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The Big Bang and Quantum Mechanics: Insights into Cosmology

This lecture explores the intricate relationship between the Big Bang theory and quantum mechanics, emphasizing the wave nature of matter and energy. It discusses the Friedmann Equation, cosmic evolution, and the emergence of structured matter from singularities. Highlighting concepts like energy-mass equivalence, symmetries in particle physics, and the role of the Large Hadron Collider, it delves into dark matter, vacuum states, and cosmic inflation. Ultimately, it addresses the fate of the universe and the implications for life in our cosmos.

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The Big Bang and Quantum Mechanics: Insights into Cosmology

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  1. ASTR 2010 Cosmology • Week 14: • Lecture 38 (30 Nov. 2012) • The Big Bang - 2

  2. Quantum Mechanics: Relativistic Quantum Field Theory : All matter & energy are waves: E= h = hc /  = mc2  = h / mv non-relativistic (V <<c)  = h / mv relativistic: V ~ c;  = 1 / (1 - v2 / c2)0.5 Energy <=> mass Symmetries:matter <=> anti-matter: Charge symmetry neutral neutral charge <=> opposite charge For h511keV:hhe-+e+ 1 eV = 1.6 x 10-12 erg  For h1 GeV:hhp++p- Super-Symmetry:bosons <=> fermions (at > 1013 eV) Bosons (force carriers):photons (h, W+, W-, Z0, gluons, gravitons || | || | EMweak forcestrong gravity Fermions (“matter”):electrons, quarks (neutrons, protons), neutrinos Dark matter ? - photinos, neutralinos, selectons, squarks …. ?

  3. Large Hadron Collider (LHC) Geneva, Switzerland

  4. Large Hadron Collider (LHC) vacuum tubes in tunnel

  5. Large Hadron Collider (LHC)- CMS detector

  6. Large Hadron Collider: TeV (1012 eV) proton - proton collision [u+2/3 u+2/3 d-1/3] <=> [u+2/3u+2/3 d-1/3] => u+2/3, d-1/3, s+2/3, c-1/3, t+2/3, b-1/3 =>short-lived particles => p+, n, e-, h, 

  7. Large Hadron Collider: TeV (1012 eV) proton - proton collision Example: top, bottom quarks => decay to p+, n, e-, h, 

  8. The “Big Bang” Cosmology: Theory: - Friedmann Equation: Cosmic Evolution depends on density ofmatter + energy Space expands (gravitationally unbound systems only!) Emergence from a compact (dense) state: A singularity as in a black hole? - The “Lambda Cold-Dark-Matter” (-CDM) cosmology Ultra-hot energy emerges from singularity 10-33 sec Inflation 10-26 sec Matter-antimatter asymmetry (matter dominates!) 10-3 sec Quark-gluon condensate 10-1 sec neutrons, protons 1 sec nucleosynthesis 300 sec Atomic Hydrogen + CMB 3.8 x 105 years Stars + galaxies ~3 x 108 years

  9. Omega ordinary matter = 0.04 Omega darkmatter = 0.23 Omega matter = 0.27 Omega = [density] / [critical density]

  10. ASTR 2010 Cosmology • Week 15: • Lecture 39 (3 Dec. 2012) • The Young Universe

  11. Cosmology topics to be covered: - Black holes, worm holes, & Singularities: non-rotating, rotating - White holes, enthropy, & the arrow of time. Time reversal in singularities? - Inflation: Higgs field: false vacua, origins of mass, Higgs mechanism - Matter-antimatter asymmetry - Quark-gluon plasma => P, n, => H, He => stars & stellar nucleosynthsis - Acoustic oscillations, radiation pressure vs. gravity, “BAO” - CMB formation: Harmonics in the CMB: Roles of dark matter - Dark ages - Galaxy formation, evolution, cosmic structure formation - Fate of the Cosmos - String theory: Cosmic dimensionality - Multiverses: Type I, II, III, OIV (Tegmark classification) - Cosmic “Natural Selection & Reproduction” (Smolin & Darwinian evolution) - Black holes and cosmic reproduction: Roles of dark energy - Origin and fate of life. - The Anthropic principle: Why is the Universe friendly to life? - Engineering the next Universes: The Smolin-Harrison cosmology

  12. … a black hole Escape speed = speed of light R = ~ 3 km/s x Mass [Solar masses]

  13. Andrew J Hamilton: jila.colorado.edu/~ajh/insidebh/rn.html

  14. Connected black holes? “Worm holes” ?

  15. Planck Scale: - Singularity in Black holes, worm holes, Big Bang E = h c /  = h c / 2 r Quantum mechanics ( = 2 r) E = mc2 Relativity => m c = h / 2 r m = h / 2 c r r = 2Gm / c2 Black holes => m = rc2 / 2G h / 2 c r = rc2 / 2G=>r2 = h G /  c3=>r = (h G /  c3 )1/2 r = ([6.626x10-27][6.67x10-8] / [3.14 ][2.998x1010]3 ) 0.5 = 2.3 x 10-33 cm Planck Length Planck mass ~ 10-5grams Planck time ~ 10-43sec

  16. ASTR 2010 Cosmology • Week 15: • Lecture 40 (5 Dec. 2012) • The Young Universe

  17. F D C B A

  18. Paul Gaugain “Where do we come from? What are we? Where are we going?”

  19. Camille Flammarion 1888

  20. The History of our Universe

  21. Cosmic Inflation • How does 1 side of the CMB know the temperature and • density on the other side of the sky ? • They have never been in contact ….. Or maybe they have! • Inflation (circa 1980) Driven by the decay of the `Inflaton’ or `Higgs’ field? Alan Guth

  22. Standard Model of particle physics: Interactions: Electromagnetic, weak,strong

  23. ASTR 2010 Cosmology • Week 15: • Lecture 40 (7 Dec. 2012) • Quantum Gravity: • - String theory (Witten +) • - Loop quantum gravity (Smolin +) • …. Cubism .. Picasso …

  24. String Theory: 6 compact + 3 large space dimensions (D) + time Solution to Einstein Vacuum equations: Ed Witten 10-33 cm 10-33 cm

  25. Kalabi-Yau manifold: Vibrating string 6 compact + 3 large space dimensions + time Solution to Einstein Vacuum equations: Shing-Tung Yau

  26. 10-33 cm Planck Length Curled-up dimension Flat space Compactification: 6 compact + 3 large space dimensions (D) + time Solution to Einstein Vacuum equations: Kalabi-Yau spaces (6 D) Spheres (2 D) Donuts (2 D) 10-33 cm

  27. Knots “Super-Strings”: Space-time Knots in 6 Compact Dimensions

  28. Loop Quantum Gravity Space & time are discrete at the Planck scale: A spin network Lee Smolin spin Space-time (spin foam)

  29. Loop Quantum Gravity Smallest length: ~10-33 cm “ area: ~10-66 cm2 “ volume: ~10-99 cm3 Shortest time ~ 10-33 cm/ 1010 cm/s = 10-43 sec Heisenberg Uncertainty principle => Zero point energy in a Planck length / c2 ~ 10-5 grams

  30. Loop Quantum Gravity Space & time are discrete at the Planck scale: A spin network Lee Smolin spin Space-time (spin foam)

  31. Artists view of The world at the Planck scale Loop Quantum Gravity “spin foam” String Theory “Planck-scale Quantum fluctuations in Space-time”

  32. A loop quantum gravity (LQG) physicist Looking at a Picasso painting: Jerzy Lendowski in the Manhattan Museum of Modern Art

  33. Rockwell Picasso

  34. As you approach the Planck Scale: …. Space-time becomes highly structured and dynamic (John Archibald Wheeler) also as you approach the singularity in a black hole ….

  35. Probing the Planck length with Gamma-rays bursters: High energy gamma-ray photons may travel slower than X-ray photons. Doubly special Relativity: In all frames of motion …. Speed of light = constant Planck-length = constant (Lee Smolin)

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