Physics 270 – The Universe: Astrophysics, Gravity and Cosmology

1. Physics 270 – The Universe: Astrophysics, Gravity and Cosmology

2. The History of Cosmology • Mythology vs the scientific method • Cosmos = Earth  solar system  Milky Way  Hubble sphere • Copernicus, Brahe, Kepler, Galileo

3. Newton: Cosmology as a Science • Galileo: The Scientific method & the universality of scientific laws • Newton’s laws • Newton’s gravity: The heavens and the Earth follow the same scientific principles • Galileo: Relativity before Einstein

4. Einstein’sTheories of Special and General Relativity • Principle of Relativity • Giving up absolute space and time • Space and time: where common sense makes no sense • what is here and there or now and then ?

5. Special Relativity • All inertial frames of reference are equivalent • The speed of light is absolute (invariant) • Maxwell’s equations are invariant under Lorentz transformation • Newton’s laws, which are based on absolute space and time, need to be modified

6. Some open problems • How to treat accelerations ? • How to deal with gravity ? • Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s conclusion that information cannot be communicated faster than the speed of light. • Distance is relative, so which distance to use in computing the gravitational force ?

7. Non-inertial reference frame • Non-inertial frames  fictitious forces • centrifugal force • Coriolis force

8. Why is the Space Shuttle orbiting? • The space Shuttle is continuously falling towards the Earth

9. Is there no gravity in space ? No, there is gravity (actu- ally Earth’s gravity at the orbit of the Shuttle is still ~80-90% of its strength on the ground • So why do astronauts appear to be weightless ?

10. What effect does mass have? • Gravity: tendency of massive bodies to attract each other • Inertia: resistance of a body against changes of its current state of motion

11. Is gravity and inertia the same thing ? • No. They are completely different physical concepts. • There is no a priori reason, why they should be identical. In fact, for the electromagnetic force (Coulomb force), the source (the charge Q) and inertia (m) are indeed different. • But for gravity they appear to be identical  Equivalence Principle

12. Eötvös experiment Coriolis Gravity

13. Result of the Eötvös experiment • Gravitational and inertial mass are identical to one part in a billion • modern experiments: identical to one part in a hundred billion

14. What effect does mass have? • Source of gravity • Inertia

15. =1 Principle of Equivalence

16. Strong equivalence principle The laws of physics are precisely the same in all inertial and freely falling frames, there is no experiment that can distinguish them. Weak equivalence principle The laws of mechanics are precisely the same in all inertial and freely falling frames. In particular, gravity is completely indistinguishable from any other acceleration.

17. Consequences of the equivalenceprinciple: mass bends light Observer in freely falling reference frame

18. Consequences of the equivalenceprinciple: mass bends light Outside Observer

19. Examples for light bending

20. Some effects predicted by the theory of general relativity • gravity bends light • gravitational redshift • gravitational time dilation • gravitational length contraction

21. Least action principle • light travels on a path that minimizes the distance between two points for flat space: straight line • a path that minimizes the distance between two points is called a geodesic • Examples for geodesics • plane: straight line • sphere: great circle

22. What is the shortest way to Europe?

23. Spacetime • Fourth coordinate: ct • time coordinate has different sign than spatial coordinates • spacetime distance: • , ,  :metric coefficients

24. Strong equivalence principle The laws of physics are precisely the same in all inertial and freely falling frames, there is no experiment that can distinguish them. Weak equivalence principle The laws of mechanics are precisely the same in all inertial and freely falling frames. In particular, gravity is completely indistinguishable from any other acceleration.

25. General relativity • Mass tells space how to curve • Space tells mass how to move

26. Why does space curvature result in attraction ?

27. Euclidean (flat) geometry: • Given a line and a point not on the line, only one line can be drawn through that point that will be parallel to the first line • The circumference of a circle of radius r is 2 r • The three angles of a triangle sum up to 180

28. Spherical geometry: • Given a line and a point not on the line, no line can be drawn through that point that will be parallel to the first line • The circumference of a circle of radius r is smaller than 2 r • The three angles of a triangle sum up to more than 180

29. Hyperbolic geometry: • Given a line and a point not on the line, an infinite number of lines can be drawn through that point that will be parallel to the first line • The circumference of a circle of radius r is larger than 2 r • The three angles of a triangle sum up to less than 180

30. Tidal forces (I)

31. Tidal forces (II)

32. Tidal forces (III)

33. Tidal forces (IV)

34. So does the existence of tidal forces violate the equivalence principle ? • there is no freely falling frame of reference in which gravity vanishes globally • there is a freely falling frame of reference in which gravity vanishes locally • equivalence principle holds for small labs, “small” in comparison to distances over which the gravitational field changes significantly. • spacetime is locally flat

35. Towards a new theory for gravity ... Requirements: • it should locally fulfill the equivalence principle • it should relate geometry of space to the distribution of mass and energy • it should be locally flat • it should reduce to Newtonian gravity for small velocities (compared to c) and for weak gravitational fields

36. Distribution of mass and energy in the universe (stress-energy tensor) Geometry of spacetime (Einstein tensor) The entire Universe in one line

37. Why is general relativity (GR) difficult ? • conceptually difficult (relativity of space and time, curvature of spacetime) • set of 10 coupled partial differential equations • non linear (solutions do not superpose) • space and time are part of the solution  exact solution known only for a very few simple cases

38. Checklist • How to deal with accelerations ? • How to deal with gravity ? • Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s conclusion that information cannot be communicated faster than the speed of light. • Distance is relative, so which distance to use in computing the gravitational force ?    

39. So what is left to do ? • Show that general relativity provides a consistent and accurate description of nature test it by experiment/observation

40. Some open problems • How to deal with accelerations ? • How to deal with gravity ? • Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s conclusion that information cannot be communicated faster than the speed of light. • Distance is relative, so which distance to use in computing the gravitational force ?

41. general relativity: Boost factor • special relativity:

42. First test: bending of light • Star light should be bend as it passes through the gravitational field of the Sun, i.e., it should be possible to see a star behind the Sun

43. First test: bending of light • Star light should be bend as it passes through the gravitational field of the Sun, i.e., it should be possible to see a star behind the Sun • General relativity predicts an angle of 1.75”, twice as big as that predicted by Newtonian gravity • measured by Arthur Eddington in 1919. Key event for Einstein’s elevation to a celebrity.

44. Test 2: Perihelion shift of Mercury • Planets do not move on perfect ellipses, but ellipses are precessing. This effect is due to the gravitational force exerted by the other planets

45. Test 2: Perihelion shift of Mercury • Planets do not move on perfect ellipses, but ellipses are precessing. This effects is caused by the perturbing effect of the other planets gravitational field. • Mercury’s precession amounts to 5600” per century, but only 5557” can be explained by Newtonian gravity, leaves a discrepancy of 43” per century. • General relativity predicts exactly this additional precession

46. Test 3: gravitational time dilation and redshift • Can be measured by experiments on Earth (challenging, but feasible) • Better: White Dwarfs(very compact objects; mass comparable to that of the Sun, radius comparable to that of the Earth), because they have a stronger gravitational field • Even better: Neutron Stars and Pulsars(very compact objects; mass comparable to that of the Sun, radius only 10-100 km), because they have a very strong gravitational field

47. Test 4: Binary pulsar PSR 1913+16 • Pulsar: a rapidly rotating highly magnetized neutron star that emits radio pulses at regular intervals • Discovered by Bell and Hewish in 1967 • Nobel Prize in physics (1974)

48. Test 4: Binary pulsar PSR 1913+16 • Pulsar:

49. Test 4: Binary pulsar PSR 1913+16 • Binary pulsar: two pulsars orbiting each other • Orbital time: 7.75h • Discovered by Hulse and Taylor in 1974 • Nobel Prize in physics (1993)

50. Test 4: Binary pulsar PSR 1913+16 • Precession: 4.2º per year