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Major Concepts in Physics Lecture 23.

Major Concepts in Physics Lecture 23. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring. Announcements. HW6 due in recitation this week Final 1 May 5-7:00 pm in Stolkin. Comprehensive. Same style, format to mid terms.

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Major Concepts in Physics Lecture 23.

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  1. Major Concepts in Physics Lecture 23. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring PHY102

  2. Announcements • HW6 due in recitation this week • Final 1 May 5-7:00 pm in Stolkin. Comprehensive. Same style, format to mid terms. • Review Monday 28th in class. Also this week in recitation PHY102

  3. Motion • Whenever we talk about motion we implicitly use a frame of reference • Just a coordinate system and a clock which is used to measure distances and times path t P1 P2 x PHY102

  4. Inertial frames • There is a special class of frames of reference used in mechanics (PHY101) • Inertial frames • Move at constant velocity (special case v=0) • Eg Otto viewed from Stolkin looks to be moving at constant velocity and also from the moving camera – an inertial frame. • Such frames do not accelerate PHY102

  5. Newtonian relativity principle • Laws of mechanics have same form in all inertial frames • All inertial observers agree when a force acts on some object and also agree on the magnitude and direction of that force. PHY102

  6. Is the Earth an inertial frame ? • A: yes • B: no Earth rotates … Coriolis force, rotation of hurricanes, … PHY102

  7. Fig. 26.1 PHY102

  8. How to add velocities in inertial frames • A car is travelling at 5 m/s in a straight line as observed by Fred who is stationary • Lucie follows the car on a bicycle moving at speed 2 m/s as seen by Fred. • What is speed of the car as seen by Lucie ? 2 m/s 5 m/s PHY102

  9. Light • Play the same game with a light beam. If light travels at speed c away from Fred • Lucie travels after it at speed v • Speed of recession as measured by Lucie should be c-v • Right ? Wrong …. PHY102

  10. Ether • Maxwell’s equations of EM contain a velocity as a fundamental parameter • c=3x108 m/s • What inertial frame is this measured with respect to ? • Prior to 1905 the ether invoked as substance permeates throughout space (even vacuum of space) which defines this special frame of reference PHY102

  11. What is this ether ? • Noone in 19th century knew – it had no observable properties • Purpose was entirely to provide special frame in which to use Maxwell’s equations • Notice – laws of electricity seem to violate the Newtonian principle of relativity • Michelson and Morley set out to measure the speed of Earth relative to the ether … PHY102

  12. Fig. 26.3 PHY102

  13. Michelson interferometer demo • See interference fringes by combining the light beams in 2 arms • If apparatus moves  fringes should shift according to Newton – since wavelength changes for waves in direction of motion PHY102

  14. How it works • Suppose apparatus moves to R at speed v • Light moves at c-v on outward trip and c+v after reflection from mirror with respect to lab • Time to go to mirror = L1/(c-v) • Time to return = L1/(c+v) • No cycles of wave along this path: (L1/l) x2/(1-v2/c2) PHY102

  15. Result • After waiting for the interference fringes to move over many months (1881) came to startling conclusion: Could not detect any motion of Earth relative to the ether ! PHY102

  16. Einstein’s relativity principle • The null result of MM expt constituted a crisis for physics – since it followed from apparently obvious truths – how to add velocities • Einstein resolved the problem by extending Newton’s principle of relativity: All laws of physics should look same to all inertial observers Speed of light should have same value for all such observers independent of their motion! PHY102

  17. Consequences • Demanding that the speed of light be the same independent of motion of observer has dramatic consequences • Consider 2 frames A with coords (x,t) and B (X,T) which move at relative speed v • Constant speed of light means: Dx/Dt=c=DX/DT or (Dx)2 – c2 (Dt)2 =0 same for both frames PHY102

  18. Spacetime • We are familiar in Newtonian physics with notion that all observers agree on the distance between 2 points in space • In relativity theory we need to generalize this notion. Talk about the distance in spacetime between 2 events • Event=(position and time at which something occurs) PHY102

  19. Spacetime distance • Einstein postulated that all inertial observers agree NOT on the distance in space but the distance in spacetime (Dx)2 – c2 (Dt)2 = Ds2 • Mixes space and time together. Observers may not agree on the time interval between two events or their spatial separation but they will agree on their separation in spacetime! PHY102

  20. Consequences … next lecture • Will see that this leads to very bizarre results • Time moves more slowly for moving bodies • Lengths shorten for bodies in motion • Energy and mass become interchangeable • The velocity of light is a maximum speed. • Explains naturally the null result of the MM expt (and many others) • Tested very accurately in modern expts PHY102

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