11Black HolesA 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 1905.27In 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 speedregardless 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 source12313So 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 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=mc².15Events• 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:16Reference 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.17 18419 20Lorentz 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 Contraction21More 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.22The 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 with respect to space has no meaning.23The 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 apparent at high velocities24525What Happens to Simultaneous Events?• Are events which