The time interval Ato measured by the observer(s) relative to whom the clock is at rest is called the proper time正确时间)”,and△t0<At That is the observer relative to whom the clock is in motion measures a greater interval between ticks. this effect is called time dilation all observer in motion relative to the clock measure onger intervals” Eg 20-3) is valid for any direction of the relative motion of s and s
The time interval measured by the observer (S’) relative to whom the clock is at rest is called the “proper time(正确时间) ”, and . That is, the observer relative to whom the clock is in motion measures a greater interval between ticks. This effect is called “time dilation”. All observer in motion relative to the clock measure “longer intervals”. 0 t t t 0 Eq(20-3) is valid for any direction of the relative motion of S and S’
2. The relativity of length Fig 20-6 shows the sequence of events as observed by s for the moving clock which is on the train sideway so that the light now travels along the direction of motion of the train According to s the length of the clock is L, which is different from the length Lo measured by S relative to whom the clock is at rest
2. The relativity of length Fig 20-6 shows the sequence of events as observed by S for the moving clock which is on the train sideway, so that the light now travels along the direction of motion of the train. According to S the length of the clock is L, which is different from the length measured by S’, relative to whom the clock is at rest. L0
Fig 20-6 (A) FD S E (C) L+a△t1=c△t1 C△t,=L-l△
(A) (B) L S (C) S’ S’ S’ →u →u 1 u t 2 u t 2 c t 2 2 c t = L − u t 1 1 L + u t = c t Fig 20 - 6 →u M F D L 0 FD FD FD
In the process from A, B to C, the total time taken is 2L1 △t=△t1+△t From Eq(20-3), setting 4, ilg c-u C+u (-)2(20-6) △t 2L 2 (20-7) Setting Eqs (20-6)and(20-7)equal to one another and solving, we obtain L=Lo 1-c) (20-8) Eg(20-8 summarizes the effect known as "length contraction
In the process from A, B to C, the total time taken is (20-6) From Eq(20-3), setting (20-7) Setting Eqs(20-6) and (20-7) equal to one another and solving, we obtain (20-8) 2 1 2 1 ( ) 2 1 c c u L c u L c u L t t t − = + + − = + = 2 0 2 0 1 ( ) 2 1 1 ( ) c c u L c u t t − = − = c L t 0 0 2 = 2 0 1 ( ) c L = L − u Eq(20-8) summarizes the effect known as “length contraction
(a The length Lo measured by an observer who is at rest with respect to the object being measured is called the rest length"or proper length. (b)All observers in motion relative to S measure a shorter length, but only for dimensions along the direction of motion; length measurement transverse to the direction of motion are unaffected (c)Under ordinary circumstances, u<<c and the effects of length contraction are too small to be observed
(a) The length measured by an observer who is at rest with respect to the object being measured is called the “rest length” or “proper length”. (b) All observers in motion relative to S’ measure a shorter length, but only for dimensions along the direction of motion; length measurement transverse to the direction of motion are unaffected. L0 (c) Under ordinary circumstances, and the effects of length contraction are too small to be observed. u c