Lecture 28: TUE 04 MAY 2010Lecture 28: TUE 04 MAY 2010Physics 2102Jonathan DowlingCh. 37 EinsteinCh. 37 Einstein’’s Theory of Relativitys Theory of RelativityCh. 38: Ch. 38: Photons and Matter WavesChapter 37 RelativityRelativity is an important subject that looks at the measurement of whereand when events take place, and how these events are measured inreference frames that are moving relative to one another.In this chapter we will explore the special theory of relativity (which we willrefer to simply as "relativity"), which only deals with inertial reference frames(where Newton's laws are valid). The general theory of relativity looks at themore challenging situation where reference frames undergo gravitationalacceleration.In 1905, Albert Einstein stunned the scientific world by introducing two"simple" postulates with which he showed that the old, commonsense ideasabout relativity are wrong. Although Einstein's ideas seem strange andcounterintuitive, e.g., rate at which time passes depends on the speed ofreference frame, these ideas have not only been validated by experiment,they are also being used in modern technology, e.g., global positioningsatellites.(37-1)The Postulates1. The Relativity Postulate: The laws of physics are the same forobservers in all inertial reference frames. No frame is preferredover any other.2. The Speed of Light Postulate: The speed of light in vacuumhas the same value c in all directions and in all inertial referenceframes.Both postulates tested exhaustively, no exceptions found!(37-2)The Relativity of TimeFig. 37-5The time interval between two events depends on how far apartthey occur in both space and time; that is, their spatial andtemporal separations are entangled.( )02 SallyDtc! =( )( )( ) ( )22122 21 102 22 SamLtcL v t DL v t c t! == ! += ! + !( )02 (37-7)1ttv c!! ="(37-8)The Relativity of Time, cont'dWhen two events occur at the same location in an inertial referenceframe, the time interval between them, measured in that frame, iscalled the proper time interval or the proper time. Measurements ofthe same time interval from any other inertial reference frame arealways greater.( )2 21 1 (37-8)11 v c!"= =##Lorentz factor:0 (time dilation) (37-8)t t!" = "v c!=Speed Parameter:(37-9)Lorentz factor γ as a function of the speed parameter βThe Relativity of Time, cont'dFig. 37-6(37-10)2. Macroscopic Clocks. Super precision atomic clocks (large systems) flownin airplanes β~7x10-7 (Hafele and Keating in 1977 within 10%, and U. Marylanda few years later within 1% of predictions) repeated the muon lifetimeexperiment on a macroscopic scaleIf the clock on the U. Maryland flight registered 15.00000000000000 hours asthe flight duration, how much would a clock that stayed on earth (lab frame)have measured for the duration? More or less? Does it matter whether airplanereturns to same place?Two Tests of Time Dilation, cont'd( )( )720801if 7 10 1.00000000000024511.000000000000245 15.00000000000000 hr 15.00000000000368 hr1 10 s!t tt t! "!"##= $ % = =#& = & ==& # & = $(37-12)Twin ParadoxThe Relativity of LengthThe length L0 of an object in the rest frame of the object is its properlength or rest length. Measurement of the length from any otherreference frame that is in motion parallel to the length are always lessthan the proper length.2001 (37-13)LL L!"= # =(37-13)Does a moving object really shrink?Fig. 37-7You must measure front and back of moving penguin simultaneously to get its length inyour frame. Let's do this by having two lights flash simultaneously in the rest frame whenthe front and back of the penguin align with them.In penguin's frame, your measurements did not occur simultaneously. You firstmeasured the front end (light from front flash reaches moving observer first as in slide37-7) and then the back (after the back has moved forward), so the length that youmeasure will appear to be shorter than in the penguin's rest frame.(37-14)A New Look at Energy20 (37-43)E mc=Mass energy or rest energyObject Mass (kg) Energy EquivalentElectron ≈ 9.11x10-31 ≈ 8.19x10-14J (≈ 511 keV)Proton ≈ 1.67x10-27 ≈ 1.50x10-10J (≈ 938 MeV)Uranium atom ≈ 3.95x10-25 ≈ 3.55x10-8J (≈ 225 GeV)Dust particle ≈ 1x10-13 ≈ 1x104J (≈ 2 kcal.)U.S. penny ≈ 3.1x10-3 ≈ 2.8x1014J (≈ 78 GWh)Table 37-3 The Energy Equivalents of a Few Objects (37-25)A New Look at Energy , cont'd20 (37-47)E E K mc K= + = +Total energy2 (37-48)E mc!=The total energy E of an isolated system cannot change0 0system's initial system's finaltotal mass energy total mass energyor (37-49)i iQE E Q! " ! "= +# $ # $% & % &= +2 2 2 (37-50)i fQ M c M c Mc= ! = "2 2i fM c M c Q= +(37-26)Fig. 37-2Experiment by Bertozzi in 1964 accelerated electrons and measured theirspeed and kinetic energy independently. Kinetic energy →∞ as speed → cThe Ultimate SpeedUltimate Speed→Speed of Light:299 792 458 m/sc =(37-3)Chapter 38Photons and Matter WavesThe subatomic world behaves very differently from the world of our ordinaryexperiences. Quantum physics deals with this strange world and hassuccessfully answered many questions in the subatomic world, such as: Whydo stars shine? Why do elements order into a periodic table? How do wemanipulate charges in semiconductors and metals to make transistors andother microelectronic devices? Why does copper conduct electricity but glassdoes not?In this chapter we explore the strange reality of quantum mechanics.Although many topics in quantum mechanics conflict with our commonsenseworld view, the theory provides a well-tested framework to describe thesubatomic world.(38-1)Quantum physics:•Study of the microscopic world• Many physical quantities found only in certain minimum (elementary)amounts, or integer multiples of those elementary amounts•These quantities are "quantized"•Elementary amount associated with this quantity is called a "quantum" (quantaplural)Analogy example: 1 cent or $0.01 is the quantum of U.S. currency.Electromagnetic radiation (light) is also quantized, with quanta called photons.This means that light is divided into integer number of elementary packets(photons).The Photon, the Quantum of Light(38-2)The energy of light with frequency f must be an integer multiple of hf. In theprevious chapters we dealt with such large quantities of light that individualphotons were not distinguishable. Modern experiments
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