1Phy 107, Lecture 16 1Relativity and Modern Physics• Physics changed drastically in the early 1900’s• New discoveries — Relativity and Quantum Mechanics• Relativity– Changed the way we think about space and time• Quantum mechanics– Changed our conceptions of matter.Phy 107, Lecture 16 2Special Relativity• From 1905 to 1908, Einsteindeveloped the special theoryof relativity.• Came up completely differentidea of time and space.• Everything is relative.No absolute lengths, times,energies.Showed that our usual conceptions of space andtime are misguided.Phy 107, Lecture 16 3Frames of reference• Frame of reference:– The coordinate system in which you observe events.– e.g. The room around you.– You judge how fast a thrown ball goes by its velocityrelative to some stationary object in the room.– You judge how high athrown ball goes by distancefrom the floor, ceiling, etc.– You judge how fast you aremoving by looking at objectsaround youPhy 107, Lecture 16 4Which reference frameSuppose you are on the bus to Chicago driving at 60 mph,and throw a ball forwards at 40 mph.From your seat on the bus,the speed of ball is the same as in this classroom.To the major league scout on the side of the road,your 40 mph throw has become a 100 mph fastball.Who is correct?You wouldn’t last long in the majors.The important velocity in a baseball game isthe relative velocity of ball with respect topitcher or the batter.Phy 107, Lecture 16 5• Earth spins on its axis– One rotation in (24 hrs)(60 min/hr)(60 sec/min)=86400 sec– Point on surface moves 2πRE in one rotation.– Surface velocity = 2π(6.4x106 m)/86400 sec = 465 m/s• Earth revolves around sun– One revolution in (365 days)(86400 sec/day)=3.15x107 sec– Earth velocity = 2π(1.5x1011 m)/ 3.15x107 sec=3x104 m/s• Sun moves w/ respect to center of our galaxy– Sun velocity = 2.3x105 m/s But what exactly is the absolute velocity of the ball?Phy 107, Lecture 16 6Galilean relativity• Absolute velocity not clear, but we canseemingly agree on relative velocities.– In all cases the ball moves 40 mph faster than I do.• Examples of two different reference frames– On the bus– Off the bus• In both cases we could talk about– the forces I put on the ball,– the acceleration of the ball, etc2Phy 107, Lecture 16 7Newton’s laws in moving frames• In both cases,the acceleration of the ball is the same.• This is because the two reference frames move at aconstant relative velocity.• Newton’s laws hold for each observer.• Which is good, because we apparently can’tdetermine our absolute velocity,or even if we are moving at all!This is an example of Galilean RelativityPhy 107, Lecture 16 8Example of Galilean relativity• Observer on ground• Observer in plane• Experiment may look differentto different observers, but bothagree that Newton’s laws hold– Can make observations agreeby incorporating relativevelocities of frames.Phy 107, Lecture 16 9Galilean relativity: example• Experiment performed…– in laboratory at rest with respect to earth’s surface– in airplane moving at constant velocity…must give the same result.v=0v>0• In both cases, ball is observed to rise up and returnto thrower’s hand– Process measured to take same time in both experiments– Newton’s laws can be used to calculate motion in both.Phy 107, Lecture 16 10Some other examples• On an airplane:– Pouring your tomato juice.– Throwing peanuts pretzel sticks into your mouth.– But when the ride gets bumpy…• In a car:– Drinking coffee on a straight, smooth road– But accelerating from a light,or going around a curvePhy 107, Lecture 16 11Turning this around…• No experiment using the laws of mechanics candetermine if a frame of reference is moving atzero velocity or at a constant velocity.• Concept of absolute motion is not meaningful.– There is no ‘preferred’ reference frameInertial Frame: reference frame moving in straight line with constant speed.Phy 107, Lecture 16 12QuestionYou riding in a car at 30 mph, and you throw a balldirectly backwards at 20 mph just as you pass astationary observer. The observer seesA. Ball drops directly to the ground with nohorizontal motionB. Ball moves backwards at 20 mph and fallsC. Ball moves forwards at 10 mph and falls to ground.3Phy 107, Lecture 16 13QuestionYou riding in a car at 30 mph, and you throw a balldirectly backwards at 30 mph just as you pass astationary observer. The observer seesA. Ball drops directly to the ground with no horizontal motionB. Ball moves backwards at 30 mph and fallsC. Ball moves forwards at 60 mph and fall to ground.Phy 107, Lecture 16 14What about electromagnetism?• Maxwell equations say that– Light moves at constant speed c=3x108 m/sec in vacuum• Seems at odds with Galilean relativity:– Jane would expect to see light pulse propagate at c+v– But Maxwell says it should propagate at c, if physics is same in allinertial reference frames.– If it is different for Joe and Jane, then in which frame is it c?JaneJoePhy 107, Lecture 16 15The Ether• To resolve this, 19th century researchers postulatedexistence of medium in which light propagates,rather than vacuum.– i.e. similar to gas in which sound waves propagate orwater in which water waves propagate.• Then Maxwell’s equations hold in the etherNo experimental measurement hasever detected presence of etherLight then becomes like otherclassical waves,Ether is absolute reference frame.Ether must be rigid, masslessmedium, with no effect onplanetary motionAllows speed of light to bedifferent in different frames(Maxwell’s eqns hold in frame atrest with respect to ether).MinusesPlusesPhy 107, Lecture 16 16The Michelson-Morley experimentPhy 107, Lecture 16 17The idea of the experiment• If the earth moves thru amedium thru which lightmoves at speed c, alongthe direction of theearth’s motion, lightshould appear from earthto move more slowly.Phy 107, Lecture 16 18Einstein’s principle of relativity• Principle of relativity:– All the laws of physics are identical in all inertialreference frames.• Constancy of speed of light:– Speed of light is same in all inertial frames(e.g. independent of velocity of observer, velocityof source emitting light)(These two postulates are the basis of thespecial theory of relativity)4Phy 107, Lecture 16 19The constancy of light speedJane is in spaceship traveling at 0.25c relativeto Earth and turns on her
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