PHYM432 Relativity and Cosmology fall Introduction. Dr. David K. Sing

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1 PHYM432 Relativity and Cosmology fall Introduction Dr. David K. Sing 1

2 PHYM432 General Relativity and Cosmology Fall Instructor: Dr. David K Sing Office: Physics building room 514 sing@astro.ex.ac.uk Website: CATS Credit Value: 10 ECTS Credit Value: 5 Duration: T1 - T11 Newman D 26 Sept 2012 to 13 Dec 2012; Wednesday 10:00, Thursday 15:00 20 x 1 hour Lectures, 2 discussion and problems classes Private Study Time: 78+ hours Assessment: One 90-minute examination (100%) T2:00 (week of 13 Jan 2013) Notes: On ELE & on my personal website 2

3 Aims The module aims to introduce the student to the special and general theories of relativity, emphasizing the geometrical interpretation of the theory. Application of the general theory to the standard cosmological model is also included at the end of the course. The course aims to develop the minimum necessary advanced mathematical topics needed to understand the concepts behind the theory, and students will require a good level of mathematical fluency and intuition in order to fully engage with the material. Core Text Lambourne, Robert J., Relativity, Gravitation, and Cosmology, Cambridge University Press, (2010) Supplementary Text Hartle, J., Gravity: An Introduction to Einstein s General Relativity, Addison-Wesley Benjamin Cummings, 1st edition (2003) Roos, Matts, Introduction to Cosmology, 3rd edition, Wiley Kenyon, I. R., General Relativity, Oxford Science Publications Assignments The student is expected to work through a set problems. BUY THE BOOK!!! only 30 quid 3

4 I. Introduction II. Key aspects of special relativity (2-5) 1. Galilean and Lorentz transformations 2. Length contraction and time dilation 3. Doppler effect 4. Relativistic mechanics 5. 4-Vectors 6. SR Mechanics III. From SR to GR (6-10) 1. Differential Geometry 2. Accelerated reference frames 3. Spacetime tells matter how to move 4. Geodesics IV. Curved spaces 1. Differential Geometry 2. Euclidean spaces 3. Curvature in one and two dimensions 4. Intrinsic and extrinsic curvature 5. Riemannian curvature 6. Introduction to tensors V. GR (11-16) 1. Einstein Field Equations 2. Newtonian Limit 3. Schwarzschild Solution 4. Orbits 5. Black Holes VI. Cosmology (17-21) 1. The cosmological principle (M10) 2. Robertson-Walker metric 3. Red-shift distance relation 4. The Friedmann equations (M11) 5. Cosmic microwave background VII. Review class (22) 4

5 BUY THE BOOK!!! only 30 quid Link for PDF of Chapter 1 and homework solutions on ELE & on my website 5

6 BUY THE BOOK!!! only 25 quid Homework problems will be given primarily from Lambourne (contains complete solutions) I will also likely give problems from Hartle two classes dedicated to discuss problems 6

7 BUY THE BOOK!!! only 25 quid These are for your own benefit, to gain practice working with the equations and gaining insight into GR Assignment: Read Lambourne Chapter 1 do problems 1.1, 1.2, 1.3 7

8 Many many good books on this subject Hartle is highly recommended Subject matter can be Difficult to understand Different viewpoints can be Very useful to understand the material 8

9 Gravity and Modern Physics Modern Physics is essentially now two separate, very different, fundamental theories, GR and QM GR is a classical theory (not quantized) The entire rest of Modern physics is currently explained by Quantum Field Theories (standard model) Short Range (quantum) Long Range Gravity? GR E&M QED Maxwell Weak QFT - Strong QFT - 9

10 Gravity Universal attraction between ALL mass and all Energy (E=mc 2 ) Only attractive, Gravity is Unscreened Long Range (1/r 2 ) Weakest of the 4 forces Short Range (quantum) Long Range Gravity? GR E&M QED Maxwell Weak QFT - Strong QFT - 10

11 Gravity Where does GR theoretically break down? r G~ c 3 r G~ c 5 r ~c 5 = cm = s G = GEV Short Range (quantum) Long Range Gravity? - Theory of Everything GR E&M QED Maxwell Weak QFT - Strong QFT - c 5 ~G 2 = g/cm 3 11

12 Gravity Quantum A fundamental Challenge to bring them together Measurements: cosmological mm Requirements: dynamic spacetime no preferred reference frames space-time Time Problem: time comes in only through metric, describing curved spacetime Technical Difficulties: highly non-linear theory mm meters fixed background (flat spacetime geometry) splitting of space & time Not a predictive theory, obvious QG wave functions are not normalizable Quantization of space-time itself, what does that even mean? Non-linear Schrodinger s equation, principle of superposition of states breaks down. Without Quantum Gravity (Does grav. wave lead to wavefunction collapse?) Yes. Uncertainty principle violated No. Gravitational interactions with quantum (use gravitational measurements quantized matter could be used for to give exact time & space locations) faster than light signals Alternatively, instead of quantizing GR, Quantum Mechanics would have to change 12

13 General Relativity works: Einstein hard to prove wrong 13

14 FLT - violation Lorentz invariance Neutrino result almost certainly wrong worth checking (latest update: wrong, bad cables) Einstein formulated GR from fundamental philosophical reasoning & deep insight into the laws of Nature FTL would put causality under question space-like world lines reference frames where they appear to move back in time (effect before cause) exotic physics to explain 14

15 dual views of Gravity Gravity is a field (force) Gravity is a manifestation of spacetime curvature (geometry) Both views useful when solving problems Geometric interpretation is stressed here 15

16 General Relativity Arguably, the geometric interpretation used to explain gravitational forces is the most elegant, most beautiful, most insightful view into the laws of nature anyone has ever had. 16

17 Gravity = Field mass tells the gravity field what to be g = GM ˆr r 2 the gravity field tells the mass how to accelerate F = m d2 X dt 2 = mg 17

18 Gravity = Geometry matter tell spacetime how to curve G µ = 8 G c 4 T µ curvature of spacetime (curve) = energy & momentum (matter) spacetime tells matter how to move m d2 X d 2 = m dx d dx d move = curvature ( straight line in curved space) 18

19 General Relativity Consequences are Very rich in unique weird physics Black Holes Worm Holes Time warps Space-time coordinates flip/switch roles inside Blackhole 19

20 Cosmology Mathematical model of the large-scale feature of the Universe All you need is GR E&M screened out, SF/WF to short range Well... for all except the first tinniest fraction of a second (Inflation.. GUT scale) Short Range (quantum) Long Range Gravity? GR E&M QED Maxwell Weak QFT - Strong QFT - 20

21 Cosmology Currently in a Golden age of Cosmology Now have a standard model ΛCDM cosmology Basic parameters of the universe are now fairly well known... how old, how much matter, dark energy, dark matter ± 0.17 yr 21

22 Burning Questions? List of questions we ll try to address before the end of class - What happens when you fall into a black hole? 22