Special Relativity Quiz 9.4 and a few comments on quiz 8.24. Topics in Special Relativity in this course: Inertial frame of reference and the definition of an “event”. The Lorentz Transformation equations of spatial coordinates or time. The Doppler effect: transformation of spatial coordinates and time. Velocity transformation: the derivative of coordinates with respect to time. Momentum and Energy, a step into dynamics. A glimpse into General Relativity if we have time. √ √

The Doppler effect: transformation of spatial coordinates and time Doppler effect (review): When the light source is moving away at a velocity v with respect to the observer, the frequency the observer measures relates to the frequency the light source emits through this formula: Here θ is the angle between the velocity v and the line defined by the observer and the source. When θ =0, the course is moving away from the observer. A discussion about redshift and the measurement of stars motion relative to the Earth. Example 2.6: direct application of the above formula. O S Reminder:

Velocity transformation: the derivative of coordinates with respect to time When a particle moves in frame S with a velocity u, and in frame S’ with a velocity u’, and S’ moves in frame S with a velocity v: Classical mechanics: Special relativity: The 3 dimensional space: still assume S’ moves in S, along its x-axis with velocity v: Example 2.7 Derive on the blackboard

Momentum and Energy, a step into dynamics Momentum of a particle of mass m, velocity in frame S: The total energy of a particle mass m, velocity in frame S: When , that is ,the particle has an energy that is its mass: So the kinetic energy of the particle is: How do you get to remember When x is small.

Momentum and Energy, a step into dynamics Example 2.9: Example 2.10: momentum conservation and Example 2.11: The reference independent energy and momentum formula: Derive it:

Review questions You accelerate two protons with mass m to a speed of 0.98c and then make them collide head-on. What is the approaching speed one proton sees the other? What are the total momentum and energy of this two particle system? (a real example: http://lhc2008.web.cern.ch/lhc2008/) By what factor would a star’s characteristic frequencies of light be shifted if it were moving away from the Earth at 0.01c?

Preview for the next class Text to be read: In chapter 3: Section 3.1 Section 3.2 Section 3.3 Questions: What is wave-particle duality? How Planck propose to modify the classical spectral energy density formula to make it match experimental data? What is the formula that brings Einstein the Nobel Prize in physics in 1921? Check those that are correct: Roentgen discovered X-ray and obtained a patent for it to make him rich. Roentgen won the Nobel Prize in physics in 1901 for his discovery of the radiation he named the X-rays. The X-rays are produced by smashing a laser beam on a target.

Homework 3, due by 9/11 Derive this formula with the condition in slide 3. Problem 54 on page 66. Problem 59 on page 66. Problem 81 on page 67.