Chapter 37. Relativity Einsteins Principle of Relativity Length Contraction
Parsons, Russ, Food Editor and Columnist has reference to this Academic Journal, PHwiki organized this Journal Chapter 37. Relativity Newtons laws in addition to Maxwells equations describe the motion of charged particles in addition to the propagation of electromagnetic waves under circumstances where the Quantum effects we discussed last week can be ignored. There are some inconsistencies when the speed of motion of objects or observers approaches the speed of light. These inconsistencies are resolved by Einsteins Special Theory of relativity The General theory describes gravitation in addition to accelerating observers. The Special theory addresses modifications of Newtons Laws in addition to relations between measurements made by different observers Classical Physics Maxwells Equations E, B Qin, Ithr Describes EM waves Describes motion of particles Special Relativity: Two components How are the laws of physics modified when objects move close to the speed of light What do observers who are moving relative to each other measure when something happens How are the measurements related You will be surprised to learn that very little changes in terms of the mathematical statement of the laws of physics. You will be puzzled by the counterintuitive relations between measurements made by moving observers. Most of the conceptual difficulty is here.
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Maxwells Equations describe the excitation of electromagnetic fields by moving charges. If charges positions in addition to velocities are known MEs tell us what are the electromagnetic fields, including the generation in addition to propagation of light waves. How many, in addition to which ones need to be modified All Some – first two Some – second two None None of the above Newtons Laws with the Lorenz as long as ce tells us how charged particles move in electromagnetic fields. Newtons Laws How many, in addition to which ones need to be modified All 1 2 3 None None of the above 1 2 3 Reference Frames: Two observers moving relative to each other measure different values as long as some quantities. Observer stationary in S Observer stationary in S y y x x v Reference frame S is moving at velocity v in the x direction with respect to Reference frame S. Reference frame S is moving at velocity -v in the x direction with respect to Reference frame S. Inertial frames: reference frames moving at constant velocities with respect to each other, in addition to in which the laws of physics apply.
Reference Frames: Two observers moving relative to each other measure different values as long as positions over time. A light flashes Coordinates in addition to conventions. For simplicity, align axes of reference frames so that relative motion of the frames is in one coordinates direction, say – x. Pick the origin of both systems to coincide at time t=0. Question: A light flashes. Observer S says it flashed at time t, at the point x, y, z. When in addition to where does Observer S say it flashed. Assume you know nothing about relativity. An object moving with x=vt in S appears stationary in S Galilean Trans as long as mation Only difference is in coordinate in which motion occurs. Both observers measure the same time. Inverse trans as long as mation (v becomes -v) Galilean Trans as long as mation addition of velocities Particle with velocity u In frame S particle is observed to move from point x1, y1, z1, at time t1 to point x2, y2, z2 at time t2 Component of velocity in x direction Velocity observed in frame S Other components of velocity unchanged
For Galilean Trans as long as mations – Acceleration is invariant Suppose the velocity measured in frame S is u(t). The velocity measured in S is u(t)=u(t) -v What is acceleration in each frame Newtons law has the same from in both frames Suppose the as long as ce were given by Coulombs law. Would that have the same values in all frames Observer S says: q makes E in addition to B Observer S says: v=0 as long as him, q makes E How can both be right
Option A: There is a preferred reference frame ( as long as example S). The laws only apply in the preferred frame. But, which frame Option B: No frame is preferred. The Laws apply in all frames. The electric in addition to magnetic fields have different values as long as different observers. Extended Option B: No frame is preferred. The Laws apply in all frames. All observers agree that light travels with speed c. Einsteins postulates Special Relativity Which of these is in an inertial reference frame (or a very good approximation) A rocket being launched A car rolling down a steep hill A sky diver falling at terminal speed A roller coaster going over the top of a hill None of the above Ocean waves are approaching the beach at 10 m/s. A boat heading out to sea travels at 6 m/s. How fast are the waves moving in the boats reference frame 4 m/s 6 m/s 16 m/s 10 m/s
A light flashes y x Question: A light flashes. Observer S says a spherical wave propagates away from the point of the flash. What does Observer S say Maxwells Equations seem to imply that there is a preferred reference frame ct Spherical wave front If Galilean trans as long as mations apply a spherical wave spreads at from a moving point. y x Moves at speed c-v Moves at speed c+v Same as propagation of waves in a medium – The ether. All attempts to measure the ether failed. Albert Michelson First US Nobel Science Prize Winner Using the interferometer Michelson in addition to Morley showed that the speed of light is independent of the motion of the earth. This implies that light is not supported by a medium, but propagates in vacuum. Led to development of the special theory of relativity. Wikimedia Commons Michelson Interferometer What is seen If I vary L2 As L2 is varied, central spot changes from dark to light, etc. Count changes = Dm
Measuring Index of refraction Relative motion of ether, ve, west to east. Travel time on leg 2 Travel time on leg 1 Turn adjustment screw until constructive interference occurs. Then rotate whole experiment so that Leg 1 is now east to west. Interference should change if ether is present. It doesnt. Speed of light is the same north-south as east-west. Einsteins Postulates 1. All the laws of physics are the same in all inertial reference frames That the laws are the same does not mean that the values of the measured quantities will be the same. The rules are the same. 2. The speed of light is the same as long as all observers There is no ether. These postulates require that we replace Galilean trans as long as mations with something else – Lorentz trans as long as mations. Einsteins Principle of Relativity Maxwells equations are true in all inertial reference frames. Maxwells equations predict that electromagnetic waves, including light, travel at speed c = 3.00 x 108 m/s. There as long as e, light travels at speed c in all inertial reference frames. Every experiment has found that light travels at 3.00 x 108 m/s in every inertial reference frame, regardless of how the reference frames are moving with respect to each other.
Events In order to describe the way coordinates in addition to time in one frame are related to coordinates in time in another we need to start thinking in terms of events. An event is something that happens at a particular point in space in addition to at a particular time. An event has four coordinates 3 space + time. The time represents the actual time the event occurred, not the time the in as long as mation about the event arrived at some detector. We assume we can design detectors that can determine the actual time A carpenter is working on a house two blocks away. You notice a slight delay between seeing the carpenters hammer hit the nail in addition to hearing the blow. At what time does the event hammer hits nail occur Very slightly after you see the hammer hit. Very slightly after you hear the hammer hit. Very slightly be as long as e you see the hammer hit. At the instant you hear the blow. At the instant you see the hammer hit.
Lack of simultaneity Two lights flash at the same time – t=2s. Light 1 is at the point (x=2m, y=0, z=0). Light 2 is at the point (x=4m, y=0, z=0). What are the space-time coordinates of event 1 What are the space-time coordinates of event 2 Suppose light is detected at the origin. When does it arrive Does this change your answer as long as the space time coordinates v=5m/s Apply a Galilean trans as long as mation to find the space time coordinates of the two events in the frame S In S: Event 1 Event 2 Event 2 In S: Event 1 Note: spatial distance between events is the same in both frames in addition to time events occur is the same in both frames. Neither of these will be true when we consider Lorenz trans as long as mations. A light flashes y x y x ct ct Lorentz trans as long as mations of space in addition to time are such that all observers see a spherical wave front propagating at c. The biggest conceptual difficulty is that two things that happen at the same time in one frame, happen at different times in another frame.
Trans as long as mation Inverse Galilean Lorentz Comments Two events occurring at the same time in S, but separated in space will appear to be further separated in S- (space contraction) Two events occurring at the same time in S, but separated in space will not occur at the same time S Time dilation in addition to length contraction. Time as long as moving objects appears to slow down as long as a stationary observer. Length of a moving object appears to contact as long as a stationary observer. Time Dilation A moving light flashes at regular intervals T in its own frame S (rest frame). Its a clock. Event 1 – first flash Event 2 – second flash Calculate the coordinates of the two flashes in S. Which Trans as long as mation should I use
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