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The Universe

The Universe. The Expanding Universe. Edwin Hubble, 1920’s and 1930’s: Galaxies receding from us The farther away they are, the faster they recede Velocity increase seems to be linear Implies that at some point in the past, everything was in a small space

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The Universe

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  1. The Universe

  2. The Expanding Universe • Edwin Hubble, 1920’s and 1930’s: Galaxies receding from us • The farther away they are, the faster they recede • Velocity increase seems to be linear • Implies that at some point in the past, everything was in a small space • 24 km/sec per million l.y.  1019 km/24 km/sec  4.5 x 1017 sec = 13 b.y.

  3. The Alternative • British Astronomer Fred Hoyle derisively coined the term “Big Bang” • He proposed that matter was continuously created in space • Rate very small: One H atom per cubic meter per billion years • Universe always has same density • Problem: Where do light nuclei come from? • Problem: Where Are All the Baby Galaxies?

  4. Cosmic Background Radiation • 1965: Universe is filled with faint microwave radiation, temperature 3K • Highly diluted radiation left over from origin of universe (Cosmic Microwave Background: CMB) • Smaller Universe would be hotter • One million l.y. radius = 1300 x 1300 x energy/area of sky = 170 million times present CBR • Stefan-Boltzmann Law: radiation = T4 • T = 3K x 4√ 170 million = 340 K

  5. Cosmic Microwave Background

  6. Cosmic Microwave Background

  7. Time Line • T proportional to 1/√time • > 1 b.y. (T=11k) Stable stars and galaxies • 300,000 years (T=600 K): atoms form • Space becomes transparent • The CMB dates from this time • 70,000 years (T=1300 K): Matter dominates over radiation • 3-20 minutes (T=50 million K): Nucleosynthesis of He and Li

  8. Time Line • 1 second – 3 minutes: Leptons (electrons) sort out • 10-6 – 1 second: Hadrons (protons, neutrons) form • 10-12 – 10-6 second: Quarks dominate • Before that: Electromagnetic, weak nuclear and strong nuclear forces become distinct • Inflation

  9. Travel to the Stars? • Kinetic Energy = 1/2 Mv2 • What does it take to get a 1000-ton spaceship to 10% of the speed of light? (43 years to Alpha Centauri) • M=106 kg, v = 3 x 107 m/sec • KE = 1/2 x 106 x 9 x 1014 = 4.5 x 1020 joules • Equals U.S. Energy Use for 4.5 years • Once you get there, you have to stop. • You are planning on coming back, right?

  10. Relativity • Speed of Light is Independent of Source • Michelson and Morley, 1887 - Speed of Light Independent of Observer • “One of the Most Unexpected Results in the History of Science” - Isaac Asimov • Conclusion: Speed of Light is the Same for All Observers • Implication: Space and Time Must Change to Keep Speed of Light Constant

  11. Pioneers of Relativity • Joseph Larmour • Hendrick Lorentz • Henri Poincare • They worked out the mathematical implications of light always having a constant speed • Einstein took it to the next level

  12. Frames of Reference

  13. Frames of Reference • Frames of Reference that are moving at constant speed and direction are called inertial • Laws of physics are the same in all inertial reference frames (Galilean invariance) • There is no “right” frame of reference

  14. What is Light?

  15. Catching the Wave

  16. What Would Einstein See?

  17. Electrical and Magnetic Fields

  18. Riding A Light Wave • You’d See Alternating Strips of + and – Electric and Magnetic Fields • We Don’t See Anything Like That In Our World • The Alternating Strips of + and – Electric and Magnetic Fields Are Just There • All Electric and Magnetic Fields in Our World Come From a Source • The Electric and Magnetic Fields of Light Generate Each Other – Cannot Be Static • Conclusion: There is no reference frame where light is at rest

  19. Why the Speed of Light is a Speed Limit • Energy of a Moving Object in Relativity:E = mc2------------------------------------------------------------------------------- 1 - v2/c2 • One consequence: as v approaches c, Energy goes to infinity • Also, as we approach c, Energy goes up very fast

  20. Beating c?

  21. Beating c?

  22. Beating c?

  23. Faster Than Light (But Not c)

  24. Beating c? • Lots of things can travel faster than light • They are not material objects • They do not carry information between two points faster than light • In a material where light is slower than c, it is possible to travel faster than light • Superluminal Jets • Appear to travel faster than light • Perspective effect of coming at us at an angle

  25. What is Relativity? • All the relationships observed in science hold for all observers (cause-effect, conservation of energy, etc.) • This is why it’s called “relativity.” • There is no frame of reference where light is at rest.

  26. Doppler Shift = Time Dilation • Source = green (1.8 x 1015 sec per wave) • We see it as red (2.4 x 1015 sec per wave) • It’s the same wave • Things take 50 per cent longer for us than for the source • Our clock is faster, theirs is slower

  27. Time Dilation and Muons • Muons are short-lived particles created in the upper atmosphere by cosmic ray collisions • Their lifetime is 2 microseconds • At c they could travel 600 m and should decay before reaching the surface • Actually observed in abundance • At 0.998c, time dilation = 16x

  28. Special and General Relativity • You might think the “special” theory is more “special” and the “general” theory is generic • “Special” means “special case”: No changes in velocity, direction, etc. • “General” means it covers everything: acceleration, gravity, etc.

  29. The Equivalence Principle • Gravity and Uniform Acceleration are equivalent • Nobody knows exactly why, but it is true to very high precision • Gravitational and uniformly accelerating frames of reference are also inertial • After all, every inertial framework we’ve ever experienced has included gravity

  30. The Equivalence Principle

  31. Einstein and Gravity • Common Sense: What we observe from gravity, we will also see in an accelerating spaceship • No Surprises Here • Einstein: What we see in an accelerating spaceship, we will also see from gravity. • We See Unexpected Things • Redshift • Time Dilation

  32. Redshift and Acceleration

  33. Gravitational Redshift

  34. E = mc2

  35. E = mc2 • Stationary observer sees light emitted in both directions • Moving observer sees more energy emitted in one direction than the other • Kinetic energy of emitter as seen by moving observer must change • Velocity doesn’t change • Therefore mass of emitter must change

  36. Fuel Economy of a Starship • At 0.1 c, energy is 0.7% greater than Newtonian formula • At 0.5 c, 24% greater • At 0.9 c, 3 x greater • At 0.99 c, 12 x greater • At 0.999 c, 43 x greater • Each extra 9 more than triples the energy • Getting our 1000 ton ship to 0.9 c takes 1.1 x 1023 joules = U.S. energy use for 1100 years

  37. Another Consequence of Relativity- Gravitational Lenses

  38. “Curved Space” • Distance relationships in relativity aren’t always the same as in ordinary life • The overall geometry of the Universe might not be the same as small-scale geometry • The rules for measuring distance in a given system are called a metric • We use different metrics all the time, even outside of relativity.

  39. The Urban Metric

  40. Warped Space

  41. Gravity and “Curved Space”

  42. What Does The Universe Look Like?

  43. What Does The Universe Look Like?

  44. As Far Out as We Can See - Ten Days With the Hubble Telescope

  45. The Faint Outer Universe • For nearby stars and galaxies, brightness varies as 1/r2 • Distant galaxies are fainter than we’d expect from distance • Redshift: Photons packing less energy • Time Dilation: Galaxies seem to be emitting photons more slowly than they really are • Apparent distance from brightness is hundreds of billions of light years

  46. A New Name for the “Big Bang?”(Sky and Telescope, 1995) • The Big Boot • God’s Log-On • Fred Withair Day (“Nobody ever named anything else after me, so why not?”) • What Happens If I Push This Button? • You’re Never Going To Get It All Back In There Again

  47. 90% of the Universe is “Missing” • Outer Stars in Galaxies revolve faster than expected • What holds clusters of galaxies together? • Conclusion: There must be a lot of invisible mass in the Universe • Not really “missing”, just non-luminous

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