10-8 s.
REMINDER Muons are unstable particles produced in the upper atmosphere (around 30 km above us). They move at about 0.995 c. How long do they take to travel to the Earth’s surface? A. ~10-4 s. B. ~10-5 s. C. ~10-6 s. D. ~10-7 s. E. ~10-8 s. REMINDER Muons are unstable particles produced in the upper atmosphere (around 30 km above us). They move at about 0.995 c. How long do they take to travel to the Earth’s surface? A. ~10-4 s. B. ~10-5 s. C. ~10-6 s. D. ~10-7 s. E. ~10-8 s. L 3 10 4 4 t 10 s 8 c 3 10 REMINDER Muons are unstable particles produced in the upper atmosphere (around 30 km above us). They move at about 0.995 c. Their halflife at rest is t1/2=1.5 10-6 s. What fraction of N them arrive to the Earth’s surface N ? surf Earth A. 10 20 ; 10 B. 10 ; 2 C. 10 ; D. 1; E. 10 2. upper atm REMINDER Muons are unstable particles produced in the upper atmosphere (around 30 km above us). They move at about 0.995 c. Their halflife at rest is t1/2=1.5 10-6 s. What fraction of N them arrive to the Earth’s surface N ? surf Earth A. 10 20 ; 10 B. 10 ; 2 C. 10 ; D. 1; E. 10 2. upper atm s, not t! N surf Earth 1 N upper atm 2 s / t1 / 2 1 s 2 t 2 x 2 x 2 2 1 v PROBLEM: However in the frame of the muon its halflife is 1.5 ms. The muon moves at constant speed so the “twin paradox resolution” does not help us here. So, does an observer in the frame of the muon see the trip taking about 10-4 seconds? NO: in this frame the Earth is moving toward the muon and the distance appears shorter by a factor of 10!! Length contraction A pole at rest has length 3 (light seconds) L0 xP xO 3 light s In the other frame (b=0.5) the length is the distance between O and Q: L' x'Q x'O x'Q xQ ( x'Q t 'Q ) x'Q L' L0 / 3 / 1.15 2.61 light s In general: The other frame moves at b=0.5 L' L0 / Pole and barn paradox A pole at rest has length 3 light s, but moving at b=0.5 its length is 2.61 light s. It does fit in a barn with length 2.61 light s. However, looking at this in the frame at rest w.r.t. the pole: the pole length is 3 light s, but the barn has length 2.61/1.15=2.27 light s so it doesn’t fit! WHICH IS CORRECT?? Pole and barn paradox A pole at rest has length 3 light s, but moving at b=0.5 its length is 2.61 light s. It does fit in a barn with length 2.61 light s. However, looking at this in the frame at rest w.r.t. the pole: the pole length is 3 light s, but the barn has length 2.61/1.15=2.27 light s so it doesn’t fit! WHICH IS CORRECT?? BOTH! But the event (Q) in which the front of the pole goes by the back of the barn is NOT SIMULTANEOUS with the event O when the back of the pole aligns with the front of the barn. Pole and barn paradox (insistence) A pole at rest has length 3 light s, but moving at b=0.5 its length is 2.61 light s. It does fit in a barn with length 2.61 light s. However, looking at this in the frame at rest w.r.t. the pole: the pole length is 3 light s, but the barn has length 2.61/1.15=2.27 light s so it doesn’t fit! WHICH IS CORRECT?? BOTH! Ok. But suppose this barn is more like a real barn with no back door, so the pole can not get through and the front door is closed once the pole fits. What happens in the frame of the pole? The front of the pole hits the back of the barn but it keeps compressing until the back end goes by the front of the barn. The compression wave can not transmit faster than c so there is no contradiction (even if there is destruction). The most important reason that an object is observed to be shorter in a frame where it is moving than in a frame where it is at rest is that A. The force of motion strongly compresses an object that is moving at relativistic speeds; B. “Simultaneity” is not frame-independent; C. The measuring sticks used by the moving observer are Lorentz-contracted; D. The clocks used by the moving observer run slower. The most important reason that an object is observed to be shorter in a frame where it is moving than in a frame where it is at rest is that A. The force of motion strongly compresses an object that is moving at relativistic speeds; B. “Simultaneity” is not frame-independent; C. The measuring sticks used by the moving observer are Lorentz-contracted; D. The clocks used by the moving observer run slower. In the pole-and-barn problem, the barn never actually encloses the pole in the barn frame, True or False? A. True; B. False; C. Don’t know. In the pole-and-barn problem, the barn never actually encloses the pole in the barn frame, True or False? A. True; B. False; C. Don’t know. An object is at rest in the Home Frame. Imagine an Other Frame moving at a speed of =4/5 with respect to the Home Frame. The object’s length in the Other Frame is measured to be 15 ns. What is its length as observed in the Home Frame? A. 15 ns B. 12 ns; C. 9 ns; D. 19 ns; E. 25 ns. An object is at rest in the Home Frame. Imagine an Other Frame moving at a speed of =4/5 with respect to the Home Frame. The object’s length in the Other Frame is measured to be 15 ns. What is its length as observed in the Home Frame? A. 15 ns L L0 / B. 12 ns; C. 9 ns; D. 19 ns; E. 25 ns. L0 L 15 (5 / 3) 25 R7R.1 Space wars paradox. Two spacecraft of equal rest length, L=100 ns, travel in opposite directions with =3/5. Laser cannon shot from ship O when its bow is lined with the tail of O’. Anne is on the ground and Brad aboard a train moving at =0.6. Which best represents a light wave front from a flash as seen in Anne’s frame? Anne is on the ground and Brad aboard a train moving at =0.6. Which best represents a light wave front from a flash as seen in Anne’s frame? Anne is on the ground and Brad aboard a train moving at =0.6. Which best represents a light wave front from a flash as seen in Brad’s frame? Anne is on the ground and Brad aboard a train moving at =0.6. Which best represents a light wave front from a flash as seen in Brad’s frame? Now Anne asks Brad to draw a circle representing his view of the light wave front at a given time (Brad can draw very fast so he draws all the points simultaneously in his frame.) Which best represents the drawing as seen by Anne (Brad never stops)? Now Anne asks Brad to draw a circle representing his view of the light wave front at a given time (Brad can draw very fast so he draws all the points simultaneously in his frame.) Which best represents the drawing as seen by Anne (Brad never stops)?
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