1. Imperial College, LONDON, 12-15 SEPTEMBER, 2008 From local to global relativity Tuomo Suntola, Finland Physical Interpretations of Relativity Theory XI

2. T. Suntola, PIRT XI, London, 12-15 September, 20082 Newtonian space defines no limits to space or physical quantities; - the velocity of an object increases linearly under the influence of a constant force - the state of rest is inseparable from the state of rectilinear motion On board of Galileo ship …

3. T. Suntola, PIRT XI, London, 12-15 September, 20083 c velocity time Newtonian space defines no limits to space or physical quantities; - the velocity of an object increases linearly under the influence of a constant force - the state of rest is inseparable from the state of rectilinear motion On board of Galileo ship …

4. T. Suntola, PIRT XI, London, 12-15 September, 20084 c velocity time c velocity kinetic energy Newtonian space defines no limits to space or physical quantities; - the velocity of an object increases linearly under the influence of a constant force - the state of rest is inseparable from the state of rectilinear motion On board of Galileo ship …

5. T. Suntola, PIRT XI, London, 12-15 September, 20085 Relativistic space: - increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration From Galileo ship to space craft … c velocity time c velocity kinetic energy

6. c velocity time T. Suntola, PIRT XI, London, 12-15 September, 20086 Relativistic space: - increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration c velocity From Galileo ship to space craft … kinetic energy

7. c velocity time T. Suntola, PIRT XI, London, 12-15 September, 20087 c velocity kinetic energy Relativistic space: - increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration Mathematical description (SR): redefinition of coordinate quantities: From Galileo ship to space craft …

8. T. Suntola, PIRT XI, London, 12-15 September, 20088 Schwarzschild solution of GR field equations: Gravitation in modified coordinates … via equivalence principle ct’ dd M ds r' ds  r'

9. T. Suntola, PIRT XI, London, 12-15 September, 20089 Schwarzschild solution of GR field equations: ct’ dd M ds r' ds  r' Gravitation in modified coordinates … via equivalence principle

10. T. Suntola, PIRT XI, London, 12-15 September, 200810 Schwarzschild solution of GR field equations: ct’ dd M ds r' ds  r' Gravitation in modified coordinates … via equivalence principle  ff= v ff /c

11. T. Suntola, PIRT XI, London, 12-15 September, 200811 Schwarzschild solution of GR field equations: The (coordinate) velocity of free fall in Schwarzschild space goes to zero at the critical radius 0 0.5 1 010203040 ct’ dd M ds r' ds  r' Gravitation in modified coordinates … via equivalence principle  ff= v ff /c

12. T. Suntola, PIRT XI, London, 12-15 September, 200812 Hypothetical homogeneous space The system of nested energy frames local galaxy group frame Milky Way frame Solar frame Earth frame “Relativity of rest energy”

13. T. Suntola, PIRT XI, London, 12-15 September, 200813 Hypothetical homogeneous space The system of nested energy frames Milky Way frame Solar frame Earth frame local galaxy group frame “Relativity of characteristic frequencies”

14. T. Suntola, PIRT XI, London, 12-15 September, 200814 Satellite in Earth gravitational frame

15. T. Suntola, PIRT XI, London, 12-15 September, 200815 Satellite in Earth gravitational frame 0 0.2 0.4 0.6 0,8 1 00.20.40.60.8 GR DU  2 =  1 f ,  /f

16. T. Suntola, PIRT XI, London, 12-15 September, 200816 Local relativity:Global relativity (Dynamic Universe): Distinctive characteristics of local and global relativity by local momentum via insert of mass equivalence by gravitation via tilting of space Rest energy Kinetic energy Description of finiteness Total energyVelocity in spaceWhat is finite ?

17. T. Suntola, PIRT XI, London, 12-15 September, 200817 Velocity of mass object on board Jump to Galileo ship … Velocity of light on board ? characterized as a velocity frame …

18. T. Suntola, PIRT XI, London, 12-15 September, 200818 Velocity of mass object on board Jump to Galileo ship … Velocity of light on board ? Momentum of mass object on board characterized as a velocity frame … characterized as a momentum frame …

19. T. Suntola, PIRT XI, London, 12-15 September, 200819 Velocity of mass object on board Jump to Galileo ship … Velocity of light on board ? Momentum of mass object on board Momentum of light on board (as reduced by the Doppler-effect) characterized as a momentum frame … characterized as a velocity frame …

20. T. Suntola, PIRT XI, London, 12-15 September, 200820 Velocity of mass object on board Jump to Galileo ship … Velocity of light on board ? Momentum of mass object on board Momentum of light on board (as reduced by the Doppler-effect) characterized as a momentum frame … characterized as a velocity frame … The observed phase velocity is conserved

21. T. Suntola, PIRT XI, London, 12-15 September, 200821 Momentum of mass object on board Momentum of light on board (as reduced by the Doppler-effect) characterized as a momentum frame … Phase velocity, group velocity, observed frequencey

22. T. Suntola, PIRT XI, London, 12-15 September, 200822 Phase velocity, group velocity, observed frequencey MkMk A (k+3) A (k+2) A (k+1) B (k+1)  B(k+1)  A(k+2)  A(k+1)

23. T. Suntola, PIRT XI, London, 12-15 September, 200823 Phase velocity, group velocity, observed frequencey MkMk A (k+3) A (k+2) A (k+1) B (k+1)  B(k+1)  A(k+2)  A(k+1)

24. Propagation and observation of electromagnetic radiation B BB C CC A AA

25. C CC A AA

26. T. Suntola, PIRT XI, London, 12-15 September, 200826 Phase velocity, group velocity, observed frequencey c0c0 B AA C BB AA Frequency observed B AA

27. T. Suntola, PIRT XI, London, 12-15 September, 200827 Propagation and observation of light Milky Way frame Earth Hypothetical homogeneous space Bending of light path - D is increased due to local bending of space -  T is increased (Shapiro delay) - c is reduced - is reduced - f = c/ is conserved - p = h 0 f is conserved - redshift of wavelength  =  D /D

28. T. Suntola, PIRT XI, London, 12-15 September, 200828 Velocity of mass object on board Jump to Galileo ship … Velocity of light on board ? Momentum of mass object on board Momentum of light on board (as reduced by the Doppler-effect) characterized as a momentum frame … characterized as a velocity frame … Michelson - Morley interferometer: no change in momentum in different arms – zero result guaranteed

29. T. Suntola, PIRT XI, London, 12-15 September, 200829 Local relativity:Global relativity: Distinctive characteristics of local and global relativity Energy – momentum four-vector Planck constant energy momentum mass wave number Quantum of radiation

30. T. Suntola, PIRT XI, London, 12-15 September, 200830 Mass object as a closed energy structure (resonator) Internal (rest) momentum

31. T. Suntola, PIRT XI, London, 12-15 September, 200831 Mass object as a closed energy structure (resonator) Internal (rest) momentum Back wave Front wave

32. T. Suntola, PIRT XI, London, 12-15 September, 200832 Mass object as a closed energy structure (resonator) Internal (rest) momentumExternal momentum Back wave Front wave

33. T. Suntola, PIRT XI, London, 12-15 September, 200833 Mass object as a closed energy structure (resonator) Internal (rest) momentumExternal momentum Back wave Front wave

34. T. Suntola, PIRT XI, London, 12-15 September, 200834 Mass object as a closed energy structure (resonator) Internal (rest) momentumExternal momentum Back wave - Doppler shift Front wave +Doppler shift

35. T. Suntola, PIRT XI, London, 12-15 September, 200835 Mass object as a closed energy structure (resonator) Internal (rest) momentumExternal momentum

36. Unified expression of energy Coulomb energy A cycle of radiation The rest energy of matter B q2q2 q1q1 r icic F EM icic Intrinsic Planck constant T. Suntola, PIRT XI, London, 12-15 September, 200836

37. T. Suntola, PIRT XI, London, 12-15 September, 200837 ImInternal (rest) momentumExternal momentum Re – Re +  c c  c c Mass object as a closed energy structure

38. T. Suntola, PIRT XI, London, 12-15 September, 200838 ImInternal (rest) momentumExternal momentum Re – Re +  c c  c c The double slit experiment Mass object as a closed energy structure Absorption pattern

39. T. Suntola, PIRT XI, London, 12-15 September, 200839 Signal transmission from Earth satellite Sagnac delay