WEBVTT 00:00:13.190 --> 00:00:15.350 PROFESSOR: Welcome back to A20 special relativity. 00:00:15.350 --> 00:00:18.680 In this last section of this chapter, 00:00:18.680 --> 00:00:22.400 we talked about applications and implications 00:00:22.400 --> 00:00:23.810 of special relativity. 00:00:23.810 --> 00:00:26.930 We talked about the global positioning system. 00:00:26.930 --> 00:00:30.920 You all have used GPS before, be it in your car 00:00:30.920 --> 00:00:34.430 when you're trying to find your way through town 00:00:34.430 --> 00:00:37.760 or when you go for a run and you want to measure how long 00:00:37.760 --> 00:00:41.260 and how fast you actually are running. 00:00:41.260 --> 00:00:43.960 The global positioning system is a set 00:00:43.960 --> 00:00:47.320 of satellites all equipped with atomic clocks. 00:00:47.320 --> 00:00:51.280 And they're used for navigation and have been developed first 00:00:51.280 --> 00:00:53.920 under the name of Napster GPS. 00:00:53.920 --> 00:00:59.180 And GPS is one of many global or few global navigation system. 00:00:59.180 --> 00:01:06.460 Others are GLONASS, BDS, Galileo Systems developed in Europe, 00:01:06.460 --> 00:01:09.920 in Russia, in Japan, and so. 00:01:09.920 --> 00:01:12.530 This picture here shows you how you 00:01:12.530 --> 00:01:16.910 want to view this view of Earth and then at around 20,000 00:01:16.910 --> 00:01:21.380 kilometer, GPS has about 31 satellites, 00:01:21.380 --> 00:01:23.930 which zooms around the Earth. 00:01:23.930 --> 00:01:26.750 And as soon as you have three satellites, which 00:01:26.750 --> 00:01:28.910 you can see from your viewpoint, you 00:01:28.910 --> 00:01:33.590 can actually figure out where that viewpoint is. 00:01:33.590 --> 00:01:37.940 Think about each satellite gives you an information of a sphere. 00:01:37.940 --> 00:01:41.370 The cross section between two spheres is a line. 00:01:41.370 --> 00:01:44.900 And if you have three spheres crossing, 00:01:44.900 --> 00:01:49.280 that gives you three-dimensional information about location 00:01:49.280 --> 00:01:52.060 on which you're looking at this. 00:01:52.060 --> 00:01:56.560 GPS was-- the first satellites were launched in 1978. 00:01:56.560 --> 00:02:02.960 Again, 31 satellites in orbit at the time right now. 00:02:02.960 --> 00:02:04.790 So how does this work? 00:02:04.790 --> 00:02:06.790 So the satellite transmits information 00:02:06.790 --> 00:02:09.530 about position in time in regular intervals. 00:02:09.530 --> 00:02:10.880 It's does have a clock. 00:02:10.880 --> 00:02:14.770 They use a specific frequency or multiple frequency 00:02:14.770 --> 00:02:16.870 to send signals. 00:02:16.870 --> 00:02:21.490 And then the receiver calculates how far away the satellite is 00:02:21.490 --> 00:02:24.430 and how long it took the message to arrive 00:02:24.430 --> 00:02:26.440 at the place of the receiver. 00:02:26.440 --> 00:02:31.870 Again, three satellites are used to extract the exact location. 00:02:31.870 --> 00:02:33.940 However, as you can imagine, the reason 00:02:33.940 --> 00:02:35.530 why I bring this up in this class 00:02:35.530 --> 00:02:37.660 is that we have to consider effects 00:02:37.660 --> 00:02:41.650 of special relativity and also, general relativity, 00:02:41.650 --> 00:02:44.960 as we will discuss later in this class. 00:02:44.960 --> 00:02:48.490 So you have clocks on the satellites. 00:02:48.490 --> 00:02:50.680 And you have identical clocks on Earth. 00:02:50.680 --> 00:02:53.410 And they do tick differently as we discussed many times 00:02:53.410 --> 00:02:54.910 in this class. 00:02:54.910 --> 00:02:58.270 If you were to calculate the effect of special relativity, 00:02:58.270 --> 00:03:00.130 the prediction is that the clocks 00:03:00.130 --> 00:03:05.880 take about 7 microseconds a day slower on the satellite 00:03:05.880 --> 00:03:08.450 then compared to the one on Earth. 00:03:08.450 --> 00:03:12.260 However, the satellite at a higher orbit. 00:03:12.260 --> 00:03:15.590 And the gravitational pull at a higher orbit 00:03:15.590 --> 00:03:18.200 is less strong as on Earth. 00:03:18.200 --> 00:03:21.770 And that then, as a result, is the clocks 00:03:21.770 --> 00:03:26.120 on the satellites actually run faster than the ones on Earth. 00:03:26.120 --> 00:03:28.700 And that effect is larger, very larger 00:03:28.700 --> 00:03:31.100 than the effect of special relativity, which 00:03:31.100 --> 00:03:35.540 is effect from then just moving relative to the observer. 00:03:35.540 --> 00:03:37.850 The fact is 47 microseconds a day. 00:03:37.850 --> 00:03:41.000 And then you can just calculate the net correction, 00:03:41.000 --> 00:03:44.870 which is 38 microseconds a day, which corresponds 00:03:44.870 --> 00:03:47.120 to about 11 kilometers. 00:03:47.120 --> 00:03:50.940 Now imagine on your run and there's 00:03:50.940 --> 00:03:52.880 11 kilometer difference a day. 00:03:52.880 --> 00:03:54.770 I don't expect you to run for a day, 00:03:54.770 --> 00:03:56.420 but you might run for an hour. 00:03:56.420 --> 00:03:58.610 Still the effect is rather large. 00:03:58.610 --> 00:04:01.040 So you want to have a more precise system. 00:04:01.040 --> 00:04:04.400 And therefore, those effects need to be corrected, 00:04:04.400 --> 00:04:05.240 and they are. 00:04:05.240 --> 00:04:07.760 They're typically built in into the electronics 00:04:07.760 --> 00:04:09.920 and automatically corrected. 00:04:09.920 --> 00:04:13.190 The precision achieved with GPS system 00:04:13.190 --> 00:04:16.700 ranges a little bit based on how you use the information, what 00:04:16.700 --> 00:04:18.200 kind of transceiver you use. 00:04:18.200 --> 00:04:21.800 It's in the order of 505 meters to 30 centimeters, 00:04:21.800 --> 00:04:24.360 so about this of a distance. 00:04:24.360 --> 00:04:28.040 So anywhere on this planet you can pinpoint your location 00:04:28.040 --> 00:04:31.760 by about this with this precision. 00:04:35.200 --> 00:04:37.180 Well, this concludes the discussion 00:04:37.180 --> 00:04:42.660 of implications and applications in special relativity.