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Astronomy 350 Cosmology

Astronomy 350 Cosmology. Professor Lynn Cominsky Department of Physics and Astronomy Offices: Darwin 329A and NASA EPO (707) 664-2655 Best way to reach me: lynnc@charmian.sonoma.edu. Group 14. Mike Lightner Emily Ogden Donald Siemon. A big hand for Group 14!. Extra credit.

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Astronomy 350 Cosmology

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  1. Astronomy 350Cosmology Professor Lynn Cominsky Department of Physics and Astronomy Offices: Darwin 329A and NASA EPO (707) 664-2655 Best way to reach me: lynnc@charmian.sonoma.edu Lynn Cominsky - Cosmology A350

  2. Group 14 • Mike Lightner • Emily Ogden • Donald Siemon A big hand for Group 14! Lynn Cominsky - Cosmology A350

  3. Extra credit • You can earn one extra point for each Space Mystery that you try out and evaluate at http://mystery.sonoma.edu • Evaluation forms are found at: http://mystery.sonoma.edu/resources/teachers/evaluation.html • The mysteries are: • Live! From 2-alpha • Alien Bandstand • Starmarket • Evaluation forms must be turned in by 5/27/03 (day of final exam) Lynn Cominsky - Cosmology A350

  4. Big Bang Timeline Today’s lecture We are here Lynn Cominsky - Cosmology A350

  5. Big Bang? Lynn Cominsky - Cosmology A350

  6. Distance in 3 Dimensions Distances in three dimensions are easily found from an extension of the 2D Pythagorean theorem for right triangles a2 + b2 = c2 In 3D: d = a2 + b2 + c2 • We all experience three spatial dimensions (usually referred to as x, y and z) Lynn Cominsky - Cosmology A350

  7. Vectors abc d = • Vectors are used to mathematically represent quantities which have both size and direction This vector d has components (a, b, c) in the (x, y, z) directions and magnitude d Lynn Cominsky - Cosmology A350

  8. Vector Fields • Vector fields are physical quantities which have magnitudes and directions at each point This is a 2D vector field where the direction at each point is given by What is the magnitude (length) of the vector at each point? Lynn Cominsky - Cosmology A350

  9. Tensors Push here • It is difficult to visualize a tensor • This is a visualization of the stresses in a 3D material when force is applied at two points on the top surface • The stress tensor is a 3 x 3 matrix of numbers Lynn Cominsky - Cosmology A350

  10. Tensors • Einstein unified the 3 spatial dimensions with the dimension of time to make a four dimensional space time (x, y, z, ct) in which gravity is defined by a 4x4 tensor Components of the tensor down the diagonal are the coefficients in d2 = g11x2 + g22y2 + g33z2 + g44c2t2 They are (1,1,1,-1) for flat space Lynn Cominsky - Cosmology A350

  11. Tensor Fields 0 Bz -By -iEx -Bz 0 Bx -iEy By -Bx 0 -iEz iEx iEy iEz 0 • The electromagnetic field is another example of a 4D tensor field. It has 4x4 components, which tell you the magnitude of the components in 3 different directions for both the electric and magnetic field. Lynn Cominsky - Cosmology A350

  12. Flatland • It’s hard to visualize 4 dimensions, so let’s start out by examining the lives of the characters in Edwin A. Abbott’s Flatland Rank in Flatland is a function of increasing symmetry: A woman, soldier, workman,merchant, professional man, gentleman, nobleman, high priest Lynn Cominsky - Cosmology A350

  13. Flatland • What do they see when a 3D being (Lord Sphere) comes to visit? 3D cross-sections of Lord Sphere float through the 2D world of Flatland Lynn Cominsky - Cosmology A350

  14. Troubles in Flatland • It’s hard to eat in a 2D world! • It is also impossible to tie your shoes! Why? A digestive tract cuts a 2D being in half! Lynn Cominsky - Cosmology A350

  15. Troubles in Flatland • A Square and his wife alone in their 2D house, when Lord Sphere drops in from the third dimension There is no privacy in 2D from a 3D being! Lynn Cominsky - Cosmology A350

  16. Troubles in Flatland • A 3D being would be able to change the symmetry of a 2D resident or help him escape from jail! The 3D being can lift the 2D resident up out of Flatland! Lynn Cominsky - Cosmology A350

  17. Troubles in Flatland movie • How do Flatlanders know the shape of their Universe? • A flat plane (with edges) is an open 2D Universe • Is there a closed 2D Universe? A Moebius strip is a 2D closed universe Lynn Cominsky - Cosmology A350

  18. Exploring Geometries • Take the newspaper • Cut a long skinny strip • Twist one end of the strip once and tape together • Congratulations – you have just made a Moebius strip! • How many sides does this have? Try drawing on it to see. • What happens to it when you cut it all around the strip direction? Lynn Cominsky - Cosmology A350

  19. Troubles in Flatland • What would happen if Flatlanders walked all the way around a closed 2D world? • They would be mirror-reversed! • Flat torus – another example of a closed 2D world Lynn Cominsky - Cosmology A350

  20. The 3D Universe • Open (W<1) Hyperbolic geometry • Flat (W=1) Euclidean geometry • Closed (W>1) Spherical geometry Lynn Cominsky - Cosmology A350

  21. Infinite Universe? • Is the Universe infinite or just really, really, really big? • Some scientists (like Janna Levin) prefer to think of the Universe as finite but unbounded. An example of such a space is a 3D torus. • With such a topology, we could see the backs of our heads, if we could see far enough in one direction Lynn Cominsky - Cosmology A350

  22. Curved Space • This is not an infinite series of reflections, but is caused by light traveling all the way around the hyperdonut • A hyperdonut is one example of a curved space in 3D Lynn Cominsky - Cosmology A350

  23. 3D Torus games • Play game here Lynn Cominsky - Cosmology A350

  24. The 4D Universe • Many cosmologists believe that our Universe is a 4D hypersphere • This is a 3D movie projection of a 4D hypersurface movie Lynn Cominsky - Cosmology A350

  25. Geometry in the 4th dimension • A 2D square is created by moving a line in a perpendicular direction • A 3D cube is created by moving a square in a perpendicular direction Lynn Cominsky - Cosmology A350

  26. Geometry in the 4th dimension • A Flatlander can only visualize a cube, if it is unfolded in 2D • If you move a 3D cube in a fourth perpendicular direction, you get a hypercube • A 3D being can only visualize a hypercube by unfolding it in 3D into a tesseract Lynn Cominsky - Cosmology A350

  27. Geometry in the 4th dimension • Christus Hypercubus was painted by Salvador Dali in 1955 –it features a tesseract • A 4D hypercube is bounded by 8 3D cubes, has 16 corners and a volume L4 Lynn Cominsky - Cosmology A350

  28. Geometry in the 4th dimension • Here is another 2D projection of a 4D hypercube • At each face, you can see a cube in different directions as you change your perspective d2 = x2 + y2 + z2 + w2 Lynn Cominsky - Cosmology A350

  29. Troubles in Spaceland • Thieves from the fourth dimension could steal things from locked safes (or operate without cutting you open!) There is no privacy in 3D from a 4D being! Lynn Cominsky - Cosmology A350

  30. Visitors from the 4th dimension • Try the “digustoscope” to see yourself as a 4D being in a 3D world! Do powerful beings such as a Cosmic Creator (or the Devil) live in the Fourth Dimension? Lynn Cominsky - Cosmology A350

  31. Angels and Devils • This 2D exercise from U Wash helps you to visualize the effects of different geometries • But first, let’s see how 2D beings would see a 3D object passing through their world (e.g. Flatland by Abbott) • Cube movies • Sphere movies Lynn Cominsky - Cosmology A350

  32. Geometry in higher dimensions • Here is 2D projection of a 5D hypercube • It obeys the same mathematical laws as objects in worlds with a lower number of dimensions d2 = x2 + y2 + z2 + w2 +v2 Lynn Cominsky - Cosmology A350

  33. Physics in higher dimensions • Kaluza was the first to try to unify the fields of (Maxwell) electromagnetism and (Einstein) gravity by rewriting the laws of physics in 5D (or a 5x5 tensor) • In this theory, light was caused by a ripple in the 5th dimension Lynn Cominsky - Cosmology A350

  34. Kaluza-Klein Theory • Theodor Kaluza’s original idea was refined by mathematician Oskar Klein • At each point in 4D spacetime, another curled up or “compactified” dimension is present, but it is so small that it is not observable At each point in spacetime, a curled up dimension exists Lynn Cominsky - Cosmology A350

  35. Physics in Higher Dimensions • Grand Unified Theory expands the 5x5 tensor to include the Yang-Mills field, which describes the weak and strong interactions in N dimensions • The resultant tensor has 4+N dimensions N is 5 for the standard model of particle physics Lynn Cominsky - Cosmology A350

  36. Physics in Higher Dimensions • Supersymmetry allows particles with different types of spin (fermions and bosons) to interchange • Each particle has a supersymmetric partner called a “sparticle” • No “sparticles” have yet been detected The WIMP (weakly interacting massive particle) is the lightest “sparticle” Lynn Cominsky - Cosmology A350

  37. Physics in Higher Dimensions • Supergravity theory includes supersymmetry as well as interactions with matter (gravity) • It requires an 11D Kaluza-Klein theory • However, it still does not have enough complexity to explain all the interactions that we see in the Standard Model Meanwhile, searches for “sparticles” continue at higher energies Lynn Cominsky - Cosmology A350

  38. Superstrings • Strings are little closed loops that are 1020 times smaller than a proton • Strings vibrate at different frequencies • Each resonant vibration frequency creates a different particle • Matter is composed of harmonies from vibrating strings – the Universe is a string symphony “String theory is twenty-first century physics that fell accidentally into the twentieth century” - Edward Witten Lynn Cominsky - Cosmology A350

  39. Superstrings • Strings can execute many different motions through spacetime • But, there are only certain sets of motions that are self-consistent • Gravity is a natural consequence of a self-consistent string theory – it is not something that is added on later Self-consistent string theories only exist in 10 or 26 dimensions – enough mathematical space to create all the particles and interactions that we have observed Lynn Cominsky - Cosmology A350

  40. Superstring Dimensions • Since we can observe only 3 spatial and 1 time dimensions, the extra 6 dimensions (in a 10D string theory) are curled up to a very small size • The shape of the curled up dimensions is known mathematically as a Calbi-Yau space Lynn Cominsky - Cosmology A350

  41. Superstring Universe • At each point in 3D space, the extra dimensions exist in unobservably small Calabi-Yau shapes Lynn Cominsky - Cosmology A350

  42. Superstring Interactions 2 strings split into 2 joined • Strings interact by joining and splitting Lynn Cominsky - Cosmology A350

  43. Superstring Interactions 2 strings 2 strings annihilation eruption 2 virtual strings • Strings annihilate and erupt repeatedly subject to the quantum mechanical uncertainty principle, just like particle pairs Lynn Cominsky - Cosmology A350

  44. Superstrings and Gravity • Gravitational force is represented by the exchange of closed strings • Even if an infinite number of string-like Feynman diagrams are added up, the theory stays finite Lynn Cominsky - Cosmology A350

  45. Superstring Motions Sliding Winding • Strings can have two different types of motions in a universe where some dimensions are curled up and others are extended Lynn Cominsky - Cosmology A350

  46. Superstring Theories • There are at least five different versions of string theory, which seem to have different properties • As physicists began to understand the mathematics, the different versions of the theories began to resemble each other (“duality”) • In 1995, Edward Witten showed how all five versions were really different mathematical representations of the same underlying theory • This new theory is known as M-theory (for Mother or Membrane) Lynn Cominsky - Cosmology A350

  47. M-Theory • Unification of five different types of superstring theory into one theory called M-theory • M-theory has 11 dimensions Lynn Cominsky - Cosmology A350

  48. Some questions • Can we find the underlying physical principles which have led to us to string theory? • Does the correct string (or membrane) theory have 10 or 11 dimensions? • Will we ever be able to find evidence for the curled up dimensions? • Is string theory really the long-sought “Theory of Everything”? • Will any non-physicists ever be able to understand string theory? Lynn Cominsky - Cosmology A350

  49. Print Resources • Elegant Universe by Brian Greene (Norton) • Hyperspace by Michio Kaku (Anchor Books) • Fourth Dimension by Rudy Rucker (Houghton Mifflin) • Surfing through Hyperspace by Clifford A. Pickover (Oxford) Lynn Cominsky - Cosmology A350

  50. Web Resources • VROOM visualization of 4 dimensions http://www.evl.uic.edu/EVL/VROOM/HTML/PROJECTS/02Sandin.html • Ned Wright’s Cosmology Tutorial http://www.astro.ucla.edu/~wright/cosmolog.htm • Fourth dimension web site • http://www.math.union.edu/~dpvc/math/4D/welcome.html Lynn Cominsky - Cosmology A350

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