Transcript of a2-l03
==========


_0:10_: Hello everybody.

_0:12_: OK, technology sorted out. Possibly and possibly sorted out

_0:17_: because

_0:19_: although these electrodes are being recorded on X360, I am not

_0:24_: 100% sure which microphone they are taking things from. It may

_0:28_: be that one, it may be this one. When I've listened to the

_0:33_: recordings they're a bit faint, but I can't find a button to

_0:37_: switch the input, so we'll just have to hope for the best. But

_0:42_: anyway, I am making separate recordings of these so we can

_0:46_: fall back on those if necessary. No, the plan today is to go

_0:50_: through the the, the, the last section of the axioms bit we got

_0:55_: last time we got as far as,

_0:60_: uh,

_1:05_: as this question, this rather mysterious question about people

_1:10_: moving, moving past each other. Plans to finish off this chapter

_1:14_: go straight into chapter 3, and the plan is to spend lectures

_1:18_: 3-4 and five on chapter 3:00 and 4:00, so that should be about

_1:22_: the right length of time. That's the goal. Anyway, we'll see what

_1:26_: happens in actuality,

_1:29_: so the ruining bit, so, so on to the the last part of Chapter 2.

_1:34_: The remaining bit here is there's not a lot to say about

_1:38_: it in a way, but the important bit is the consequence of the

_1:42_: second axiom.

_1:45_: Before I go, I go, I go into that. I want to just

_1:48_: recapitulate this. This quick question that we asked we

_1:51_: address at the very end of last time because it is so very

_1:54_: important.

_1:55_: So if you recall, I have a friend moving past me a rocket

_1:59_: and rush for 6 speed, and relativistic speed means

_2:01_: something moving at some appreciable fraction of the

_2:04_: speed of light.

_2:06_: Observe her watch be taking slower than mine for reasons

_2:09_: that we haven't come to yet but which we will get to very

_2:12_: shortly.

_2:15_: She examines my watches I at the same time and the question was

_2:18_: it's taken faster or slower than hers and asked you to think

_2:22_: about that a little bit and then I came back and said that the

_2:26_: answer is my watch. We're taking slower than hers,

_2:30_: so her watch is ticking slower than mine, and my watch is

_2:33_: ticking slower than hers.

_2:35_: How can that be

_2:38_: the we'll come to the reasons why that is not insane in a

_2:42_: moment, but the point is that you don't even have to go on and

_2:46_: talk about next chapter

_2:49_: or the second of the of the of the second section of relativity

_2:52_: to know the answer to that. Because the first axiom says you

_2:55_: can't tell you're moving.

_2:57_: And if one of us could discover that the others watch was moving

_3:00_: slow in an absolute sense, then we could tell that we were the

_3:03_: one that would move,

_3:06_: or vice versa, or whatever, like that. So just by itself, the

_3:08_: first axiom tells you that something weird happening here.

_3:11_: I mean, extra weird, but it's really more than the usual, more

_3:14_: than the obvious weirdness happening here.

_3:18_: I'm sorry, we'll come back to that. What will we return to

_3:20_: That? Definitely. But I wanted to impress upon you the last

_3:23_: thing I said last time,

_3:28_: and this is also a very important remark.

_3:34_: This is Einstein's version of the of Galileo's principle of

_3:40_: relativity and the

_3:43_: following on from.

_3:45_: But he says, and also there's a second postulate

_3:49_: who's only apparently only apparently irreconcilable with

_3:52_: the. With the former, they appear to be inconsistent with

_3:54_: each other. When you look at them first, the he's saying that

_3:57_: they're only apparently inconsistent with each other.

_4:01_: The light is always propagated in empty space with the definite

_4:03_: velocity C which is independent of the state of motion of the

_4:06_: emitting body.

_4:08_: We have to understand what that means.

_4:11_: There's a number of things

_4:14_: I could be going.

_4:17_: All the other more, there are a number of things that the speed

_4:20_: of light could mean.

_4:22_: It could mean if I have a torch and a shame it against the wall,

_4:26_: how fast does the light leave? It could mean how fast did the

_4:29_: light go through empty space like like like water waves on

_4:33_: water they have a speed and that speed is relative to the to the

_4:37_: to the water.

_4:38_: OK. Or the speed of light could mean

_4:42_: how fast is light moving? Quite nice. Very nice when I see it,

_4:46_: or when I detect it, or when I do an experiment which involves

_4:49_: light.

_4:50_: These are all three different things. In principle, that light

_4:53_: could mean

_4:54_: and the first two. They both seem fairly obvious.

_4:58_: It's the third one that is the case

_5:01_: the speed of light. The the the major speed of light is the

_5:04_: speed of light that

_5:06_: when you detect it, when it enters your your eye or your

_5:10_: camera or your physical apparatus, and it's that that's

_5:14_: independent of the state of motion. So if I am going on a

_5:18_: train going through a station at hospital light and I shine a

_5:23_: light forward,

_5:24_: then it'll leave

_5:27_: and it'll leave my my my torch at the speed of light.

_5:31_: He didn't think the 2nd, 2nd and anyone on the on the on the on

_5:35_: the train who measures the speed of that light. However, we'll

_5:39_: get three to 10/8 metres a second and someone on the

_5:42_: station platform

_5:45_: who sees this light being shown from the train

_5:49_: to them to their eyes on the station platform, If they

_5:51_: measure the speed of light, they will see it not as at the speed

_5:54_: of light plus 1/2 plus the speed of the train. They'll see it as

_5:57_: just the speed of light.

_5:59_: So bizarrely what what the second action was saying is that

_6:03_: speeds don't add the way you expect when you get when you're

_6:06_: talking about light. But more generally when you talk things

_6:10_: needs people like,

_6:11_: so I'm this shining the torch forward to shining it into the

_6:15_: eyes of someone on the on the station platform. It's not it's

_6:19_: not like plus the train. It's just the speed of light, and

_6:22_: there's something is happening there

_6:25_: that makes those speeds not add in the way you expect.

_6:29_: So I'm. I'm, I'm. I'm adding up weirdness here.

_6:34_: I think it is. Is that having a say though? Because

_6:39_: a mic

_6:44_: I see,

_6:46_: right? That's not helpful.

_6:50_: I'll try.

_6:53_: I'll try there.

_6:59_: That's not really working, is it?

_7:04_: Well, touching it. The wire,

_7:07_: you think. The wire.

_7:15_: I'll try touching myself some differently.

_7:22_: Perfect.

_7:25_: OK, so I'm adding up. Weirdness is here, and the resolution is

_7:29_: coming soon. I promise,

_7:31_: and so the the point here is that that that is basically all

_7:35_: I have to say about the 2nd axiom. It's strange, but go with

_7:39_: it for the moment.

_7:42_: The the last point that is important to mention in the

_7:48_: in the notes is just. I'll I'll point you towards section 221 on

_7:52_: the idea of synchronising clocks. I'm not gonna say much

_7:55_: about it

_7:57_: because it's there as a sort of pre placed footnote.

_8:02_: So when you think start thinking this through and go hang on. But

_8:07_: how do we have the same time everywhere? Because remember I

_8:11_: said that when we make observations on the station

_8:14_: platform of the train moving past, all the observers have

_8:17_: synchronised clocks.

_8:20_: You know they're all, they all know where they are on the

_8:22_: station platform because there's a scale marked long station

_8:24_: platform

_8:25_: and all the watch the synchronised because that's how

_8:28_: we do it and you may think how and how do we organise that is

_8:31_: that is there is there a problem there and no there isn't there's

_8:35_: process mentioned in the notes section 21, just for when you

_8:38_: start worrying about that go back and have a look at that. It

_8:41_: all works out,

_8:44_: but it's not. But it would distract us to, you know, step

_8:48_: through it. Just here. Just here.

_8:51_: OK, that is

_8:56_: so the. So just to be absolutely clear, what is the key, the key

_9:00_: points here, there are only two postulates we're going to talk

_9:04_: about, only two physical statements, 2 new things about

_9:08_: the universe you didn't know and all the rest is in a sense

_9:11_: logic. It's the deductions.

_9:15_: I mean that the physical statements, not logical

_9:17_: statements. You know, they could, you can imagine them

_9:19_: being otherwise. That's what I mean by physical sickness,

_9:22_: garlic, principal activity. You can tell you're moving.

_9:25_: Push it to the speed of light of the same value in all reference

_9:29_: frames,

_9:30_: and

_9:32_: I'll just mention in passing that there are a number of a

_9:34_: number of different things that postulate 2 could be. There's a

_9:37_: number of alternatives there.

_9:40_: One could spend a lot of time talking about this, but that is

_9:43_: the probably the most useful way to what wanted me to make

_9:47_: progress with. So before I go, I go on while I'm changing the

_9:50_: slides,

_9:52_: are there any puddles that are, that are that are outstanding

_9:55_: there

_9:56_: talk to me.

_10:02_: I don't. I mean,

_10:05_: I think it's possible for you to think, OK this is all

_10:07_: transparent, clear why making so much of A fuss about this,

_10:11_: that's perfectly reasonable.

_10:14_: Some of the puzzles are maybe yet to come and maybe over

_10:17_: egging this. It's weird bit but but don't worry. Just you

_10:22_: and

_10:25_: what we're going to talk about quite a lot, the idea of

_10:28_: simultaneity.

_10:29_: That's the question of two things happening at the same

_10:33_: time. And again, why do you think that was a big issue? The

_10:36_: reason it's a big issue is because there's a variety of

_10:41_: types of confusion

_10:43_: that you that that that that happened if you don't think

_10:46_: about these things in exactly the right way. So what what I'm

_10:49_: doing here is sort of training you to think about things of

_10:53_: this type.

_10:54_: We would be in the right way to avoid confusion

_10:57_: and a lot of the the you you will see on the Internet. I

_11:01_: think Oh my God relatively wrong because X or someone to come up

_11:05_: with a new theory which which doesn't involve Rushton dilation

_11:09_: or something because X. In almost all cases, these

_11:12_: confusions, these wrong

_11:15_: accounts of why relatives is wrong, come from not

_11:18_: understanding

_11:19_: the importance of thinking in the right way about simultaneous

_11:22_: events. So that's where the confusion comes from and it's

_11:25_: again, it seems like we're making more of a fuss about this

_11:28_: that we want, but it is terribly important

_11:31_: objectives.

_11:34_: So this is a tree garage

_11:38_: just

_11:40_: either sitting in this inflation or we're just thinking about it

_11:44_: from the point of view of people in the train carriage. There's

_11:47_: two observers,

_11:48_: one each. End

_11:51_: and there are light flash in the centre, like a strobe or

_11:56_: something whatever. A flash of light, an event,

_12:01_: and the light goes off. No directions. In particular. It

_12:04_: goes off toward the front of the tree of shrinkage and towards

_12:07_: the back of the garage,

_12:10_: and it takes 3 units of time

_12:14_: to get there. What are these units? We'll come to that, but

_12:18_: they're very small units. Clearly it all takes 3. It takes

_12:22_: three of them to get flight travel, say 3 metres, then

_12:28_: then that's the time on the clock of the person this end,

_12:30_: the 10:00 on the person at the end. And there's absolutely

_12:33_: nothing surprising about what I've just said there or what you

_12:36_: can see there, because this light flash is in the middle of

_12:39_: the carriage,

_12:40_: so it takes the same amount of time to get to the to each end.

_12:45_: So both the people, each end will record the same time, the

_12:50_: same time of arrival time of the light at the end. Nothing

_12:54_: complicated there,

_12:60_: no.

_13:01_: Let's imagine the same thing happening, but this time not

_13:05_: from the point of view of the people in the

_13:08_: carriage train carriage, but from the point of view of people

_13:12_: standing on the station platform watching this train go past.

_13:16_: How does that? How is that different?

_13:19_: Get the top one. There,

_13:21_: that's the late flashing,

_13:25_: Then a, you know, visual world leader.

_13:28_: The light has

_13:30_: travelled a bit, a little bit forward and backwards and the

_13:33_: train characters moved forward because it's moving

_13:37_: a little while later,

_13:39_: the late has travelled further out from the the, the, the, the,

_13:43_: the flash and the

_13:45_: indeed, and at the same time the train characters move forward.

_13:49_: So at this point the light flashes. Hit had arrived at the

_13:52_: end of the back of the train carriage

_13:56_: and the you remember Einstein's remark. All our measurements of

_14:00_: time are remarkable simultaneous events.

_14:04_: So here the light arriving at the end at the back of the train

_14:07_: carriage and that reservoir of what showing three our

_14:10_: simultaneous events they have. They are true events which

_14:13_: happen in the same place at the same time. It's like 2 cars

_14:17_: crashing.

_14:18_: There's no ambiguity about that

_14:21_: so the late so so we have to know this argument is saying we

_14:24_: have. It has to be the case that this observer what shows three

_14:28_: when the light arrives at the

_14:31_: and the. The way we've drawn this has used the second, the

_14:35_: the the 2nd postulate. Because you see here,

_14:39_: the light isn't moving forwards faster than it's moving

_14:42_: backwards. It's not getting, it's not picking up some extra

_14:45_: speed from the speed of the train

_14:48_: is moving forward at the speed of light,

_14:50_: which is why

_14:52_: the back runs into it before the light going forward has reached

_14:56_: the front.

_14:58_: If you if you think of that a Galilean world,

_15:01_: then the late moving forward would have picked up some extra

_15:04_: speed of the train, and so it would catch up at the front. 2nd

_15:07_: axiom says that's not what happens.

_15:10_: The light arrives at the back, but the light hasn't arrived at

_15:13_: the front yet.

_15:14_: So if we were to sort of take a photograph of this moving train,

_15:18_: at the instant when this arrives at the back,

_15:22_: the watch that we can see, so we can see the window of the train

_15:26_: carriage and we can see that the servers watch that can't be

_15:29_: written 3 yet

_15:30_: because it hasn't got there yet. It has yet to arrive, so has yet

_15:34_: you got as far as three. In other words,

_15:39_: although in the train carriage,

_15:44_: the back watch, but the back was ever reading back observers

_15:46_: watched reading three and the front observers watched reading

_15:49_: three are simultaneous events. They happen at the same time

_15:51_: coordinate

_15:53_: in the station platform.

_15:56_: The back was ever watch reading three and this front was

_15:59_: watching something like one. They are simultaneous events.

_16:03_: They happen at the same time coordinate because you imagine

_16:06_: this photograph taken of the train that goes past. In other

_16:09_: words, simultaneity

_16:11_: is relative.

_16:17_: These events are simultaneous in this frame.

_16:20_: These events three, one or similar things in this frame.

_16:23_: Depending on

_16:26_: what frame you're in,

_16:28_: things are simultaneous at different places.

_16:32_: Are relative. There's no, there's no there's no There's no

_16:35_: question about the the the the light arriving at the back and

_16:37_: that clock reading 3 because they happened at the same place.

_16:41_: That's the two cars, you know. There's no, there's no

_16:43_: ambiguity. Two cars crashing

_16:45_: but two vents which are separate?

_16:50_: It depends.

_16:52_: You're at this point allowed to go gasp. OK,

_16:56_: but we have this is a straightforward reduction from

_17:00_: the two

_17:03_: most of the the the the 2nd axiom.

_17:10_: OK, that's a bit strange.

_17:13_: So now imagine you know everyone goes back to where they started

_17:16_: off and we we we now have two trains going through the station

_17:19_: at the same time

_17:21_: at the same rustic speed going in opposite directions and we

_17:24_: can see both of them. So the top one that's the the the trains

_17:28_: heading off in in that direction and and by the same argument

_17:32_: there was ever Barbara for the back there was ever afraid at

_17:36_: the front there three and one are simultaneous in our frame.

_17:40_: But we'll set things up so that at the same time with actually

_17:44_: passed through the train station there's another train Yvette and

_17:47_: 70 who going to do the same thing but in the other direction

_17:51_: and of course it's quite symmetrical. So in that case,

_17:54_: the reader observer,

_17:56_: the watcher showing three, the front observer Yvette, what we

_17:59_: showing one.

_18:01_: OK. So that's that makes sense.

_18:05_: Right now I've got to make sure I see the next bit in the right

_18:09_: order.

_18:10_: Umm,

_18:13_: because it's possible to confuse things

_18:18_: and

_18:19_: keep,

_18:21_: and we're going to pause a moment and take another

_18:25_: a set of observations just a short fraction later. With both

_18:30_: trains have moved slightly onwards and there's some

_18:33_: observer in the top carriage who can see,

_18:38_: who can see. Deputies watch at that point and we're going to

_18:42_: leave that? There for the moment. But what we're going to

_18:46_: assume by the way is that these two trains are going past like

_18:50_: that

_18:51_: we thought the the very close to each other so that Elaine or

_18:56_: whatever is you know knows glued up against the the train window

_19:01_: and can seize everybody's watch as if as if she were Co located

_19:06_: with it. So these are in principle at the same position.

_19:10_: OK, so there's no time flight stuff

_19:14_: to hold on to that. Thought for more.

_19:17_: And they're a little bit later

_19:19_: and the trains have moved further, further, further

_19:22_: forward and Barbara and Zebedee see each other's clocks and

_19:25_: they're both showing 11.

_19:28_: OK, there's that. No.

_19:33_: And I said, what's in the order?

_19:42_: So everyone calms down,

_19:46_: come back together, have a cup of tea and discuss their

_19:49_: results.

_19:51_: And

_19:54_: Barbara

_19:55_: says I I saw the front of the other train

_19:59_: at time 3.

_20:04_: And Fred says, oh that's interesting, I saw the back of

_20:07_: that train at time 1.

_20:10_: So but the about time three,

_20:12_: you know when Barbara saw the front of the train at time 3,

_20:16_: the back of the other carriage was well past Fred.

_20:21_: And if you remember last time I talked to how we would measure

_20:24_: the length of of a of a moving train if that bench we're moving

_20:27_: it or something we're moving through here at high speed. The

_20:30_: way we measure the length of the moving thing.

_20:33_: If everyone had you know we're looking at the watch and I'd

_20:36_: appreciate a pre arranged time they looked up and if they see

_20:39_: the the the the the the the the the the train in front of them

_20:42_: they they write that down and we should we we measure the length

_20:45_: of the moving object by asking did you see the end of the

_20:47_: train. You saw the end of the train. Subtract 1 distance from

_20:50_: one coordinate from the other, and that's the length of the

_20:53_: moving of the moving train.

_20:55_: That's our procedure for measuring the length of a moving

_20:57_: object.

_20:59_: But look what happened here at time 3.

_21:02_: Barbara Singh

_21:04_: for another cage was was level with me and Fred, said Ohh at

_21:07_: time 3 the front those guys was was passed to me.

_21:11_: We don't exactly weird but it was certainly passed trade. In

_21:13_: other words, at time 3, the front of the carriage

_21:17_: was levelled in the server down over here.

_21:20_: In other words, the people in the top carriage

_21:23_: have measured the other carriage, the bottom carriage,

_21:27_: to be shorter than theirs.

_21:30_: OK.

_21:33_: And

_21:36_: umm,

_21:39_: the next thing they can do is, you know, they'll park that for

_21:42_: the moment,

_21:43_: Fred remarks.

_21:46_: I I noticed the deputies watch was 2 units faster than mine.

_21:49_: Ohh, they they're what they watched a faster than ours. They

_21:52_: watched a set ahead of ours,

_21:55_: but Barbara goes

_21:58_: no, because when I looked as if he's watch, you know, colocation

_22:02_: with me watch wasn't faster at all.

_22:06_: So Fred has seen deputies watched by two units fast.

_22:09_: Barbara sees deputies watched not be fast at all.

_22:12_: In other words, these watches going slow,

_22:16_: they have and that's a measurement. It's not, it's not

_22:18_: some weird optical illusion the the point of all this, you know,

_22:21_: making an observation local to you and blah blah blah that that

_22:24_: is saying we are making observations here measurements.

_22:27_: It's not just this is not optical illusions.

_22:30_: So

_22:31_: the people of the top top carriage have measured the

_22:34_: bottom carriage to be shorter than theirs and this clock to be

_22:38_: moving slowly.

_22:40_: But again I see this. Hope everything here is symmetrical

_22:45_: through the exactly the same.

_22:47_: Like, no argument

_22:48_: could be made by Yvette and Liberty. So they would measure

_22:52_: the top carriage to be moving slower, to be shorter than

_22:55_: theirs,

_22:57_: its length to be contracted, and they would measure Barbara's

_23:00_: clock to be initially ahead of theirs and later in time. So

_23:04_: they would measure Barbara's watch to be moving slower than

_23:08_: theirs,

_23:09_: and it has to be and and and it has to be the case. This isn't

_23:12_: just a symmetry symmetry argument that has to be the case

_23:14_: by the 1st, 1st axiom, because if one of them could make could

_23:17_: see that the other was absolutely shorter than, they

_23:19_: could tell they're moving.

_23:21_: This has to be symmetric,

_23:23_: and this is so. So what's happening here is that both of

_23:26_: these sets of observers measure the other to be less contracted

_23:30_: and both of them measure the other to be time dilated. Let's

_23:34_: contraction things get shorter. Time dilation clocks go slow.

_23:39_: Umm,

_23:41_: and you're you. And that's another thing you are quite

_23:44_: permitted to be to to to gasp and stretch your eyes at.

_23:52_: So a Porter moment. There are the other outstanding puddles

_23:56_: that that probably can't be right because

_24:02_: you will reread this and you'll it'll percolate into your

_24:05_: percolation.

_24:07_: So

_24:09_: which of the following statements are true, referring

_24:12_: to the preservers at the front of the train carriage?

_24:16_: So Fred and Bubbles watch the mission synchronised with each

_24:19_: other and measured their frame.

_24:21_: Friend bubble watches. Do you synchronise with the clocks in

_24:23_: the other frame?

_24:24_: Fred and Barbara measure the garage to get shorter when

_24:26_: they're moving.

_24:30_: True or false. The the first statement all those states true.

_24:35_: Obviously it's false.

_24:38_: Second statement

_24:39_: very much always synchronised with the clocks and the other

_24:42_: carriage. True.

_24:44_: False.

_24:47_: Friend Bob Major. The case to get shorter when they're moving

_24:50_: true.

_24:52_: False.

_24:54_: Good

_24:57_: excellent mother I think the the the majority of the the come

_25:00_: from majority of everyone's got that right. So we won't deny

_25:04_: other than say yes the whole thing about because friend

_25:07_: Barbara aren't mutually aren't mutually moving

_25:11_: the the the synchronizer watched by a procedure which we can talk

_25:14_: about and this dating advice there's no complication there.

_25:17_: You can hold on to that thought when you thinking through these

_25:20_: things.

_25:21_: And yes, the whole point of this is, is that there's a difference

_25:24_: in the measurement of the passage of time.

_25:28_: And yes, it cannot be the case that Fred and Barbara measure

_25:32_: the character you shorter when they're moving A because that

_25:35_: would violate productivity

_25:38_: be because as far as they're concerned, they're not.

_25:42_: They're standing and shrinkage, OK, happens, the world is moving

_25:45_: past them at high speed. But nothing, everything that happens

_25:49_: when you're stationary has to happen in the train characters

_25:52_: as well. So that can't happen.

_25:54_: Excellent.

_25:57_: I should be going faster.

_25:60_: Key points, right? We'll move on

_26:03_: and talk about the light clock. Now this isn't a useful clock,

_26:07_: but it's a way of materialising the passage of time in a way

_26:11_: which depends on the moving speed of light or the speed of

_26:15_: light. So this is our light clock.

_26:18_: It consists of

_26:20_: when we were flashes

_26:22_: a mirror at the top and observer back at the bottom again and and

_26:26_: one tick of the lake clock is flash buying detected OK

_26:31_: and the person who's standing by the lake clock so that they are

_26:35_: Co located with the with the flash rather the code with the

_26:38_: flash. They have a stopwatch, they see the late flash start

_26:41_: the stopwatch, the late travels a distance. L bounces off the

_26:44_: miracles back troubles since 2L and they stop the stopwatch so

_26:48_: they they time how long it takes for that in their framework. In

_26:51_: the watch of the person on the on the on the watch, the person

_26:55_: standing by the by the sector.

_26:58_: Nothing complicated there. So so delta T prime is 2 / C distance

_27:02_: between time, distance, speed times time is another thing that

_27:06_: you can hold on to.

_27:11_: Now imagine that late clock is moving or had to rise for 6

_27:14_: speed or treating carried through station blah blah.

_27:18_: And now what is being observed by someone who by a set of

_27:23_: observers

_27:25_: and including this one on the station platform.

_27:29_: The light flashes,

_27:32_: but the time makes it across the to the side, the leap of of the

_27:36_: light clock. The whole thing has moved, moved along because it's

_27:39_: moving at a significant fraction of the speed of light and so but

_27:43_: it bounces off the middle at the top. It's bouncing off the

_27:46_: middle. When it's over here,

_27:48_: he's moved on the track a bit and bouncy comes back and

_27:51_: eventually rise back at you know

_27:54_: where it started more or less in that frame. And the same being

_27:57_: observed by someone on the station platform.

_28:02_: But again, second axiom,

_28:06_: the light moves

_28:08_: at to be late.

_28:10_: It doesn't. It doesn't get a speed boost from the fact that

_28:14_: the light the flashlight here is moving seems speed, but it

_28:17_: travels a longer distance,

_28:20_: so the time it takes to go

_28:25_: it's good. That longer distance is.

_28:29_: It is

_28:32_: speed times time.

_28:35_: It seems that that that time so that so that triangle from the

_28:41_: play here is C dot t / 2

_28:44_: is the total time it takes divided by two.

_28:47_: And if the whole thing is moving at

_28:50_: at speed V,

_28:51_: then that distance from there to here it of course

_28:55_: we just does this be template. So that thing is, it's half V

_29:00_: dot of. TI

_29:04_: thought it was the theorem.

_29:07_: Umm,

_29:09_: would you to?

_29:11_: And

_29:14_: yeah, I thought one of the only one of these recorded on E360

_29:17_: and I don't know which one it is. So just have to

_29:25_: hope it's the right one.

_29:30_: Ohh, how are you? Hello

_29:46_: So what we have is

_29:52_: and

_29:54_: see delta t / 2 V delta t / 2

_30:02_: that distance is L

_30:04_: Now why is it L primed?

_30:08_: Does that I've just written only that L the same as in in the

_30:13_: light clock when we

_30:18_: was stationary. So there isn't an LNL primed. You may or may

_30:22_: not have noticed.

_30:25_: And that's because that doesn't change. And we can think we can

_30:30_: work out that it can't change by using the principle relativity.

_30:35_: Because imagine

_30:38_: I've said that the length contraction along the direction

_30:40_: of motion.

_30:42_: Perhaps there's length contraction perpendicular to the

_30:44_: direction of motion.

_30:47_: OK,

_30:48_: let's go with that for a moment. Say you're you're you're driving

_30:53_: along, you're in this on the on the stream and see

_30:58_: the the length contraction, see length traction exists and it

_31:02_: had the effect of making that train actually shorter.

_31:06_: The trick then the training wheels will fall into the train

_31:11_: tracks and the whole thing will crash. That's a very bad thing

_31:15_: because there's been a length contraction that way.

_31:20_: But from the point of view of the people on the train, it's

_31:23_: the world that's moving past them.

_31:27_: So the the the the train tracks are the ones that are moving, so

_31:30_: they're going in the other direction. But if there's a

_31:32_: perpendicular length contraction then what will happen is the

_31:35_: train track, the sleepers on the train will get shorter

_31:38_: and the and the distance between the tracks will get shorter. So

_31:42_: the train wheels will end up outside. The train track will

_31:45_: crash, it will be it will be a crash. But in one case because

_31:48_: from one point of view it's because the the train actual

_31:51_: have we have got shorter and they end up inside the train the

_31:54_: train tracks and the other view is the sleepers be shorter. The

_31:58_: train wheels have ended up outside. You can't have both.

_32:02_: It's not possible for them to be both

_32:04_: and that argument depended on the assumption that perhaps

_32:06_: there was a a perpendicular length contract

_32:08_: to the camper.

_32:11_: So that's L and not L prime.

_32:15_: OK, so Pythagoras theorem we have. Well first of all from the

_32:22_: simple case

_32:25_: and the detector that we know that

_32:29_: 2L is equal to

_32:32_: see

_32:33_: delta T prime. That's where delta T prime is the time that

_32:36_: the round trip time on the on the watch of the person standing

_32:39_: by this.

_32:41_: So now we have C

_32:44_: delta t ^2 / 2 ^2 plus is equal to L ^2 plus

_32:52_: the Delta t

_32:54_: / 2 ^2. Just Pythagoras theorem.

_32:59_: So or in other words, C ^2 delta T ^2 is equal to two L ^2 +

_33:09_: D delta

_33:13_: square.

_33:16_: But we know what L is, so that's C

_33:22_: debt primed squared

_33:25_: plus C ^2 delta T ^2.

_33:29_: I'm going to, you know, just ignore the cancel out the seas

_33:32_: and we end up. So I've written the wrong thing. I've said

_33:36_: that's V ^2. Why did no one stop me?

_33:39_: Eastwood.

_33:41_: All right, I need V ^2, Delta t ^2,

_33:49_: v ^2, Delta t ^2

_33:53_: or Delta t ^2 is equal to

_33:56_: Delta T prime squared plus v ^2 / C ^2

_34:02_: go to t ^2. I'm rather middle of this of this algebra, but

_34:07_: therefore delta T is equal to

_34:10_: and you know 30 primary equal to Delta T 1 -, V ^2 / C ^2.

_34:21_: It's about 1/2 square root of.

_34:24_: So this simple construction has allowed us to work out

_34:29_: the relationship between the time between these two clicks as

_34:32_: measured in the on the watch of the person.

_34:36_: Umm,

_34:38_: conversation platform

_34:40_: and the time between You seem to Click to events on the watch of

_34:44_: the person in the in the train and that they are different.

_34:52_: And we're going to write that as Delta T is equal to

_34:56_: gamma,

_34:58_: Delta T primed where gamma is equal to 1 -, E ^2 / C ^2,

_35:05_: tomato half. And you'll see that factor appearing again and again

_35:09_: and again.

_35:12_: So we've already got a

_35:16_: mathematical expression for the time dilation effect,

_35:19_: just for the two axioms and a bit of ancient Greek geometry.

_35:28_: It was aghast at that

_35:31_: Question

_35:34_: Time in the stationary no dirty prime. That's the time on the

_35:38_: watch of the person who's standing by the light clock. So,

_35:41_: so, so, so, so the light clock is, is on the on the train, the

_35:45_: standing by there with, with, with, with, with with with

_35:48_: their. Their.

_35:50_: So so so this in standard configuration

_35:54_: is X prime X.

_35:59_: That's the the frame moving at speed V The light clock is

_36:07_: is there and

_36:10_: delta T prime in that frame. And these two events are

_36:16_: because the key in this in in in this room standard figuration,

_36:21_: meaning that the **** prime axis are lined up together and the

_36:27_: clocks are synchronised to to zero at the point where the that

_36:31_: the the the the the frames.

_36:36_: We'll call it heated,

_36:39_: as you can check at this point. This is a good prompt for you to

_36:42_: go back and look at the section in chapter one which said

_36:45_: exactly what the standard configuration was.

_36:50_: OK.

_36:55_: Yeah.

_36:59_: Um,

_37:03_: so I mean and and and. This is essentially that that question.

_37:09_: When discussing the lake clock we saw the phrase one tickets

_37:12_: time at delta T seconds.

_37:14_: So

_37:15_: that which is that what your person on the train the watch of

_37:18_: person in the platform edge station, the station clock or

_37:21_: the OR the temperature of the photon of light? Who would say

_37:24_: it was watching a person on the train?

_37:27_: Who was the Was the watch person on the platform edge?

_37:31_: Who was it? Was the station clock

_37:33_: who received the time attacks the fortune of late

_37:37_: Who hadn't put the hands up yet?

_37:40_: OK, I'll do that again. Put your hand up at something. Guess it

_37:43_: doesn't matter. I'm not keeping track of who says what. No one

_37:46_: keeps track track. I'll just make some sort of commitment to

_37:49_: yourself but we'll which it is who say with the watch of a

_37:52_: person on the train.

_37:54_: OK, who was the? It was the watch of some of the platform

_37:56_: age

_37:57_: who was there with the station clock.

_37:60_: Who is he? With the time of the Fortune of Light

_38:03_: chat, you never tell them why. You're right.

_38:53_: OK,

_38:58_: so asking that again,

_39:01_: doesn't she? Doesn't in that construction I remember we're

_39:05_: talking about is

_39:07_: the setup here.

_39:09_: There's tea. There is the water person on the train,

_39:13_: the watcher personal at the platform edge,

_39:16_: the station clock.

_39:18_: What time is your fortune of late?

_39:21_: OK, it's the watch of a person on the platform edge

_39:25_: because, and this is, it's always very important.

_39:30_: It doesn't matter what what his tea, what's tea framed the all

_39:34_: the frames are equally good.

_39:37_: But then, This is why when you're working through problems

_39:40_: like exercise like this, you always have to say

_39:44_: T is the time in this frame, T prime in the time in this frame.

_39:47_: You have to be explicit about it because you know all options are

_39:50_: are OK. In principle there's a sensible way of doing it, but

_39:52_: the sensible ways of legitimate too.

_39:55_: So the way I set this up,

_39:57_: I could have set up a different way. The way I did set it up was

_40:01_: that delta T was the same with observers, plural on the, on the

_40:04_: on the station.

_40:07_: Does TT Prime were the the watch at the time when the watch this

_40:10_: person standing by the light clock and that's moving and the

_40:13_: different times we could define them differently. We didn't in

_40:17_: that we set them up

_40:20_: and it's not

_40:23_: on the station clock. Can anyone see why it isn't the time on the

_40:26_: station clock?

_40:27_: It's not like the same reference frame. Well, it's not in the

_40:30_: same session. Yes, that's it. It is in the same reference frame.

_40:34_: So the station and the station clock are not moving with

_40:37_: respect to each other,

_40:39_: so the decision from clock is fixed to the station. So it's

_40:43_: going to be synchronised with the with delta T with all the

_40:47_: observers who are at rest in the station but the one we are

_40:52_: looking at the the, the the the the the person who's who's, who

_40:56_: notes

_40:57_: we are we we are recording in Delta T is is the the watch of a

_41:01_: person who is standing by the bit where the the light came

_41:04_: back to the bottom bottom like light lock

_41:08_: that is simultaneous in their frame with everyone else in that

_41:11_: frame. But it's their watch we're looking at. They are the

_41:15_: observer that matters.

_41:17_: So that's why a question there, Why does it matter so much that

_41:20_: the

_41:22_: ohh right.

_41:24_: That's a very good question. Why does it matter? And I think it

_41:29_: matters. It matters because

_41:35_: if we all would make sure that's the only person we're talking

_41:37_: about, then we know exactly what we mean by the time of the

_41:40_: event.

_41:42_: It would be possible to see that and look at the look at the

_41:45_: station clock at the same time and you could walk it out. But

_41:49_: it would involve do also extra sums about the light travel time

_41:52_: and worrying about what what simultaneous and what's not. So

_41:56_: the person who's at the whose Co located with the event in

_41:59_: question, the event being the like getting back to the

_42:02_: detector. There's no ambiguity there. There's no question about

_42:05_: there's no light travel time. There's no question about there

_42:08_: are complications about simultaneity because we've said

_42:12_: things which are

_42:12_: contains the same position automated. Absolutely. So it

_42:15_: just it it ties up with the boys. There's no there's no

_42:18_: there's no quibbles at this point. So and that's why we have

_42:21_: this, this profligate collection of observers everywhere. So that

_42:24_: anything that happens in our frame, we've gotten Observer Co

_42:27_: located and it's their watch we pay attention to.

_42:31_: So we could do otherwise, but we don't. So be it. But I think

_42:34_: it's important to to to to to to to to mention. And that last

_42:38_: one. A bit of a red herring,

_42:41_: because it's hard even to talk about the time of photon. A

_42:44_: photon doesn't have a clock.

_42:46_: I mean, you know, in a trivial sense, but also because it's

_42:49_: moving, actually atmosphere, light, everything goes a bit,

_42:52_: you know, 1 / 0 at that point. So we end up just not really

_42:55_: being able to say anything sensible about this time

_42:57_: attached to a photon because there's a sort of 1 / 0 problem.

_42:60_: Basically when it comes down to it, it's not mathematically

_43:03_: sensible thing to talk about

_43:08_: blah blah.

_43:10_: So that's what I wrote. I scribbled down, written down

_43:14_: that the time the moving frame is or the same in the quarter

_43:19_: stationary frame is gamma times the time in the in the moving

_43:23_: frame or or whatever. And when you do exercises and you will be

_43:28_: doing exercises

_43:30_: right, there's something like that,

_43:33_: but you will lose marks if you are not clear what you mean by

_43:36_: T&T frame

_43:37_: because it can be other either way up. And the thing you

_43:41_: remember is that it's called timed deletion. Moving clocks

_43:45_: run slow and you will work out. Do I multiply divide based on

_43:49_: that?

_43:51_: I mean, really, I suppose I should write delta T prime

_43:54_: equals delta T over gamma and let's say that that factor of

_43:56_: gamma you'll see again and again and again enough that you won't

_43:59_: even have to memorise it. You write down so many times it will

_44:02_: just stick in your head

_44:04_: and that's what it looks like as a function. And you can see it's

_44:09_: pretty close to to one for most speeds, from zero up to the

_44:14_: speed of light.

_44:16_: It's only it only gets to two at about just under .9 of the speed

_44:21_: of light. So, and This is why we never we never noticed it before

_44:25_: the 19 century, because it doesn't make any difference

_44:29_: until you're 90% spotlight, at which point it could have been.

_44:34_: So it shoots up to Infinity at at this beautiful

_44:38_: so that you have that picture in your head.

_44:43_: He points

_44:45_: right.

_44:46_: Um,

_44:48_: now that is. I've gone through through that rather quickly

_44:51_: actually,

_44:52_: and

_44:54_: more quickly than I worried about, so

_44:58_: it's not worth starting on Chapter 4. But I I will post

_45:02_: chapter 4 promptly

_45:04_: and in the last couple of minutes rather than hurry on

_45:08_: other other questions I think are really good questions like

_45:12_: that, that, that, that that are

_45:16_: boiling over in your head.

_45:21_: OK then

_45:23_: think of some.

_45:25_: I'll post the notes, have a look at them for next time. I I think

_45:29_: it's quite important to to to go through these, the the, the the

_45:32_: notes afterwards and make sure they make sense because it's

_45:36_: sort of thing where ohh, yes, it made perfect sense and then in

_45:39_: half an hour you'll explain to someone else and we'll go. I

_45:43_: have no idea what's going on, so it's just it needs to settle