1Mon. Mar 5, 2007 Phy107 Spr07 Lecture 181From Last Time…• Electromagnetic waves• Special relativity– Reference frames– Inertial reference frames– Physical laws hold in all reference frames– In particular, speed of light constant in allreference frames.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 182Einstein’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)Mon. Mar 5, 2007 Phy107 Spr07 Lecture 183Light speedJane is in spaceship traveling at 0.25c relativeto Earth and turns on her headlights.Joe is on Earth, and observes the lightfrom the headlights travel atA. 0.75cB. 1.25cC. 1.0cD. 1.50cMon. Mar 5, 2007 Phy107 Spr07 Lecture 184Consequences of Einstein’s relativity• Many ‘common sense’ results break down:– Events that seem to be simultaneous are notsimultaneous in different inertial frames– The time interval between events is not absolute.it will be different in different inertial frames– The distance between two objects is not absolute.it is different in different inertial frames– Velocities don’t always add directlyMon. Mar 5, 2007 Phy107 Spr07 Lecture 185Time and simultaneity• What does it meanfor two things to happen at the same time?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 it.When you ask me, I cannot tell it. — St. AugustineMon. Mar 5, 2007 Phy107 Spr07 Lecture 186QuestionYou hear two gunshots exactly 1/2 second apart.Did the gunshots occur at the same time?A. NoB. YesC. Maybe2Mon. Mar 5, 2007 Phy107 Spr07 Lecture 187Analogy with sound• Suppose you hear two loud shotsabout 1/2 second apart.• Did they occur at the same time?• Obviously not.• But suppose you find out one of the shots wasfired closer to you than the other.• Sound travels at 340 m/s.• The sound pulse closer to you would arrivefirst, even if they were fired at the same time.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 188But everyone can agree• 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 at themidpoint between x1 and x2.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 189Relativistic simultaneity• Similar definition for relativistic simultaneity.• Simultaneity of separated events:– Event (x1, t1) is simultaneous with event (x2, t2) if light signalsemitted at t1 from x1 and at t2 from x2 arrive simultaneously atthe midpoint between x1 and x2• BUT, due to the constancy of the speed of lightwe are forced into the conclusion that not everyone willagree that two events are simultaneous (occurred at thesame time).Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1810Simultaneity thought experiment• Boxcar moving with constant velocity v with respect to Jane standingon the ground.• Joe rides in exact center of the boxcar.• Two lightning bolts strike the ends of the boxcar, leaving marks on theboxcar and the ground underneath.• On the ground, Jane finds that she is halfway between the scorchmarks.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1811Simultaneity, continued• Jane (on the ground) also observes that light waves from each lightningstrike at the boxcar ends reach her at exactly the same time.• Since each light wave traveled at c, and each traveled the same distance(since O is in the middle), the lightning strikes are simultaneous in theframe of ground observer.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1812When do the flashes reach Joe?• Jane can see when the two flashes reach Joe on the boxcar.• When light from front flash reaches Joe,he has moved away from rear flash.—Front and rear flashes reach Joe at different times• Since speed of light always constant• Joe is equidistant from lightning strikes—Joe is equidistant from the lightning strikes—Light flashes arrive at different times—Both flashes travel at c• Therefore for Joe, lightning strikes are not simultaneous.3Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1813Simultaneity and relativity, cont• Means there is no universal, or absolute time.– The time interval between events in one referenceframe is generally different than the interval measuredin a different frame.– Events measured to be simultaneous in one frame are ingeneral not simultaneous in a second frame movingrelative to the first.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1814Ether again• If there were an ether, this wouldn’t be a problem.• The ether would be the medium that transmits EM waves.• Speed of light is c relative to the ether.Suppose ether stationary with respect to Jane on ground.• Joe sees the flash from the front of the train first becausehe is rushing towards it. The ether is rushing backwards,carrying the flash along with it. The train observer measuresthe wave from the front to travel faster than from the back.• After accounting for this,he agrees with Jane that the strikes were simultaneous.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1815But there is no ether•No stationary ether, no absolute reference frame.•Joe sees that the train is stationary,and that Jane is rushing backwards.•Joe sees the light pulses from the front and rear travel atexactly the same speed.•Since the flashes arrive at different times,and Joe is equidistant between them, Joe is forced toconclude that the flashes occurred at different times.Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1816No universal simultaneity• Assumption: speed of light is constant in allinertial reference frames• Consequence: simultaneity not universal• Also time interval between two events is notuniversal.• For example,– the two events are two beats of an astronauts heart.– Number of heartbeats in time interval depends onobserver.– Aging depends on observer!Mon. Mar 5, 2007 Phy107 Spr07 Lecture 1817Time dilation• Laser bounces up and down from mirror on train.• Joe on ground measures time interval w/ his clock.• Joe watches Jane’s clock on train as she measuresthe time
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