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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.
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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. S O 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.
