《special relativity - rtftechnologies：特殊相对论rtftechnologies》由会员分享，可在线阅读，更多相关《special relativity - rtftechnologies：特殊相对论rtftechnologies（15页珍藏版）》请在金锄头文库上搜索。
1、Special RelativitySpring 2006Foundations of RelativityThe first introduction of a special relativity concept occurs in Maxwells equations for the relation between E and B in a vacuum. This equation gave insight to a relation between electric fields, magnetic fields, and the speed of light.Voigt firs
2、t introduced the concept of EM waves being observed in a moving frame of reference in 1887 with his “Elastic-Solid Theory” of light and introduced some important mathematical ideas.Consider the coordinate system and the wave equationVoigt introduced a moving set of coordinates or “reference frame” =
3、 Observer frame moving at V in the X directionand a new time coordinate where t is unity with no scaling of time and X is a linear function of space.Voigt demanded that the wave equation preserve its form in the new coordinate frame such that Thereforesoclearly we needthen Transverse coordinates sca
4、le in Voigts calculation, however they do not in the Lorenz transformation which will be used for special relativity. This is the main discrepancy between Voigts and Lorenzs calculations. Classical reference frames is obeyed by a free particleConsider two frames S and SS moves with velocity V with r
5、espect to frame S, therefore the relation of x between the two frames is , however in the classical explanation, time is absolute between the two frames The velocity transformation between the two classical frames is given byAnd both frames are inertial framesIn mechanics an inertial frame is one wh
6、ere Newtons first law holds. That is a “free fall frame” in which a particle in that observer frame will continue in a straight line with out accelerating unless an external force is applied to it.Mechanical WavesMechanical wave motion (eg sound waves) results from the Newtonian inertia among the me
7、dium which carries the wave. the speed of a wave measured in S is the speed of the wave measured in S minus the velocity difference between frames.By measuring changes in the speed of the mechanical wave we can detect motion of the host fluid with respect to our inertial reference frame in which the
8、 wave is traveling. Michelson-Morley experimentAttempted to determine velocity with respect to the either using an optical interferometer.In the early 19th century mechanical waves were well known, however electromagnetic waver were new. Physicists attempted to use a classical explanation to show th
9、at light propagates through an invisible substance called “either”.By observing EM waves in different inertial frames they hoped to observe the motion of the host medium “either”.To do this they attempted to measure the speed of the earth with respect to the either by taking one measurement, weighti
10、ng 6 months and taking another. Since the earths orbital velocity is about 3E4 m/s the ratio and that the measured speed of the earth with respect to the either should be on the order of The Michelson-Morley interferometer consists of a two mirrors at right angles a set distance away from on a split
11、ting cube. If the interferometer is moving with respect to the either, the wavelength on one of the arms will shift and the observed interference fringe pattern will change.If the interferometer were moving vertically with velocity V with respect to the eitherThe time of flight can be calculated on
12、the paths PS1P On path PS2P the observed light path would be at an angleBy the Pythagorean theoremThe time difference is now given by where Now rotate the interferometer by 90 degreesThe interferometer should register n fringe shifts given bySince we expect the first order approximation is sufficien
13、tly accurateThe number of fringe shifts can be calculated by where is approximately 1E-4However the results did not indicate a fringe shift showing that there was no either that light propagated in.Fitzgerald and Lorentz contractionsLorentz argued that since the fields of moving charges contracted a
14、long the direction of motion, the chemical bonds of matter should contract as well, reducing the objects length.In mechanics the Galilean relativity principle was enforced by the Galilean transformation. in the sense that Newtons laws hold However in electromagnetics, Maxwells equations do not prese
15、rve their form under the Galilean transformation. Following Lamor in 1900 and Lorentz in 1905, Poincare showed that Maxwells equations were invariant under the Lorentz transformation. where In 1905 Einstein derived the Lorentz transformation from his own axioms involving the principle of relativity and the statement that different inertial observers measure the same value for c.In the limit where vc the Lorentz transformation becomes the Galilean transformation.Einsteins axioms allowed all physical phenomena to obey the relat
