1 / 17

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

roch
Download Presentation

Special Theory of Relativity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related