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GRAVITATIONAL WAVES

Utrecht University. GRAVITATIONAL WAVES. Gerard ’t Hooft VSV `Leonardo da Vinci’ Symposium, TU Delft, March 16, 2007. J.C. Maxwell 1864. The electro-magnetic force. Gravitation. The fourth force:. Gravity is an accumulative force !. All atoms in the Earth

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GRAVITATIONAL WAVES

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  1. Utrecht University GRAVITATIONAL WAVES Gerard ’t Hooft VSV `Leonardo da Vinci’ Symposium, TU Delft, March 16, 2007

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

  3. 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) !

  4. hight time Coordinates Curved coordinates

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

  6. General Relativity

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

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

  9. 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 !

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

  11. The Black Hole Electromagnetism: like charges repel, oppositecharges attract → charges tend to neutralize Gravity: like masses attract → masses tend to accumulate

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

  13. The Schwarzschild Solution to Einstein’s equations Karl Schwarzschild 1916 “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”

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

  15. Stephen Hawking’s great discovery: the radiating black hole

  16. Electro-magnetic radiation gravitational radiation

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

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

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

  20. (Figure from Weisberg et al. 1981) Orbit shinks 3.1 mm per orbit

  21. Violent events in the cosmos

  22. LISA A gravitational antenna

  23. LIGO Hanford, Wa Laser Interferometer Gravitational wave Observatory 4 + 4 km

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

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

  26. The END

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

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

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

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

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

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

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