00:01
In this problem, we're going to be looking at time dilation, and we have an observer attached to frame s.
00:08
We have an observer attached to frame s prime, which is moving at point speed, 0 .5c, away from s.
00:16
And equivalently, from s prime's perspective, s is moving to left, the speed 0 .5c.
00:22
So it all depends on what perspective you want.
00:25
This is the perspective of s.
00:27
That's what we're trying to answer first.
00:30
Now, let's talk.
00:32
Talk about this.
00:33
Let's say we have a device.
00:35
Let's not even talk about it being an type of clock, just a device that it has some type of indicator, a needle of some type.
00:47
And that both when s and s prime are together, they agree that the needle in position a corresponds to t equals zero, zero hours.
01:01
And now, let's leave s out of this.
01:04
So we got that device.
01:06
So they both have agreed on that when they're together that this first position, position a, is the zero time.
01:15
Now, s prime, again, we're just working in s prime for a second.
01:20
S prime has a real clock.
01:23
Like i said, this is another device.
01:25
It's not even think about it as a timekeeper clock of any time.
01:28
It's got a separate clock.
01:30
They brings over and basically waits for that clock to read 20.
01:34
And he says, position b on that.
01:36
That needo, that indicates on this device 60 minutes, one hour.
01:42
So now going from position a to position b on that device is one hour.
01:48
So yes, we could then use that as a clock.
01:52
We have calibrated it, if you like.
01:55
So he discards the, he's got that other clock, and now he's got this device.
02:00
Now, clocks in s prime, they give him proper time.
02:07
And so we've constructed it.
02:09
So his proper time between a and b, seeing that they take place at the same point in space.
02:16
So he can use a single clock, as i just did, between the two.
02:20
That, by definition, is proper time.
02:22
Same position in the place, space.
02:24
So you can use a single clock to time, the interval between the two events.
02:29
So the needle being at a, the needle being at b are my two events, took place at the same spot.
02:34
So one hour is the proper time.
02:36
So clocks in s prime give proper time.
02:41
Now, from s's standpoint, they're seeing moving.
02:47
They're seeing these events are not taking place at the same place in space.
02:55
So they give, for those two events, dilated time, longer time.
03:04
So we know what the proper time is between position a and position b.
03:08
That's one hour.
03:10
What is the time between those events from the standpoint of observer in s? well, that's this.
03:20
Delta t, it's delta t prime.
03:23
This is the proper time.
03:26
Square root, 1 minus v squared, c squared.
03:30
So it's one hour, h for hour, square root, 1 minus 0 .5c over c squared.
03:40
And this gives to three digits, 1 .15 hours.
03:49
So he says between the needle being at a to b is 1 .15 hours.
03:56
Though as prime observer, i'm talking about s said that, as prime observer said between those two is one hour.
04:04
So that's why you hear them, that's why s would say, your clock's running slow.
04:10
Your clock's running slow.
04:14
I get 1 .15 hours, you're only getting one hour between those two.
04:19
So your clock's slow.
04:24
Okay.
04:25
Now, so that's what s says...