Relativity and Modern Physics Special Relativity

1 1 Phy 107, Lecture 161 Relativity 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 107, Lecture 162 Special Relativity From 1905 to 1908, Einsteindeveloped the Special theoryof Relativity . Came up completely differentidea of time and space. Everything is absolute lengths, times, that our usual conceptions of space andtime are 107, Lecture 163 Frames of reference Frame of reference: The coordinate system in which you observe events. The room around you. You judge how fast a thrown ball goes by its velocityrelative to some stationary object in the room.

2 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 164 Which reference frameSuppose you are on the bus to Chicago driving at 60 mph,and throw a ball forwards at 40 your seat on the bus,the speed of ball is the same as in this the major league scout on the side of the road,your 40 mph throw has become a 100 mph is correct?You wouldn t last long in the important velocity in a baseball game isthe relative velocity of ball with respect topitcher or the 107, Lecture 165 Earth spins on its axis One rotation in (24 hrs)(60 min/hr)(60 sec/min)=86400 sec Point on surface moves 2 RE in one rotation.

3 Surface velocity = 2 ( m)/86400 sec = 465 m/s Earth revolves around sun One revolution in (365 days)(86400 sec/day)= sec Earth velocity = 2 ( m)/ sec=3x104 m/s Sun moves w/ respect to center of our galaxy Sun velocity = m/s But what exactly is the absolute velocity of the ball?Phy 107, Lecture 166 Galilean 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, etc2 Phy 107, Lecture 167 Newton s laws in moving frames In both cases,the acceleration of the ball is the same.

4 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 168 Example 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 107, Lecture 169 Galilean Relativity : example Experiment in laboratory at rest with respect to earth s surface in airplane moving at constant give the same >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 107, Lecture 1610 Some other examples On an airplane.

5 Pouring your tomato juice. Throwing peanuts pretzel sticks into your mouth. But when the ride gets In a car: Drinking coffee on a straight, smooth road But accelerating from a light,or going around a curvePhy 107, Lecture 1611 Turning this 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 107, Lecture 1612 QuestionYou riding in a car at 30 mph, and you throw a balldirectly backwards at 20 mph just as you pass astationary observer. The observer drops directly to the ground with nohorizontal moves backwards at 20 mph and moves forwards at 10 mph and falls to 107, Lecture 1613 QuestionYou riding in a car at 30 mph, and you throw a balldirectly backwards at 30 mph just as you pass astationary observer.

6 The observer drops directly to the ground with no horizontal moves backwards at 30 mph and moves forwards at 60 mph and fall to 107, Lecture 1614 What 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 1615 The Ether To resolve this, 19th century researchers postulatedexistence of medium in which light propagates,rather than vacuum. similar to gas in which sound waves propagate orwater in which water waves propagate.

7 Then Maxwell s equations hold in the etherNo experimental measurement hasever detected presence of etherLight then becomes like otherclassical waves,Ether is absolute reference 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 1616 The Michelson-Morley experimentPhy 107, Lecture 1617 The 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 107, Lecture 1618 Einstein s principle of Relativity Principle of Relativity : All the laws of Physics are identical in all inertialreference frames.

8 Constancy of speed of light: Speed of light is same in all inertial frames( independent of velocity of observer, velocityof source emitting light)(These two postulates are the basis of thespecial theory of Relativity )4 Phy 107, Lecture 1619 The constancy of light speedJane is in spaceship traveling at relativeto Earth and turns on her headlights. Joeis on Earth, and observes the light fromthe headlights travel 107, Lecture 1620 Consequences of Einstein s relativityMany common sense results break down: Events simultaneous for observer in one referenceframe not necessarily simultaneous in differentreference frames. The distance between two objects is not for observers in different reference frames The time interval between events is not for observers in different inertial framesPhy 107, Lecture 1621 Time and simultaneity What does it meanfor two things to happen at the same time?

9 I do not define time, space, place, and motion,as being well known to all. NewtonIf you do not ask me what is time, I know you ask me, I cannot tell it. St. AugustinePhy 107, Lecture 1622 QuestionYou hear two gunshots exactly 1/2 second the gunshots occur at the same time?A. NoB. YesC. MaybePhy 107, Lecture 1623 Simultaneity If you know your distance from the shots, you caneasily determine if they were simultaneous. And everyone will agree with you, after doing thesame correction for distance. You might even come up with a definition Event (x1, t1) is simultaneous with event (x2, t2) if sound pulsesemitted at t1 from x1 and at t2 from x2 arrive simultaneously atthe midpoint between x1 and x2.

10 Einstein came up with a similar definitionfor relativistic simultaneity. Due to the requirement of the consistency of speed of light noteveryone agrees events are simultaneousPhy 107, Lecture 1624 Simultaneity thought experiment Boxcar moving with constant velocity v with respect toJane standing on the ground. Joe rides in exact center of the boxcar. Two lightning bolts strike the ends of the boxcar, leavingmarks on the boxcar and the ground underneath. On the ground, Jane finds that she is halfway between thescorch 107, Lecture 1625 Simultaneity, continued Jane (on the ground) also observes that light waves fromeach lightning strike at the boxcar ends reach her at exactlythe same time.