Geodetic VLBI Lecture 2 18 October 2010

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

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

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

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

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

Galileo transformations 18 October 2010

Hendrik Lorentz Lorentz transformation 18 October 2010

Hermann Minkowsky Minkowski space or Minkowski spacetime 18 October 2010

Henri Poincare Poincaré group of symmetry transformations 18 October 2010

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

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

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

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

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

Special relativity Minkowsky metric 18 October 2010

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

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

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

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

Aberration of light 18 October 2010

Conventional group delay model 18 October 2010

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

General relativity Geometric theory of gravitation Einstein, October 2010

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)

Gravitational deflection (lensing) 18 October 2010

Gravitational delay for VLBI 18 October 2010

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

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

Conventional group delay model 18 October 2010

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