1. Geodetic VLBI Lecture 2 18 October 2010

2. Lecture plan 1. From measurement of space and time to measurement of space-time 2. Elements of the Special and General Relativity 18 October 2010

3. Lecture plan 1. From measurement of space and time to measurement of space-time 2. Elements of the Special and General Relativity 18 October 2010

4. From measurement of space and time to measurement of space-time 3 dimensions 1 dimension Space Time 3 & 1 18 October 2010

5. From measurement of space and time to measurement of space-time 3 dimensions 1 dimension Space Time x(t), y(t), z(t) – equations of motion 3 & 1 18 October 2010

6. Space Time X Z X’ Z’ Y Y’ t’ t r=r’ 2 1 V 18 October 2010

7. Galileo transformations 18 October 2010

8. Hendrik Lorentz Lorentz transformation 18 October 2010

9. Hermann Minkowsky Minkowski space or Minkowski spacetime 18 October 2010

10. Henri Poincare Poincaré group of symmetry transformations 18 October 2010

11. Albert Einstein "On the Electrodynamics of Moving Bodies” 1905 Main postulates and final formulae 18 October 2010

12. Lecture plan 1. From measurement of space and time to measurement of space-time 2. Elements of the Special and General Relativity 3. Exercises 18 October 2010

13. Postulates of Special relativity The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body." 18 October 2010

14. Newton theory vs special relativity 1. The existence of infinitely many inertial frames. Each frame is of infinite size (covers the entire universe). Any two frames are in relative uniform motion. 2. The inertial frames move in all possible relative uniform motion. 3. There is a universal, or absolute, time. 4. Two inertial frames are related by a Galilean transformation. 5. In all inertial frames, Newton's laws, and gravity, hold. 1.Same as the Newtonian assumption. 2. Rather than allowing all relative uniform motion, the relative velocity between two inertial frames is bounded above by the speed of light. 3. Instead of universal time, each inertial frame has its own time. 4. The Galilean transformations are replaced by Lorentz transformations. 5. In all inertial frames, all laws of physics are the same (this leads to the invariance of the speed of light). 18 October 2010

15. Space Time X Z X’ Z’ Y Y’ t’ t r = r’ ? 2 1 V 18 October 2010

16. Special relativity Minkowsky metric 18 October 2010

17. Lorentz transformation X Z X’ Z’ Y Y’ 2 1 V 18 October 2010

18. Aberration Star γ Dra – change of position (Bradley, 1727) 18 October 2010

19. Aberration, not parallax Bradley was searching for parallax, but discovered aberration of light. Parallax was found only 100 years later. Parallax depends on distance Aberration does not depend on distance 18 October 2010

20. Aberration of light c – speed of light A V 18 October 2010

21. Aberration of light 18 October 2010

22. Conventional group delay model 18 October 2010

23. Possible modification of the conventional group delay model Constant acceleration 18 October 2010

24. General relativity Geometric theory of gravitation Einstein, 1916 18 October 2010

25. Contribution to fundamental science Geoscience Australia 18 October 2010 Test of General Relativity (deflection of the quasar position by the Sun or planet) First experiment (Eddington, 1919) – Solar eclipse First VLBI experiment (Schuh et al, 1988) – Jupiter passage near quasar VLBI experiment for “speed of gravity” (Kopeikin, Fomalont, 2002)

26. Gravitational deflection (lensing) 18 October 2010

27. Gravitational delay for VLBI 18 October 2010

28. Gravitational delay for VLBI For geodetic VLBI this is a difference of the Shapiro delays for the both ends of baseline Sun: ~40 nsec for 1º from Sun; ~400 psec for 180º 18 October 2010

29. Gravitational delay for VLBI Non-zero for all radio sources irrelevant to their closeness to Sun For the Earth it is ~20 psec 18 October 2010

30. Conventional group delay model 18 October 2010

31. Lecture plan 1. From measurement of space and time to measurement of space-time 2. Elements of the Special and General Relativity 18 October 2010