9 Relativity 9 1 The principle of Newtonian

9. Relativity 9 -1. The principle of Newtonian Relativity • Inertial frame : The frame is moving with a constant velocity v. y´ y x´ x z z´ Galilean transformation of Coordinates 1

9 -2. Michelson-Morley Experiment • Mechanical waves and sound waves need a media. • In 19 C, light is Electromagnetic wave and need a media. Luminiferous ether : massless but rigid • Absolute frame : at rest with respect to the luminiferous ether. • A. A. Michelson and E. W. Morley Determine the velocity of the Earth with respect to the ether. Using Interferometer No change in the light speed by the motion of the Earth. 2

9 -3. Einstein’s Principle of Relativity • Failure of Galilean transformation. (failure of the consideration through Ether. ) • Two postulates 1. The principle of Relativity : All the law of physics are the same in all inertial reference frame. 2. The Constancy of the Sped of Light : c = 3. 00 × 108 m/s. No change in the speed of light. • Postulate 1: Generalize the Newtonian Relativity (No absolute frame) • Postulate 2: Light always moves with a speed c in all inertial frame. 9 -4. Consequences of Special Relativity the distance between two points the time interval between two events Depends on the measurement frame No absolute time, No absolute length!! Newtonian No absolute Coordinate Absolute time interval (Inertial frame) Einsteinian No absolute Coordinate No Absolute time interval (Measurement frame with Coordinate and time) But the speed of light is always c = 3. 00 × 108 m/s. 3

• Time dilation The time interval Dt at the moving frame is longer than the interval Dt ´ at the rest frame. Proper time The proper time is always the time interval measured with a single clock at rest in the frame in which the events takes place at the same position. 4

Example of a Muon decay Muon : -e, 207 me (unstable, created by collisions between cosmic rays and atoms) decay lifetime t = 2. 2 ms e- + neutrinos v = 0. 99 c In the Muon frame: In the Earth frame: • Length Contraction Proper length : the length of the object measured by someone who is at rest relative to the object. LP Length Contraction 5

v L v 10 years 북극성 (the North Star) 1000 light year If an astronaut travels to the north star and return, it takes 20 years. But the clock at the earth: 2000 years. • Twin paradox Speedo and Goslo 6

9 -5. The Lorentz Transformation Equations y y´ P O z x O´ z´ v x´ When v << c , Galilean transformation 7

• Velocity If If 8

Example 9. 5 Relative velocity of Spaceship v = 0. 75 c A v = -0. 85 c B Velocity of B with respect to A? v = 0. 75 c ux = -0. 85 c 9 -6. Relativistic Momentum and Newton’s Laws Newtonian mometum But a momentum as is not conserved !! must be conserved in all collisions. The relativistic momentum is defined as 9

9 -7. Relativistic Energy At low velocity Newtonian Kinetic Energy Total Energy Rest Energy 10

If ; Photon Rest Energy ; Electron ; Proton ; Neutron 11

9 -8. Mass as a Measure of Energy L Momentum conservation L v c Kinetic mass of Pulse of light (Center of mass of the box is fixed) If a body gives off the energy E in the form of radiation, its mass diminishes by E/c 2. Conservation of mass-energy 12

9 -9. General Relativity Einstein’s assumptions for the general relativity • All the laws of nature have the same form for observers in any frame of reference, whether accelerated or not. • The Gravitational field is equivalent to an accelerated frame of reference. 13