Transcript for a2-l02

We're a bit tighter in this room than where we are in the other0:08

room, so we will, well, we'll all be friends.0:12

I think we're alternating. We're more or less alternating between0:17

this room and the boys room from from day-to-day. So keep track0:22

of the application to where you are0:27

after the confusion, technological confusion of the0:34

beginning of last time didn't get all the way through chapter0:37

one. So what I'm going to do is quickly touch on the last bits0:41

of chapter one.0:45

I'm going to go over them quite quickly,0:47

not talking them in as much detail as they as they would0:52

would deserve, because as I said last time, there are sections0:56

that you'll want to go back to in in coming weeks when it when1:00

the the point of you know why do we fight about time, why do we1:05

make a fuss about clocks becomes a little clearer. So I'm1:09

introducing these ideas to you, what you to have them in your1:13

head at this point. But the the texture of them will will arrive1:18

later, I think1:22

so, so quite promptly I I I expect to go on to chapter 2 in1:26

this section. So, so1:31

I'm just warning you that this will feel a bit rushed because I1:35

I expect you to be going back to this later.1:39

The last thing we did more or less last time was talk about1:43

this quick question of measuring times. And1:47

rather counterintuitively, I said that the only1:51

observer of the three involved whose time we are interested in1:55

right now, we put up with answering the question what is1:59

the time of the event in this frame? The only observer the2:03

relevant is the observer who was stationary in our frame and Co2:07

located with the event.2:12

OK, the driver has a can describe a time to that event2:14

because they were Co located with the event within the2:20

sneezing2:23

and they were stationary in that frame. They were sitting2:25

stationary in the car. So there are two frames here just to2:28

drive this point home, 2 frames here, the motorway and the car.2:31

They are both perfectly good frames.2:34

Different people are stationary in them and and different2:37

people. And there are two people Co located with the event.2:40

The policeman and the driver are both Co located with the event,2:44

even though they're in different frames. OK, so we're imagining2:48

the sneeze, the driver and the people all in the same the same2:51

spot of the same location and location. Even though you know,2:54

because it's a car driving past, they're not literally in the2:58

same spot. But for the purposes of this, they are the same3:01

sport.3:04

I will watch up. You signing somewhere else?3:06

Um,3:12

watching this happen is not3:14

a way in which we measured the time of that event.3:17

Partly because if we see that event happen, things like we've3:20

got to wait for the light to get to our eye, so there's an extra3:25

correction would have to apply. But also because as woke become3:29

clear, the question of what is the time, what is the time?3:33

Becomes a complicated question3:37

and we are simply avoiding that question. You know in a good way3:40

by saying the only time that matters is a time of person3:44

collocated with an event. So I'm seeing this again and again and3:47

again just to drive it home that the time at which only happens3:50

at the time of an observer Co located with the event.3:53

So you'll forget that and you get confused. But I've said to3:59

you several times, so bank those up and listen to them in your4:02

head,4:05

intended to come,4:07

so that how we measure time,4:09

we make a big fuss about it.4:11

How do we measure distance? How do you measure lengths? And this4:13

also is something that will4:17

become4:20

a bit more complicated4:22

that you think that you expect.4:24

If I wanted to measure the length of this bench here,4:27

then there's a variety of where they could do it.4:34

I could get a a tape measure4:36

or he'll get better stick and lay it out. And there's also the4:41

ways I can think of doing it.4:44

But the way we are, you will think of of measuring. That4:46

is if I get me and a lot of friends line it up along the4:50

front here in previous years I've made this an audience4:54

participation but4:57

activation front bench you if this is a a coordinate frame, it4:60

is room, it's a coordinate frame.5:04

Then this observer here has you know, you know your coordinates,5:08

that you're this far from this wall, this far from this wall,5:11

this far from the ground. You know the same.5:14

Everyone knows their coordinates in the room,5:19

and there's another observer at the other end of the bench5:23

who knows their coordinates. And you know and the timings are5:26

one.5:29

And the way we measure the length of the bench is we5:30

arranged beforehand that everyone will walk. It will will5:34

look at the bench at a certain time5:39

and everyone I said tape ever looks at the bench and the two5:42

people who are at the end knew it down. I was at the end of the5:45

bench5:47

and then we subtract the coordinates.5:48

OK and the length of the bench is.5:51

This was every coordinates mine, this was average coordinates,5:56

but that seems a very long winded way of doing it. But it's6:00

very precise. It's very and it's precise enough that we can6:03

really think, think through what what happens here.6:07

It's over. It's over complicated for this further set of6:11

situation where the bench is just sitting there. There are6:13

all sorts of other ways we could do that.6:16

What about the case where the bench wasn't just sitting there,6:19

it was flying through the room.6:22

OK, so it is zooming along6:25

at some relatively speed.6:28

How then6:30

do we measure the length? What is the length of the bench in6:31

that sense?6:36

And there's a variety of ways you could think of doing that.6:38

But the way that hangs together, and the way that it is6:41

productive for relativity is this we do basically the same as6:44

we did before.6:47

So imagine you're all sitting where you are6:50

and the bench is moving, moving past you.6:54

OK, so you're standing clear.6:57

And as before we say, OK, everyone,7:00

get you synchronise your watches.7:04

At a certain time we're going to look in front of our, in front7:06

of our noses7:09

and as this bench, you fly through the room,7:11

everyone goes7:14

do, do I see a bench in front of me?7:16

And depending on where the bench is, some foot wouldn't.7:19

Some thought would7:23

so we see that the first person who spotted where we saw the7:25

bench in front of them and we see the last person who saw the7:28

bench in front of them and we surprised those coordinates7:32

and that's the length of the bench in this frame7:36

seemed over complicated.7:39

But the point that the crucial thing is at the same time,7:42

OK, so we prearranged what time the observation were going to be7:47

made. Everyone made an observation just in front of7:51

their nose. Do I see the bench or do I not and we collected the7:54

data afterwards7:58

and that the the the reason why we're doing it that way is8:01

because it makes it clear where time comes into it.8:03

Everyone made the observation at the same time in the with their8:07

synchronised watches and everyone in the in the room8:11

has synchronised watches,8:16

OK and and we can talk about the the, the, the process of of8:18

doing that. It's interesting, but8:22

play parenthesis8:26

and that and that of the very other other options you might8:29

think of. That is the way we measure the length.8:32

What we'll discover is that gets a bit more that that that that8:35

has interesting consequences when it comes to8:38

thing moving at Russia 6 speed. So I'm not going to explore8:42

those consequences right now. I'm going to explore them8:46

shortly in probably chapter three or more Lecture 3,8:49

but this is the picture I want you to have in mind.8:52

We have among the people standing on a platform that we8:58

could hear an awful lot of trains going through stations.9:01

People are standing on a station platform. They've marked off9:05

the coordinates along the platform. So there's the origin9:10

of the X axis is at one end of the platform, and there's a grid9:13

on the platform. There are two observers are stationary.9:17

They're standing on the platform and the train goes past at a9:20

certain time. The same time9:24

they observe where the train is, you know, where trained and the9:26

and the two extremes 2. At the end of the train, subtract the9:29

coordinates and that's the length. That's what we are9:32

taking to be the length of the train in the in that in that9:35

frame.9:38

We're going to explore that more in a bit, but I want to log that9:40

with you right now as what we mean we have, we have a we we do9:43

we we mean a very specific thing. We'll talk about9:46

measuring a length.9:48

Any questions about that?9:51

And9:56

and and and and sneak preview. The reason why we are making a10:00

fuss about this10:05

is because it turns out that the question of of of simultaneous10:07

is what is what turns out to be more complicated than we10:11

thought. We're measuring the end of this, of this train end to10:15

this bench, whatever at two points for just simultaneous in10:20

our frame.10:24

It turns out that isn't A-frame dependent thing. That that is a10:25

is A-frame dependent thing. It's not a frame independent thing.10:29

Different frames10:32

have different notions of what is simultaneous10:35

and that's where a lot of the there's a lot of stuff about10:38

length contraction possibly comes from.10:41

So that's a picture of a, I think an engine change odometer10:47

that I I talked to the the10:52

observers and their10:55

distance measuring sticks. I think that was a sort of10:57

imperial distance measure in10:60

available now. The other thing I want to talk about is clocks.11:02

Clocks are nice and simple things. Of course you have one11:08

on your phone, on your wrist, or on the wall.11:11

We're going to abstract the notion of a clock. A clock is a11:16

thing which tells you the time and nice and complicated way.11:20

What is the time? It's a11:24

um,11:27

this is where you know the whole thing can start to go off rails11:29

and people get off go. What is time and all that stuff? Time.11:32

Time is a distance. Time is a distance through time. We're11:36

going to be very simple minded about what? What time is it?11:39

It's. It's11:43

how far from in time from something you have moved. And a11:45

useful image, I think is this thing and this thing is it's11:50

called11:56

Ohh God, what is11:58

And12:01

a tough real log.12:03

If you are on a sailing boat and you want to know how far you've12:05

sailed, then one way you can do that is to a propeller behind12:09

you.12:13

And as it pulled through the water it turns and you discover12:15

how much water you've you've moved through and you can use12:18

that to navigate your position if you have GPS or whatever. And12:21

that's a picture of old fashioned taffrail log, and I12:25

think it is useful to have in mind the idea of a clock as a12:28

taffrail log. It a clock tells you how much time you have gone12:31

through.12:35

And again, this sounds as if I'm making things over complicated.12:38

You know how How is that a complicated notion?12:40

It's. It turns out to be important, and it turns out that12:43

we have to be precise about it12:47

because at the12:50

the question of how much time have I moved through?12:53

Is very straightforward from the point of view of being a clock.12:55

It gets more complicated when you want to step back and talk12:60

about things moving around at speed.13:02

So again I want to lodge that thought in your head I13:05

in in the next chapter and one after that we'll we'll we'll13:11

start to use that13:13

and and see why we have to be so precise about that. So I'm I I'm13:16

this this this whole first chapter is a whole a whole bunch13:20

of of of sneak previews13:23

and you may see mention of the clock hypothesis. The clock13:26

hypothesis sounds grand is just clocks are unison simple the the13:29

they they don't they don't malfunction you we we assume13:33

that clocks are working that they don't get suddenly break13:36

when you got when they got high speed or with their accelerators13:39

That's obviously not true all clocks but the the the clocks we13:43

imagine our heads for the purposes of this of this whole13:46

study are uncomplicated and and and people are careful enough13:49

about this whole area people need to see that13:53

OK13:57

I think almost you're getting good progress here13:59

then one of the one of the last points is as you saw that same14:03

are we in the right place.14:12

No we are not14:14

and I was all I was saying14:19

Yeah14:22

that we can talk of14:24

frames yes see X&Y and a14:27

observer14:32

stationary in that frame14:34

with an order order there and coordinates X&Y.14:37

And we could talk of14:41

another frame,14:45

it's primed with coordinates X prime, Y primed and Z prime and14:48

T primed. And we presume there will be observer, one or more14:52

observers stationary14:57

in that frame14:59

and that frame15:00

is moving at speed V in15:02

with respect to the frame S along the X axis.15:06

And that is that's a setup we're going to, we're going to see15:14

that diagram again and again and again in one other variant. OK.15:17

So get used to it.15:21

That setup is called standard configuration.15:23

So when I say 2 frames are in standard configuration, that's15:27

the picture that jumps into your head,15:30

plus15:34

the constraint that at time zero15:35

time t = 0. That's the time on the watch of the observer in S15:42

the15:49

the origin of the moving frame.15:53

At the origin of the15:57

stationary frame,15:59

the origin of the16:03

moving frame is there as well. So sorry that that makes our16:04

over complicated. The origins coincide at time t = 0 we we we16:08

set the clocks and set the the coordinate systems so that the16:12

origins are the same. At time t = 0. So at time t = 0, T prime16:16

is equal to 0 as well and the true origins are at the same16:20

place.16:23

OK, so that that, that the, the, the, the setup, that everything,16:25

all the equations we end up using not too many of them and16:31

presume. OK. And so16:35

and16:38

there is16:43

basically there's approximately in round numbers, there's16:45

approximately 1 relativity question and it comes to the16:49

exam.16:52

It's Here's a puddle16:54

cast into standard configuration.16:57

Here are some coordinates you know extract from from from the16:59

the some the corners of the various events. Identify the17:03

events. Work out what they're they're those coordinates are in17:06

the other frame.17:10

That's what so many of the exercises about is basically17:12

what the what the all of the exam questions are about. You'll17:14

see that again and again and again17:17

and and and it sounds, you know, why is that important? You you17:19

might ask him. We would. Do we have to worry about the17:23

coordinates of this event in of in two different frames?17:26

Specific that specific problem? No. But that's the the tool that17:30

we use, that the mental tool we use to work out things like the17:34

the the way that Russia's momentum works, relativistic17:40

force, Russia energy and and so on. So that that toy problem in17:43

a sense is the one that drives all the all the all the other17:47

things.17:51

So step one of all of those17:52

that variance of that more same puzzle is draw diagram, put it17:56

inside configuration.18:01

OK. So again, you'll see this lots and lots of times I'm18:03

seeing it now to say it's important make sure you're18:06

you're more or less have that more or less right way up in18:08

your head.18:11

OK.18:13

Yeah.18:17

Um,18:18

what's the definition of that?18:20

I'm also going to mention,18:23

as I said, I I hope I made clear last time the notes and the18:26

lectures are the same material, just delivered in different18:31

ways.18:36

I hope the lecture is a bit more vivid than the notes, but the18:39

the notes are more, you know, more careful than the the the18:42

the the the precise wording is quite carefully thought through18:46

and revise from year to year based on what people have found18:49

puzzling.18:53

So there's a sort of fast and slow stream of the material, but18:54

another source of material is books.18:58

The library has books. Wonderful thing.19:02

The web has stuff stuff on it,19:06

not always equally good, but I will mention a couple of books19:09

which are on the which, some of which are on short loan in the19:14

library and are available for as ebooks.19:19

So if you go I I see that there's a link in the middle to19:23

the A book list which in the notes to a booklist which it was19:27

actually turns out to be out of date last year's. But on the19:30

Moodle you'll find a link to the book list books at the library19:33

or something. It's called and that's a link to recommended19:37

books and including electronic texts.19:40

The Colonoscopy is the A2 course recommended book. It talks19:44

relativity. It's not wrong. I don't find it terribly exciting19:48

the way it talks relativity. And there are and it makes some19:52

slightly19:56

aspect notational changes, but still worth reading to get a19:58

different way of of making sense of this.20:02

Tyron Wheeler is an excellent book. It's a book though you20:06

it's worthwhile looking looking through that. It's a book you20:15

read all of the more or less. I think it's a great book but a20:18

bit of a proposition20:22

that book Rindler if you're getting if stuck in puddles and20:26

but deep subtleties here you know what is time and and so on20:30

then I might well you say go and have a look at that I might in20:34

the notes points will bits of of of renderer could render is very20:38

careful about things like that20:42

it's a book that goes on to well beyond this course but for for20:45

deep things that that that's useful. The book called French,20:49

which is very old fashioned but in portable, quite a good way20:54

and I think quite different from from me. There's a long way of20:58

saying read other things.21:02

Don't know,21:05

I think. I think the way I teach relativity is the best way,21:08

but that's the way it makes more sense to me and I am not you.21:12

I hope you will agree that the way I teach relativity is a good21:17

way, but other views are possible21:20

so I don't I I encourage you to to to to find other ways of21:24

thinking it through. Be aware though, there are some there.21:27

There's more than one routine, not all of them are completely21:31

compatible, and there are a few rotational differences, so just21:34

be a bit alert to that when reading other other sources.21:38

OK, that's the end of last week's lecture21:45

a while ago into Chapter 2. Are there any questions?21:49

Everyone has21:56

any worries,21:57

he thoughts.21:59

OK, I'll take that as a I mean, my essay isn't terribly good,22:02

but I don't think I would put hand up. I'll show, I'll show22:06

it. I don't mind audience participation within limits.22:09

OK,22:14

so22:22

I mentioned22:26

and the last time that the entire physical physical content22:28

of this course is comes into two axioms.22:32

And by physical content by I mean things about our universe22:36

that could be otherwise.22:41

The mathematical statements are, and we admit, a bit of the22:45

philosophy of mathematics here. Mathematical statements are true22:48

if the things that the22:53

are based on are true. So there's a there's a logic to22:57

maths. You can't. If you agree with this statement, then this23:00

deduction from it, you can't disagree with. So those are23:04

mathematical statements.23:07

Physical statements are things about our universe that could be23:09

otherwise.23:12

So gravity, you know,23:14

if he goes me, for example, you can imagine a universe where23:17

that wasn't true. And before Newton, Aristotle did imagine a23:20

universe where that wasn't true and everyone went, oh, that's23:22

fair enough. That's clearly how it works.23:25

So Newton saying23:28

using first law in second and third law, we're making a23:30

statement about the world. He using a statement. This is about23:32

how our universe is,23:35

although it could be otherwise.23:37

And the two axioms are23:39

relatively interesting because the the the physical content of23:42

it is so tiny23:45

it is a large chunk of23:47

of relatively going to learn. For the first five chapters, C23:51

consist of just these two bits of physical information.23:54

And that's amazing. I mean, relatively is is weird23:58

and the most so parenthesis and most physical theories version24:01

one of them when they were first produced by by Newton or Galileo24:06

or Maxwell or whoever.24:11

Yeah, I'm largely an intelligible and if you go back24:13

to the original papers you know you they don't make sense. You24:16

know because folks since then have gone. I know that's a24:18

really weird weird way of explaining it. He had a much24:21

better way of explaining it that that turns out to be a much more24:24

productive way of doing so. So the original version of24:27

Microsoft equations which underlie all of electromagnetism24:29

are unintelligible. You can't read that paper unless you're a24:32

historian in physics basically because it just doesn't make24:35

sense. Why would you even think of it that way?24:37

Relativity is,24:41

I think, almost unique in the Einstein 1905 paper is still24:43

basically readable,24:47

and that's 120 years ago.24:49

Einstein's version. One overactivity will basically24:55

that it you know that's it done24:59

and that's that's very strange. I mean that and and and and that25:01

in a way what made Einstein weirdly good that you got the25:04

right answer from the very beginning25:07

and all this stuff but trains as well everyone talks about trains25:11

through relativity because it's a very convenient. It's a great25:14

example to use. Actually did that first in a popular book25:18

talking about relativity.25:21

It's enough enough25:23

fandom,25:27

SO2 axioms and the consequences.25:29

Objectives, power, blah. And25:35

I want to see25:38

that we're talking about Einstein, Special relativity.25:40

The principle of relativity, which is actually one, was not25:44

Einstein's, but Galileo's,25:48

and in the notes I quote a passage from25:50

and from from Galileo's account which Book Awards and which is a25:57

long party. We describes imagining26:02

being below decks in a ship with all sorts of stuff.26:06

Both. You could roll, roll around small animals, whatever,26:13

and and they all do their thing26:17

and if the if the boat then starts sailing out so it's26:21

moving26:24

at a constant speed,26:26

everything works as before,26:28

Agario said. Ohh, that's actually quite significant.26:30

That's telling something about the world that you can't tell26:33

you're moving26:36

and that is the the the the that that Galileo is relatively26:38

principle is26:42

axiom one. You're like of Einstein's special relativity26:45

that you can't tell you're moving. And so if we say the the26:49

if we see that same thing and we pinned down your intuitions in26:53

the the, the, the, the terminology we're just starting26:60

to use here.27:02

We're saying that if you are,27:04

if you if you describe physics,27:07

describe a physical process like someone throwing the ball27:10

using the coordinates27:15

of some understanding on on the harbour,27:17

the ship goes past someone on the board could be throwing a27:20

ball from hand to hand and it's uses laws work perfectly well.27:24

You know things weren't going to parabola blah blah blah blah27:28

blah. You know how to do that sort of stuff. So you could27:31

describe it perfectly successfully using the X27:35

coordinate along the harbour or or the train platform and the27:38

time when you watch27:41

and the person in the porch or on the train platform or on the27:44

train27:47

throwing the ball from hand to hand could do exactly the same27:48

thing. They could also describe what's happening using Newton's27:52

laws and, but they would be using the coordinates X prime,27:56

which are the coordinates attached to the boat.28:01

And both of these are good descriptions and it's very easy28:04

if you know one of these28:07

to to work out the other one. Because28:09

for this boat instant configuration,28:13

because the frame is moving at speed V along the X axis28:17

at any for any event, the ex prime coordinate of that event28:23

see the observer clapping the hands.28:29

The ex prime coordinate of that is the X coordinate of that28:33

minus the distance that the thing has travelled. This sounds28:36

insultingly obvious. OK, I'm. I'm not telling you anything28:40

sophisticated here. I'm telling you something you are very28:43

familiar with.28:46

I'll say that a lot, A lot of times as well.28:47

A lot of one of the ways people get confused about relativity is28:51

they they hear something like that said and they think, Oh my28:54

God, that much more complicated than I thought.28:57

It's not what we're doing, What I'm doing there in describing29:01

something you do understand that you understood when you were in29:04

school.29:08

But I'm using the terminology of this rather elaborate29:09

terminology of changes of frames and stack configuration to do29:13

it. So what I'm doing is I'm, I'm letting you translate, I29:17

mean you already understand, into slightly different29:20

conceptual rotation. OK, so I'm not telling you anything funky29:24

there.29:28

OK.29:29

And this transformation of coordinates29:31

is known as the Galilean transformations. Galileo didn't29:35

call that, and no one called it that until after people talked a29:37

little bit relativity. In fact, they had to give a name to that29:40

perfectly obvious thing, that perfectly obvious transmission29:43

coordinates. OK, so I talk about the Guardian transformation. I29:46

just mean that the obvious thing29:49

and that is the guardian transformation written out29:52

again. It looks like I'm making a meal of this,29:56

the X coord X prime coordinate. So the coordinate of this event30:01

in the moving frame is. Is that the why part? Prank coordinates,30:05

how high up it was? Blah, blah, they're the same time as the30:08

same the speed of the ball being thrown.30:12

If I threw a ball from the back of the ship to the front or the30:15

back of the train to the front, then it speed in the train and30:19

its speed as viewed by the station platform are going to be30:23

different.30:26

Not surprisingly and and the different by that amount you30:28

know the, the, the, the, the, the, the, the speed on the train30:31

is the speed on the platform minus the speed of the of of the30:34

train. Not a big surprise.30:37

Nice and simple. Too simple even did writing down30:40

sue relative principle. Is is actually one30:46

quick question.30:50

Suppose I have a fancy new cosmological theory that says30:52

the special point in the universe. See halfway between30:55

here and Andromeda.30:58

And the gravity should constant G changes depending on how far31:01

you are31:05

from that point there. So there's a sort of a sort of, I31:07

don't know what you call it, but that that my wonderful wonderful31:10

idea. This solves dark matter. I I see if the graphic content31:14

varies according to distance from the special point31:17

to that idea of a chance of being right,31:21

who is the chance being right?31:27

Who didn't have a chance to be right?31:29

Who had put the hands up yet?31:32

How about we chat between you and I31:34

whichever way you think that could be. Why?31:39

OK,32:14

how many folk would say that idea? Yeah, is a is a gore.32:17

How may we see it? Couldn't work work.32:23

OK,32:26

that the reason it can't work32:29

because if that worked it would violate the relativity32:32

principle.32:36

So that Richard principle that that that that that axiom you32:38

can't tell you're moving had already done some work.32:41

Why did it violate the right principle? Because if32:44

if you if that theory were true, then what you could do is32:49

measure. Measure G, Measure big. Not very easy. You could measure32:53

big and and find a value for it and then you sort of think what32:57

was a wonder about a bit and you measure again. I think I didn't33:01

get right the first time. You measure it again and it's33:06

changed.33:09

You know, Either you made a mistake in your measurement or33:12

you've got closer to this, this magical point in half. In other33:15

words, you'll be able to tell you we're moving33:18

so, so, so there are two principle, says33:22

Ohh. There are multiple ways of of reframing the relativity33:27

principle, and one of the books I point to in the in the33:30

biography is a book about the relativity principle about, you33:33

know, how you can think about this and what and what its33:37

consequences are. Just that one axiom.33:40

So it's already doing work just by by saying that because it33:44

effectively says all coordinate frames are equal, you can't pick33:48

one that's special, and you can't pick one that's absolutely33:52

moving.33:55

So it's useful to think back on that and think33:57

and I think that's that's a very that looks rather silly question34:01

but it's very productive question.34:04

We've got two things puzzle about and if you make sure you34:07

understand why they're principle is it's getting there34:11

and the other thing that I'll that's important is the idea of.34:15

Ohh go this is not I'm gonna get through all through all the34:22

changing have to have to go faster and is34:25

I, I, I I said that we can analyse physics in one frame and34:33

and and equally well in another we'll get different numbers34:37

the the velocity of the ball of the throwing ball will be34:42

different in in in in these two cases but it would be the34:44

there'll be the same you know but there'll be the same34:47

physics. It would be the same equation.34:50

For example, the constant acceleration equations are just34:52

X prime equals34:57

UT plus half a t ^235:01

as you don't recall,35:05

and35:08

the executive square35:10

even apply the35:13

the35:18

gully and transmission to that35:20

I will get.35:24

So that's X = X X prime equals X35:26

-, b T and we end up with. What is it?35:32

And the X35:38

goes P minus35:42

then we say that X = X prime plus35:46

PT equal to UT primed plus35:51

half35:57

a T primed squared. Because remember the the T prime equals35:58

T was one of the other.36:03

You need to go in transmission or X prime is equal to U -, v36:08

she primed plus36:15

half a36:17

T prime squared.36:18

So what I've done there36:21

is I have changed frame,36:24

I change coordinates using the Galilean transformation36:27

equations. I've gone from the description of this accelerated36:31

motion36:35

in the platform frame36:36

or the harbour frame whatever, to the description of the same36:39

motion in the36:42

train frame and I've got an equation which is different36:45

because it has a different speed. Here I have the same36:50

form.36:52

In other words, the explanation of the acceleration acceleration36:53

equations work just as well in the 2 frames. It's as if I just36:58

swapped added primes to everything37:02

and that looks what you're going. You know what the why37:05

that surprising.37:09

It's not surprising because you you've been you have you intuit37:11

quite a lot of the principle. But the point being that the is37:15

important here is that the description of of the physics37:19

that's happening as described by an equation in the platform37:22

frame37:26

and the description of the physics that's happening as37:27

described in the37:30

train frame37:32

are the same.37:34

The equation has the same form, the number of different, because37:35

the velocity has picked about a term from the speed of the37:40

frames.37:45

But the form of the equation is the same, and that turned out to37:46

be a. That's your first look at a deeply important principle if37:50

you're going to do general activity in 4th, 4th or 5th37:55

year. If you stick with this area,37:59

then that becomes38:02

the the the principle that guides essentially all of38:04

general relativity, The fact that that the form of the38:07

equations has to say the same in different frames.38:10

The court is basically we are seeing the coordinates you've38:14

picked. The coordinates you pick don't matter,38:16

they're just a calculation or two.38:19

So the next thing that's interesting here is38:24

you've heard of Maxwell's equations. Is that right? Yep.38:30

Is that is that, is that right or is that wrong? I saw some38:35

notes there, but there were. I'm not, I'm not. I'm not going to38:38

ask you questions about them but you've heard of them and you38:41

you very good and they they describe electromagnetism. So38:45

they they unify all of the the electric and magnetic laws that38:49

were developed through the century and that's a way of of38:53

of writing them down. I'm not going to you know that that's38:56

math beyond portable point but they are they are nice macro39:00

creations are great. They were developed during the next39:04

century and they were found very quickly to be, OK, that's the39:07

answer. That's that's how electromagnetism works.39:11

But the problem39:17

which is that the speed of light,39:19

it's sort of built into those equations39:22

and people discovered that if you do39:25

the Galilean transformation39:31

on macro equations and that's a mathematical quite intricate39:33

thing to do. But that's not the point. If you do this39:37

transformation39:40

that what you get afterwards39:42

is microaggressions.39:44

In other words, what that appear to be saying was the macro39:46

equation that didn't work when you were moving.39:50

But what that means is that you can tell if you're moving39:54

because if that were true.39:58

Then you could just do an electrical experiment. The40:00

experiment and if maximum equations work then you're40:03

stationary. If they don't work, then you know you're moving and40:05

that breaks. Breaks the relative. France40:08

and folk were disturbed by this because that's clearly40:11

not right, because a radio still works when you're moving40:16

light still works removing that electronically radiation.40:22

So there was a big problem40:27

at the end of the next century,40:29

and this was highlighted in the very first sentence of of of40:32

Einstein's 1905 paper.40:36

It is known that Maxwell's equations, as usually understood40:39

at the present time, making five would apply to moving bodies,40:42

least asymmetries who should not appear to be inherent in the40:46

phenomena. That's a long way of saying they break40:49

the IT looks like Maxwell tweeted don't work is the40:52

problem.40:55

So at this point there are were four possibilities.40:58

Either41:02

Maximilian is wrong,41:03

perhaps41:05

could try. It didn't work.41:06

One possibility.41:08

Perhaps the relativity principle is wrong. Perhaps you can tell41:10

you're moving in some circumstances. But that seems41:14

very that's not comfortable motion because that seems so,41:17

so, so fundamental to our idea of how the universe works,41:20

pops the Galilean transformation is wrong.41:25

Perhaps the the the this41:28

thing here, perhaps that perhaps there's more to it than that.41:30

Perhaps there's some new physics happening here,41:34

and the answer you will not be surprised to discover it.41:37

Migrations are right.41:40

The relativity principle is right. Is the Galilean41:42

transformation. That's wrong.41:45

And special activity is the new physics that comes out of this.41:48

So this, it turns out, is this bit that's wrong or assumption41:51

that that was how you went from one frame to another. That's the41:55

bit that broke41:58

you know to everyone surprise and horror and and it it42:02

although it's relativity was adopted as the answer and it was42:05

agreed organically the right answer in a remarkably short42:10

time. It was about a decade it took for basically everybody to42:14

to be on board with saying ohh right that that solves the42:18

problem. There were holdouts were a long time and there's an42:22

interesting story to talk about about the whole thoughts, but42:26

the the acceptance of what was in fact faced with42:30

and in that paper.42:39

I think it was on to talk about42:43

example of the sort together with unsuccessful attempts to42:47

discover any motion of the earth related to the light medium.42:49

And this is the idea of the ether, because with one of the42:52

ways of making sense of Maxwell equations and undergoing42:56

transformation would see our maximum speeds only work in42:59

this. There is a reference in an apparent reference frame, sort43:02

of which is this idea of the ether, which is the the thing43:06

that that electromagnetism wiggles in, in the same way that43:10

water we wiggle and water43:13

we waves on wiggle in ether and had strange properties. We43:16

didn't really make a lot of sense. But there's another long43:19

story there. But it was experiments such as the famous43:22

Michael Small experiment, which we could, which you may have43:24

heard of but we're not going to talk about. We did try to try to43:27

actually detect that movement in the ether and failed43:30

and failed again. And failed again and everyone was going43:33

well. This can't fail. This can be wrong, but that is what is43:37

being referred to here43:40

and43:44

and what43:47

Einstein. Einstein then in the paper upgrades this principle,43:49

relativity,43:52

to not being just a statement about mechanical motion, but to43:54

say all the national frames are equivalent for the performance43:57

of all physical experiments,44:01

so that it absolutely nothing you can do. It's not just that44:03

this works from mechanics, but for trains going through44:06

stations, it works for all of physics. There's no physical44:09

experiments there, no chemistry experiment, no biological44:12

experiment, no social experiment that you can do that works44:14

differently when you're moving. And that's a very bold44:17

statement, is saying we're not talking about Marxism here.44:20

We're not talking mechanics here. We are talking about all44:23

of physics.44:26

Umm,44:31

this. This will be a point to to to to to, to, to finish on.44:37

So I'm44:41

I'm standing here with a friend moving past me in a rocket. So44:46

some some huge speed. Let's see.44:49

Very high speed.44:51

And I observe her watch to be ticking slower than mine.44:53

Let's see it's a good it has magically broken because of the44:58

rocket. But I unless don't worry how we observe that that watch45:01

taking slower because that also the complicated thing. But one45:05

way or another observed that what should be moving more45:09

slowly than mine,45:12

you just I'm going to tick, tick, tick. She's going to tick45:14

take, take.45:17

No.45:19

These windows are too easy.45:20

She could look and see my watch,45:22

OK, and she would she see my watch moving faster than hers,45:25

or slower than hers?45:30

Who says you might watch moving faster than hers?45:33

Who says you see my watch moving slower than hers?45:36

Who had put the hand up yet?45:39

I'm not. I'm not taking notes of Hubert the hands up the the45:43

reason I was able to put the hand. But I want you to guess45:45

when we're another just just to write the company self. So in45:48

the last couple of minutes,45:50

just talk to your neighbours about what that should be.45:52

Why does it bother?46:17

Yeah.46:30

OK.46:33

Think of the question again.46:37

Whoops,46:40

books.46:43

I watched the movie slower than mine.46:47

Who would see? She sees my watch moving slower than hers.46:51

Who sees? You see my watch moving faster than hers,46:56

fairly evenly split. There46:60

the answer is47:02

that although there's clearly quite quite interesting to47:05

analyse47:08

and47:09

the watch must be moving slower.47:11

So I see her watch moving through the main,47:13

and she must see my work moving slower than hers, because if she47:16

didn't,47:19

then47:21

one of us would know which one was moving47:22

and that we find the right principle. And that makes no47:24

sense. I mean, come on, how can my watch moving faster than47:27

hers? And how Watch moving faster, faster than mine47:30

That's so. So we don't. We have. We haven't even got the second47:34

action yet.47:38

Already the47:40

first. The first action was telling us this extraordinary47:43

thing about time47:47

that that we can, the two of us can make observations of each47:49

other, other clocks, and come to opposite conclusions. But what's47:52

happening47:55

and this sort of thing is why people go no brothers can't be47:57

right. That doesn't make any sense. Oh my God, it does. But47:60

you have to be quite careful. But what questions you're48:03

asking? Because I said let's not worry about how we measure the48:06

measure. How her watch.48:09

There's a lot of missing out there.48:12

OK48:13

and and and so it's it's when we ask the question what do you48:15

actually mean by measuring the other person's watch48:18

that when you discover you can step through this and you can48:22

come to something that does make sense and hangs together and and48:26

that's what we're going to be doing in starting in chapter 3.48:30

I have the other half of this chapter to go, but I will be, I48:34

think displaying myself about taking more. So I'll see you48:38

next Wednesday, next Tuesday.48:41