Special Relativity Lecture 25 F2013 Lorentz transformations 1

2 Einstein’s Postulates The Relativity Postulate: The laws of physics are the same for observers in all inertial reference frames. No frame is preferred over any other. 2. The Speed of Light Postulate: The speed of light in vacuum has the same value c in all directions and in all inertial reference frames. These postulates lead to new relationships for time, length, mass, momentum, and energy. At low relative speeds (<< than speed of light) the relativistic relationships reduce to the relationships we know from classical mechanics.

3 Measuring an Event 37- Fig Event: something that happens, can be assigned three space coordinates and one time coordinate Where something happens is straightforward, when something happens is trickier (for example the sound of an explosion will reach a closer observer sooner than a farther observer.) Space-Time Coordinates 1. Space Coordinates: three dimensional array of measuring rods 2. Time coordinate: Synchronized clocks at each measuring rod intersection How do we synchronize the clocks? Event A: x=3.6 rod lenghts, y=1.3 rod lengths, y=1.3 rod lengths, z=0, time=reading on nearest clock All clocks read exactly the same time if you were able to look at them all at once!

4 Lorentz Factor 37- Lorentz factor  as a function of the speed parameter  Fig. 37-6

Galilean transformations 5

Lorentz transformations 6

7

Representing Lorentz transformations graphically 8 Here are the lines for x=0 and t=0 in an x-t cartesian plot. ct x x The line for t=constant is dashed.

Worldline for a traveling particle. Representation of a fixed object. (t=constant) Observation in a moving frame? 9

Representing Lorentz transformations graphically 10 ct x x’ ct’

11 A New Look at Energy Mass energy or rest energy EXAMPLES ObjectMass (kg)Energy Equivalent Electron≈ 9.11x ≈ 8.19x J(≈ 511 keV) Proton ≈ 1.67x ≈ 1.50x J(≈ 938 MeV) Total energy

A New Look at Kinetic Energy Classical Kinetic energy Relativistic Kinetic energy For a given speed, relativistic kinetic energy is greater than classical kinetic energy.