Chapter 1
1 Introduction
2 Testable Models for Experiments
3 Lunar Laser Ranging
4 Geodetic Precession and NASA ’s Gravity Probe –B
5 Interplanetary Laser Ranging
6 A STEP Experiment
Acknowledgement
References
Chapter 2
1 Introduction
2 Currently Running Experiments
3 The Principle of Our Experiment
4 The Experimental Setup
5 The Measuring Procedure and First Results
6 Outlook
Acknowledgment
References
Chapter 3
1 Introduction
2 Rotation
3 Equation of Motion for Angular Momentum
3.1 The Motion of Gyroscopes
3.2 Motion of an Elementary Particle with Spin 1/2
4 Gravitational Field of a Rotating Body
4.1 Stationary Gravitational Field
4.2 Gravitational Field of a RotatingSource
5 Lense –Thirring Effect
5.1 Motion of a Point Particle
5.2 Motion of a Gyroscope
6 On the Observation of Gravitomagnetic Effects
6.1 Lense –Thirring Effect for Point Particles
6.2 Lense –Thirring Effect for Gyroscopes
6.3 Lense –Thirring Effect in Quantum Physics
Appendix: Theory of Congruences
References
Chapter 4
1 Gravity Probe B: An Experiment in Physics – and Management
2 Shape of the Experiment
3 Incremental Prototyping
4 Risk Mitigation and Verification Matrix
5 Probe-C Assembly March –August 1999
6 Probe-C Testing in Science Mission Dewar August –December 1999
7 The Four Discrepancies and Their Resolution August 1999 –June 2000
8 Spacecraft,Electronics Systems,Integration &Test
8.1 Spacecraft
8.2 Payload Electronics
8.3 Integration &Test,Ground Station,and Launch
Acknowledgement
Chapter 5
1 Introduction
2 Gravitoelectromagnetism
2.1 Gravitational Larmor Theorem
2.2 Gravitoelectromagnetic Field
2.3 Free Fall Is Not Universal
2.4 GEM Stress-Energy Tensor
2.5 Oscillations of a Charged Rotating Black Hole
3 Structure of Time and Relativistic Precession
4 Clock Effect in the PPN Approximation
5 Detection of the Gravitomagnetic Temporal Structure
6 Quantum Origin of Inertia
7 Discussion
Appendix: Mach and the Absolute Motion of Light
References
Chapter 6
1 Introduction
2 Covariant and Noncovariant Equations of Motion of a Spinning Particle in an Electromagnetic Field
2.1 The Problem with the Covariant Equations of Motion
2.2 What Is the Correct Definition of the Coordinate of a Spinning Particle?
2.3 The Noncovariant Formalism
3 Spin Precession in a Gravitational Field
3.1 General Relationships
3.2 Spin –Orbit Interaction
3.3 Spin –Orbit Interaction in the Schwarzschild Field
3.4 Spin –Spin Interaction
3.5 Spin Precession in a Plane Gravitational Wave
4 E .ects of Higher Order in Spin
4.1 Outline of the General Formalism
4.2 Second-Order Spin Effects in an Electromagnetic Field
4.3 Second-Order Spin Effects in a Gravitational Field
5 Multipoles of Black Holes
6 Gravitational Interaction of Spinning Bodies, and Radiation of Compact Binary Stars
6.1 Spin Interactions in a Two –Body Problem
6.2 Contribution of Spin Interactions to Gravitational Radiation
Acknowledgements
References
Chapter 7
1 Introduction
2 The GEO 600 Concept
3 Noise Contributions
3.1 Seismic Noise
3.2 Thermal Noise
3.3 Laser Noise
4 Shot Noise
5 The GEO600 Sensitivity
6 Interferometry
7 Civil Engineering
7.1 Construction
7.2 Electronics and Data Management
8 The Vacuum System
8.1 Vacuum Pumps
8.2 Vacuum Tubes
8.3 The Vacuum Achieved
8.4 Vacuum Tanks
9 The 30 Meter Prototype
10 Data Management
11 Outlook
References
Chapter 8
1 Introduction
2 Wave generation from Isolated Sources
2.1 Einstein Field Equations
2.2 Multipole Expansion in Linearized Gravity
3 The Quadrupole Moment Formalism
3.1 Multipole Expansion in the Far Region
3.2 The Far-Field Quadrupole Formula
3.3 Energy Balance Equation and Radiation Reaction
4 Post-Newtonian Gravitational Radiation
4.1 The Multipole Moments in the Post-Newtonian Approximation
4.2 Post-Newtonian Radiation Reaction
5 Light Propagation in Gravitational Fields of Isolated Sources
5.1 General Solution of the Light Propagation Equation
5.2 Time Delay and Bendingof Light
6 Detection of Gravitational Waves
References
Chapter 9
1 Introduction
2 Cosmological Gravitational Waves
3 Cosmological Pump Field
4 Solving Gravitational Wave Equations
5 Theoretical and Observational Constraints
6 Detectability of Relic Gravitational Waves
7 Conclusion
Acknowlegements
References
Chapter 10
1 Equivalence Principles and the Structure of Gravitation Theories
1.1 From the Weak to Einstein ’s Equivalence Principle
1.2 Theoretical Contexts for Analyses of the EEP
1.3 The Role of Locality
1.4 Relevant Observables
2 Theoretical Frameworks for the Analysis of EEP Tests
2.1 The TH µ–Formalism
2.3 The Kostelecky Formalism
2.4 Formalisms Based on Matter –Field Equations of Motion
3 Motivations for Continued Testing of the EEP
3.1 StringTheory
3.2 Loop Quantum Gravity
3.3 Gauge Theories of Gravity and Other Possibilities
4 Experimental and Observational Tests of the EEP
4.1 Tests of the Universality of Freefall
4.2 Spectroscopic and Atomic Clock Tests of the EEP
4.3 EEP Tests Involving Observations of Wave Propagation
References
Chapter 11
1 Background
2 STEP Concepts
3 STEP Instrument Configuration
3.1 Test Mass Shapes and Con .guration
3.2 Differential Accelerometer Operation
4 Experiment Operations and Timeline
4.1 Test for Systematic Effects
5 Error Analysis and Mission Tradeoffs
5.1 Orbit Height Effects in the Model
5.2 Satellite Rotation and EP Signal Detection in the Error Model
6 Conclusion
References
Chapter 12
1 Introduction
2 Experiment Description
2.1 Drop Tower Bremen
2.2 Experimental Set –Up and Timing
2.3 Main Error Sources
3 SQUID Based Position Detector
3.1 The DC SQUID
3.2 SQUID Control Unit
3.3 Detector Principle
4 Experimental Results
4.1 Inductance Measurements
4.2 Performance of the Detector
4.3 Free Fall Measurement System
4.4 Free Fall Tests of the Measurement System
5 Conclusions
Acknowledgement
References
Chapter 13
1 Introduction
2 Accelerometers Dedicated to Space
3 Electrostatic Servo –Controlled Accelerometer Operation
4 The ASTRE and STAR Accelerometers
5 From CHAMP to GRACE and GOCE Instrument
6 Electrostatic Accelerometers to Test the Equivalence Principle in Space
7 Space Gravity Wave Antenna
8 Perspective
References
Chapter 14
1 Introduction
2 Theoretical Motivation and Phenomenology
2.1 Overview
2.2 Yukawa Potentials
2.3 Current Constraints on New Yukawa Forces
3 Problems in Testing Gravityat Very Short Distances
3.1 General Problems
3.2 Quantitative Example:Parallel Plate Gravity Experiment
4 Very Short Distance Null Gravity Experiments
4.1 Null Experiment #1
4.2 Null Experiment #2
5 Discussion
Acknowledgments
References
Chapter 15
1 Introduction
2 Restricted Three-Body Problem in General Relativity
3 Discussion
Acknowledgments
References
Chapter 16
1 Introduction
2 Dynamical Equations for Bodies,Light,and Clocks
3 New Long Range Force?
4 LLR ’s Science –Related Range Signals
5 The Gravitomagnetic Interaction
6 Inductive (Inertial)Forces
Acknowledgement
References
Chapter 17
1 Introduction
2 ASTROD Payload Concept and Technological Development Requirements
3 Orbit Simulation
3.1 Post –Newtonian Ephemerides and ASTROD Orbits
3.2 Simulation of ASTROD Ranging Data
3.3 Estimation of Parameters
4 Solar Angular Momentum and Solar Oscillations
5 G –Wave Detection
6 Mini –ASTROD and Super –ASTROD
7 Outlook
References
Chapter 18
1 Introduction
2 Basics of Atomic Clocks
2.1 Definitions
2.2 Perturbing Effects and Remedies
3 Clocks Based on rf Transitions
3.1 Cs Beam Machine
3.2 Optically Pumped Cs Clocks
3.3 Atomic Fountain Clocks
3.4 Clocks Based on Ion Traps
4 Optical Clocks
4.1 Clocks Based on Ion Traps
4.2 Optical Frequency Standards Based on Neutral Atoms
4.3 ExpandingCloud of Cold Ballistic Ca Atoms
5 Measurement of Optical Frequencies
6 Optical Frequency Standards for the Realization of the Meter
Acknowledgements
References
Chapter 19
Chapter 20
1 The Pulsar Population
2 Pulsar Timing
3 Binary Pulsars and Gravity Experiment I Double –Neutron –Star Binaries
3.1 PSR B1913+16
3.2 PSR B1534+12
4 Binary Pulsars and Gravity Experiment II. Small –Eccentricity Binary Pulsars
4.1 Gravitational Dipole Radiation
4.2 Violation of the Strong Equivalence Principle
4.3 Violation of Local Lorentz Invariance and Conservation Laws
5 Geodetic Precession
References
Chapter 21
1 Introduction
2 Lagrangian Theory
3 Quantization
3.1 Dificulties with the Derivative Coupling
3.2 A Coherent Method f Quantization
4 Interaction Picture and the S –Matrix
4.1 Evolution Operator and Transition Amplitudes
4.2 S –Matrix
5 Calculation of the Relativistic Phase Shifts in the Weak –Field Approximation
5.1 Calculation in Configuration Space
5.2 Calculation in the Momentum Representation
5.3 Analogy with the Electromagnetic Interaction
Appendix A: Dirac Equation in Curved Space –Time
Appendix B: Weak-Field Approximation
Appendix C: A Stationary Phase Calculation
Appendix D: Derivation of the Wave Function Using the Momentum Representation
Acknowledgement
References
Chapter 22
1 Introduction
2 WEP,EEP and the Axial Interaction
3 Spin and Gravitation
4 Spin, Equivalence Principle,and Long –Range Forces
5 Experimental Searches for Photon Polarization Coupling and Tests of EEP
6 Experimental Searches for Electron Spin –Coupling
6.1 Weak Equivalence Principle Experiments
6.2 Finite –Range Spin –Coupling Experiments
6.3 Spin –Spin CouplingExperiments
6.4 Cosmic Spin –Coupling Experiments
7 Outlook
References
Chapter 23
1 The Dirac Equation
2 Spin and the Poincaré Group
3 General Relativity
References
Chapter 24
1 Introduction
2 The Model: A Modification of the Dirac Equation
3 Plane Wave Solutions and Neutrino Propagation
4 The Non –relativistic Limit
4.1 The Non –relativistic Field Equation
4.2 Modifications of the Energy Levels
5 Conclusion
Acknowledgement
References
Chapter 25
1 Introduction
2 On the Equivalence Principle
3 A Caveat
4 Electric Charge and Magnetic Flux Conservation
5 No Interaction of Charge and Flux “Substrata” with Gravity
6 Constitutive Law of Electrodynamics and Its Relation to Gravity
6.1 Non-local
6.2 Non-linear
6.3 Linear: Abelian Axion, inter Alia
6.4 Isotropic
6.5 Centrosymmetric
7 Non-minimal Coupling Involving Curvature, Nonmetricity and Torsion?
7.1 Non-minimal Coupling Violating Charge and/or Flux Conservation
7.2 “Admissible” Non-minimal Coupling
8 Outlook
Acknowledgments
References