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Special Theory of Relativity

Special Theory of Relativity. Chapter 26. Modern Physics. Albert Einstein (1879-1955) Began with theory of relativity (1905) Classical Physics Before 1900 Newtonian Mechanics, Wave Motion, Kinetic Theory, etc. Time and lengths are constants Modern Physics After 1900

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Special Theory of Relativity

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  1. Special Theory of Relativity Chapter 26

  2. Modern Physics • Albert Einstein (1879-1955) • Began with theory of relativity (1905) • Classical Physics • Before 1900 • Newtonian Mechanics, Wave Motion, Kinetic Theory, etc. • Time and lengths are constants • Modern Physics • After 1900 • Theory of Relativity, Quantum Mechanics • Time and lengths depend on motion

  3. Galilean-Newtonian Relativity • Inertial Reference Frames • Not accelerating • Earth is considered inertial even though it rotates • Non-inertial Reference Frames • Accelerating • Relativity Principle • The basic laws of physics are the same in all inertial reference frames • All inertial reference frames are equivalent

  4. Galilean-Newtonian Relativity • Classical Physics • Space and time are absolute • Do not change from one reference frame to another • Mass and forces also do not change • Complication • Which frame of reference is the speed of light measured to be 3E8 m/s? • Ether: predicted medium light travels through • Speed is with respect to ether • Maxwell’s equations: laws of EM did not obey relativity principle • Michelson-Morley experiment

  5. Postulates of Special Theory of Relativity • What would I see if I rode a light beam? – Einstein • Two Postulates • The laws of physics have the same form in all inertial reference frames. (relativity principle) • Light propagates through empty space with a definite speed, c, independent of the speed of the source or observer. (constancy of the speed of light)

  6. Simultaneity • If two events are simultaneous in one inertial reference frame, are they simultaneous in all others? • NO! Simultaneity is relative.

  7. Time Dilation • Clocks moving relative to an observer are measured by that observer to run more slowly as compared to clocks at rest. • Δt = Δto/√(1 - v2/c2) • Δt = time of stationary object • Δto = time of moving object (“rest time”) • v = speed of moving object

  8. Example • What will be the mean lifetime of a muon as measured in the laboratory if it is traveling at 1.8E8 m/s with respect to the laboratory? Its mean lifetime at rest is 2.2 μs. • How far does a muon travel in the laboratory, on average, before decaying?

  9. Example • A car travels 100 km/h covering a certain distance in 10 seconds according to the driver’s watch. What does an observer at rest on Earth measure for the time interval?

  10. Example • A space traveler is moving at a speed of 0.999c. How many years pass for the space traveler after 100 years pass on the Earth?

  11. Twin Paradox • One twin gets in a space ship and travels around the moon and returns home. Since no frame of reference is privileged, which twin will be older when they meet?

  12. Length Contraction • The length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest. • Occurs only along the direction of the motion • L = Lo√(1 – v2/c2) • L= length of object measured with respect to stationary observer • Lo= length of object measured with respect to moving observer (“rest length”) • v = speed of moving object

  13. Example • A rectangular painting measures 1 m tall and 1.5 m wide. It is hung on the side wall of a spaceship which is moving past the Earth at a speed of 0.9c. • What are the dimensions of the picture according to the captain of the spaceship? • What are the dimensions as seen by an observer on the Earth?

  14. Relativistic Momentum and Mass • Mass increases as the speed increases • mrel = mo/√(1 – v2/c2) • mrel = relativistic mass • mo = rest mass • v = speed of object • Momentum increases as the speed increases • p = mov/√(1 – v2/c2) • p = momentum of moving object • mo = rest mass • v = speed of object • According to Newton’s second law of motion, the c is the fastest speed an object with mass can travel.

  15. Example • Compare the momentum of an electron when it has a speed of 4E7 m/s and 0.98c.

  16. Mass and Energy • Energy and mass are the same thing, only in different forms. • Eo = moc2 • Eo = rest energy (joules) • mo = rest mass (kg) • c = speed of light in a vacuum (3E8 m/s) • E = moc2/√(1 – v2/c2) • E = total energy

  17. Example • Calculate the rest energy of a proton in joules and MeV.

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