Relativistic Effects In The Absolute Gravimeters

Absolute gravimeters are devices that determine the local acceleration due to gravity.The precision of the measured gravitational acceleration not only depends on the control of various experimental conditions,but also on the accuracy of theoretical model which relates the measured results with the gravitational acceleration.With the improving technology of gravity measurement and the experimental conditions being optimized,smaller and smaller effects can be detected with the absolute gravimeters.Thus,it is extremely necessary to establish a high precise theoretical model.Currently,in Special Relativity,research on the theoretical model focus on the finite speed of light effect,which gives different results,arising a fierce controversy.In addition,studies on the theoretical models in General Relativity are rather rare,and the results they gave have some limitations.Therefore,developing a more complete and general relativistic theoretical model for absolute gravimeters is of significant importance.It can not only help to resolve the controversy on the finite speed of light effect,and improve the precision of absolute gravimeters,but also to serve for testing the general relativistic effects experimentally,such as gravitational wave detection with atom interferometry.This thesis mainly studies the relativistic effects in free-fall corner-cube absolute gravimeters and atom interferometric gravimeters.Our studies mainly contain the following points:(1)combining the work principle of free-fall corner-cube absolute gravimeters,four dimensional time-space diagrams and the theory of relativistic measurement,we calculate the controversial finite speed of light effect in this absolute gravimeter in a "relativistic geometry" method,which can be used as a theoretical reference to solve the controversy.(2)Extending the "relativistic geometry" method,we further analyze the relativistic effects in free-fall corner-cube absolute gravimeters.In this work,we focus on the relativistic effects related to the devices,which haven't been perfectly considered before,and develop a complete and relativistic theoretical model for this absolute gravimeter.(3)Combining the work principle of atom interferometric gravimeters and four dimensional time-space diagrams,we thoroughly perform a coordinate transformation for the reference system to simplify the calculation,analyze the finite speed of light effect in atom gravimeters still existing controversy in current research,and finally give a more complete expression.According to our results,current research on finite speed of light effect in atom gravimeters has neglected a correction term,which is in fact far too important to be ignored.This analysis plays a critical role on estimating the related systematic errors.(4)Extending the calculations in(3)to general relativistic frame,and introducing the earth's rotation effect,gradient effect,gravitational potential effect and so on,we also establish a more complete and general relativistic model for atom gravimeters.This universal model discusses about the atoms moving spatially in three dimensions,and can provide a theoretical support for the research programs on testing general relativity with the atom interferometry.Choosing typical parameter values to estimate various relativistic effects in the absolute gravimeters,we find:according to the current precision of absolute gravimeters,only the finite speed of light effect can be detected,and the other relativistic effects such as the transverse doppler effect,the gravitational red effect,and the relativistic effects related to earth's rotation are so tiny that can be neglected in current gravity measurement.With the technology development of gravity measurement in the future,the transverse doppler effect in free-fall corner-cube absolute gravimeters and some of the relativistic effects related to the earth5s rotation in atom gravimeters,which are at 10-3 ?Gal level,may have a great potential to be detected.