Special Relativity Ch 37 n Modern physics n

Special Relativity (Ch 37) n Modern physics n n special relativity quantum mechanics Both were developed to explain the “few remaining puzzles” of classical physics Special relativity n n length contraction time dilation simultaneity energy-mass equivalence 1

Maxwell’s Equations

Michelson & Morley experiment n Hypothesis was that the speed of light must = c in the rest frame of “ether” n n ether was material proposed to fill all space and it allowed light to travel (waves need a medium) M&M tried to measure shift in speed of light due to earth’s orbital motion around sun Did not detect any shift!!! Michelson thought his experiment failed, but really there was no ether. 3

Postulates of Special Relativity n The laws of physics have the same form in all inertial reference frames. n inertial frame - not accelerating n n all reference frames are equivalent n n general relativity deals with acceleration car is at rest and earth is moving The speed of light in a vacuum is constant and the same for all observers. n required by Maxwell’s equations 4

The Galilean Transformations The Galilean transformations of position are: The Galilean transformations of velocity are:

Simultaneity n n Time is not absolute time interval between 2 events depends on observer Observer 2 sees lightning strikes as simultaneous Observer 1 does not 6

Time Dilation On spaceship n Moving clocks run slow n t 0 = proper time n frame where two events occur at same place 7

Lifetime of a moving muon n n When at rest, the lifetime of a muon is 2. 2 E-6 s. What will be the mean lifetime of a muon as measured in the laboratory if it is traveling at v=0. 60 c. How far does the muon travel in the laboratory, on average, before decaying? 8

Twin Paradox n One twin travels on spaceship at v=0. 5 c for 20 years, then turns around and returns. n n Twin on earth ages 40 yrs Twin in spaceship ages less 9

Length Contraction n The length of an object is measured to be shorter when it is moving n proper length, L 0 n n length of object as determined by observers at rest with respect to object contraction occurs only along direction of motion 10

Group Problem n A certain star is 10. 6 light-years away. How long would it take a spacecraft traveling 0. 960 c to reach that star from Earth, as measured by observers: (a) on Earth, (b) on the spacecraft? (c) What is the distance traveled according to observers on the spacecraft? (d) What will the spacecraft occupants compute their speed to be from the results of (b) and (c)? 11

Relativistic Momentum & Mass n Relativistic Momentum n n conservation of momentum in special relativity requires Relativistic Mass 12

Relativistic KE & Total Energy n Relativistic Kinetic Energy n Total energy 13

Mass and Energy n Equivalence of mass and energy n Pair production n n electron and positron annihilate to create gamma rays Nuclear energy n n products have less mass than reactants change in mass released as energy 14

Group Problem n A certain chemical reaction requires 4. 82 E 4 J of energy input for it to go. What is the increase in mass of the products over the reactants? 15

Group Problem n n Calculate the rest energy of an electron in joules and Me. V (1 Me. V = 1. 60 E-13 J). Calculate the velocity of an electron whose energy is equal to the rest-mass energy of a proton. 16

Group Problem n The total annual energy consumption in the United States is about 8 E 19 J. How much mass would have to be converted to energy to fuel this need? 17

Relativistic Addition of Velocities n n n v = vel of 1 WRT earth u’ = vel of 2 WRT 1 u = vel of 2 WRT earth n can’t just add velocities! 18

Group Problem n A person on a rocket traveling at 0. 50 c (WRT the Earth) observes a meteor come from behind and pass her at a speed of 0. 50 c. How fast is the meteor moving WRT the Earth? 19

Group Problem n Using MATLAB, plot (a) length/proper length and (b) time/proper time as a function of speed, as speed approaches the speed of light. At what speed do the special relativistic values differ classical values by 1. 00%? Express velocities in terms of c. 20

Mastering Physics n n Start on in-class assignment for Ch 37. Complete by Wed, 11 pm Physics 140 21