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