torques Conclusion Acknowledgements References Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models Introduction The Measurement of Gravitomagnetism with LAGEOS, LAGEOS 2 and the GRACE Earth Gravity Models Method of the 2004 Analysis of LAGEOS and LAGEOS 2 Data Using the GRACE Models Results of the Measurement of the Lense-Thirring Effect LARES Introduction A New Laser-Ranged Satellite at a Lower Altitude than LAGEOS and LAGEOS 2 Structural Requirements for LARES Satellite Gravitational Uncertainties and Even Zonal Harmonics A Reply to the Critical Remarks by Iorio on the Error Analysis and Error Budget of the Gravitomagnetism Measurements with LAGEOS, LAGEOS 2 and LARES Orbital Inclination Determination Comparing Different Earth Gravity Field Models Uncertainties in the Higher Degree Even Zonal Harmonics Uncertainties in the Rate of Change of J4 and of Higher Even Zonal Harmonics Measurement of the Orbital Inclination of LAGEOS-type Satellites and Atmospheric Delay Modeling Errors in SLR Conclusions Acknowledgements References Lense-Thirring Precession in the Astrophysical Context Introduction Quasi Periodic Oscillations in Accreting Neutron Stars and Black Holes QPO Models and Lense-Thirring Precession Relativistic Precession in Binary Pulsars The Outstanding Case of the Double Pulsar Relativistic Precession of the Spin of PSR J0737-3039B References New Frontiers at the Interface of General Relativity and Quantum Optics Introduction Rotation Sensors Foucault Pendulum Sagnac Interferometer Atom Interferometer Enhancement Factor Cold Atoms and the Need for Microgravity Present Activities and Goals Bose-Einstein Condensates A Brief History BEC and Microgravity Gravito-magnetism The Relativistic Notion of Rotation Lense-Thirring and Geodetic Precession Experiments on Gravito-magnetism Gravity Probe B LAGEOS Satellites Observation of Gravito-magnetic Effects in a Two-Body System Gödel's Universe Basic Features Time Travel Visualization of Light Propagation Possible Analogies Summary Acknowledgements References The Pioneer Anomaly in the Light of New Data Introduction New Doppler Data and Their Preliminary Analysis The Extended Pioneer Doppler Data Set A Strategy to Find the Origin of the Pioneer Anomaly Direction of the Pioneer Anomaly Study of the Planetary Encounters Study of the Temporal Evolution of the Anomaly Analysis of the Individual Trajectories for Both Pioneers Investigation of On-Board Systematics Using Flight Telemetry to Study the Spacecrafts' Behavior The Pioneer Spacecraft Compartment Temperatures and Thermal Radiation Telemetry Overview RTG Temperatures and Anisotropic Heat Reflection RTG Power Electrically Generated Heat The Thermal Control Subsystem Studying the Pioneer Anomaly with New Horizons Electrically Generated Heat Heat from the RTG Acceleration Due to Emitted Heat Conclusions Acknowledgements References The Puzzle of the Flyby Anomaly Introduction Gravity Assist Maneuvers The Earth Flyby Anomaly Conclusions Acknowledgements References Time-Dependent Nuclear Decay Parameters: New Evidence for New Forces? Introduction Evidence for Correlations Between Nuclear Decay Rates and Earth-Sun Distance Implications of the Solar Flare of 2006 December 13 Phenomenology of a Time-Dependent Decay Parameter lambda(t) Modifications of Decay Constants in External Fields General Features of Decays in External Fields Decays in External Electromagnetic Fields Weak Electromagnetic Fields Furry's Formalism for Static Fields; The Phase-Space Prescription Extension of Furry's Formalism to Time-Dependent Fields Decay Modifications by Constant Fields beta-Decay in a Static, Homogeneous, Isotropic Field beta-Decay in a Static, Homogeneous, Spin-Dependent Field Decay Modifications from Time-Dependent External Fields Modeling The Interaction Potential Calculational Results Seasonal Variation of the Fine Structure Constant and alpha-Decay Discussion of Critical Papers Discussion of 14C Decay Ongoing and Future Experiments Implications for Detecting the Relic Neutrino Background Summary and Conclusions Acknowledgements References Tests of the Gravitational Inverse Square Law at Short Ranges Introduction Detecting Anomalous Forces Laboratory ISLV Tests at Ranges Greater than a Millimeter ISLV Tests from 1 μm to 1 mm Torsion Pendulum Sub-mm Experiments Non-Torsion-Pendulum Sub-mm ISLV Tests General Considerations for Very Short Range ISLV Tests ISLV Tests Below 1 μm Theoretical Ideas Suggesting Inverse Square Law Violation Acknowledgements References The Equivalence Principle and the Constants of Nature Introduction Are the Constants Constant? Varying Constants and Equivalence Principle Violations Scenarios for the Selection of Coupling Constants Dynamics versus Anthropics Conclusions References Laboratory Tests of the Equivalence Principle at the University of Washington Introduction, Motivation The Apparatus Torsion Balance Torsion Angle Readout Vacuum Vessel and Shields Turntable Data Taking Data Reduction Systematic Effects Gravity Gradients Gravitational Gradient Compensators Pendulum Gravitational Moments Tilt Effects Temperature Effects Magnetic Effects Preliminary Results Differential Acceleration Towards Astronomical Sources Constraints on Long-Range Yukawa Interactions Conclusions Acknowledgements References Lunar Ranging, Gravitomagnetism, and APOLLO Introduction LLR Science Gravitomagnetism Introduction to Gravitomagnetism Familiar Examples Generalized Gravitomagnetism and Application to the Moon's Orbit More than a Coordinate Effect? Inside LLR Analysis Experimental Conflict Scenario Summary Statement APOLLO Acknowledgements Open Access References Atom-Based Test of the Equivalence Principle Open Access References Testing General Relativity with Atomic Clocks Introduction Tests of General Relativity Atomic Clock Ensemble in Space (ACES) SAGAS Acknowledgements References Fundamental Constants and Tests of General Relativity-Theoretical and Cosmological Considerations Introduction Physical Systems and Constraints Physical Systems Setting Constraints Constraints on the Fine Structure Constant Unification and Correlated Variations Theories with "Varying Constants" Making a Constant Dynamical General Dangers Ways Out Links with Cosmology Cosmological Evolution About Dark Energy Beyond the Copernican Principle Testing General Relativity on Astrophysical Scales Toward a Post-LambdaCDM Formalism Conclusion References Testing the Stability of the Fine Structure Constant in the Laboratory Introduction Precision Optical Spectroscopy and Optical Frequency Measurements Laser Stabilization Ultra-Short Pulse Lasers and Frequency Combs Extending the Frequency Comb Self-Referencing Frequency Conversions Frequency Measurement of the 1S-2S Transition in Atomic Hydrogen High-Precision Laboratory Measurements and Variation of the Fine Structure Constant Upper Limit for the Drift of the Fine Structure Constant from Optical Frequency Measurements Absolute Frequency Measurements Coupling to Gravity Direct Comparison of Optical Frequencies Frequency Combs for Astrophysics Conclusions Acknowledgements Open Access References Constraining Fundamental Constants of Physics with Quasar Absorption Line Systems Introduction The Method Atomic Data Quasar Absorption Line Systems Source of Errors Variation of the Fine-Structure Constant alpha The Many-Multiplet Method The Alkali Doublet (AD) Method Variation of the Proton-to-Electron Mass Ratio μ H2 HD NH3 Combinations of Constants The 21 cm Absorbers Other Molecules: CO, OH, NH3, HCO+ Conclusion Acknowledgements References The Role of Dark Matter and Dark Energy in Cosmological Models: Theoretical Overview Introduction: Urbain Jean Joseph Le Verrier: Neptune Discovery (1846) & Mercury's Anomaly (1859) (an Invisible ("Dark") Object or a Violation of the Newtonian Gravity Law) Dark Matter in the Galactic Clusters and in Spiral Galaxies Different Components of Matter Indirect Searches of DM Dark Matter in the Galactic Center Lambda-Term, Dark Energy or Alternative Theories of Gravity Lambda-Term Revisited Lambda-Term or Dark Energy? Standard Cosmology vs. f(R) Gravity Conclusions Acknowledgements References Some Uncomfortable Thoughts on the Nature of Gravity, Cosmology, and the Early Universe Introduction Spontaneous Birth of the Universe Primordial Cosmological Perturbations Cosmological Perturbations in Inflationary Theory Discovering Relic Gravitational Waves in the Cosmic Microwave Background Radiation Field-Theoretical Formulation of General Relativity Generalizing the General Relativity Conclusions Acknowledgements References The Cosmic Microwave Background and Fundamental Physics Introduction The CMB Current CMB Observations The CMB and the Nature of Gravity The Generation of Perturbations Inflation and String Theory Further Links with Fundamental Theory-Parity Violation? Constraints on alpha Variation Constraints on MOND and Modified Gravity Primordial Non-Gaussianity A Bianchi Model Universe? Bianchi Polarisation Could the Cold Spot Be a Cosmic Texture? Effects of Anisotropy During Inflation? Conclusions Acknowledgements References Perspectives on Dark Energy Introduction Cosmological Constant Cosmological Constant Problems Regulating the Gravitation of the Quantum Vacuum Cosmological Parameters The Shape of New Physics Parameterizing the Equation of State New Gravitational Phenomena A Fundamental Change in Our View of the Universe Summary Acknowledgements References An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging Introduction The Systematic Error of Gravitational Origin in the LAGEOS-LAGEOS II Test A New Approach to Extract the Lense-Thirring Signature from the Data On the LARES Mission A Conservative Evaluation of the Impact of the Geopotential on the LARES Mission The Impact of Some Non-Gravitational Perturbations Conclusions Acknowledgements References Misalignment and Resonance Torques and Their Treatment in the GP-B Data Analysis Introduction Misalignment Torques Observations Explanation and Calculation of Torque Data Analysis in the Presence of Misalignment Torques Resonance Torques Observations Explanation and Calculation of Torque Data Analysis in the Presence of Resonance Torques Summary and Conclusion Acknowledgements References Polhode Motion, Trapped Flux, and the GP-B Science Data Analysis Introduction Gyroscope Polhode Motion, Trapped Flux, and GP-B Readout Free Gyroscope Motion: Polhoding GP-B Readout: London Moment and Trapped Flux GP-B High Frequency Data Changing Polhode Period: On-Orbit Discovery and Its Explanation Trapped Flux Mapping: Concept and Importance Trapped Flux Mapping Key Points of TFM Trapped Flux Mapping: Three Analysis Levels Level A: Asymmetry Parameter, Polhode Phase and Angle Level B: Spin Phase Level C: Trapped Field Distribution and Polhode Phase Refining Trapped Flux Mapping: Results Conclusions Acknowledgements References The Gravity Probe B Data Analysis Filtering Approach Introduction "Simple" GP-B Data Analysis: Pre-Launch Concept Inertial Frame and the Relevant Vectors Measurement Model Two-Floor Structure of Data Analysis Modification of the Pre-launch Scheme Floor 1: One-Orbit Batch Data Reduction Floors 1 and 2: Readout Scale Factor Modeling Gyroscope Orientation Profiles: Moving Window Method Floor 2: Misalignment and Roll-Resonance Torque Modeling. Torque Compensation and Relativity Estimation Misalignment and Roll-Resonance Torque Model Elimination of Torque Contributions from the 1st Floor Orientation Profiles: Proof of Concept Step 1. Independent Kalman filter/smoother for each segment and each gyroscope Step 2. Reconstruction of "Relativistic Trajectory": Subtracting Torque Contributions Two-Floor Analysis Results Data Analysis Expansion: Two-Second Filter Conclusion Acknowledgements References GP-B Systematic Error Determination Introduction Approaches to Estimating Experiment Uncertainty Bottom-up Analyses Sensitivity Tests Gyro-to-Gyro Variation Data Selection Tests Two Independent Analysis Methods and Teams Initial Models of Scale Factor, Torques, and the Associated Early Science Results Model Improvements Sensitivity Tests Roll Phase Uncertainty Coupling to Science Result Gyroscope Position Coupling to the Science Result Electromagnetic Interference (EMI) SQUID Non-linearity Torques Other than Those Due to Patch Effect Potentials Summary Acknowledgements References Space-Time Metrology for the LISA Gravitational Wave Observatory, and Its Demonstration on LISA Pathfinder Introduction LISA Measurement Scheme The Basic Element: The Doppler Link Noise in the Doppler Link Noise in LISA Acceleration Noise Acceleration of Fiducial Points Interferometer Noise Proving Space-Time Metrology with LISA Pathfinder Acknowledgements References The Microscope Mission and Its Uncertainty Analysis Introduction The MICROSCOPE Space Experiment Satellite Configuration Instrument Concept and Design Instrument Performances Experiment Systematic Errors and in Orbit Calibration Mission Performance and Discussion Acknowledgements References The STEP and GAUGE Missions Introduction The STEP Mission Introduction The STEP Experiment Spacecraft and Operations The GAUGE Mission Proposal Introduction Technological Concept Scientific Objectives Macroscopic Equivalence Principle Microscopic Equivalence Principle Inverse Square Law Spin-Coupling Quantum Decoherence Summary References Satellite Test of the Equivalence Principle Uncertainty Analysis Motivation Program Design Description of Representative Analysis Connectivity Tradeoffs Error Budgets Description of Error Terms with Specific Conclusions from GP-B Conclusions References What Determines the Nature of Gravity? A Phenomenological Approach Introduction How to Explore Gravity The Structure of Dynamics Existence of Inertial Frames The Inertial Law Order of Equations of Motion Linearity Law of Reciprocal Action The Structure of Gravity The Foundations of Metric Gravity Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance The Constancy of the Speed of Light The Relativity Principle The Consequence Motivating Einstein's Field Equations Proving Consequences of General Relativity Solar System Effects The Gravitational Redshift Light Deflection Perihelion/Periastron Shift Gravitational Time Delay Direct measurement Measurement of frequency change Lense-Thirring Effect Schiff Effect The Strong Equivalence Principle Strong Gravity Effects Open Problems-Unexplained Observations Dark Matter Dark Energy Pioneer Anomaly Flyby Anomaly Increase of Astronomical Unit Quadrupole and Octupole Anomaly The Search for Signals of Quantum Gravity Theoretical Approaches Experimental Approaches Extreme Situations Extremely high energy Extremely low energy Large distances Weak accelerations Strong accelerations Strong gravitational fields Better Accuracy and Sensitivity New Tests "Misusing" High Precision Devices The Need for Improved Tests Acknowledgements References