Chapter 20 The special theory of relativity Albert Einstein(1879-1955)
Chapter 20 The special theory of relativity Albert Einstein ( 1879 ~ 1955 )
20-1 Troubles with classical physics The kinematics developed by galileo and the mechanics developed by Newton, which form the basis of what we call"classical physics, had many triumphs. However, a number of experimental phenomena can not be understood with these otherwise successful classical theories 1. Troubles with our ideas about time The pions( or z created at rest are observed
20-1 Troubles with classical physics The kinematics developed by Galileo and the mechanics developed by Newton, which form the basis of what we call “classical physics”, had many triumphs. However, a number of experimental phenomena can not be understood with these otherwise successful classical theories. 1. Troubles with our ideas about time The pions ( or ) created at rest are observed + −
to decay( to other particles)with an average lifetime of only 26.0ns In one particular experiment, pions were created in motion at a speed ofv=0.913c. In this case they were observed to travel in the laboratory an average distance of D=17.4m before decaying, from which we conclude that they decay in a time given by D/=637ns, much larger than the lifetime measured for pions at rest This effect. called time dilation", which cannot be explained by Newtonian physics. In Newtonian physics time is a universal coordinate having identical values for all observers
to decay ( to other particles ) with an average lifetime of only . In one particular experiment, pions were created in motion at a speed of . In this case they were observed to travel in the laboratory an average distance of before decaying, from which we conclude that they decay in a time given by , much larger than the lifetime measured for pions at rest. This effect, called “time dilation”, which cannot be explained by Newtonian physics. In Newtonian physics time is a universal coordinate having identical values for all observers. 26.0ns v = 0.913c ns v D = 63.7 D =17.4m
2. Trouble with our ideas about length Suppose an observer in the above laboratory placed one marker at the location of the pion's formation and another at the location of its decay The distance between the markers is measured to be 17.4m. Now consider the observer who is traveling along with the pion at a speed of u=0.913c This observer, to whom the pion appear to be at rest, measures its lifetime to be 260ns, and the distance between the markers is (0913c)(260×103)=71m Thus two observers measure different value for the same length interval 3. Troubles with our ideas about light
2. Trouble with our ideas about length Suppose an observer in the above laboratory placed one marker at the location of the pion’s formation and another at the location of its decay. The distance between the markers is measured to be 17.4m. Now consider the observer who is traveling along with the pion at a speed of u=0.913c. This observer, to whom the pion appear to be at rest, measures its lifetime to be 26.0ns, and the distance between the markers is Thus two observers measure different value for the same length interval. (0.913c)(26.0 10 ) 7.1m 9 = − 3. Troubles with our ideas about light
20-2 The postulates of special relativity 1. Einstein offered two postulates that form the basis of his special theory of relativity o The principle of relativity: The laws of phys are the same in all inertial reference frames. sics (D The principle of the constancy of the speed of light The speed of light in free space has the same value c in all inertial reference frames 2. The first postulate declares that the laws of physics are absolute, universal, and same for all inertial observers
20-2 The postulates of special relativity 1. Einstein offered two postulates that form the basis of his special theory of relativity. (I) The principle of relativity: “The laws of physics are the same in all inertial reference frames.” (II) The principle of the constancy of the speed of light : “ The speed of light in free space has the same value c in all inertial reference frames.” 2. The first postulate declares that the laws of physics are absolute, universal, and same for all inertial observers
The Second postulate is much more difficult to accept, because it violates ourcommon sense which is firmly grounded in the Galilean kinematics that we have learned from everyday experiences It implies that it is impossible to accelerate a particle to a speed greater than c
The Second postulate is much more difficult to accept, because it violates our “ common sense”, which is firmly grounded in the Galilean kinematics that we have learned from everyday experiences. It implies that “it is impossible to accelerate a particle to a speed greater than c
20-3 Consequences of Einstein' s postulates 1.The relativity of time We consider two observers: S is at rest on the ground, and S is in a train moving on a long straight track at constant speed u relative to s The observers carry identical timing devices, illustrated in Fig 20-4, consisting of a flashing light bulb F attached to a detector d and separated by a distance Lo from a mirror m The bulb emits a flash of light that travels to the mirror when the reflected light returns to d, the clock ticks and another flash is triggered
20-3 Consequences of Einstein’s postulates 1.The relativity of time We consider two observers: S is at rest on the ground, and S’ is in a train moving on a long straight track at constant speed u relative to S. The observers carry identical timing devices, illustrated in Fig 20-4, consisting of a flashing light bulb F attached to a detector D and separated by a distance from a mirror M. The bulb emits a flash of light that travels to the mirror, when the reflected light returns to D, the clock ticks and another flash is triggered. L0
The time interval At between ticks is 2L (20-1) The interval At is observed by either s or s when the FD clock is at rest respect to that observer Fig 20-4
The time interval between ticks is: (20-1) The interval is observed by either S or S’ when the clock is at rest respect to that observer. M F D Fig 20-4 L0 0 t c L t 0 0 2 = 0 t
We now consider the situation when one observer looks at a clock carried by the other. Fig 20-5 shows that s observes on the clock carried by s on the moving train B L Fig 20-5 FIDI S FID uAt s
We now consider the situation when one observer looks at a clock carried by the other. Fig 20-5 shows that S observes on the clock carried by S’ on the moving train. F D S A B C L L ' S ' S ' S ut Fig 20-5 F D F D
According to s, the flash is emitted at A, reflected at b. and detected at c This interva△tis 1s2l2/n2 +(l 2 △ (2020) Substituting for Lo from Eg(20-1)and solving Eq(20-2)for At gives △ △t (/)2 (203)
According to S, the flash is emitted at A, reflected at B, and detected at C. This interval is (20-20) Substituting for from Eq(20-1) and solving Eq(20-2) for gives (20-3) c t L u c L t 2 2 0 ) 2 2 ( 2 + = = 2 0 1 ( ) c u t t − = t t L0
