PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 25:

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Presentation transcript:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 25: Start reading Chap. 11 Equations in cgs (Gaussian) units Special theory of relativity Lorentz transformation relations 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

03/20/2018 PHY 712 Spring 2018 -- Lecture 25

03/20/2018 PHY 712 Spring 2018 -- Lecture 25

03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Notions of special relativity The basic laws of physics are the same in all frames of reference (at rest or moving at constant velocity). The speed of light in vacuum c is the same in all frames of reference. y’ y v x x’ y’ x’ y x 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Lorentz transformations y’ y v x x’ y’ x’ y x 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Lorentz transformations -- continued 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Examples of other 4-vectors applicable to the Lorentz transformation: 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

The Doppler Effect 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

The Doppler Effect -- continued x y x’ v y’ k’ k 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Electromagnetic Doppler Effect (q=0) Sound Doppler Effect (q=0) 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Lorentz transformation of the velocity For an infinitesimal increment: 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Lorentz transformation of the velocity -- continued 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Example of velocity variation with b: ux/c uy/c 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Velocity transformations continued: Velocity 4-vector: 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Some details: 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Significance of 4-velocity vector: Introduce the “rest” mass m of particle characterized by velocity u: Properties of energy-moment 4-vector: 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Properties of Energy-momentum 4-vector -- continued 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Summary of relativistic energy relationships 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Special theory of relativity and Maxwell’s equations 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

More 4-vectors: 03/20/2018 PHY 712 Spring 2018 -- Lecture 25

Lorentz transformations 03/20/2018 PHY 712 Spring 2018 -- Lecture 25