1 00:00:00,000 --> 00:00:01,984 [SQUEAKING] 2 00:00:01,984 --> 00:00:04,464 [RUSTLING] 3 00:00:04,464 --> 00:00:07,936 [CLICKING] 4 00:00:19,350 --> 00:00:22,372 MARKUS KLUTE: Welcome back to 8.20, Special Relativity. 5 00:00:22,372 --> 00:00:24,330 In this section, you're going to take a journey 6 00:00:24,330 --> 00:00:27,300 through our solar system and beyond. 7 00:00:27,300 --> 00:00:30,780 1977 marks the first flight of the Voyager program. 8 00:00:30,780 --> 00:00:35,220 Voyager is an MIT-led program with the original mission 9 00:00:35,220 --> 00:00:37,770 to study planetary systems. 10 00:00:37,770 --> 00:00:41,340 Now, Voyager 1 and Voyager 2, two spacecrafts, 11 00:00:41,340 --> 00:00:43,920 are studying the interstellar space. 12 00:00:43,920 --> 00:00:46,770 Those two probes are still sending back now, 13 00:00:46,770 --> 00:00:49,800 more than 40 years later, information 14 00:00:49,800 --> 00:00:54,210 about measurement of their surroundings back to Earth. 15 00:00:54,210 --> 00:00:58,830 Those are the two furthest-away objects we were able to send. 16 00:00:58,830 --> 00:01:00,690 What we have here in 8.20-- 17 00:01:00,690 --> 00:01:04,580 and it's IAP, so we are a little bit more ambitious-- 18 00:01:04,580 --> 00:01:07,790 our mission is to bring us to Alpha Centauri. 19 00:01:07,790 --> 00:01:10,850 Alpha Centauri is the closest star and planetary 20 00:01:10,850 --> 00:01:14,150 system to our solar system. 21 00:01:14,150 --> 00:01:17,330 It's actually not just one star, but multiple stars. 22 00:01:17,330 --> 00:01:20,750 And our journey brings us to Proxima B, 23 00:01:20,750 --> 00:01:25,860 which is a planet in the Alpha Centauri system. 24 00:01:25,860 --> 00:01:28,380 So we have a very fancy spacecraft. 25 00:01:28,380 --> 00:01:33,710 It's able to travel with a constant velocity of 0.943 c, 26 00:01:33,710 --> 00:01:35,720 speed of light. 27 00:01:35,720 --> 00:01:40,790 The gamma factor is 3, and the path which it's going to take 28 00:01:40,790 --> 00:01:43,700 is 5 light years long. 29 00:01:43,700 --> 00:01:47,420 Alice is our ground control. 30 00:01:47,420 --> 00:01:49,010 She is going to stay on Earth. 31 00:01:49,010 --> 00:01:53,720 And Bob is going to take this journey with Virgin Galactic. 32 00:01:53,720 --> 00:01:58,180 After some time, Bob is going to arrive on Proxima B. 33 00:01:58,180 --> 00:02:02,570 So your first challenge is to now calculate 34 00:02:02,570 --> 00:02:06,410 how long does this trip take from Alice's and Bob's 35 00:02:06,410 --> 00:02:08,280 perspective? 36 00:02:08,280 --> 00:02:11,780 So I ask you to stop the video here and just work this out. 37 00:02:14,640 --> 00:02:18,570 So for Alice, the time needed is 5 light years 38 00:02:18,570 --> 00:02:22,320 divided by 0.9, by the velocity of 0.943, 39 00:02:22,320 --> 00:02:23,700 times the speed of light. 40 00:02:23,700 --> 00:02:26,490 And that gives us 5.3 years. 41 00:02:26,490 --> 00:02:32,070 So after 5.3 years, Alice is observing Bob's arrival 42 00:02:32,070 --> 00:02:36,970 on Proxima B. For Bob, the length of this path 43 00:02:36,970 --> 00:02:40,270 is Lorentz contracted-- 44 00:02:40,270 --> 00:02:42,460 5 light years divided by 3, which 45 00:02:42,460 --> 00:02:47,500 is the gamma factor, which results to 1.67 light years. 46 00:02:47,500 --> 00:02:51,610 So for him, the journey takes only 1.77 years-- 47 00:02:51,610 --> 00:02:57,380 1.67 light years divided by 0.943 times the speed of light. 48 00:02:57,380 --> 00:03:01,690 So apparently, the time experienced by Alice and Bob 49 00:03:01,690 --> 00:03:04,700 for the very same journey is different. 50 00:03:04,700 --> 00:03:06,490 So this now is the first part, where 51 00:03:06,490 --> 00:03:10,690 we enter discussions of paradoxes 52 00:03:10,690 --> 00:03:12,130 in special relativity. 53 00:03:12,130 --> 00:03:13,810 And this will bring us, ultimately, 54 00:03:13,810 --> 00:03:18,720 to an understanding of the twin paradox later in this course.