Black Holes A Matter of Gravity 1 Guiding Questions 1 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 2 Good to Know 3 Introduction 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 Kinematics 4 The 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 5 The 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 6 In Water Things Look Like This A boat moving through water will see forward going waves as going slow and backwards going waves as going fast 7 8 Michelson 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 c 299792458 m s This is strange 9 Michelson 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 10 is moving A 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 source 11 12 So 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 13 invariant Welcome 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 than c the speed of light in vacuum A stationary observer will see a moving clock running slow A moving object will be contracted along its direction of motion Mass can be shown to be a frozen form of energy according to the relation E mc 14 Events In physics jargon the word event has about the same meaning as it s everyday usage An event occurs at a specific location in space at a specific moment in time 15 Reference Frames A reference frame is a means of describing the location of an event in space and time To construct a reference frame lay out a bunch of rulers and synchronized clocks You can then describe an event by where it occurs according to the rulers and when it occurs according to the clocks 16 17 18 19 Lorentz Transformation Space and time are not absolute as in Newtonian physics and everyday experience The mathematical relation between the description of two different observers is called the Lorentz transformation Some phenomena which follow from the Lorentz transformation are Relativity of Simultaneous events Time Dilation Length Contraction 20 More on Reference Frames What is the relation between the description of an event in a moving reference frame and a stationary one To answer this question we need to use the two principles of relativity 21 The First Principle of Relativity An inertial frame is one which moves through space at a constant velocity The first principle of relativity is The laws of physics are identical in all inertial frames of reference For example if you are in a closed box moving through space at a constant velocity there is no experiment you can do to determine how fast you are going In fact the idea of an observer being in motion 22 with respect to space has no meaning The Second Principle of Relativity The second principle of relativity is a departure from Classical Physics The speed of light in vacuum has the same value c in all inertial frames regardless of the source of the light and the direction it moves This is what the MM experiment shows The speed of light is therefore very special This principle is not obvious in everyday experience since things around us move much slower than c In fact the effects of relativity only become 23 apparent at high velocities 24 What Happens to Simultaneous Events Are events which are simultaneous to one observer also simultaneous to another observer We can use the principles of relativity to answer this question Imagine a train moving at half the speed of light 25 View from the Train 26 The View From The Ground 27 Simultaneous Events Thus two events which are
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