Hello, I'm Norman Gray.
You are a 345 as we have,
just fairly conclusively established.
We're all back to face face teaching.
It's been a very hard couple of
years and I think some of you will.
None of your third years, is that right?
You're all 4th and 5th years, right?
So all of you will have had at
least one year at university.
But your second and third years
maybe have been a bit complicated,
but well done cleaning,
making it through one of some of you
I think I may have taught special
relativity to in a 2 two years ago.
Yep, I'm seeing some nods.
Good, good, good. Then you are you.
Some of the diagrams you will
will be familiar to you.
OK, without too much further ado, no.
Before I talk about that,
what I do want to do is mention
as Professor Contar did,
the Moodle and a couple of things
that are on the relevant page.
So.
Um.
We go there, we go there. Umm.
Well.
No, I haven't forgotten my.
OK, right, as long as equal 5.
Cycle B. I want to draw
attention to a couple of things.
First is there's a folder of lecture
notes there which contains lecture notes.
A whole little more say
about these in a moment,
so I'll come back to that.
Very shortly, I also want to
draw attention, however. 2.
Padlet. And padlet is.
And. Either to show them to describe
it's various bits of fragments of
questions if you have a question.
Double click on that. Ask a question,
but a bit of extra content context.
It's all anonymous,
have no idea who's asking questions.
I will sporadically,
but not entirely reliably check that
and trying to update the questions
that are there or just ask me.
This is for the shy.
For those who think they are
slightly complicated question,
they want to to to to work
out what how to get down.
So all all modes of asking
questions are good. Umm.
There's also a Microsoft Stream channel.
Unlike previous years,
that's not a core part of the whole thing,
but there will be one or two things there.
I do have from previous years
some brief 5 minute videos,
actually overviews of the various
parts and I will post them there.
I think they're quite useful just
to to be useful to let you getting
over all impression of what the
the uppermost part is going to be.
So we'll post them there,
but that's not a big going to
be a big deal for this year.
OK, let's move away from the middle.
Get back to the slides.
I don't have a a bigger big thing
with slides because the other
pages ohh I'd mentioned ESR.
I I think you should be able to see that
my A2 like special election notes you might.
Enjoy those.
If you if you want to see those you
can't see them then let me know.
And.
Now before I go on to the onto this,
I'll say that the the way I've developed
of teaching this and added at the SSR is.
Feeling specific?
I do put the lecture notes,
which are, you know,
quite a lot of text up beforehand.
And what I want you to do is
look at those beforehand,
not read them through and
digest and fully understand,
but look at them to get an impression of
what's coming up so that in the lecture,
the lecture isn't a surprise.
The the notes there are spoiler
alerts all the way through.
You know they're there for you
to to to not be surprised when I
start talking something, right?
The lecture is the main event.
That's me explaining it to you.
I will. I will often allow details.
I'll say the details are on the notes,
or read about this year,
or read this in this book.
I'll aim to communicate the
main idea in the lecture,
but I won't always fill in the details,
because after the lecture you'll be
able to go back to the notes and go.
Now I see the point.
So it will be possible I think.
To just go to the lectures
and ignore the notes and pass.
It would be possible, I think,
to ignore the lectures and just read
the notes and pass, but it'd be harder.
In both cases.
The expectation of the plan is that
the two can complement each other.
There's not a huge amount of
stuff to learn in this course,
it's just what there is is quite hard.
And it's a case of understanding
rather than accumulation of knowledge.
And that means a couple of things.
It means you do have to think.
It means you do have to assemble
an understanding from the various
resources that are available.
And it also means you can't cram it all
at the end. That really doesn't work.
I mean, with some courses, you know,
OK, don't do that, but you know,
you can sort of get away with it.
And this one I will Part 2 bills on part one,
Part 3 builds on Part 2, Part 4,
absolutely build on part three.
So if you're not, you know,
getting some sort of idea of what's going on,
it will get progressively harder.
OK. Um, I do record the lectures.
Audio, however, that depended on
batteries and me not accidentally
turning the recording off and stuff,
so don't depend on that.
I'll put those up once I sort of
got a couple of technicalities,
but so there's sort of revision aid rather
than as something should depend on.
I'm getting going with the the
actual relativity in a moment,
but the last thing I want to mention
in a sort of pedagogical sense is
that although it's a couple of of
pedagogical fashions that are date,
I do like aims and objectives.
And the distinction to them
between them is clear to me.
In the aims are the point of the
course that the things that the
why you're doing this course,
the why I'm teaching it,
that the things you'll remember
after the course is finished,
you know, in years to come.
And there are things they appreciate,
understand.
Quite general, quite general things,
quite high level things.
The problem, that's the point
that that's why you're doing this.
The aims.
The problem with that is it's easy to say,
Oh yes, I understand that,
I appreciate that, but.
You can't do an examiner appreciation so.
There are also companions to them,
not a one to one relation,
but companions objectives and
these are the party tricks.
These are the things that you can do.
They are explained, quote, explain.
There are things you can do,
which are the sort of things
you can do in an exam.
So when I write the exam,
I have the list of objectives in front of me.
And the exam is basically conformant
or consistent with those objectives.
Not a sort of precise 1 to one thing.
But if somebody is clearly not
covered in the objectives,
then I think that's for the.
If it's broadly mentioned, you know,
alluded to in the objectives
then that's in there possible?
So that's the distinction for me.
So these are not exciting things.
But the things you can do and the
exercises that are attached to the.
To debate,
parts are keyed fairly precisely
to these objectives.
OK.
I think I'm about to start
doing relativity now,
so the administrative and
pedagogical things are over.
Are there any questions about
where we've got to so far?
Any questions, anxieties, worries,
neuroses or other dislocations,
psychological dislocations of that type?
None of the English people admit to OK.
That's not necessarily good.
I mean,
I like questions because the
questions are good because they
help me understand if I'm going
too quickly or too slowly.
So I like questions.
OK.
Still nothing. OK, well,
that's that's that's good,
that's good, that's good. Right.
You've seen this before.
This is Newton's second law.
Force is proportional. It is.
It is proportional to the
rate of change of momentum.
You're familiar with that.
That's not wrong.
We're going through,
we're more safe with that,
but that's that's good.
And I did have the other one,
I thought another version of that.
The key thing about this,
from our point of view is
that it's a vector relation.
It says that the force vector is.
Proportional to the rate of
change of momentum vector.
And you say, well, yeah,
that's is that that's not really
a big it is a big deal because
that is a geometrical statement.
It's seeing these are these things
have a magnitude and A and a direction,
and that side is proportional to that.
We're not talking about coordinates,
we're not talking numbers here.
Just saying that's proportional
to that is a physical statement.
You can imagine a world, but that's not true.
A science fiction world, but that's not true.
But in this universe, that's true,
and that's a very big deal.
And it's true whatever the coordinates.
Either you pick. I mean it in most cases.
And in most cases you you'll solve that,
but using Cartesian coordinates.
It might be that the case where you
solve that using what you know,
fair polar coordinates and the masks will
look very different in each of those cases.
Possibly very hellish
complicated one of those cases,
but the basic geometrical
statement is the same in both,
and that's what we're holding on to
all the way through this course.
And indeed, that is the principle that
that that statement is the principle
of general covariance, which the grand
we have seen what I've just said.
Which is that all physical laws have
been under coordinate transformations.
All physical laws must look
the same or be the same.
Independent of the coordinates
you choose to describe them.
So it doesn't matter if I choose Cartesian
coordinates to do to to to work out the
consequences of F equals of people,
city or or use spherical pullers,
they're just numbers.
That's just maths the physics,
the physical laws must be independent
of the choice of coordinates.
You think and and that doesn't
sound like a big deal.
I mean you think, well,
that's sort of could be us in next mean.
That's certainly been my experience in in
in the physics I've learned in the past,
but it's not just a nice thing.
It turns out to be massively important,
and Einstein beast the whole of GR on that.
That's that's where all of GR comes from,
that statement.
The principal general comedians the
demand that that be true is where
everything else is right falls out from.
Um and? And the principle relativity here,
I don't see anything that I
forgot to say here. Yeah.
And we can combine that with
the principle of relativity.
Which is that? That's not I mean,
I illustrated that with F equals PDT using.
Basically accommodation
first and second laws.
It's not just through mathematics or
mechanics, it's true of all physics.
So Einstein here is saying, you know,
we the principle companion applies to
all of physics, not just mechanics.
What we'll we'll talk about mechanics
most of the time because it's
straightforward talk about and we
can all understand that very well,
but it's placed all of physics. And.
What? Although the although the
equivalently but not obviously identical.
It is a. It is equivalent,
but is that the link between them
is not trivial.
No experiment performed wholly
within one local national frame.
Can detect its motion related to
any other local natural frame now?
The words local,
inertial and frame are all important there.
A-frame just a coordinate frame.
It's. It's a coordinate system.
It's an XY and Z. Very little he's been.
A Freeman just coordinate system.
It's a choice of where your origin is and
where and where the axes are. Inertial.
From your recollection of special relativity,
you will remember inertial natural
means it's something we're using.
Laws work basically.
We'll have more to say over that is
what we'll we'll we'll complicate
that a little bit in a moment,
but that's basically the same idea
or most of the same idea as you've
as you know from special activity.
And local is important because
what we're talking here is the
local part of our national frame.
We're not talking with things
that are far away from us.
Because and and that will
become more important later on.
Um, but the word local is is meant to
mean within a short distance of here.
Now, what does short mean? Short?
Depending on the experiment you're doing,
the moment you're doing should be a meter.
It could be a party,
but the point is, it's not infinite.
And it also means short in terms of time.
Could be 10 seconds or it could be years.
Or millennia, whatever.
So the the point is it's it's it's a bounded,
the bounded box within which your your,
which is your local and national,
the local part of your national frame.
And this says in that you can't tell.
You can't tell which of the of the of
the base bottleneck frames you're in.
That is equivalent to the thing you
might remember from special activity.
You can't tell if you're moving,
but this is more profound than that.
And so. Yeah.
Are there any questions at that point?
OK.
And.
Another thing that is unexpected here,
which could drop in here but and
and leave slightly hanging.
No, I'm ugly saying,
but we're going to pick up again,
which seems to be unrelated to
the the two statements I've just
made is the strange business of
inertial and gravitational masses.
No. You don't love gravitation?
That's F = g Big M / r ^2.
Says that the gravitational force
between two objects is proportional.
To the gravitational mass of those objects.
With the gravitational mass, that's the
amount of gravitational charge you like.
That's the amount of stuff that
the gravitational field acts on.
OK, so that's a it's how.
How? How? Coupled based?
How coupled with gravitational
fields is this mass?
And the government voted proportional to.
Accelerate the acceleration.
Is proportional.
Invest proportional to the mass,
the inertial mass.
So if you push something.
Then how much accelerates is a
function of how inertial it is.
A heavier thing, I think with
more inertial mass will resist the
pushing more and accelerate less.
And that inertial mass is is that is
the amount of resistance to being pushed.
Nothing to do with gravity.
It is resistance but and and and and and and.
Galileo's contribution to
physics was essentially walking,
discovering that and and Newton
something tied that down
mathematically in in existing laws.
But girly with this business of
dropping things over the Leaning
Tower of Pisa should this is what
you thought you were showing.
But what he did show was that
this gravitational mass.
And this inertial mass?
Are precisely proportional.
So if you double the amount of
resistance a mass has to being pushed.
The only way of doing that?
Also double s the coupling
to the gravitational force.
Even though these two things have nothing
to do with each other as far as we can see.
You know what?
What would you've never thought of that of,
of, of them being distinct.
But in fact they have nothing
to do with each other.
And yet they are precise,
proportional to each other.
And This is why you've never heard
of these terms of gravitational mass,
international mass?
Because I saw some of you looking so worried.
Am I supposed to know the national mass?
No, you're not.
Because it's never been used before?
Because I introduced here in
order to remind you that that
distinction doesn't matter.
But there's no explanation for that.
In your in Newton physics.
That's a completely unexplained
thing in Newtonian physics.
And and and I'm not sure
it's a question of history,
of of science and how how much
Newton was worried about that.
I think there were some things Newton
didn't like the law of universal gravitation.
He thought, he thought,
that can't be right.
But the there are physiological
problems with this,
with it from his point of view.
But I don't know if he would
worry about that.
But he should be because there's
no explanation for that.
Insurance physics.
So that's a puzzle.
How do we approach that?
Imagine you are in a box.
A special out in floating around somewhere,
very far away from gravitating masses,
and in there there's a
bit of mechanical stuff.
Watch, but of biological stuff.
Some, some, some,
some other bits of energy,
photons and so on,
and they're all wondering they're
floating around because you're floating
well away from the application masses,
you're just floating around.
And if you push him off the wall,
you move in a straight line at a constant
speed until you hit the other wall.
Nuisance laws work.
In other words, they really, genuinely work.
I mean you.
You push him off and you stay.
You move in a straight line at a
constant speed until until you hit something.
And so on.
So Newton's laws work there.
Good. No, I trust no one surprised at that.
OK, so you, you've got that picture.
I'm not telling you anything new here,
I'm just reminding you that that that's
in fact you do think of that picture
and see that makes that makes sense.
No, we put our.
A rocket under this very big rocket,
but a small rock. And we push the the box.
We don't push things in the box,
we just push the box. So what happens?
The people stay where they are,
or people in the and and and the
and the clock and the and the and
the pot plant stay where they are,
but the box moves around them.
And they don't.
And what we're doing this
is there's no air in this.
Rain is complicating,
but the box will just move around
them until they hit the ground,
until they hit the bottom surface,
and then they'll stay there
and they will accelerate at
the same rate as the box does.
That's not surprise.
So, and if the rocket is designed
to with the right force,
then it can make accelerate
this at 9.81 meters per second
squared and even inside will go.
I can't tell good Earth or not.
And they will be uncertain.
I like to think what experiment you might do.
They would let you tell
the difference between.
Being in that situation and being on Earth.
You would think of what an
experiment that would be.
How would you tell you where you were in
the situation rather than being on Earth?
The only one I can think of is having
someone in this side of the box,
that side of the box with
very precise inclinometers.
And if you're on Earth,
then they would sleep.
They point toward the center of the.
And if they were in this situation,
they point they both point down,
but that wouldn't be a local frame.
Because the word local here,
and we're talking to the local frame,
the word local means it's small enough
that you can't do that sort of stuff.
That your experiments aren't precise
enough to be able to detect that so
within the bounds of your of your
experiments that you can do 2nd
order effects like that you can't,
you wouldn't.
I defy you to think of any real term
that is with that and be on Earth.
And I'm confident you will not be able
to come up with something because
it is a foundational principle,
GRR, that you can't.
That there is no difference.
Between that and being on Earth.
That the.
Experience of being accelerated at
constant speed and the experience of being.
In our.
And St. Gravitational field
are equivalent. Not just close.
Not just the same, but equivalent.
They are the same thing.
It's what it seems.
OK. And that but and that's and
that's a physical statement,
that's that. You know,
this is called the equivalence principle.
Uniform gravity.
I will put these slaves and there's
nothing in these slides isn't in the notes.
These slides are just here.
So I've got something to Peter
in front of and talk about,
and I will put the size up in the lecture
notes folder just because why not?
But but I encourage you to write things down.
Writing things down is engaging and
putting things in in the notes.
The equivalence principle.
Uniform gravitational fields that you
know that's just straight up and down,
not ones which are pointing inwards,
are equivalent to frame that accelerate
uniformly relative to an. 2 frames.
There's that word national happening again.
What an inertial frame.
An inertial frame.
Is.
One like that.
It's one where Newton's laws work.
Now there are more elaborate
way of of putting that,
but in that frame Newton's laws work.
If he goes a precisely right if
if you leave something, it stays.
If you push something,
it moves at constant speed.
So that's a national,
you're prototype national frame?
And uniform graphical fields are equivalent
to 1 accelerate relative to that.
So. Um, where we going with this next thing?
So open parenthesis. And the
critical general comedians is?
It restricts the IT it
it had critical content,
it has physical and mathematical content.
It's not just a beautiful philosophy
that we can think about and and
and debating the pub it had.
It had consequences.
It restricts the category of mathematical
statements that we prepared to countenance.
As Portal scriptions of nature.
So if you have a theory which violates
the equivalence principle, is wrong.
You would have to think about it.
It's just wrong because the
ethical principle is true.
Then it supervenes on on those,
so it restricts what you can see.
The relativity principle.
I just mentioned picks out
inertial frames as special those
frames like the floating box.
In which nuisance laws work.
Are special.
They have a special status and
we'll carry on talking with them
again and again and again they are.
There's things we could say about
them that we can't see other things.
And the equivalence principle further
constrains the set of the set of, of,
of, of, of these special frames by.
Seeing that those frames.
The acceleration business
for the constraints what the?
What the frames can be.
I I forget what the for the quite what I put.
Why I've written that thing
probably in the notes. Right.
And so I'm going through the course,
talk about things, certain things,
physical statements.
And what I mean by that.
A physical statement is a statement
that picks out one possible universe.
From all the ones you can think
of mathematically or in some sort
of dream state and says this,
one of all the ones that
mathematical insistent is ours.
Other universes are possible.
They're not this one.
And so physical statement is a
statement that says the universe
could be otherwise logically,
but it's not.
And when I see physical statement
that that is that notion that
I mean there are plenty of
mathematical statements in this.
Mathematical statements just follow
from what came before and they can't be
otherwise other or else logic is wrong.
Physical statements could be otherwise.
There's a contingency to physical statements,
and there is,
and that's where the physics is.
So that's a good point.
At which you mention.
Some of you will be doing maths,
some of you will do maths, yes.
And you do months.
Well, if you OK so.
This is of course in interactivity.
It's course we therefore also
covers different geometry.
It's nonetheless a physics
course or astrophysics course.
It's not a maths course,
and so we will be sloppy.
From the point of view of map additions,
there's gracefully so.
But we don't care because we're physicists.
And everything's done.
Being a physicist means the
entire universe is analytic,
that that's being a physicist means.
It nonetheless, nonetheless it is,
I will mention just parenthetically to
that and they take mathematical course,
so, so yeah, hold on to your,
hold on to your seats.
So close parentheses.
Would you do badly OK?
Let's go back to this floating box.
So we're going to know is 3 thought
experiments, 3 things that we.
Fancy scenarios which we can analyze
using what we've learned so far and
and discover the physical content.
The consequent consequence of those
statements, we're back to the
to the box floating in in space.
On the observer floating in the middle.
And we. Flash a light bulb
on one side of the box.
And we have a detector of some type,
perhaps another observer on the
other side of the box and given
that this this light is pointing
across the across the box,
then you know of course it's going
to go straight across the box and
be detected the same distance down.
No surprises there.
There are no surprises there, OK?
No, let's do the same thing.
But in our box which is falling.
No, that box is in free fall.
And I think the first time I've
mentioned this that phrase. Um.
I think there is a link to
to to to to that there's a.
There's a site link of I think
I've forgotten from the note.
Check the notes for the for,
for the for the little bridging movement,
but the. The point here is that we
are also taking things just that's it,
things which are. Things which are
moving only under gravity like.
Which is floating out in a way
more gravity gravitating bodies.
They are inertial frames.
They are in freefall, so-called.
Moving all into gravity and they we
are saying are also inertial frames.
I'm sure there's bridging a little
bridging statement I I've skipped
here that doesn't matter. So this.
Falling box and imagine it's a
lift and the keeble's been cut.
It's falling, in other words,
moving purely under under control of gravity.
And so it's a national frame.
And the equivalence principle says that.
Situation there with the box
falling down the lift shaft.
And the people in it is equivalent.
To being in the national frame well
with gravitating sources, therefore.
And.
This person can't tell the difference
between these two these situations.
They can't tell which inertial
frame they're in.
Therefore,
when the they they see this that this light.
Yeah, shown across the across the box.
What they see is this.
And for the late Good Cross and.
Hits.
I'll I'll little bit don't know
from the top as you'd expect,
but the point of view someone
standing by this watching.
In horror as this lift shaft plummets
to the ground and hoping that this
person is paying attention to their
relative lectures and taking notes,
hopefully very quickly.
The light takes a finite time to cross.
Not much, but a finite time to cross and so.
The would it reach his,
the other side will be slightly lower.
By the time the light gets there.
It must get there because
the observer in the box,
if it didn't get to that point,
that expected point,
which is the same distance down from the top,
then this person would tell
that something was missed.
So it does get to that point,
but from this person's point of view.
That point is lower than the starting point.
In other words,
the light has followed a curved path.
And the only things we've used in
that argument are the equivalence
principle and the relativity principle.
In other words, light is bent by gravity.
It has no mass.
But it's still bent by gravity.
And that's strange.
But that conclusion I mean it.
Which is true.
But that conclusion comes only
from the physics we've learned
in the last half hour.
Um. I don't change to work through this,
but I I I have a few of
these quick questions here.
No, no, I will ask this question.
The question just this point in
following lift. I am a spring gun.
Just do not have a light.
Not a relativistic spring gun,
just an ordinary, you know.
Charles Toy across the lift
intend to hit the bulb.
I want to hit hit the bulb
which is BEM above the bulb.
Should aim directly at the bulb or should it?
In below the bulb, who would see a?
Who would say be? Who say see?
Correct. OK.
And you've all been paying
excellent attention more than.
This isn't just a a story about light,
it's a story about things falling and
you're not being able to tell the.
The difference?
So there's no difference between
this and do the same thing with
the weightless cabinet in orbit.
OK, next.
So you have a mass.
Here. And you? Drop it.
And it drops it acquire kinetic energy from
transitional energy into kinetic energy.
So it ends up down here. With.
Oh oh, C is 1. OK, just like in
special relativity as we use natural units.
I'll have a little more to that in a moment.
I better hurry up or I won't get to that bit.
See series one. So E is equal to M, right?
So the energy of this of of this
thing is equals MC squared C is 1.
Andrew there. When it gets down to here,
the energy has gone up by the amount of
potential energy loss in going down here.
OK, then we take this slightly
more energetic mass.
And convert it into pure energy.
That's kinematically impossible,
but energetically perfectly reasonable.
OK, and we send that photon.
You know the energy equivalent
of that mass back upwards.
Until it gets to the top here
itself with energy and the energy
E primed at the top there no.
Either we have invented a way of extracting
free energy from the universe, or.
E is the same as M.
So that this must be a closed cycle.
Or else we've got perpetual motion machine.
In other words, what that means is
that photon which starts off with
energy E here which is bigger than M.
Ends up with energy E prime,
which is the same as it was a photon
climbing through a gravitational field.
Loses energy. Simply because of
that could have special activity,
an argument and and because yes.
So that's another thought experiment that
that that that that that says interesting
physical things have to happen just
because of what we've learned so far.
And. Let's do that twice.
So this is a setup called Shields photons
because some someone Shields you use
this example to as part of someone
as an argument in the 50s I think.
So this is a Minkowski diagram
Z the vertical direction.
That way and time in this in this direction.
And we do the same thing as
in the previous slide.
We fired a photo on upwards in the Z
direction. And it loses energy. OK.
In which it goes from frequency F energy HF.
To frequency F prime and F probably
because F prime at the top.
OK, just like what we said before.
Then we could hit.
Wait, and periods?
We'll do it again.
OK, so we do the exact same thing again.
We send a photon of frequency F up
and it arrives the top frequency.
Different frequency,
a lower frequency because that's lost energy
by climbing through relational field.
So that time difference. Is north over F.
Obviously because we we
had that many periods.
This time difference is also
the same number of periods.
But the frequency is different
so the period is different.
So the time interval between B&amp;B primed.
Is not the time interval between A&amp;E Prime?
You're entirely surprised at that.
What that is telling you is that isn't.
This isn't a parallelogram.
The. You know the the the
distance is in both cases,
but the the time distance on opposite of
the parallel or parallel is not the same.
In other words, this is not a Euclidean.
Um. Uh. Surface is like are
you clicking in space now?
It's because of space.
We didn't expect it to be anyway,
but the the the point here
is that just with that.
Gravity redshift argument.
You can just,
you can just discover the first hint
of that and there be lots more of that.
OK, I think that's. Well, things to see. Um.
I have a quick question with that which you
can look at in the in the in the notes.
Yep. And another one to we don't have
time to do have have votes and and and.
This is also an important diagram
which you will see again in about.
10 lectures.
And it's two objects. And.
Well up above above the earth.
And they both fall down towards
the center of the Earth,
direct towards center of the Earth.
But this frame is big enough,
there's not a local inertial frame,
so the two balls will fall directly
toward the center of the Earth.
Now they're both. And if we fall,
they're both in inertial frames locally.
But if you ask what's the separation
between them, what's that sigh.
Distance?
Then you discover that the second derivative
of Phi with respect to T is non 0.
So the second derivative of the
position is known as zero.
But they're not accelerating.
So the the the the they are in freefall,
so they are non accelerated frames
and yet the second derivative
position is is known as zero.
What's happening here?
What's happening here is the secondary
position is just a coordinate number.
It's just a number.
Which is not the same as being pushed
in the back and being accelerated.
So I will aim to keep the sanctions separate.
When I mean acceleration,
I mean pushing the back.
I mean something that you can detect
locally and unequivocally and absolutely.
And there is a difference between.
That, and I think we've been different.
And the reason why this happens,
the reason why you can tell
why if you if you were,
if you were these two people in
radio contact with each other,
you could say,
ohh,
we appear not to be in our
uniform gravitational fields.
It's because this frame is big
enough that it's not local.
So there's a a tidal effect
so-called happening here,
which lets you detect that
you're not in in this case.
There is an international frame
which covers both of these.
OK, this is an important slide
because it's meant to be reassuring.
So that's the end of of
the thought experiment.
A few a few final remarks.
That's the definition of differentiation.
That you are very familiar with
because you learn about it in school.
OK. The derivative of F with respect
to X is the limit of F X + H -,
F of X / H as you take that H to 0.
You really understand that?
The will be doing the same a lot,
the part, but a large part of the
mathematical structure of this course
is learning to do the same thing.
In a curved. Space-time.
And the the 10 lectures gets you to the
point where the where you learned that
mathematical practice like I'll just do
that G2 which comes next semester is OK,
what follows from that in in physical terms.
So this first semester is
basically learning how to do that.
Intercourse.
Beasting and it's difficult because.
In this case, it's easy to know to to
think about what F of F at a different
point is and how subtract it it.
It needs to know what what
dividing by H means.
In a country's time,
both of those things are tricky,
so we have to learn how
to say the same thing.
But it's the same thing happening.
It's fundamentally the same thing happening.
It's just it will look hellish because the.
The coverage does that does that for you.
In terms of overall structure,
this Part 1 lecture one almost done it is.
Setting the scene,
saying why there's a problem,
say what the problem is.
Part 2 is introducing tensors,
mathematical structures that you
may have somewhat across before,
but have always seemed a little
bit exotic and and you don't
necessarily have much to do with them.
They are vital to an understanding
of of of generativity.
Part three is letting her to
differentiate those sensors.
Which is each of them,
one might think,
but but still not not easy.
And then part 4 is actually using
all this mathematical apparatus to
do what Einstein did and describe
a theory of gravity in these terms.
So today's been physics.
The next 7 lectures were basically maths.
The last few lectures are back to physics.
So say bye to physics for seven lectures.
We will look forward to coming back,
but that's what's happening.
At the last thing I'll mention natural units.
I've lost more than natural units.
Natural units are the units you
choose when you say C is equal to 1.
So you measure distance in meters
and time in meters.
A meter of time is the is the
light meter is the time it takes
for light to travel a meter,
and in those units in light meters,
light meters in meters per light meter.
The speed of light is a nice,
easy to remember one and I have noticed it.
You will find stuff on the
way by have a natural unit.
How terribly confusing.
Oh my God,
awful.
But it's just a matter of picking the right
units in which back to the sea disappear.
And I think that's the
last thing I've got to say.
And I know you have to rush
off to gallop around the that
you'll be so fit this semester,
galloping around the the, the,
the the campus trying to find things.
I have a section in the notes about reading.
There are many good books on
relativity on general relativity.
This course is highly compatible with shoots.
Highly compatible said.
I'll even refer to it as the
same overall set of ideas,
or so.
It's it's a good book to use cattle
is very it's it's slightly different,
and that's a good thing,
because a nice contrast,
it might treat you better.
Rindler is very old fashioned as far
as the treatment of generativity goes,
but the first half of that book is
really all about explanation of
this of of subtleties and the things
you three different subversions
of the government principle.
Rindler knows all about the physics of GR.
Little thought Wheeler.
Great big doorstop.
Wonderful book which irritates
the hell of some people,
but good and and some of these
books are on available at that URL,
which in the notes which you can
find at the library, there are.
There are electronic versions of some
of these books and you might be able to.
The wild. OK, I think that's the end.
It better be. Yes it is. I will see you next.