Black Holes A Matter of GravityGuiding QuestionsSlide Number 3Introduction to Special RelativityThe Speed of LightThe Speed of LightIn Water Things Look Like ThisSlide Number 8Michelson-Morley Experiment Michelson-Morley Experiment (cont.)A Thought ExperimentSlide Number 12So how is this possible??Welcome to The Strange World of Albert EinsteinEventsReference FramesSlide Number 17Slide Number 18Slide Number 19Lorentz TransformationMore on Reference FramesThe First Principle of RelativityThe Second Principle of Relativity Slide Number 24What Happens to Simultaneous Events?Slide Number 26Slide Number 27Simultaneous EventsSlide Number 29Slide Number 30Time Dilation Time Dilation (cont.)Time Dilation (cont.)Slide Number 34So How Much Does The Moving Clock Run Slow?Slide Number 36The Factor called GammaSome Time Dilation FactorsTime Dilation (cont.)FitzGerald Length ContractionSlide Number 41Why Length Contraction?The Twin ParadoxSlide Number 44Slide Number 45Twin ParadoxThe Concept of Space-timeSpace-Time DiagramsSlide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54A trip to the StarsSlide Number 56Slide Number 57EnergyGeneral RelativityEnergyRelativity and Magnetism Relativity and Magnetism (cont.)The Equivalence PrincipleGeneral RelativityWhy Curvature?Slide Number 66Black HolesGravity and TimeWhat Al and Bill seeDust orbiting a black holeSlide Number 71Black HolesSlide Number 73Curved in What?Again, the special theory of relativity changes our conceptions of space and timeThe speed of light is the same to all observers, no matter how fast they are movingAn observer will note a slowing of clocks and a shortening of rulers that are moving with respect to the observerThe general theory of relativity is our most accurate description of gravitationSlide Number 79Slide Number 80Slide Number 81The general theory of relativity predicts black holesSlide Number 83Slide Number 84Slide Number 85Slide Number 86Certain binary star systems probably contain black holesSlide Number 88Slide Number 89Slide Number 90Supermassive black holes exist at the centers of most galaxiesA nonrotating black hole has only a “center” and a “surface”Just three numbers completely describe the structure of a black holeSlide Number 94Falling into a black hole is an infinite voyage Slide Number 96Black holes evaporate Jargon1Black Holes A Matter of Gravity2Guiding Questions1. What are the two central ideas behind Einstein’s special theory of relativity?2. How do astronomers search for black holes?3. What are super massive black holes, and where are they found?4. In what sense is a black hole “black”?5. In what way are black holes actually simpler than any other objects in astronomy?6. What happens to an object that falls into a black hole?7. Why do some pulsars emit fantastic amounts of X rays?8. Do black holes last forever?3Good to Know4Introduction to Special Relativity• Motivation– Michelson-Morley Experiment– Induction versus Force Law• The Basics– Events– Principles of Relativity– Giving up on absolute space and time• What Follows from the Basics– Time Dilation – Length Contraction– Twin Paradox?• The Big Picture– Spacetime– Kinematics5The Speed of Light• Special Relativity becomes important in systems which are moving on the order of the speed of light• The speed of light is c=3X108 m/s is very fast:– Is exactly 299,792,458 m/s (how can they know this is the exact speed?)– 1 foot per nanosecond– 1 million times the speed of sound.– Around the earth 7 times in a second– Earth to sun in 15 min.• Galileo was the first person to propose that the speed of light be measured with a lantern relay. His experiment was tried shortly after his death. • In 1676 Ole Roemer first determined the speed of light (how can this be done with 17’th cent equipment.6The Speed of Light• In 1873, Maxwell first understood that light was an electromagnetic wave.• It was the the understanding of the nature of EM radiation which first led to a conceptual problem that required relativity as a solution.• According to his equations, a pulse of light emitted from a source at rest would spread out at velocity c in all directions.• But what would happen if the pulse was emitted from a source that was moving?• This possibility confused physicists until 1905.7In Water Things Look Like This• A boat moving through water will see forward going waves as going slow and backwards going waves as going fast89Michelson-Morley Experiment• Albert Michelson and Edward Morley were two American physicists working at Case Western Reserve University in Cleveland • They constructed a device which compared the velocity of light traveling in different directions (1887). • They found, much to their surprise that the speed of light was identical in all directions!• This is strange????smc /29979245810Michelson-Morley Experiment (cont.)• If the aether theory were correct, light would thus move more slowly against the aether wind and more quickly downwind. The Michelson-Morley apparatus should easily be able to detect this difference.• In fact, the result was the exact opposite: light always moves at the same speed regardless of the velocity of the source or the observer or the direction that the light is moving!11A Thought Experiment• A person on a cart moving at half the speed of light will see light moving at c.• A person watching on the ground will see that same light moving at the same speed, whether the light came from a stationary or moving source1213So how is this possible??• In the 18 years after the Michelson-Morley experiment, the smartest people in the world attempted to explain it away• In particular C.F. FitzGerald and H.A. Lorentz constructed a mathematical formulation (called the Lorentz transformation) which seemed to explain things but no one could figure out which it all meant.• In 1905, Albert Einstein proposed the theory of Special Relativity which showed that the only way to explain the experimental result is to suppose that space and time as seen by one observer are distorted when observed by another observer (in such a way as to keep c invariant)14Welcome to The Strange World of Albert Einstein• Some of the consequences of Special relativity are:– Events which are simultaneous to a stationary observer are not simultaneous to a moving observer.– Nothing can move faster