Physics 2102 Jonathan Dowling Lecture 28 TUE 04 MAY 2010 Ch 37 Einstein s Theory of Relativity Ch 38 Photons and Matter Waves Chapter 37 Relativity Relativity is an important subject that looks at the measurement of where and when events take place and how these events are measured in reference frames that are moving relative to one another In this chapter we will explore the special theory of relativity which we will refer to simply as relativity which only deals with inertial reference frames where Newton s laws are valid The general theory of relativity looks at the more challenging situation where reference frames undergo gravitational acceleration In 1905 Albert Einstein stunned the scientific world by introducing two simple postulates with which he showed that the old commonsense ideas about relativity are wrong Although Einstein s ideas seem strange and counterintuitive e g rate at which time passes depends on the speed of reference frame these ideas have not only been validated by experiment they are also being used in modern technology e g global positioning satellites 37 1 The Postulates 1 The Relativity Postulate The laws of physics are the same for observers in all inertial reference frames No frame is preferred over any other 2 The Speed of Light Postulate The speed of light in vacuum has the same value c in all directions and in all inertial reference frames Both postulates tested exhaustively no exceptions found 37 2 The Relativity of Time The time interval between two events depends on how far apart they occur in both space and time that is their spatial and temporal separations are entangled 2D t0 c 2L t c L 1 2 L 1 2 t Fig 37 5 Sally Sam v t D 2 v t c t0 2 2 2 1 2 t0 1 v c 2 37 7 37 8 The Relativity of Time cont d When two events occur at the same location in an inertial reference frame the time interval between them measured in that frame is called the proper time interval or the proper time Measurements of the same time interval from any other inertial reference frame are always greater Speed Parameter Lorentz factor t t0 v c 1 1 2 1 1 v c 2 37 8 time dilation 37 8 37 9 The Relativity of Time cont d Lorentz factor as a function of the speed parameter Fig 37 6 37 10 Two Tests of Time Dilation cont d 2 Macroscopic Clocks Super precision atomic clocks large systems flown in airplanes 7x10 7 Hafele and Keating in 1977 within 10 and U Maryland a few years later within 1 of predictions repeated the muon lifetime experiment on a macroscopic scale If the clock on the U Maryland flight registered 15 00000000000000 hours as the 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 airplane returns to same place if 7 10 7 1 1 2 1 000000000000245 t t0 1 000000000000245 15 00000000000000 hr 15 00000000000368 hr t t0 1 10 8 s 37 12 Twin Paradox The Relativity of Length L0 L L0 1 2 37 13 The length L0 of an object in the rest frame of the object is its proper length or rest length Measurement of the length from any other reference frame that is in motion parallel to the length are always less than the proper length 37 13 Does a moving object really shrink Fig 37 7 You must measure front and back of moving penguin simultaneously to get its length in your frame Let s do this by having two lights flash simultaneously in the rest frame when the front and back of the penguin align with them In penguin s frame your measurements did not occur simultaneously You first measured the front end light from front flash reaches moving observer first as in slide 37 7 and then the back after the back has moved forward so the length that you measure will appear to be shorter than in the penguin s rest frame 37 14 A New Look at Energy Mass energy or rest energy E0 mc 2 37 43 Table 37 3 The Energy Equivalents of a Few Objects Object Mass kg Energy Equivalent Electron 9 11x10 31 8 19x10 14J 511 keV Proton 1 67x10 27 1 50x10 10J 938 MeV 3 55x10 8J 225 GeV Uranium atom 3 95x10 25 Dust particle 1x10 13 U S penny 3 1x10 3 1x104J 2 8x1014J 2 kcal 78 GWh 37 25 A New Look at Energy cont d Total energy E E0 K mc 2 K E mc 2 37 47 37 48 The total energy E of an isolated system cannot change system s initial system s final Q total mass energy total mass energy or E0i E0i Q 37 49 M ic2 M f c2 Q Q M i c 2 M f c 2 Mc 2 37 50 37 26 The Ultimate Speed Experiment by Bertozzi in 1964 accelerated electrons and measured their speed and kinetic energy independently Kinetic energy as speed c Fig 37 2 Ultimate Speed Speed of Light c 299 792 458 m s 37 3 Chapter 38 Photons and Matter Waves The subatomic world behaves very differently from the world of our ordinary experiences Quantum physics deals with this strange world and has successfully answered many questions in the subatomic world such as Why do stars shine Why do elements order into a periodic table How do we manipulate charges in semiconductors and metals to make transistors and other microelectronic devices Why does copper conduct electricity but glass does not In this chapter we explore the strange reality of quantum mechanics Although many topics in quantum mechanics conflict with our commonsense world view the theory provides a well tested framework to describe the subatomic world 38 1 The Photon the Quantum of Light 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 quanta plural 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 38 2 The Photon the Quantum of Light cont d So what aspect of light is quantized Frequency and wavelength still can be any value and are continuously variable not quantized c f where c is the speed of light 3x108 m s However given light of a particular frequency the total energy of that radiation is quantized with an elementary amount quantum of energy E given by E hf photon energy where the Planck constant h has a value h 6 63 10 34 J s 4 14 10 15 eV s The energy of light with frequency f must be an integer multiple of hf In the previous chapters we dealt with such large quantities of light …
View Full Document
Unlocking...