Tests of General Relativity: Equivalence Principle and Experimental Verification, Study notes of Astronomy

Download Tests of General Relativity: Equivalence Principle and Experimental Verification and more Study notes Astronomy in PDF only on Docsity! 1 Tests of the Equivalence Principle and the “Classic” Weak Field Tests  Compartmentalizing General Relativity into testable components  Tests of the Equivalence Principle  Post-Newtonian Parameterization  The classic solar system tests  Deflection of light  Precession of perihelion of Mercury  Shapiro delay 2 The Metric Tensor  Definition of (3d) metric tensor gij … the distance between points (x1, x2, x3) and (x1+δx1,x2+δx2,x3+δx3)  Can simply generalize this to 4-d spacetime  Geodesics are those paths which minimize the distance between two points A and B  For a given matter distribution, metric is determined by Einstein’s equation (ten coupled partial differential equations) 5 III.5 : Tests of the Einstein Equivalence Principle (EEP)  Weak Equivalence Principle (WEP)  Dates back to Galileo (or earlier!)  Statement: the acceleration experienced by an object in a given gravitational field is independent of the objects mass or composition.  Inertial and gravitational mass are equivalent  To test this, we need a formulism for describing deviations from the WEP. 6  Weak Equivalence Principle formulism  Consider an object as a collection of masses bound together by various interactions (weak, strong, electromagnetic)  Suppose that some part of the binding energy associated with these interactions violates the WEP  If we measure the acceleration of two bodies with different composition, we can define 7  Classic Experiment of Eotvos…  Used torsional balance to determine that η<10-8  Roll, Krotkov, Dicke (Princeton)…  Improved Eotvos method and obtained tighter limit η<10-11 The confrontation between GR and Experiment; C.M.Will 10  Classic experiment of Michelson & Morley using interferometry  Hughes-Drever experiments probe “c” through effect on energy levels in atomic nucleus  Can now directly time “one-way” trips of light signal The confrontation between GR and Experiment; C.M.Will 11  Local Positional Invariance  Is physics independent of location?  Test through gravitational redshift  Suppose two identical clocks are placed at different locations in gravitational field… we’ve seen that there is a fractional shift of frequency  But if the physics governing the clocks depends on position, then we can write 12  Pound-Rebka-Snider tower experiment (Harvard)…  frequency shift of gamma-ray emission line from Fe-57  Null redshift experiment…  Synchronization of three H-maser clocks (used changes in solar grav. potential) The confrontation between GR and Experiment; C.M.Will 15  Classic expedition by Eddington to observe solar eclipse…  First confirmation of GR  Made Einstein instantly famous!  Modern measurements of light-bending possible from VLBI observations of quasars… get GR result to 0.2%. The confrontation between GR and Experiment; C.M.Will 16 III.8: Shapiro delay  Spacetime curvature increase time taken for a photon to propagate from point A to B  Within our solar system, spacetime curvature from Sun dominates… so events that occur on far side of Sun are “late” THE PARAMETER (1+4)/2 DEFLECTION ‘OF LIGHT VLBI Y , i Hipparcos _| PSR 1937421 5s | Voyager wPir ey Radio Optical ° 1.05 | Pot | 1.00 e a s 095-- es 4 xs ly 1.05 SHAPIRO TIME DELAY | i 1.00 I" o9s|- i i 1 Lt 1920 1940 1960 1970 1980 1990 2000 YEAR OF EXPERIMENT 17