Transcript for a2-l01

Hi, I'm Norman Green0:12

and this, in case anyone having a little panic, is0:14

the relative gravitation strand of astronomy too0:19

good? You're there, we are.0:23

Now there's a couple of this first lecture is all a little0:26

bit weird because there's a bit of predatory stuff we've got to0:30

get through about how I organise the course. And the the topics0:33

I, I, I'm sort of gallop through in this first lecture seem a bit0:37

disconnected and that's this are sort of disconnected. But they0:41

are important important ideas that you've got to to get under0:44

your under your skin really more or less over the rest of the of0:48

the course. So you will come back to this material again and0:52

again over the course of of these 15 lectures,0:55

but we'll only really get properly going in the next0:59

lecture1:02

tomorrow.1:03

So with that said,1:06

that's the that's the wrong computer.1:11

With that said, there are some things I want to make sure to1:17

say1:20

which are.1:22

Um,1:24

if you look in the middle1:29

middle of the relevant page, you'll see that there are. I1:32

will show you a picture of the middle1:36

um,1:39

just so we know what we're talking about.1:40

Yeah,1:43

you will see that there are.1:45

The number of number of resources1:48

under1:51

under section 10 Medical section 10,1:54

including the lecture notes1:59

and I'd like to note2:01

include2:03

Introduction PDF,2:05

axioms.pdf. And there are2:07

some other versions of those which are the same but in a2:12

slightly laid out slightly differently. In a way, which2:15

might I I I think I think I aim to be more useful on a tablet.2:19

Whichever one that's the same in both of them. Whichever one2:22

works better for you, works best for you.2:26

And that's a theme,2:29

because these notes are fairly comprehensive. There's a lot of2:31

text in there2:35

and the way that I have ended up delivering these lectures is2:37

that the main event is the lecture,2:41

right? That's the the the the thing we focus on.2:44

But2:48

the notes others have Co main event if you like.2:50

They are Co equal. With the lecture as the way I'm I'm2:54

delivering this stuff to you because relativity makes a lot2:57

more sense the second time you do it.2:60

And if I do it in a lecture and I do it in the notes, you'd have3:03

getting two goals at once.3:08

And that's important, because it will only make sense the second3:10

time you do it. Now, if you think notes, first, I'm gonna3:13

read the notes and then just check what he says in the3:16

lecture, that's good. If you think I'm going to sit back and3:18

let it wash over me in the lecture and then check what's3:21

happening in the notes, that's good too.3:23

But you have to decide who you organise it,3:26

OK? You have to sort of take charge of your own learning here3:29

and work out how do I work out what's going on here?3:32

And if someone like Sam Goldman of the of the movie mogul who3:37

said half of the money I spend on advertising is wasted,3:40

but I don't know which half3:44

and half of what I say in the notes is irrelevant to you3:46

because you don't need that bit. But the the half that's that3:48

that is needed for you is different from for for for all3:51

of you.3:54

So the it's quite a lot of material here, a lot of pages3:56

here.3:59

Don't panic, you know it's supposed to memorise everything.4:00

OK, now the the notes are there as a resource for you to go4:04

revisit what happened to the lecture and make sense of it.4:07

Second time, it follows that it's a good idea to look at the4:10

notes before the lecture.4:14

Now you have to understand everything, but you get an idea4:16

of what to commit. This isn't a detective mystery. There are no4:19

cliffhangers.4:22

Yeah,4:24

spoilers are good. If you know what's coming up, then you can4:27

know that bit didn't make sense in the notes. I'll really pay4:30

attention in the lecture because it'll be explained in a slightly4:33

different way.4:36

OK, I could go on at this for some length and I will post. You4:38

know right now that that these slides are in there because for4:41

reasons, but I'll generally post the slides after the4:45

after the lectures. The slides unlike you know, some people do.4:49

People do have different opinions about how to lecture4:52

with slides. I don't like slides very much, so the slides I do4:55

are pretty minimal. There really is something for me to stand in4:58

front of or a diagram to point to.5:01

There's nothing in the slides that isn't in the notes. OK, so5:04

don't think Oh my God, if it's to work with those sides as5:07

well.5:11

OK. So the state-of-the-art of prop, A prop which I put, I mean5:12

I don't think the right, I don't think there's much point in5:14

putting them up here really but people want them, they feel5:17

secure if they've got a copy of the site.5:19

So I do OK, but I don't regard, I don't rate the site as a very5:22

important part of the resource. OK5:25

they're they're prop for me.5:28

The E360 I I think that means this is being recorded.5:33

I don't know where it goes after this echo through a bit of a5:37

novel thing I'm not very sure what happens. I trust it works5:40

and for the first couple of lectures I will do record record5:44

them myself. And just as a bit of a backup to do we reassure5:47

ourselves that doesn't work. Don't rely on that5:51

because some people think ohh all the lectures are recorded,5:54

just go listen to them afterwards. Doesn't make a lot5:57

of sense because being in the lecture concentrating it a part5:59

of the of the whole learning.6:02

Umm,6:04

the other big big big teaching resource is the exercises.6:07

Each of the chapters in the notes has a block of exercises6:12

which are pretty cute,6:16

clearly linked to specific parts of the notes.6:18

And relativity is something you only understand when you do the6:22

exercises.6:26

You cannot just sit back and and I think yeah, yeah, yeah, got6:28

that.6:31

You think you understood it when you sit in the lecture, but you6:32

didn't.6:35

Very probably not. OK, it's when you you you you're forced to6:38

rethink it and and it forced to buy ahead in the table a bit6:41

going through the exercises. That's where you understand it.6:45

You go ohh, it's simple really6:48

OK And that is also why it's in next semester that are released6:50

the solutions and notes to the exercises, not the semester,6:54

because OK is quite handy to check you've got the answer6:59

right, but it is more useful, you know, controlling that to7:03

bang your head on the table a bit. It's the it's the impact7:06

that get the learning in. OK,7:10

umm7:13

but boom.7:16

Um. OK,7:17

other7:23

Where are we?7:26

I although it's terrifically all fashioned,7:29

like the idea of aims and objectives, I think internally7:32

learning outcomes are one fashion later and they're out of7:35

fashion.7:38

For me. The aims and objectives are very simple and are very7:39

useful. Structuring notion7:42

definitions differ, but for me the aims are the point.7:45

They're why you're learning this7:51

and why I'm teaching it. And there are things like7:53

understand,7:56

appreciate the the other things you'll remember7:58

after you've done the exam in two years. You'll remember the8:02

aims you because that that that is why you're doing this course.8:05

And so if the exam were understand things, you went,8:09

Yeah, then we'd all be a lot happier.8:12

That'd be a nice exam,8:15

but it doesn't really work in assessment terms. So8:17

as well as the aims, there are the objectives,8:21

and the objectives are party tricks,8:25

the things you can do,8:27

things that you can be assessed on.8:29

They're not terribly exciting necessarily, but the best way of8:33

achieving the objectives.8:36

It's achieved the aims. If you understand something that the8:38

the objects would become pretty easy, OK, but they are the other8:41

other other nice concrete things which you can do. There are8:44

things like provide descriptions of such and such,8:47

describe as different an exam answer, blah blah blah and so8:51

on.8:57

So that's a very good distinction. I tend to associate8:58

exercises with objectives. When I'm making up the exam, I look9:01

at the list of objectives.9:05

So that's it's not a one to one mapping, but there is a9:08

correlation between what I think is what the objectives of what I9:11

think is fair game in the exam.9:15

Things which are clearly not objectives after the exam ask me9:18

questions. But that's the that's the basic answer I'll give you9:20

whenever you ask me that question9:23

every time and moving on very rapidly.9:25

Umm,9:30

so. And my timetable for this lecture to this lecture is9:32

timetables in a way that other ones aren't so much. It's9:37

already all short. So9:41

and we'll just press on.9:44

So the9:47

this market here because it's just backing up the the the9:49

market made that a lot of this is for you to work out what you9:53

need to read.9:57

So there's there's more material than you might like9:58

but that's because I'm sort of forcing you to to just to think.10:01

You will probably have look look at all the words in all the10:04

notes, but you your your study only says selected bits as there10:07

are signpost aims and objectives are signposts. At the end of10:11

each section, I tend to have a couple of key points, which is10:14

also signposts is what you should have picked up from that.10:17

You're very standard things.10:20

So that's sort of the other thing I've got to remember.10:23

Remember I was asked to say to you is there is no lab this10:26

afternoon. I think you know that because I think you were told10:29

that on Moodle. But to see you tracking up to Garscube, just10:33

remember, no love this afternoon, OK? They start. I'm10:36

not sure when they start. I don't have to do that, so I10:39

don't10:42

OK10:44

any questions about the other sorts of organisational things?10:45

Have I forgotten anything obvious?10:49

Nope.10:51

OK, so10:53

onward to the physics bit.10:55

I have on the next slide10:58

put all of the physics you will learn in the next 10 weeks10:60

because we do 10 weeks of special activity and five weeks11:04

on general activity.11:08

So all the physics you'll learn in the next 10 weeks,11:10

That's it.11:14

It's two sentences.11:16

There's11:20

on a national reference reference, performance of11:21

physical experiments. It's called the principle and the11:24

speed of light. The same constant value measured in any11:26

inertial frame.11:29

That's it.11:30

Why many 10 weeks talking about that? Because those are easy to11:32

state,11:37

and those are the physical, the thing, the physical statements11:38

you didn't know before. But the consequences of these are11:42

intricate, and even understanding what those words11:46

mean is a bit subtle,11:49

and so there's not a lot of volume to learn in this course.11:52

You don't memorise stuff. I have a rotten memory, so I don't11:55

think it's fair to think to play you to memorise stuff. When I11:59

can't, I can't.12:03

So demonstrating that you understand these things is the12:06

point of the objectives.12:08

So there's not a lot to learn. And12:11

this is not this is this. What is and isn't a mathematical12:14

course.12:18

The maths we we use in this course is addition, subtraction,12:20

multiplication, division, square roots.12:24

Later on we use differentiation,12:28

but it's all school physics. It's all school maths.12:31

There is no funky maths in this12:35

course.12:39

But in a different sense this is a mathematical course, because12:41

the way we start things with there's there's no seat of the12:45

pants intuitive. You know you'll get you know get this picture12:49

and you'll understand. It doesn't there. There's no see12:53

the fans intuitiveness in this in this course it's all about12:56

this axiomatic approach. This is the fundamental the fundamental12:60

insight which is expressed in logical form of feeling,13:03

mathematical style of thinking. And then you move proceed13:07

carefully and thoughtfully forward in a mathematical style.13:10

So although the the arithmetic use is very simple,13:14

the style is quite abstract and that is and and and that's I13:18

think the first course you've done. Where that's true13:21

First, your first year courses have tended to be more13:26

physically13:28

unless you know apart from say the pure pure maths courses that13:29

you've done.13:33

So that will be a bit of a jolt. OK.13:34

Also, you have done a bit of special relativity before, I13:38

think in physics one is. That's right, yeah, OK. And that's I13:42

think 2 lectures and I'm sure the word Lorentz transformation13:46

was mentioned and events and stuff. But that's just two13:50

lectures. How can I spin it out to 10 lectures?13:54

Because I want you to actually understand it,13:59

and you can't do that without good without sort of going round14:03

and round several times and and getting a bit confused. So this14:06

is quite a thorough version of of special activity14:09

that's. But these are the only14:13

physical statements, only statements about the world. The14:15

only thing about the world that could be otherwise that I'm14:19

going to make all the until a bit later. All the rest is14:22

deduction.14:25

So14:29

as I said, this first lecture is,14:31

you know, dotting around a bit what what happens next is14:36

Chapter 2, which I think is what we'll get through in one14:39

lecture, is going through those axioms and think, what do they14:42

actually mean? What do those words mean?14:46

Chapter three and four, which I think is. I think it's 314:50

lectures basically, Roughly is but the field direct14:53

consequences of those actions. OK, given those axioms, what14:56

follows,14:60

and there's quite a lot of followers pretty directly before15:01

you get into anything, any, any, anything calculational. And15:04

that's interesting. Those axioms, although they look very15:08

simple, are full of physical content.15:11

Chapter 5 is where we go onto the main apparatus.15:15

The the main. The main, Yeah, the main international tool. Or15:18

relatively how you how, given a A-frame, you're sending A-frame15:22

that's moving past you. How do you say this event that happened15:27

here happened in those coordinates, the moving frame,15:31

blah blah. Those words will mean more in a short while15:34

after that. That's that. That's sort of the the, the, the, the15:39

the first pillar of the whole thing. After that we talk about15:43

and and that we I think we'll spend 3 lectures on that. OK.15:48

The kinematic dynamics is how do you describe motion, what how do15:54

you talk about momentum and energy and conservation of15:57

things in a relativistic context. You're familiar with16:01

these things from physics. One,16:04

What do these ideas look like in a realistic context?16:07

And and and and that sort of thing. That's very important. If16:10

you do particle physics for example,16:12

and then chapter 8:00 and 9:00, the last five lectures is16:15

general relativity. We cannot go into the maths of general16:17

relativity because that is actually quite hard16:20

and that's that's an honours masters course. But what we can16:23

do is give an account of general relativity which is has much16:27

more textured, is much more substantial because we'll spend16:31

10 weeks, 10 lectures, sorry, and thinking through the16:35

terminology and thought processes of special activity.16:38

So there's a lot more substance we can say about generativity.16:42

So it's it's beyond a popular account,16:46

but we we can't get to the free technical account so we can get16:50

to that intermediate range there16:54

and that's and that's five lectures,16:58

OK.17:02

And17:03

so I'm not gonna be, I'm, I'm gonna gallop through these now17:04

really. But that's OK because I want to have said these things17:08

to you at one point,17:13

even though17:16

I it doesn't sort of matter that I'm going to go through rather17:18

too quickly because we're coming back to them again and again and17:21

again in later weeks. So I'm sort of logging these in your17:24

head17:27

just just now, but you'll come back to these, you'll come back17:28

to the notes for these bits again and again, and we will17:31

talk over them again and again.17:34

OK,17:40

key thing. Number one, what is an event?17:42

An event is17:46

that17:48

that happened there. It happened, you know, two metres17:49

from the, from that door, from that, from that wall, 1 1/217:52

metres from the floor,17:55

4 metres from there. And it happened17:57

10 seconds ago17:60

for the four numbers attached to it,18:01

3 spatial coordinates and a time coordinate.18:05

But notice that I said it happened from that wall. That18:08

war, that war someone in the street18:13

would give, would give different physical coordinates to that18:17

event.18:20

OK, obviously.18:22

So the event is in some sense absolute. There's no, there's no18:24

question that event happened, but the numbers you used to18:28

describe it are relative. So the first one that you're going to18:31

use that word a lot, that's the first time it comes in there.18:35

They are basis dependent. They are coordinate frame dependent.18:39

So my coordinate system in this room start for the order over18:44

there say blah blah blah you you you can imagine 3 axes.18:47

Someone standing in the street has a different coordinate18:51

system. My watch I I said it happened 1010 seconds ago from18:54

when it was. Someone might say it happened at rib and 11 1/218:58

hours from midnight.19:01

So the zero of position and the zero of time is up to you. It's19:03

up to the definition of the coordinate.19:09

Another sort of event is.19:14

I caught it.19:19

I didn't miss it. I caught it. So how did I catch it? I I19:21

caught it because my hand and the eraser were in the same19:25

place at the same time19:29

and it doesn't matter what coordinates you give to that19:33

quote was brought to this room quarters relative to the to19:37

buyers Rd.19:40

They were in the same place at the same time,19:42

and there's nothing relative about that. There's no point of19:45

view19:48

in which I didn't catch it. If two cars collide,19:49

then metal is bent19:53

and there's no point of view in which that metal isn't bent you19:56

there's no way you can be moving in which you you look at it in a19:59

funny way and and and they didn't. They missed each other.20:02

So two things which happened which collide which are which20:05

are at the same place at the same time are there. Absolutely,20:08

there's nothing there. So why is he saying why is he saying this20:11

again and again? Why is he making a fuss of this? It sounds20:14

it's obvious, it's obvious, but it remains obvious if you like,20:17

even when there's a lot of other things that you thought were20:20

obvious aren't obvious anymore. So it doesn't need saying.20:23

That that remains true.20:28

So which of the following events?20:33

Who says supernova explosion was an event20:36

behind?20:39

Who say it wasn't?20:40

Who's the A concert with an event?20:43

Who said it wasn't?20:46

Who see the whole country clapping its hands at once? Was20:49

an event20:52

not20:54

a collision between 2 particles in the LHC. Is that an event?20:58

No,21:02

I agree with with, with most of you, even when you you, you,21:04

you, you disagree with each other because a concert,21:08

OK, that is a sort of an event in the sense that it happens at21:13

A at a place and a time.21:16

You know you know it. It said that on a ticket you'll be here21:18

at this time and they will start. But it also has a21:22

duration,21:25

and from that sense it's not an event21:27

because it's. It's a sequence of events. It's sequence of of of21:29

notes if you're like, which are all in the individual event. So21:32

an event has no duration.21:35

So the start of the concert is unequivocally an event,21:37

but the the concept as a thing because it really and similarly21:41

the whole kind of clapping hands at once. Well, yes, that does21:45

that sort of has a,21:49

you know, I definitely I I sort of definite time, but it's also21:51

spread out in space21:55

because it's the whole country, it's it's doing it once. There's21:58

not happening at a place you can't see what is the place at22:02

which the whole country does this. OK, if you stand22:05

sufficiently far back, OK, it happened in the UK, but if22:08

you're in the UK then because it was spread out in space, it22:12

didn't happen at a place and that means and we'll go on to22:15

this next time. I think that means it didn't happen at a22:19

time.22:22

It seemed obvious that if everyone claps that they would22:25

see everyone claps their hands at once. That seems obviously.22:28

Well, I know what that means.22:31

Turns out you don't.22:33

If something is extended in space, the question of what22:35

tended to happen at becomes much more complicated and we'll come22:37

to that, I hope in a moment.22:41

It certainly will come to that again and again and again over22:43

the next few weeks.22:45

So,22:46

and there's no issue about the .4, if those things were in the22:48

same place at the same time, they decided that that that22:51

happened at a place in the time,22:54

you know and and the story.22:56

So yeah,23:00

and23:02

what is it?23:06

So next, how do we locate these events?23:10

I've alluded to this,23:16

but what we do is we have reference frames and we have23:18

observers, and these two23:23

fridges being something very specific, our reference frame.23:26

They're not exotic, but we do have a very specific meaning23:30

when we talk about these. In this context, our reference23:35

frame is a coordinate system.23:37

It's an origin and a set of axes in space and in time. So it is23:40

saying that is the zero of my coordinate system and I'm23:45

measuring all times from midnight.23:49

I've defined A coordinate system23:52

feel straight forward.23:54

Someone else could have a different coordinate system, as23:57

I've said.23:60

So there's nothing. There's a coordinate system. Is a. There24:01

are infinite many, many coordinate systems.24:04

OK, everyone gets gets a coordinate system. Everyone gets24:06

lots of coordinate systems. OK, there's coordinates from makes24:09

more sense to you. Is the one in which you where you're standing24:12

still at the minute. OK,24:14

but there's nothing special about that. And that is the24:16

thing about relativity. There's nothing special about the24:19

coordinate system that you that you choose24:22

within certain limits,24:25

because there are different observers,24:28

and observers are, well, observers.24:31

Again, not an exotic notion, but the when we're talking about an24:34

observer in special activity, we mean someone24:39

with a notebook24:43

who is very short sighted24:44

notebook and a watch and very shortsighted and and they will24:48

pay attention to things that happen in front of their nose24:50

and they will write down where they are when that happens. So24:54

OK I OK, it happened at 11:40 and I'm at this position in in24:58

the quarter. They write that down and and and make a note25:03

that that's their job.25:07

If, if, if if it happened over there, they're not interested.25:10

OK,25:13

so observers are in a coordinate system.25:14

They know where they are in the coordinate system, in space, and25:18

in time. Well, they've all got to you. They know they're all25:21

written on on the ground and they and they know what spot25:24

they're sending on. And they've all got to watch. They're where25:26

they are and what time it is, and they only pay attention to25:29

things in front of their noses,25:31

OK? They ignore things which happened elsewhere. If you want25:34

to to to work out where an event happened, you've got to have25:37

lots of friends.25:41

OK, so if I want, if there was a firecracker went off in the25:43

middle of the room,25:46

the only person I'd be interested in Who, who, who? I25:48

would ask where did that happen and when? If the person,25:52

unfortunate person, who's sort of sitting on top of it when it25:55

when it went off, everyone else ignored it but that person. I25:59

asked Where are you? What time do you go off? No one else even26:03

sought? OK, hold on to that thought.26:06

So observers are very limited people26:09

and what this is illustrating26:15

come back to is 2 reference frames.26:19

A reference stream S26:22

which has an X&AY26:26

and someone standing stationary in that reference frame with the26:28

watch26:32

and as someone in different reference frame it's frame which26:33

is a different ex prime axis, a different Y prime axis and they26:37

have a different watch and they were great. So if something26:40

happens, an event happens and this second reference frame as26:44

prime is moving with respect to the first one26:48

at a speed V.26:51

So at all times the location of the origin of this26:53

reference frame is at X26:58

in it. At X in the27:01

South frame equals Vt simply because it's moving at a27:05

constant speed VS There's a bit of school maths for you,27:09

multiplication distance speed times time. You remember that27:12

bit,27:16

So what that is showing is27:19

I'd rather elaborate way of showing a moving reference frame27:22

S prime is moving in the frame S at a speed VS the origin is at27:27

space at at a coordinate X at the origin. That point there is27:31

it. Coordinate X prime equals 0 and coordinate X equals Vt27:36

a point there is a cordon. X prime equals whatever27:42

and it coordinate. X equals whatever plus Vt27:46

keeps it. Nothing exotic there. OK, we'll get on to exotic27:49

later, but there's nothing exotic there. OK,27:53

but those two observers only pay attention to things locally.27:57

Now I've said there's there's possibly have lots and lots of28:03

different inertial frames and a different reference frames.28:05

Everyone gets a, gets a reference frame, gets a28:08

coordinate frame.28:10

But some of them are special.28:11

Some of them you can.28:14

In some of them you can take it that you are not moving.28:19

Now I'm standing here, I'm. I'm not having any difficulty28:23

standing here. I'm not being thrown about because the28:26

building isn't shaking. This is a good thing.28:28

If I were in a train28:32

and the training was just bowling along the track in a28:34

nice calm fashion, then it could also, I could stand on the train28:37

with the difficulty I could juggle28:41

or a great cup of tea, whatever. Whether difficulty, because as28:43

far as I'm concerned I can regard that steadily moving28:47

train as being stationary28:50

and it is stationary, that there's there's no, there's no28:52

experiment I can do28:54

that would tell me that that's steadily moving train isn't28:55

stationary. I can look out of a window and see the landscape go28:59

by, but all that tells me is I'm moving with respect to the29:02

landscape. It doesn't mean I'm absolutely moving. I'm29:05

absolutely moving.29:08

OK, it might sugar, but so it might be that there there are29:10

some vibration in the in this, but that's just OK that's OK29:13

vibrating29:17

and that's not that it's tricky to tell you moving. It's not29:20

that no one knows how to29:24

tell you movie. One of those axioms was you cannot tell29:27

you're moving at a constant speed29:31

and a matter of of deep physical principle, there is no physical29:34

experiment you could do that would tell you if you're moving29:37

at a constant speed29:40

that you are actually the one moving as opposed to the rest of29:42

the world moving past you. And you've seen this is happening to29:46

image and saying in a train station, in a tree, in a train,29:50

in a station, you're you're gazing blankly into space and29:54

the train next to you is moving29:57

and you don't know if you're if you're trained to start off30:00

smoothly, whether it's that train to move at the station or30:03

your train, you can't tell.30:05

And there's nothing with specially processed experiments.30:07

You could because if you had a little pendulum and you as30:10

you're trade accelerated, you could do that little pendulum30:13

would, would, would, would put to one side and in a way you can30:16

imagine or or or or a ball on the table would roll off. So you30:19

can tell you're accelerating30:23

absolutely. And there's no doubt that you're accelerating. If you30:26

are sitting in a train and it's accelerating at a station, you30:30

can feel you're being pushed the small of your back. You can tell30:33

you're accelerating unequivocally and absolutely,30:37

but once you're not accelerating,30:41

your frame is as good as anyone. Your your idea of stillness is30:44

as good as anyone else, and that's to repeat myself. That's30:47

not30:51

a curiosity. That's a fundamental physical principle30:52

that there are a lot of things and it's not, and it's called30:54

the principled relativity. It's not Einstein's principle of30:57

relativity, It's Galileo's principle of relativity. Because31:00

he31:03

spelled out quite like that. But it was. It was. Galilean physics31:04

rests on that as a notion.31:09

And so that means that those frames which are not31:14

accelerating have a special status.31:17

They are the ones that we're going to make all our31:20

measurements in.31:22

The other one will give a special name to namely inertial31:25

reference frames, because they are inertial31:27

and in our show in the sense that Newton's second law,31:30

Newton's laws work in the actual frame.31:34

If you31:38

So you're floating out in space and we'll come back to this31:40

later on. If you leave something where you just let go something,31:43

it'll stay. For it is if you give something a push, it will31:47

move in a constant, a constant speed until it hits something.31:50

Yeah, just like you see the issues. If you are moving along31:53

on a on a smoothly moving train, and you roll a ball across the31:57

the, the, the, the the table, it'll move in a straight line32:02

at constant speed until it hit something.32:06

Different laws work while the train is accelerating. If you32:09

try and roll the ball across the table and go rule it like that,32:12

there's a mysterious extra force32:16

which appears which breaks Newton's laws,32:19

doesn't break news laws. It's called inertia. And if you are32:22

on a roundabout, on a children's roundabout, you throw a ball to32:26

someone across the other than their own about, then it goes32:30

off to one side.32:34

Is there a mysterious force that reflects it? No, it's just that32:36

you're in a rotating reference.32:39

Centripetal force, central centrifugal force. It's not a32:42

force, it's a it's a32:46

an illusion caused by being a non inertial frame. So the point32:48

of a national frame is that nuisance laws work in it. So you32:52

understand the physics of national frames,32:55

Physics. No, natural frames is harder. Physical natural frames32:59

easy. And we will always stick to natural frames, especially33:02

activity. We will do the same thing. We get a general33:04

activity, but we have to change our definition of what a natural33:07

frame is. And that's exciting. But that's 10 lectures33:09

and33:15

I I I am33:18

I don't feel I have to go to go through this as a as a quick33:21

way. I have a quick question. We'll have more of these33:24

questions and other lectures and have a think about these when33:26

you're, when you're mulling over the the, the you know which of33:29

these countries national frames33:32

and33:36

we can talk about that at some point33:39

and blah blah.33:42

So how do we measure times?33:47

It's really easy. How to make, you know, we know how to measure33:50

distances. We just draw things on the ground and and and and33:53

you know, with33:56

a greater things in the ground and walk away. We are in the33:58

reference frame.34:01

How do we talk about time? Well, look at our watch. How hard can34:03

it be?34:06

But when it turns out we have to be a little more specific than34:10

that, a little more precise than that, and this remark in34:13

Einstein's remark. It comes from I think the 1905 paper34:17

because you know the the paper which introduced, you know,34:21

banks especially activity in its more of its final form to the34:24

world, all our judgments in which types apart our judgments34:27

of simultaneous events and that were simultaneous is a key one.34:31

If I see the train arrived at 7:00, what I mean is the point34:36

of view of the small hand on my watch at 734:40

and the arrival of the train are simultaneous.34:43

Simultaneous in the sense they happen at the same place at the34:46

same time,34:48

so my watch doesn't have to be right.34:50

But when I see34:54

my, it happened at seven of my watch. What I mean is the train34:57

was here in front of my nose and so was my watch and they were35:01

both doing that thing in front of my nose at the and therefore35:04

they are. They are simultaneous, absolute and absolute. Sense35:08

there were simultaneity gets more complicated if you're35:11

talking about things which are separate from each other, as we35:14

will discover.35:17

But in the same way the if you if you have two cars crashing35:20

because they are metal bending because they're the same at the35:23

same time, that's absolutely simultaneous. This is absolutely35:26

simultaneous. You can hold on to this notion,35:29

and the reason why I'm banging on about the reason why I think35:32

was banging on about is because that turns out to be a35:35

clarifying way of thinking about time.35:37

The timer event is35:40

what happened on what happened on the clock which was at the35:43

same place at the same time.35:47

OK, and again, you think this sounds like it's like excess35:50

precision. Why does this matter?35:54

This is the this is the the list of things I'm kicking off in35:57

this first lecture, which will come back with the significance35:60

of which we'll come back to next time. So we're gonna see a lot36:02

of pictures of this. These are our true observers.36:05

Well, and and we we always have multiple observers because what36:08

we're interested in the whole point of things like the36:11

transformation, are36:13

someone in that frame in that when that coordinate system says36:15

this happened at this place and this time36:18

I'm in this36:20

cordon system with respect to which that coordinate system is36:22

moving, what is the position and time of that event in my36:25

reference frame?36:28

That sounds, I think why would one care? But that36:29

that's the sort of boiled down question you have to answer in36:36

order to do things like talking about36:40

Doppler shift about about I think the general relativity36:44

that that that that it all boils down to that sort of question36:47

even though it ended up being quite an abstract question. And36:50

that in a in a way is why I I I said this was quite a36:53

mathematical course because the idea that you take a complicated36:56

thing you boil it down to the simplest thing it could possibly36:59

be that still has the property and you analyse the hell out of37:02

that. That's quite mathematical approach to this. You can37:05

understand the rest by building up from that, but you tear down37:08

in order to build up.37:11

OK.37:14

I can see some folk going, oh, this is a great some folk going,37:16

oh, there's gonna be terrible, but it's gonna be great. Yeah,37:19

it's, it's, it's it's a a tremendous intellectual37:22

experience. The point is that there are multiple observers,37:25

OK? And each of them knows where they are because they've got one37:28

of these little spheres things which let them work out where37:31

reference to the the, the, the, the origin of their frame they37:34

are so they can put mark in the ground and attach a coordinated37:38

position, Gordon, to that. And they've all got to watch,37:41

which they can look at with their short sight.37:46

OK, we'll see these people again and again.37:49

So imagine you're standing on a bridge over a motorway37:55

looking police officer standing beside the road so that you're38:01

looking down and they're standing beside the road38:03

and a car driver goes past them and sneezes.38:07

Who would watch? Do you consult to find out the time of this38:15

sneeze in your frame?38:18

And this is all happening? Artistic speed? So so. And38:22

let's, you know, hold on to our intuitions. Who says it's your38:25

watch?38:29

Who said the police officers watch?38:31

Who said the driver's watch?38:34

Who hasn't put the hand up yet?38:37

OK, I'll try again. Everyone had to put their hand up. I don't38:40

care what your answer is,38:43

but I want to see if everyone had at least once. Just don't38:46

you have a punted make a guess.38:50

Who says it's your it's your your own watch.38:52

Who's this police officer watch? Who says the drivers watch?38:55

Talk to your neighbour.38:59

Tell them why you're right.39:01

Normally Adeem,39:25

normally Odin to give you more time to to to to talk it over39:28

than that. But folks, folks, normally I didn't give more time39:31

to talk over than that. But you know we're going through at the39:35

end here. So after discussion, who would say your own watch?39:39

Who should the police officers watch?39:43

Who would say the driver's watch?39:45

It's the peace officers watch.39:49

Why? Because the police officer is in your frame.39:51

You and the police officer are both in the same frame. They're39:55

both standing stationary in the motorway frame. Neither of you39:58

are moving. That's the point.40:01

Your the driver is moving.40:05

OK, so they're not in your frame. They're not observer.40:09

You, you, you you. You want to talk to. You only want to talk40:11

to observers who are stationary. You are free.40:14

Why not you? Why not your watch? Because you're short sighted40:17

too. You can't even see this driver40:21

and and and and and so the the driver sneeze didn't happen in40:24

front of you.40:27

Well, the police officer, they were standing about standing40:28

there when the sneeze happened and the right were going past40:31

sneezed and the and the police looked to their watch. So40:34

they're the only person40:37

who can see what the time of that event was in the motorway40:40

frame.40:43

The driver of the car, they know what time it happened. And their40:45

friend, they look at their watch40:48

and it turns out they'll give a different answer from the police40:50

officer.40:53

But we don't care, you know, to begin with and measurement terms40:54

what they were. And they watch, we care what happened in our40:58

frame. And the only people we talk to are the observers in the41:01

frame. And the only one observer whose opinion matters is the41:04

observer who was next to the event when it happened. Now, the41:08

event didn't happen in the motorway frame rather than the41:11

car frame. The event didn't happen in the car frame rather41:14

than the motor we frame, it happened in all the frames. So41:17

this is a good point of which I can say don't get into this way41:20

of thinking of it happens in A-frame and event happens.41:23

It's a thing in the world.41:27

It happens in all frames41:29

but different people describe different coordinates to it.41:32

Meditate on that and and we have run out of time. So I will have41:36

to to go through the last couple of bits of of of this first41:39

chapter next time which is tomorrow which and I think we41:42

are the Adam Smith building which is the last year that we41:45

will swap back and forth between.41:48