同济大学：《大学物理》课程教学资源（电子教案，英文版）第二十一章 相对论

Special relativity

Special relativity

Newtonian Relativity Absolute motion can not be detected

Newtonian Relativity Absolute motion can not be detected

A.Einstein‘s world Common sense is the collection of prejudices acquired by age eighteen

A.Einstein ‘s world Common sense is the collection of prejudices acquired by age eighteen

Einstein's postulates of special relativity 1 The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good 2 light is always propagated in empty space with definite velocity c,which is independent of the reference system that we choose

1 The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good 2 light is always propagated in empty space with definite velocity c, which is independent of the reference system that we choose. Einstein’s postulates of special relativity

The time dilation(时间膨胀) Mirror M Mirror Event 1 Event 2 MOTION D Event 1- Event 2 △ C Sally Sam (a) ()

The time dilation（时间膨胀）

- A-C Let:t=t- △t= Moving clock runs slower

2 2 2 1 2 1 1 v C t t t t t         2 1 Let：  t t 2 2 1 v C t     Moving clock runs slower

The twin paradox(双生子悖论) (a) (b)

The twin paradox（双生子悖论）

The length contraction(尺度收缩) 1=x2-x1=Vt vt x2-x=vl= X2一X1 v-(c)v-c) 1=1V1-2/C2

The length contraction（尺度收缩） o ´ z ´ y ´ x ´ v o x y z 1 x  2 x  l  x  x  vt 2 1     2 2 1 2 2 1 1 1 ' v C x x v C v t x x v t          2 2 l  l 1 v C

Example:A rod of 1m is 45 degrees to the horizon in S'system,How about its incline angler measured in s system？(v=√3C/2) solution: -1c0os0 ly==I'sin 0 1,=V1-v2/c2=1cos0V1-v2/C2 1=Vg+=1V1-/C2cos20=0.79m) 1'sinθ t8= I'cos01-v/C2 =20=6327

solution： S S´ ´ Example: A rod of 1m is 45 degrees to the horizon in S’ system, How about its incline angler measured in s system?（ v  3C 2 ） l  lcos x l  l  lsin  y y 2 2 2 2 l x  l x  1 v C  lcos 1 v C 2 2 x y l  l  l 1  cos 0.79( ) 2 2 2  l  v C   m 2 cos 1 sin 2 2         l v C l l l t g x y      6327

The relativity of simultaneity(同时的相对性)

The relativity of simultaneity（同时的相对性） v v