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This lecture covers the postulates of special relativity, including the relativity postulate and the speed of light postulate. It explains how these postulates lead to new relationships for time, length, mass, momentum, and energy. The lecture also discusses the measurements of events and the concept of proper time and length. Examples and experiments related to special relativity are presented.
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Special Relativity Lecture 24 F2013 The Postulates Phenomenology The proper frame Time Length Mass energy Measuring events Lorentz transformations
Observations of particle decay • The pion has a lifetime of 26 ns in its rest frame. • In an experiment where it has a speed of 0.913 c, the pion is observed to travel 17.4 m, which implies a lifetime of 64 ns. • We will come back to this observation and see how it can be possible from the viewpoint of special relativity.
An experiment in terror • Hannah sits on a cart and moves a pencil back and forth while the cart moves at constant speed. • How far does the pencil move according to him? • How far does the pencil move according to the rest of the class? • How long did it take? • What was the average speed of the pencil?
A related problem • Maxwell’s theory of the electric and magnetic fields states that electromagnetic waves are the results of changing electric and magnetic fields and that they travel at v=(00)-1/2 in vacuum. • But classical kinematics does not preclude traveling along with a light wave at the speed of light. • Experiments on the speed of light (1890-1905) showed that the speed of light measured on the orbiting Earth was independent of the direction in which the light propagated.
Einstein’s Postulates 1. 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. 37-
How do things change if the speed of the pencil must be the same in every measurement frame? Either time or distance must somehow be different as measured in different frames
The Ultimate Speed Fig. 37-2 Experiment by Bertozzi in 1964 accelerated electrons and measured their speed and kinetic energy independently. Kinetic energy →∞ as speed → c Ultimate Speed→Speed of Light: 37-
Measuring an Event Fig. 37-3 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? All clocks read exactly the same time if you were able to look at them all at once! Event A: x=3.6 rod lenghts, y=1.3 rod lengths, y=1.3 rod lengths, z=0, time=reading on nearest clock 37-
Relativistic Time When two events occur at the same location in an inertial reference frame, the time interval between them, measured in that frame, is called the proper time interval or the proper time. Measurements of the same time interval from any other inertial reference frame are always greater. Lorentz factor: 37-
Relativistic Time, cont'd Fig. 37-6 Lorentz factor g as a function of the speed parameter b 37-
Concept Check Sam A B C Sam leaves point A and travels at constant velocity past point B to point C. Beatrice stays at home at point B. • Each measures the travel time from point A to C. Who measures the proper time for the trip? A) Alice B) Beatrice C) Sam D)Both E) Who is Alice?
Concept Check Sam leaves Alice at point A and travels to point C. Beatrice stays at point B. Along the way, Sam sends a light pulse from his vehicle to point C. Both Alice and Beatrice observe the sending and receiving of the pulse. Who measures the proper time for the travel of the pulse? A) Alice B) Beatrice C) Sam D)All of ‘em E) None of ‘em.
The length L0 of an object in the rest frame of the object is its proper length or rest length. Measurement of the length from any other reference frame that is in motion parallel to the length are always less than the proper length. Relativistic Length
Relativistic Momentum relativistic expression using Dt=Dt0g, where the time Dt0 to move a distance Dx is measured in the moving observer's frame 37-
A New Look at Energy Mass energy or rest energy EXAMPLES Object Mass (kg) Energy Equivalent Electron ≈ 9.11x10-31 ≈ 8.19x10-14J (≈ 511 keV) Proton ≈ 1.67x10-27 ≈ 1.50x10-10J (≈ 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.
Scientists did not accept the Special Relativity model without a “healthy discussion”. Michelson-Morley: large interferometer, rotated so arms point along or perpendicular to motion of the Earth Kennedy-Thorndike: large interferometer fixed in orientation wrt Earth Fizeau: speed of light through a moving liquid.
