Astro 201: Sept. 9, 2010

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Astro 201: Sept. 9, 2010 Do on- line prac8ce quiz #2 by 9/14 Turn in HW 2 in box in front of the room Reading: Hester Chapter 4 Today: String Theory Determinism v.

1 Astro 201: Sept. 9, 2010 Do on- line prac8ce quiz #2 by 9/14 Turn in HW 2 in box in front of the room Reading: Hester Chapter 4 Today: String Theory Determinism v. Chaos; Fractals Light STRING THEORY everything is ul8mately made of strings (sub- sub- sub atomic par8cles) How big are strings? Smaller than a Planck length, which is about cen8meters or about a millionth of a billionth of a billionth of a billionth of a cen8meter. 1

2 Strings vibrate Closed string Open string In many string theories the Universe is 10 dimensional, with the "extra" dimensions COMPACTIFIED. All HS math geeks read a book called FLATLAND: A Romance of Many Dimensions, by Edwin A. Abbo_ (1884) FLATLAND: a "first person" account of life of a 2- dimensional society a radical named Arthur Square figures out that space is really 3 dimensional. 2

3 So what the string theorists say is that in ordinary life we think we live in 3 dimensions, and we have to think of ways to detect the other 7. The extra- dimensions in string theory are Calabi- Yau figures: 3

4 4

5 Kni_ed Calabi- Yau Figures 5

solve the Three- body problem Mechanical Universe: In Newtonian physics, objects move in perfectly

6 Kepler: Empirical descrip8on of the mo8on of the planets Newton: Law of Gravity. Developed Calculus, derived orbits of the planets Solved the Two- body problem: Sun + one planet Couldn t solve the Three- body problem Mechanical Universe: In Newtonian physics, objects move in perfectly determined ways Orrery Mechanical models of planetary motions in the solar system But is the real solar system accurately described by an orrery? 6

7 "We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes." Marquis Pierre Simon de Laplace ( ) The Equa8ons Many thanks To Scott Tremaine s Notes from April

King Oscar II of Sweden (1829-1907) - Prize: How stable is the universe?

8 King Oscar II of Sweden ( ) - Prize: How stable is the universe? Jules Henri Poincaré ( ) Sun (large) plus one planet (circular orbit) Stable Added 3 rd body Strange behavior Not periodic Modern approach: Solve many- body problem with computer calcula<ons Take a distribu8on of mass Figure out the gravita8onal force on each part F=ma gives you the accelera8on on each part Compute velocity of each part Move the parts a li_le Repeat 8

Kuiper belt objects Plutinos (3:2) Centaurs comets as of March 8 2006 (Minor Planet Center) Sensi8vity to Ini8al Condi8ons "A very small cause which escapes our no8ce determines a considerable effect

9 Kuiper belt objects Plutinos (3:2) Centaurs comets as of March (Minor Planet Center) Sensi8vity to Ini8al Condi8ons "A very small cause which escapes our no8ce determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situa8on of the universe at the ini8al moment, we could predict exactly the situa8on of the same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could s8ll know the situa8on approximately. If that enabled us to predict the succeeding situa8on with the same approxima8on, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws. But is not always so; it may happen that small differences in the ini8al condi8ons produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the la_er. Predic8on becomes impossible...". (Poincaré) 9

10 Can we predict the mo8on of a single planet a billion years from now? Laplace and Newton Yes Poincare No Lorenz 1963 Bu_erfly Effect If a bu_erfly flaps its wings in Brazil, does it result in a tornado in Kansas? Two kinds of dynamical systems Regular highly predictable, well- behaved e.g. baseball, golf, simple pendulum, all problems in mechanics textbooks, planetary orbits on short 8mescales Chao8c difficult to predict, erra8c appears regular on 8mescales short compared to Liapunov 8me e.g. roule_e, dice, pinball, weather, billiards, double pendulum The Solar System 10

11 Double Pendulum: a chao8c system Consequences of chaos Posi8ons of planets are not predictable on 8mescales longer than 100 Myr the solar system is a poor example of a determinis8c universe The solar system is Chao8c 11

12 Fractals Geometric forms Deﬁne by a recursive rule Same on all scales Benoit Mandelbrot Serpinski Triangle 12

13 Von Koch Snowflake Fractals are Self- Similar : same when you zoom in 13

14 The Julia Set Gaston Julia, French mathema8cian The Mandelbrot Set 14

15 Fractals in Nature 15

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Astro 201: Sept. 6, 2010

Astro 201: Sept. 6, 2010 Do on- line prac:ce quiz #2 by 9/14 Homework #2: posted on web page, due 9/9 Reading: Hester, Chapters 2-3 Gleiser: Sec:ons 3-6 Today: Astronomical basis for calendars Why there