1
00:00:13,190 --> 00:00:15,350
PROFESSOR: Welcome back
to A20 special relativity.

2
00:00:15,350 --> 00:00:18,680
In this last section
of this chapter,

3
00:00:18,680 --> 00:00:22,400
we talked about applications
and implications

4
00:00:22,400 --> 00:00:23,810
of special relativity.

5
00:00:23,810 --> 00:00:26,930
We talked about the
global positioning system.

6
00:00:26,930 --> 00:00:30,920
You all have used GPS
before, be it in your car

7
00:00:30,920 --> 00:00:34,430
when you're trying to
find your way through town

8
00:00:34,430 --> 00:00:37,760
or when you go for a run and
you want to measure how long

9
00:00:37,760 --> 00:00:41,260
and how fast you
actually are running.

10
00:00:41,260 --> 00:00:43,960
The global positioning
system is a set

11
00:00:43,960 --> 00:00:47,320
of satellites all equipped
with atomic clocks.

12
00:00:47,320 --> 00:00:51,280
And they're used for navigation
and have been developed first

13
00:00:51,280 --> 00:00:53,920
under the name of Napster GPS.

14
00:00:53,920 --> 00:00:59,180
And GPS is one of many global
or few global navigation system.

15
00:00:59,180 --> 00:01:06,460
Others are GLONASS, BDS, Galileo
Systems developed in Europe,

16
00:01:06,460 --> 00:01:09,920
in Russia, in Japan, and so.

17
00:01:09,920 --> 00:01:12,530
This picture here
shows you how you

18
00:01:12,530 --> 00:01:16,910
want to view this view of
Earth and then at around 20,000

19
00:01:16,910 --> 00:01:21,380
kilometer, GPS has
about 31 satellites,

20
00:01:21,380 --> 00:01:23,930
which zooms around the Earth.

21
00:01:23,930 --> 00:01:26,750
And as soon as you have
three satellites, which

22
00:01:26,750 --> 00:01:28,910
you can see from
your viewpoint, you

23
00:01:28,910 --> 00:01:33,590
can actually figure out
where that viewpoint is.

24
00:01:33,590 --> 00:01:37,940
Think about each satellite gives
you an information of a sphere.

25
00:01:37,940 --> 00:01:41,370
The cross section between
two spheres is a line.

26
00:01:41,370 --> 00:01:44,900
And if you have three
spheres crossing,

27
00:01:44,900 --> 00:01:49,280
that gives you three-dimensional
information about location

28
00:01:49,280 --> 00:01:52,060
on which you're looking at this.

29
00:01:52,060 --> 00:01:56,560
GPS was-- the first satellites
were launched in 1978.

30
00:01:56,560 --> 00:02:02,960
Again, 31 satellites in
orbit at the time right now.

31
00:02:02,960 --> 00:02:04,790
So how does this work?

32
00:02:04,790 --> 00:02:06,790
So the satellite
transmits information

33
00:02:06,790 --> 00:02:09,530
about position in time
in regular intervals.

34
00:02:09,530 --> 00:02:10,880
It's does have a clock.

35
00:02:10,880 --> 00:02:14,770
They use a specific frequency
or multiple frequency

36
00:02:14,770 --> 00:02:16,870
to send signals.

37
00:02:16,870 --> 00:02:21,490
And then the receiver calculates
how far away the satellite is

38
00:02:21,490 --> 00:02:24,430
and how long it took
the message to arrive

39
00:02:24,430 --> 00:02:26,440
at the place of the receiver.

40
00:02:26,440 --> 00:02:31,870
Again, three satellites are used
to extract the exact location.

41
00:02:31,870 --> 00:02:33,940
However, as you can
imagine, the reason

42
00:02:33,940 --> 00:02:35,530
why I bring this
up in this class

43
00:02:35,530 --> 00:02:37,660
is that we have to
consider effects

44
00:02:37,660 --> 00:02:41,650
of special relativity and
also, general relativity,

45
00:02:41,650 --> 00:02:44,960
as we will discuss
later in this class.

46
00:02:44,960 --> 00:02:48,490
So you have clocks
on the satellites.

47
00:02:48,490 --> 00:02:50,680
And you have identical
clocks on Earth.

48
00:02:50,680 --> 00:02:53,410
And they do tick differently
as we discussed many times

49
00:02:53,410 --> 00:02:54,910
in this class.

50
00:02:54,910 --> 00:02:58,270
If you were to calculate the
effect of special relativity,

51
00:02:58,270 --> 00:03:00,130
the prediction is
that the clocks

52
00:03:00,130 --> 00:03:05,880
take about 7 microseconds a
day slower on the satellite

53
00:03:05,880 --> 00:03:08,450
then compared to
the one on Earth.

54
00:03:08,450 --> 00:03:12,260
However, the satellite
at a higher orbit.

55
00:03:12,260 --> 00:03:15,590
And the gravitational
pull at a higher orbit

56
00:03:15,590 --> 00:03:18,200
is less strong as on Earth.

57
00:03:18,200 --> 00:03:21,770
And that then, as a
result, is the clocks

58
00:03:21,770 --> 00:03:26,120
on the satellites actually run
faster than the ones on Earth.

59
00:03:26,120 --> 00:03:28,700
And that effect is
larger, very larger

60
00:03:28,700 --> 00:03:31,100
than the effect of
special relativity, which

61
00:03:31,100 --> 00:03:35,540
is effect from then just moving
relative to the observer.

62
00:03:35,540 --> 00:03:37,850
The fact is 47
microseconds a day.

63
00:03:37,850 --> 00:03:41,000
And then you can just
calculate the net correction,

64
00:03:41,000 --> 00:03:44,870
which is 38 microseconds
a day, which corresponds

65
00:03:44,870 --> 00:03:47,120
to about 11 kilometers.

66
00:03:47,120 --> 00:03:50,940
Now imagine on your
run and there's

67
00:03:50,940 --> 00:03:52,880
11 kilometer difference a day.

68
00:03:52,880 --> 00:03:54,770
I don't expect you
to run for a day,

69
00:03:54,770 --> 00:03:56,420
but you might run for an hour.

70
00:03:56,420 --> 00:03:58,610
Still the effect
is rather large.

71
00:03:58,610 --> 00:04:01,040
So you want to have a
more precise system.

72
00:04:01,040 --> 00:04:04,400
And therefore, those effects
need to be corrected,

73
00:04:04,400 --> 00:04:05,240
and they are.

74
00:04:05,240 --> 00:04:07,760
They're typically built
in into the electronics

75
00:04:07,760 --> 00:04:09,920
and automatically corrected.

76
00:04:09,920 --> 00:04:13,190
The precision achieved
with GPS system

77
00:04:13,190 --> 00:04:16,700
ranges a little bit based on how
you use the information, what

78
00:04:16,700 --> 00:04:18,200
kind of transceiver you use.

79
00:04:18,200 --> 00:04:21,800
It's in the order of 505
meters to 30 centimeters,

80
00:04:21,800 --> 00:04:24,360
so about this of a distance.

81
00:04:24,360 --> 00:04:28,040
So anywhere on this planet
you can pinpoint your location

82
00:04:28,040 --> 00:04:31,760
by about this with
this precision.

83
00:04:35,200 --> 00:04:37,180
Well, this concludes
the discussion

84
00:04:37,180 --> 00:04:42,660
of implications and applications
in special relativity.