Relativity Common wisdom everything is relative Is this really what the theory of relativity tells us Physics for Scientists Engineers 2 Absolutely not Spring Semester 2005 Lecture 47 April 21 2005 Physics for Scientists Engineers 2 1 April 21 2005 Interference in a Nutshell Physics for Scientists Engineers 2 2 Interferometer Simplified Michelson Morley interferometer Path length difference of n 1 2 destructive interference Path length difference of n constructive interference Interferometer can be used to measure very small path length differences between light beams Appearance of fringes light and dark April 21 2005 Physics for Scientists Engineers 2 3 April 21 2005 Physics for Scientists Engineers 2 4 1 Wave in Medium Doppler Effect Waves in a Nutshell from PHY183 The equation for all wave motion Solutions y x t v 2 2 y x t 0 t 2 x 2 2 Stationary sound source emits spherical sound waves spreading with v s y1 x t Y x vt with Y arbitrary function y2 x t Y x vt Sinusoidal waves Moving to right y x t Asin t x 0 Moving to left y x t Asin t x 0 Wave speed April 21 2005 Physical reason for Doppler Effect v Movement of sound source with v towards observer bunches up waves causing more waves to move past the observer in a given time interval perceived higher frequency f Physics for Scientists Engineers 2 5 April 21 2005 Doppler Effect 2 fo f 6 Electromagnetic Waves General formula for observed frequency of sound fo as a function of emitted frequency of sound f vs sound velocity vo velocity of observer v velocity of source Physics for Scientists Engineers 2 The speed of an electromagnetic wave can be expressed in terms of two fundamental constants related to electric fields and magnetic fields the magnetic permeability and the electric permittivity of the vacuum vs vo vs v c signs for the following cases 1 0 0 Source moves away from observer For an electromagnetic wave the wavelength and frequency of the wave are related to the speed of light Source moves towards observer c f Observer moves away from source Observer moves towards source Traveling electromagnetic waves E r t Emax sin kx t B r t Bmax sin kx t All velocities are relative to the medium air which is assumed to be at rest April 21 2005 Physics for Scientists Engineers 2 7 April 21 2005 Physics for Scientists Engineers 2 8 2 Electromagnetic Spectrum Ether So far we have not answered what medium light waves propagate in Air Not needed because light from outside the atmosphere reaches us too sun stars moon Now we know light can propagate in vacuum Around 1900 this was not known and the medium that light propagates in was postulated to be the ether Can one see something similar to the Doppler Effect for light since the Earth moves relative to the ether Michelson Morley built their interferometer to find out April 21 2005 Physics for Scientists Engineers 2 9 April 21 2005 Michelson Morley Morley s Result Michelson Morley used their interferometer and found NOTHING Light speed is the same in any direction 300 000 km s April 21 2005 Physics for Scientists Engineers 2 10 Einstein If there is motion of Earth relative to ether then the observed speed of light should be different for light in different directions Physics for Scientists Engineers 2 11 1879 Born in Ulm Germany March 14 1902 Begins work at Swiss patent office 1905 Publishes the three seminal papers on theoretical physics 1916 Proposes general theory of relativity 1919 General relativity is proved correct during a solar eclipse 1922 Awarded Nobel Prize in Physics 1933 Emigrates to US Princeton N J 1939 Urges F D R to develop atom bomb 1955 Dies in his sleep April 18 April 21 2005 Physics for Scientists Engineers 2 12 3 Einstein Einstein s Miracle Year 1905 Einstein Einstein s Postulates Postulate 1 Three seminal papers A paper explaining the so called photoelectric effect as due to the quantum nature of light This earned him the Nobel Prize in 1922 Light a quantum particle more on this in modern physics A paper explaining the effect of Brownian motion the motion of very small particles in water or other solutions as due to collisions with molecules and atoms thus proving that atoms really exist This was not at all clear before his work This would have also been worth a Nobel Prize Theory of special relativity The laws of physics are the same in each reference frame independent of the motion of this reference frame Postulate 2 The speed of light c is the same in every reference frame 2005 Celebrate 100th anniversary April 21 2005 Physics for Scientists Engineers 2 13 Reference Frame April 21 2005 Physics for Scientists Engineers 2 14 Moving Reference Frame Classical Person walking with a velocity vw as measured by an observer moving along with him on the walkway What is a reference frame It is any frame in which an observation can be made Walkway surface moves with vwt relative to terminal Any point on Earth is a reference frame Reference frames can move with respect to each other Two velocities add as vectors Let s go back to moving reference frames another review from PHY183 Velocity of person as measured by someone standing in the terminal vt vwt vw April 21 2005 Physics for Scientists Engineers 2 15 April 21 2005 Physics for Scientists Engineers 2 16 4 Galilean Transformation Galilean Transformation 2 Velocities Two coordinate systems x y z and x y z that have their axes parallel to each other and coincide at t 0 r r rT r vT t d d d r r vT t r vT dt dt dt v v vT Origin of x y z moves with constant velocity vT relative to x y z After some time t the origin of x y z is located at rT vT t Accelerations d d d v v vT v 0 dt dt dt Vector addition gives us the transformation between frames r r rT r vT t April 21 2005 Physics for Scientists Engineers 2 a a 17 April 21 2005 Physics for Scientists Engineers 2 Simple Example Beta and Gamma A spaceship moves towards Earth with speed c 2 Someone in the spaceship shines a laser speed c in the reference frame of the spaceship towards Earth Introduce a variable beta as the ratio of the speed to the speed of light v c Another useful variable that depends on the speed and the speed of light Galilean answer v c c 2 1 5 c Einstein s answer the speed of light is the same in every reference frame So the speed of the laser light measured on Earth is v c Physics for Scientists Engineers 2 It is convenient to express speeds as a fraction of the speed of light What is the speed of this laser light as measured on Earth April 21 2005 18 19 April
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