Shapiro Time Delay And Test Of Equivalence Principle

In the 1960s,I.I.Shapiro proposed one more classical test of General Relativity that there will be a relativistic time delay in the round-trip travel for radio signals[1].The single trip time delay can be written as:where ? is one of the PPN parameter[2,3].r is the distance from the source of gravity to the signal.x horizontal axis coordinates of the Cartesian coordinates in which the source is on the origin.From then on,the experiments of Shapiro time delay has been used to constrain the PPN parameter?[2-5].Recently,The best absolate bound with ? that(?-1)=(2.1±2.3)×10-5 is given by the measurement of time delay on the Cassini spacecraft[3,6].It was found by astronomers that different kind of particles emitted from the same source millions lightyears away arrived at earth at different times.They parameterized the difference on arrival time by the PPN parameter ? and thought that different particles(or some particles with different energies)have different ?.The idea was then used to test the Equivalence Principle[7-9].In the detection of GW170817,both gravitational waves and gamma-ray brust observed together from the merger of binary neutron stars[10,11].The GW and GRB emitted from the same source arrived at earth at different times.The difference of arrival time between photons and gravitational wave has been suggested as the difference of Shapiro time delay between graviton and photo by some astronomers.And it was used to test Equivalence Principle[12,13].The aim of this thesis is to show that Shapiro time delay cannot constrain the Equivalence Principle.On the one hand,there are many uncertainties such as the particles may not emitted at the same time.On the other hand,even if the Shapiro time delay for different particle is different,the Equivalence Principle may still not violated.In chapter 2,I discuss the theory of Equivalence Principle and PPN frame.Then I derive the equa-tions of Shapiro time delay for massless and massive particles.The equations for massless and massive particles are a bit different if ??1.In galactic scale,it's shown that time difference between the velocity difference of massless and massive particles is much bigger than the Shapiro time delay difference for massless and massive particles.The Shapiro time delay in Einstein frame for Brans-Dicke theory is discussed in chapter 3.The conformal transformation between Einstein frame and Jordan frame also discussed.In chatper 4,two related issues have been analysed:the first is to constrain the mass of graviton from gravitational wave.The capacity of Tianqin detector to constrain the mass of graviton has been calculated in this part.The second is the massive gravitation theory.