軸對稱時光機

1. 軸對稱時光機 「廣義相對論的物理與數學」 暑期研習營 2011.8.19 葉李華 http://www.yehleehwa.net/

2. 大綱 ●時光旅行的科與幻 ●軸對稱時光機發展簡史 ●（廣義相對論架構下）為何時光可能倒流 ●軸對稱時光機的直覺解釋 ●光錐結構的深入探討 ●容許封閉類時曲線的時空 ●淺探：究竟是物理還是數學？

3. ●時光旅行的科與幻 ●軸對稱時光機發展簡史 ●（廣義相對論架構下）為何時光可能倒流 ●軸對稱時光機的直覺解釋 ●光錐結構的深入探討 ●容許封閉類時曲線的時空 ●淺探：究竟是物理還是數學？

4. 時光旅行的科幻鼻祖 • “The Time Machine”(1895) • Herbert George Wells (1866-1946) http://en.wikipedia.org/wiki/H_G_Wells

5. Chapter One "Clearly," the Time Traveller proceeded, "any real body must have extension in FOUR directions: it must have Length, Breadth, Thickness, and--Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives."

6. 介於科學和科幻之間的時光旅行

7. Wheeler-Feynman(1940)

8. 《穿梭超時空》p319 “All You Zombies”圖解 http://drng.pixnet.net/album/photo/34253699

9. 時光機Vs時光隧道 • http://www.imdb.com/title/tt0268695/ • http://www.imdb.com/title/tt0060036/

10. 前往未來的時光旅行 • 古典物理？ • 狹義相對論 • 廣義相對論

11. 回到過去的時光旅行 • 古典物理？ • 狹義相對論 • 廣義相對論

12. ●時光旅行的科與幻 ●軸對稱時光機發展簡史 ●（廣義相對論架構下）為何時光可能倒流 ●軸對稱時光機的直覺解釋 ●光錐結構的深入探討 ●容許封閉類時曲線的時空 ●淺探：究竟是物理還是數學？

13. 最早的 • Lanczos, C. (1924) “On a Stationary Cosmology in the Sense of Einstein’s Theory of Gravitation” • van Stockum, W.(1937) “The gravitational field of a distribution of particles rotating around an axis of symmetry” • Tipler, F. (1974) “Rotating Cylinders and the Possibility of Global Causality Violation”

14. Interior Exterior A definite axis

15. 最著名的 • Gödel, K. (1949) “An example of a new type of cosmological solution of Einstein's field equations of gravitation”

16. Kurt Friedrich Gödel (1906-1978) One of the most significant logicians of all time. http://en.wikipedia.org/wiki/Kurt_G%C3%B6del

17. Gödel’s Universe • Stationary but not Static • Anisotropic but Homogeneous • Axially symmetric but without a definite axis • Inconsistent with observations

18. 最有可能的 • Kerr, R.(1963) “Gravitational field of a spinning mass as an example of algebraically special metrics” • Newman E. et al (1965) “Metric of a Rotating, Charged Mass”

19. 最善用媒體的 • Mallett, R.(2003) “The gravitational field of a circulating light beam”

20. ●時光旅行的科與幻 ●軸對稱時光機發展簡史 ●（廣義相對論架構下）為何時光可能倒流 ●軸對稱時光機的直覺解釋 ●光錐結構的深入探討 ●容許封閉類時曲線的時空 ●淺探：究竟是物理還是數學？

21. Light cones in the flat spacetime http://en.wikipedia.org/wiki/Light_cone

22. 3 inertial observers, 1 light cone http://en.wikipedia.org/wiki/Minkowski_diagram

23. How about non-inertial observers?

24. Light cones in the curved spacetime • Fairly distorted • Highly distorted

25. Timelike Curve(類時曲線) http://en.wikipedia.org/wiki/Light_cone

26. Closed Timelike Curve (CTC) (封閉類時曲線) Highly distorted cone Fairly distorted cone

27. ●時光旅行的科與幻 ●軸對稱時光機發展簡史 ●（廣義相對論架構下）為何時光可能倒流 ●軸對稱時光機的直覺解釋 ●光錐結構的深入探討 ●容許封閉類時曲線的時空 ●淺探：究竟是物理還是數學？

28. 時空拖曳效應(frame dragging) • frame dragging  distorted cones • ripples as an analogy

29. t ‧

30. t ‧

31. t ‧

32. t ‧

33. ‧

34. 　時空拖曳效應的理論與實驗證據 • Lense–Thirring precession(1918) • LAGEOS(1976) • LAGEOS 2(1992) • Gravity Probe B (2004)

35. Gravitomagnitism(重力磁性) • static charge  electric field • rotating charge  electric field+ magnetic fields • static mass  gravitational field • rotating mass  gravitational field+ gravitomagnetic field

36. ●時光旅行的科與幻 ●軸對稱時光機發展簡史 ●（廣義相對論架構下）為何時光可能倒流 ●軸對稱時光機的直覺解釋 ●光錐結構的深入探討 ●容許封閉類時曲線的時空 ●淺探：究竟是物理還是數學？

37. 玩具模型的重要性 • e.g. S2 • e.g.1-dim Ising model

38. 介於兩種相對論之間的問題平直時空中的加速度運動介於兩種相對論之間的問題平直時空中的加速度運動 • 孿生子矛盾 • 等加速座標系 • 旋轉座標系

39. 等加速座標系造成的重力假象 等效原理(equivalence principle)

46. Left http://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity) Right http://en.wikipedia.org/wiki/Rindler_coordinates

48. X X<1 X>1 X=1

50. Not unique!