825.2 the need for change and th postulates of the special theory It means that there is an ultimate speed c, the same in all directions and in all inertial reference frames. light and any massless particles travel at this speed. no particle that have mass and carry energy or information can reach or exceed this limit no matter how much or how long it is accelerated This postulate is expression of the experimental result (1)in a 1964 experiment, physicist at CERN Rapid 兀→>y+y Speed of the light was OvI same as measured at source rest in the laboratory. 825.2 the need for change and the postulates of the special theory (2)W. Bertozzi experiment(1964) 0 3 Speed10°m/s) v=0.99999999995c
11 It means that there is an ultimate speed c, the same in all directions and in all inertial reference frames. Light and any massless particles travel at this speed. No particle that have mass and carry energy or information can reach or exceed this limit, no matter how much or how long it is accelerated. This postulate is expression of the experimental result. (1)in a 1964 experiment, physicist at CERN. π → γ +γ Rapid 0 moving source Speed of the light was same as measured at rest in the laboratory. §25.2 the need for change and the postulates of the special theory (2)W. Bertozzi experiment(1964) v = 0.99999999995c §25.2 the need for change and the postulates of the special theory
825.2 the need for change and th postulates of the special theory @the fundamental laws of physics are the same for observers in all inertial reference frames No frame is preferred. Descriptions of what happens as a result of the laws of physics may different from one inertial reference frame to another, but the underlying fundamental physical principles and laws are the same Glileo assumed that the laws of mechanics were the same in all inertial reference frames Einstein extended that idea to include all the laws of physics. 8 25.3 consequences of Einsteins postulates 1. Time dilation Mirror Event 1: emission of the pulse 0,y=0,x1=0,1 Event 2: reflection of the pulse Event 2 x2=0,y2=l1,z=0,t2=l/c Event 3: detection of the pulse x3=0,y3=0,z3=0,t3=2l/c Time interval: At=To=2Lo/c Proper time interval
12 2the fundamental laws of physics are the same for observers in all inertial reference frames. No frame is preferred. Descriptions of what happens as a result of the laws of physics may different from one inertial reference frame to another, but the underlying fundamental physical principles and laws are the same. Glileo assumed that the laws of mechanics were the same in all inertial reference frames. Einstein extended that idea to include all the laws of physics. §25.2 the need for change and the postulates of the special theory §25.3 consequences of Einstein’s postulates 1. Time dilation 0l 0 τ s′ Event 1: emission of the pulse 0, 0, 0, 0 x1 ′ = y1 ′ = z1 ′ = t1 ′ = Event 2: reflection of the pulse x y l z t l c 2 2 0 2 2 0 ′ = 0, ′ = , ′ = 0, ′ = Event 3: detection of the pulse x y z t l c 3 3 3 3 0 ′ = 0, ′ = 0, ′ = 0, ′ = 2 t l c = 0 = 2 0 Time interval: ∆ ′ τ Proper time interval
825.3 consequences of Einsteins postulates Event 1: emission of the pulse MOTION 0,y1=0,x1=0,t1=0 Event 2 reflection of Event 1 even the pul x2=v/2,y2=l0, z,=0,t,=τ/2 Event 3: detection of T 2 +(vT/2)2 the pulse 3=vz,y3=0, 2L/c z3=0,t53= =n22= 8 25.3 consequences of Einsteins postulates Conclusions: the moving clock has a greater time interval between its ticks than the clock that is at rest a moving clock runs slow. This is called time dilation Time intervals in relativity are not absolute or universal but depend on whether the clock is moving or not: we say time is a relative not an absolute quantity. The proper time interval is the shortest Time dilation has been confirmed by many experiments
13 Event 1: emission of the pulse x1 = 0, y1 = 0,z1 = 0,t1 = 0 Event 2: reflection of the pulse 0, 2 2, , 2 2 2 2 0 τ τ = = = = z t x v y l Event 3: detection of the pulse τ τ = = = = 3 3 3 3 0, , 0, z t x v y s τ vτ 0l c l v 2 2 0 ( 2) 2 τ + τ = 2 2 0 2 2 0 1 1 2 v c v c l c − = − = τ τ §25.3 consequences of Einstein’s postulates Conclusions: the moving clock has a greater time interval between its ticks than the clock that is at rest ; a moving clock runs slow. This is called time dilation. Time intervals in relativity are not absolute or universal but depend on whether the clock is moving or not: we say time is a relative not an absolute quantity. Time dilation has been confirmed by many experiments: §25.3 consequences of Einstein’s postulates The proper time interval is the shortest
825.3 consequences of Einstein's postulates Microscopic clock: Muons are unstable elementary particles with a(proper) lifetime of 2.2 As they are produced with very higl speeds in the upper atmosphere when cosmic rays collide with air molecules. Take the height Lo of the atmosphere to be 90 km in the reference frame of earth, if the average speed of the muons is 0.999978c can the muons arrive the surface of the earth? 8 25.3 consequences of Einsteins postulates Solution: According to Newton's mechanics L=0.999978×3.0×103×22×10=660m The muons can not arrive the surface of the earth According to relativity, the life-time of the muon is 2.2 3317 (0.999978 The distance that muon can travel is 0.999978×3×10°×3317×10=995078m The muon can arrive the surface of the earth
14 Microscopic clock: Muons are unstable elementary particles with a (proper) lifetime of 2.2 µs. they are produced with very high speeds in the upper atmosphere when cosmic rays collide with air molecules. Take the height L0 of the atmosphere to be 90 km in the reference frame of earth, if the average speed of the muons is 0.999978c, can the muons arrive the surface of the earth? §25.3 consequences of Einstein’s postulates Solution: 0.999978 3.0 10 2.2 10 660 m 8 6 = × × × × = − L According to Newton’s mechanics The muons can not arrive the surface of the earth. According to relativity, the life-time of the muon is 331.7µs 1 (0.999978) 2.2 1 ( ) 2 2 2 0 = − = − = v c τ τ The distance that muon can travel is 0.999978 3 10 331.7 10 99507.8m 8 6 × × × × = − The muon can arrive the surface of the earth. §25.3 consequences of Einstein’s postulates
§253c。 onsequences of Einstein' s postulates Example: your starship passes Earth with a relative speed of 0.9990c. After traveling 10.0 y(your time), you stop at lookout LP13, turn and then travel back to earth with the same relative speed. The trip back takes another 10.0 y(your time). How long does the round trip take according to measurements made on Earth? (neglect any effect due to the accelerations) Solution: Event l: start from earth Event 2: stop at LP13 Proper time: To=4,=10.0 y 8 25.3 consequences of Einsteins postulates The earth measurement of the time interval is 10.0 =224(y) √1-(v/c)2√1-0.99 On the return trip, we have the same situation and the same data. thus the round trip requires 2 total =448(y) 1-(v/c)
15 Example: your starship passes Earth with a relative speed of 0.9990c. After traveling 10.0 y(your time), you stop at lookout LP13, turn, and then travel back to earth with the same relative speed. The trip back takes another 10.0 y(your time). How long does the round trip take according to measurements made on Earth?(neglect any effect due to the accelerations) Solution: Event 1: start from Earth Event 2: stop at LP13 Proper time: 10.0 y τ 0 = ∆t0 = §25.3 consequences of Einstein’s postulates The Earth measurement of the time interval is 224 (y) 1 0.999 10.0 1 ( ) 2 2 0 = − = − = = v c t τ τ ∆ On the return trip, we have the same situation and the same data.thus the round trip requires 448 (y) 1 ( ) 2 2 0 total = − = v c t τ ∆ §25.3 consequences of Einstein’s postulates