2. Gerard t Hooft VSV `Leonardo da Vinci Symposium, TU Delft, March 16, 2007 Utrecht University

3. The electro-magnetic force J.C. Maxwell 1864

4. Gravitation The fourth force: Gravity is an accumulative force ! All atoms in the Earth pull all atoms in your body to the same direction (downwards) !

5. Curved coordinates time Coordinates hight

6. Near a source of gravity (such as the Earth), space and time are curved

7. General Relativity

8. There is a curvature conservation law There is also a matter conservation law (energy, momentum and forces) In Einsteins attempts to find a formula, they did not match ! To make them match, you must assume that not only matter (or Energy ) is the source of gravity, but also pressure !

9. This you will not notice, under ordinary circumstances negative pressure (tension) pressure The total pressure always cancels out !!! Einstein had to add an extra term to his equation. grav. source

10. For light, and electro-magnetic fields, So, light couples twice as strong to gravity as matter ! Light rays bend twice as much as one might expect !

11. time Why does Dark energy make the Universe expand ? - Dark energy requires dark pressure which is negative !

12. The Black Hole Electromagnetism: like charges repel, opposite charges attract charges tend to neutralize Gravity: like masses attract masses tend to accumulate

13. horizon Where is the gravitational field strongest? The formation of a Black Hole even light cannot escape from within this region... Black Hole

14. The Schwarzschild Solution to Einsteins equations Karl Schwarzschild 1916 Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

15. As seen by distant observer As experienced by astro- naut himself They experience time differently. Mathematics tells us that, consequently, they experience particles differently as well Time stands still at the horizon Continues his way through

16. Stephen Hawkings great discovery: the radiating black hole

17. Electro-magnetic radiation gravitational radiation

18. The photon has spin = 1 The graviton has spin = 2

19. Heavy gravitating bodies emit gravitational radiation In the process, they loose energy: the orbit shrinks

20. The binary pulsar PSR 1913+16 (Figure from Weisberg et al. 1981)

21. Orbit shinks 3.1 mm per orbit

22. Violent events in the cosmos

23. LISA A gravitational antenna

24. LIGO Hanford, Wa L aser I nterferometer G ravitational wave O bservatory 4 + 4 km

25. VIRGO Gascina (near Pisa) 3 + 3 km

26. LISA Main Spacecraft Spacecraft # 3 Spacecraft # 2 Secondaries

28. photon graviton The Photon Spin = 1 Spin = 2 P P P P P P P P P P P P P P P P Equal charges repel one another... Equal masses attract one another... The Graviton

29. Moon Earth Sun strength of force This is the wave function of a spin 2 particle Graviton Force and spin

30. The Universal Force Law: Gravitation: Distance Force Maxwell & YM:

31. There are two kinds of curvature: Riemann curvature (space and time near Earth) Ricci curvature (only inside Earth, the real source of gravity) Einstein tried a formula: Ricci curvatureMatter density But there was something wrong ! (for a curved piece of paper, these are the same, only in many-dimensional space-time, Ricci is more special.

32. There is a curvature conservation law There is also a matter conservation law (energy, momentum and forces) In Einsteins original formula, they did not match ! To make them match, you must assume that not only matter (or Energy ) is the source of gravity, but also pressure !

33. This you will not notice, under ordinary circumstances negative pressure (tension) pressure The total pressure always cancels out !!! Einstein had to replace by grav. source