Hello everybody this is lecture 11 as planned.
Little bit behind schedule, but not too much
was to finish off Chapter 7 today. There's just a little bit
left to do an important bit, but it we can finish that off and
then move on
to talk about General General Relativity. In the second-half
of this lecture and in the remaining 4 lectures of this sub
course
I'll first mention I see that there are questions appearing on
the padlet as good as the one that appeared this morning. I
answered that I take the point about handwriting but the goal
is to show the maths on the on the on the scribbles rather than
you know how beautiful notes. I have in the past
put up sky and diversion of those scribbles but the folk
last year the substitute later on committee said ohh there's
too much stuff in the middle. Oh my God, I'm sorry I said not to
do that, but if folk would like would have a different opinion
this year, I can scan those if that would be useful or if that
sort of not really necessary,
you wouldn't feel strongly about that. I mean me.
So where we are now is
getting on toward, well, finishing off chapter six and
seven when kinematic endemics and
moving on.
Any questions either organisational or where we got
to last time?
Yes,
point would be examinable,
right? I
I'm not. I haven't really thought about that yet. I've
only just finished marking assignment one, right, like at
four o'clock 4:00 last night. So I haven't got as far as that,
but I think in previous years I have.
I I think in previous years I've I've only gone as far As
for six and seven, six and seven. So there's suffering
today. So class is still that's at the end of November 2020.
Third right. Ohh deadline suit.
Thank you. I have to think about that
I I will make a ruling about that shortly. I know when when
as as some point, but I think it would basically be just 66 up to
up to the stuff stuff today but they're not
possibly I'll see what I sent the thing to see, but good
question. Thank you. Anything else there?
OK, let's get going.
OK.
That and
you.
OK Where we had got to
I think was talking about
this
and uh
the
this this collision where if you're if I recall we're looking
at a simplified collision here of two of relativistic party two
things which come in with former mentor
whatever they are and merge into one outgoing object with
appropriate formentor. And we simplify things by saying that
this is going to happen along the X axis. So we're going to
ignore the the, the, the, the Y&Z components will be 0
and these things will be colliding head on into some sort
of outgoing single particle. And what we reduced
last time from the
the conservation of momentum which I said with the other
physical statement that we're making in these lectures was
this table
where the
incoming
velocity
so so the the the the target particle is stationary. The
incoming particle is at nice convenient 1517, so the speed of
light and we watched all the all the other numbers
using the the expressions we have accumulated so far.
And the point is, as we're just seeing the very end last time,
the momenta
are conserved so that you add up the incoming momenta component
by component and you get the the outgoing energy momentum of
particle.
That allows you to deduce the velocity of the outgoing
particle, because it's just the ends up being just the
the X important divided by the you can put it. You'll see the
notes for details.
And
the
masses of the incoming particles are as expected, so that if we
obtained the mass respecting the equation that E squared equals P
^2 + m ^2, which was one of the things we deduced last time. We
discovered that the mass,
the mass by that by that formula is 8, which is what we put into
this if you recall.
And the oddly enough,
the masses don't add up.
So the energy of a mentor
add up component by component, but the mass it doesn't add up.
And I introduced the terms that the
mass, the Andrew Mentum, is
conserved, meaning is the same before and after a collision.
We will discover that the that that some that things which are
the same indifferent frames such as the length of the energy
momentum vector are frame independent
or invariant is another way of putting that. So I'm introducing
terminology here. So invariant means the same in all frames,
conserved means both we means the same board before and after
a collision, and constant such as the speed of light means it's
the same everywhere. That's the folks of full House of of
invariant and conserve and everything.
That's what we got last time.
No.
That is the so-called lab frame,
and this is a particle physics term. It's called the lab frame
because you know you're hitting something which is stationary,
and if you have a target
of whatever you want and you have an accelerator, then the
target is stationed in the lab frame, obviously. That's why
it's called frame. There's nothing profound to that,
but we can change frames.
Really confusing.
So
let's do that
and.
Repeat that committee that we can see that. Let's see if we
can get this to the right.
OK.
So
by conservation of momentum, we're going to see that the
the Andrew Mentum of this outgoing particle 3
through P3
is going to be gamma 1M1 plus.
Gamma 2M2
is the key component
and
gamma 1M1V1 plus gamma 2M2V2 is the X bullet. And remember the
Y&Z components are 0 here the this gamma one is just gamma
of of of the of the you know corresponding to the velocity of
the first particle and so on. So that all that I've written down
there is the result of momentum management and conservation.
OK, if you incoming memento
PNP two then Oakland 11 is that.
But let's change frame. Now
let's go to another frame. So look at the same
a vector 4 vector in a different frame A-frame which is moving
with speed V.
So what are the components of this?
Victor? There's four vector in that new frame. That's easy,
that's just mechanical. That's just looking at the
transformation equation the the matrix expression at the
beginning of Chapter 6,
and we discover that what we can we can find what the
the 0 component of
made them three in the prime frame is. We can discover that
whatever it is, and we can look at the
one component, the X component of
particle 3 in the primed frame. So this is quite a compact
notation here.
So So what, what? And that will be gamma
V with that's the the speed of the of the new frame
times P31 minus VP3
0.
I just want to unpack that. I'm not doing. I'm not pulling a
fast one here. This is just the transformation equation that
goes from one frame to another.
So this is one of the lines of that matrix at the beginning of
chapter
6,
and this looks like
the
and the. The range transmission equation that looks like T by
SVX
is basically what that is, and notice that's P31,
not P3 part, not P3 prime.
This is where my handwriting is fairly neat because maths has to
be fairly neat even if you you can't interpret it massively.
P31 primed is the one component of momentum 3 in the other
frame.
OK, what does that look like with this expression for the for
P3? So we have this is P3
zero and this is
P31.
OK, the one component of P3 that is gamma
V
P31 is gamma 1M1V1 plus gamma 2M2,
E 2 -, V
gamma 1M1 plus gamma 2M2
like that
job done. OK, so that that's that's the the components of
this
but the same incrementum to 4 vector in the other frame
of arbitrary V, speed of that speed along the X axis at speed
V
But we can pick a. We can make a sensible choice of what that V
is, because if we decide, let's pick the frame in which P3
primed,
yeah, P31 primed is equal to 0.
Let's pick the frame in which the outgoing particle has 0
spatial momentum.
They're going the the frame in which outgoing particle is at
risk.
OK, so so so, so, so that will be not the lab frame,
but it will be the frame in which the which is moving just.
So just right for the after the collision,
you're moving alongside the outgoing particle
in that frame.
This would be 0,
and in that frame that tells us what V is,
V will be.
And
what we have that expression over that expression and using
the the velocities that that we have chosen. In this particular
example,
that will be.
Right,
so in this particular example, remember the two incoming masses
M1 and M2 are both equal.
They're both equal to 8, and so they they cancel out. We get
gamma 1V1 plus gamma 2V2 over gamma one plus gamma 2. And in
our in the using the numbers we've chosen that's equal to 3
5th
which matches what we saw
in this table
that the outgoing particle is moving at speed 3/5.
So just to reiterate, what we've done is we've chosen
to go to A-frame in which which is moving at speed 3/5 in and in
that frame the outgoing particle is dictionary.
OK. And that and
so, so, OK, hold on to that though.
In that frame,
we can look at what we can find out when you calculate what this
table is in that frame
by, you know, transforming these expressions component by
component or or otherwise. And I won't go through that step by
step. There's an exercise which encourage you to do so
and
and we get an expression like this
and here
yeah so so the term of handle turning
to get this
but you can go through it. I heartily encourage you to go
through the steps of this because very instructive just to
get those mechanics in place. What we see is
some different numbers,
but there's also a pattern to these.
You notice that in this
in this frame, the speed of the outgoing particle is 0.
That's by definition. That's because that's how we choose
this frame.
It means that the the speeds of the incoming particles are equal
and opposite because they have equal mass. So in this frame,
the particles are coming in from opposite directions, merging and
just staying there. Because momentum,
Sir,
the energies of the two particles are different, The
spatial momenta the two particles are equal and opposite
and the but they are still conserved in the collision,
so that the energy of momentum of the product particle
is still the sum of the energy momentum of the two incoming
particles. The components are different
because this is the because although this is the same
vector,
the management of it's it's the same P3
because you're looking at it in a different frame. The
components are different but the same rules applied. Andrew
Mentum still conserved
and
and notice the masses are the same,
so massive although the components E&P are
different. The masses of the incoming particles and the mass
of the product particle are as they were before,
of course, because that mass is just the squared length of the
engagement particle.
So it doesn't matter what components what what framework
you're picking. The components will will will, will change, but
they'll change in such a way that this length stays the same.
OK, so that illustrates quite a number of things about the
changing of frames and about and about four vectors.
And that seems a bit like slate of hand because because I
haven't gone through each of those calculations and that's
why I I, I encourage you to to go through those afterwards just
to reassure yourself there's nothing tricky happening here.
Any questions about that?
Thank
and part of this is good about this because there's a lot more.
For example the collisions at CERN I, the collision vertices
at the AT, the four experiments rob around around around the
LHC. They all they are designed so that you have two
conversating beams which hit each other head on. So the lab
frame in that context is the same as the as the centre of the
centre of mass
because precisely in order to maximise the energy available
for for collisions in a linear accelerator like slack, which is
just a long straight accelerator which is a target, the last
frame and the central map centre mental frame are not the same.
But this is astronomy, not particle physics, so we're not
going to go into that too much,
no?
Did anyone think there's anything odd about this
apart from the obvious things? But there's there's a a key
thing that seems very strangely odd about this
in the final column.
That's right. That's it.
So the mass is not conserved.
There appears to be more mass afterwards
in the world before,
so there's more gravity there than there was before.
Where's this mask come from?
And that is strange.
And you can push away at that
short circuited by seeing that mass is not the source of
gravity.
Gravity doesn't come from mass.
Gravity comes from energy momentum.
So it's the amount of energy momentum
that is the source of mass, not the motor stuff.
OK. And if you imagine this,
and
so how do how do we explain that? I I've I've ordered this
fairly carefully here.
Yes. So you you you you you you have this this this box. The two
human particles, this collision two incoming particles and
they're going particle and you put it in a box.
OK,
the
afterwards you've got just got this see in the centre of
momentum free.
Afterwards you've got this big lump of of stuff sitting there,
which probably very hot and and so on. There's a lot of a lot of
gravitating stuff before you seem to have less mass.
But the particles were moving very rapidly.
In other words, there was lots of oomph in there but before the
collision. So you have two things colliding and then just
stopping you. You end up with one heavy particle afterwards,
before you're too lighter particles, but they were moving
very rapidly
and so it's that energy Momentum
that is contributing to the grip, the the the gravitation.
So it's not mass that gravitates the energy momentum and the fact
that you have a lot of energy in the box,
not all of it in the form of mass is what gravitates
and we'll we'll come back to that in in, in in the other
lectures. But that's an important thing to to stress and
and and to to think about and you walk home
great. I'm I'm keen to to press on
and I'm going to.
Is not mass at the source of gravitation but the formentor?
OK
no I'm also I'm I'm going to quick fairly quickly mention
another change of units but this is much less confusing than
natural units
you will have
yeah I'm sure you'll recall I have you come across the Janski
has that been you know the Janski and the Janski just it
sounds exotic unit but all it is is a a convenient name for our
our convenient small number and a convenient small small amount
of of course of course you you observational astronomy and and
it's the it's units of flux per square metre
mumble mumble. I I think so, but it's it's given a name because
it's a convenient small quantity
in the context of particle physics.
You have particles moving around all over the place and there are
convenient unit of energy is the electron Volt which is
that number of joules is not very many joules but it's that
number of joules. And one electron Volt is the amount of
energy and electron has one that's been accelerated through
111 Volt.
So it's, you know, it's a nice sensible unit and I'm not gonna
say very much more about it other than that it's a
convenient unit to to use.
And uh,
yeah, there's there's much more that there's excitement about
that.
But if I do refer to it later on, then that's the section to
go back and remind you what I mean.
We'll finish off with a worked example.
A very important work. Example.
But Compton scattering, so-called
through this you are familiar with Thompson scattering. I
presume that's the that's why the sky is blue.
Our electromagnetic wave comes along,
accelerates our charged particle and which radiates and the
colour change and and the and the electronic wave is scattered
by different modes depending on on the frequency. That's not
we're talking about here.
We're talking here, is an electron
an incoming photon?
Which bounces off
the electron,
scattering it.
And this is a a quantum mechanical collision.
We didn't go into the details, but it is a quantum mechanical
collision in which the photon as a particle collides with
electron as a particle and the two recoil in the same way that
you are familiar with from Newtonian physics. But in this
case, we're one of the one of the the particles of the
collision is a photon,
No? We want to analyse this collision,
so we'll set up with the incoming
photon
having energy
Q1
because it has Planck's constant times
incoming frequency.
Outgoing fortune will call energy Q2HF2.
The outgoing electron will have mass M and outgoing energy E and
momentum P
at at certain
scattering angles, and this is just the.
Figure 7/3.
So we have all the the the dynamical information there. We
can write this down component by component and conserve the
incoming
momentum, energy momentum
through the collision
and find out and and and balance that balance. That
right.
What we discover is that the incoming
right?
And
what we write down is the
that before
the electron
is stationary, so the
zero the the the 0 component of the energy. Momentum is just its
mass,
there is
and it's not moving. So the XY&Z components of momentum
are 0
the.
Before
the mention of incoming photon
is going to be Q1, but it's energy and it's moving entirely
in the
X direction and so in order for the length, the length squared
of this formant to be 0, we can deduce that the
X component of its
energy momentum
is going to be the same
because it's moving and and it's all in the important because
it's moving along the X axis. So they are Q 1 ^2 -. Q one squared
is equal to 0 as a photon 4 momentum must be
afterwards
the.
Similarly the the the electron's outgoing electron has energy. E
mean we've just decided to label that component east and the
components of their spatial momentum
are going to be peak Cos Theta & Cos Theta.
We're just doing the same thing that you've you've done, you've
rehearsed in previous years with
conservation of momentum. The only different thing, the only
difference here is we've got a fourth, a fourth component in
here,
Peter. Gamma is going to be
Q2 the energy of the outgoing photon and similarly the the the
the 2X and Y components of the spatial momentum Q2
course Phi Q2.
Fine, fine.
And again you can see that Q 1 ^2 -, Q two Cos Cos Phi squared
minus Q2 sine Phi squared is going to be equal to 0
as it has been the case for a photon.
And we can balance this component by component
M
M plus Q1 is equal to east plus Q2,
Q1
If you could do a P
Cos Theta
plus Q2.
Of course Phi
0
is equal to
app sine Theta
plus Q2
saying Phi and so on
and I won't go through the IT would a little more time. I
would go through the the the the step by step. I won't. I won't
do that. It's in the notes. The the point is that what we're
doing here is exactly the same as what you've done in previous
years in Newtonian physics. And we
add everything up, Do a bit of algebra, Slightly fiddly
algebra, but not not hard,
and discover that
went over
Q 2 -, 1 over
Q1 is equal to 1 minus
cost 5 over
M
Or in terms of. You know, if you remember that the
Q is just the
in terms of frequency and thus in terms of the wavelength. So
that Lambda
2 minus Lambda one is equal to
thanks constant over M
1 minus
course 5
Compton Compton formula.
And this is not
a a Doppler shift. So the the the outgoing photon has changed.
Its
a wavelength, it changes its energy.
But it's not a Doppler shift because we we're not, we're not
talking about changes of frames here. There's no Lorentz
transformation here.
What we're doing here is conserving momentum, the rest of
us momentum. But we we can discover the prediction for the
change in the photon energy in this case, which is amply
verified by experiment. And this is you can do this in the lab.
This process is also important Astro physically because the
process of of so-called inverse competence gathering where you
go the other way around and
thermal in Blackpool accretion discs are thermal photon can be
scattered off a high energy electron. So this is the
opposite process where our photon collides with our a
realistic electron and increases its its energy. So you get X-ray
emission from Blackpool accretion discs because of the
inverse of this process.
Yeah,
in a way that a particle physicist would would relate at
an astrophysicist would like delight at.
So I I skimmed over a couple of of of of algebraic details, but
you can sort those out.
So that brings us to basically the end of the special activity
part of this course.
We're going to go into Gianni in just a moment, but
it brings, it brings it then rather neatly with an
application of all this stuff that you've been learning about
relativistic trains and and and so on in a way which is
important for particle particle physics and for astrophysics.
There are other sorts of other applications of this to.
To to the realistic version of quantum mechanics is Rossford.
Quantum mechanics is what allowed people to discover the
idea of the of the neutrino and so on. Quantum field theory,
which modern particle physics is based heavily on, is founded on
special activity.
So in the sense that
review theory is just particle, it just quantum mechanics redone
in with the assumption that the universe is based on special is
structured and special relativity.
So you won't. So in a sense you might not use special whatever
again in a specific in this is where my special effects come
in. You won't have to to calculate the speed of rustic
trains,
but in order to understand where Rusty 1 mechanic comes from, in
order to understand where quantum field theory comes from,
you will have to be thinking in a in a special artistic world.
And the interesting thing and interesting thing is that what
we've covered here
is basically all the special activity there is
that isn't sort of advanced special relativity,
right overly in the special case of new acceleration is
sort of done
OK.
The the more general case of relativity with acceleration or
relativity with gravitation is what general relativity is, that
that's what the general is in general relativity. And that's
what we're going to go and talk about that in a moment.
But there's not more of it as such. And I hope that you have
at the beginning of an actual one. I said that that there
wasn't a lot of
hard maths in this course in the sense that what the what would
addition to fraction, multiplication, division and
square root. And OK, we got 4 vectors as a sort of extension
to three vectors and that's a bit of maths but that's
basically all there is.
I hope you realise that's that's true, I said. But also I think
you're also congratulate yourself having got here.
Because although the the the mathematical bricks and mortar
that you're using are quite simple, the way that you've had
to put those together and think in our from
very apparently straightforward principles, you know the two
axioms
to some really quite strange ideas is quite hard work
and in some ways equip mathematical way of approach.
And I think it is strange to look back and think those two
axioms are both plausible.
But you get those. You put those into your head,
step forward and dropped in a rabbit hole
and you think what we is up.
It's very strange. So it is strange and discomforting. But I
hope you have the the haven't been any missing steps along the
way. We're sort of tiptoed through that whole landscape
and got somewhere really quite exotic
step by step. So well done.
Umm,
any questions before we move on?
OK
then we shall. Let's go back to here,
did the picture of conference gathering, right.
Thank you. No,
at this point we somewhat change gears because we we have to
chapters one to seven about special activity. As I've just
said chapters 8 and 9 out about general activity. Now I said
I've just finished seeing that the maths of special relativity
is nice and simple. It's school maths.
The same is not true for GR.
The master GR is advanced undergraduate or graduate level
maths, and if you carry on with doing astronomy, masters or the
theoretical physics course or a couple of other things of map, I
think maths and astronomy, I'm not sure the variety of courses.
Then you will have the opportunity to do the general
activity course in either your 4th or 5th year for you. It'll
be in your fifth year if you if you do that. And I actually
teach that course as well, but it kept it to there because it's
it's the maths is challenging enough that you need a lot of
practise to go up to that point. So we're not going to touch that
maths here.
But because of the way I've done special activity
focusing on the geometry, it's not the only way you can
introduce special activity, but we're focused on the geometry
because of that I think. Well, the point of that, the reason
why I've done it that way is because I think it makes a
Natural Bridge into talking about GR.
So we're not going to do many of the details of GR here, but
because of the last 10 lectures in the last few weeks of of of
of relativity, we can go into a lot of the ideas
with a lot more sophistication than any sort of popular
account.
OK, so, so pop accounts, you know, we'll we'll leave the
hands about, you know, curved rubber sheets and all that
stuff. And I'm sure you've seen those sort of things on
television or or or whatever. We can do better than that.
So in a sense the the payoff OF11 payoff of the the last 10
lectures is that we can cover quite sophisticated if not very
technical or if not high not although not hyper technical
account of GR.
So enough rubbing.
One other thing. And so there are a very important aims to
this
appreciate, understand, understand. And those are the
point of all this.
The objectives, however, are thin
because it's not terribly easy
to
right
exercises or homework or class tests or exams which cover this.
So there's a limited number of things that I'm going to be able
to say that are accessible,
but I'm not gonna let that stop me.
So in these, in this part of the course, I will be seeing things,
a lot of things that aren't basically accessible because
they're not on that list.
So don't panic, right. I I'm going to go fairly rapidly
through this. This part I'm going, I'm going to be, we're
going to be jogging in in these last five lectures, but don't
get stressed because a lot of it isn't examinable, right. And I'm
telling you this because it's wonderful and beautiful and good
for your intellectual and moral development, right. It makes you
better people for having struggled with this, right? But
don't get anxious.
I I feel it's important to see that right, because people do
get anxious, right.
But pay attention to the objectives. Those are the things
that I think are fair, that I think will be fair. Again,
generativity. As I said, the general in general relativity
is not the special case of no acceleration and not the special
case of no gravity.
Because although when we've been talking about special activity,
we talk about trains move through stations,
You know, the trains are on the Earth and are held down by
gravity and and so on. But we've ignored the gravity bit, the
gravity but hasn't been important to the to to to to to
what's happening. Things are going all, all all the trains
are being moving along level train tracks. There's been no
gravity. We're just ignored it.
Newton has a theory of gravity which works very well. You can
get to the moon and back
with Newton theory of gravity.
OK, so it's not wrong. It's just as we discover about to discover
doesn't quite get to tell the full story.
But Newton
it's something false if I have an apple to pick an example at
random and I drop it.
Then, as you know,
the force of gravity
acting on that apple is proportional to the mass of the
Earth and proportional to the mass of the apple.
Much GM1 M 2 / R ^2. OK. So the bigger the apple they have or
the apple, the more the forces in proportion to the mass.
So there's a force,
so the apple then accelerates toward the ground.
How much is accelerate
if you go there? Me
the apple accelerates in
proportion to or inverse proportion to its mass.
So if I double the mass of the apple,
the force acting on it of gravity doubles
I think, but the acceleration halves,
you know, so they they they they they just balance out. In other
words, if I have a an apple and dirty great gold bar
or an apple and a feather in a vacuum, they will fall at the
same rate because those things cancel out.
That's not surprising. You may well have seen videos of of
Apollo 16 or whatever it was and and whichever astronaut was
dropping a hammer and a feather on the on the moon. I believe
they got terrible, terrible trouble from Mission Control for
doing that. They weren't supposed to do that. They
smuggled on board just because it was so much, so much fun to
do it on the moon.
But this is strange.
You think that's that's fairly obvious, right? But this is
strange because the two masses there are different things.
The mass that is acted upon by gravity is a sort of
gravitational charge. That's a that's a you can think of as the
gravitational mass of an object. It's how how much is it affected
by gravity.
The mass in the second equation
is inertial mass. It's a different thing really. That's
that's the the, the, the the the the the property of the Apple
hires that that lets it resist being accelerated and there's no
reason why they should have to do with each.
So you could imagine them being quite having quite different
relationships to the dynamics.
But it turns out in Nuisance Britannica nuisance and
dynamics, they are exactly proportion,
not just proportional ish, they are exactly proportional. So it
seems to be no difference between these two on the face of
a completely different things, a national mass and gravitational
mass. And that is strange. And Newton thought it was strange.
He noticed it and said I had. I have no idea why that's true
in the in the general scholium at the end of of of interview he
basically says. I don't know why that's true.
I don't know how gravity works, she said.
As Newton did not claim to understand gravity, he said I've
got an equation which describes it, and if I start with the
right place, all the maths works out and and and all works, but I
don't know what gravity is, he said.
And that puddle remained.
But let's step aside from that for a moment and go out into
space.
And imagine you're in a box
out in space,
breathable, see, So you're you're you're well away from
everything. You're in orbit or you're in between the stars or
or something. So there's no gravity,
right? And everyone just floats around
and if you, there's you, there's a clock, there's photons, the
electromagnetism, there's biology happening. There's
anything like happening in that box
and everyone's just floating around
and the thing that's the thing that is still true in that box
is that
Newton's three laws work. So if you
if if you sort of push the a clock across the across the
cabin, it'll move at a constant speed until it hits until it
hits the end.
If you pull something, it'll accelerate according to if it
was me, and so on. So nuisance laws work in that box in exactly
the way you'd expect,
of course,
because why wouldn't?
Then let's start a little rocket motor under the box
and you turn it on and then the box would move
but we are floating around inside it and nothing happens
until the the box reaches us
and and start pushing it. So before the box touches us,
we're not going to
be affected by the book obviously.
But when we get home at the box does reach us, then we'll be
pushed by the floor of the box. And if the rocket motor is is
set so that it produces an acceleration of 9.81 metres per
second squared, then we are going to feel as if we're
standing on Earth. We're going to be accelerated in the exact
same way
and that's exactly the same we
it's not ish,
it is exactly the same. We, we will not be able to tell the
difference
between
being accelerated in that way
and
being on being on Earth,
OK, And that is a physical statement. That's not a
mathematical statement. That's a physical statement. That's true.
But our universe?
In our universe, we cannot tell the difference between a uniform
gravitational field and an acceleration like that, and
that's called the Equivalence Prince.
And that explains the whole gravitational mass versus versus
inertial mass thing.
Because
in the case where everyone's floating around,
the methods aren't involved.
In the case where the rocket
is pushing the cabinet that that the cabinet up towards us,
everyone's going to inside the cabin is going to be
accelerating towards the base of the cabin in exactly the same
way, independent of their mass.
So the statement that these two things are equivalent
explains why the the the different gravitational national
mass doesn't matter.
And this statement, they equivalence principle, was
enunciated by Einstein and it's what is in it. It is what the
general theory of relativity is based on
that that that variant of that principle is what the whole
thing that that's the the starting point. If you're like
like the two accidental activity, there's equivalence
principle is the starting point for the whole rest of the
elaborate apparatus,
right? OK.
And as I say, I want it just I said I said at the end of it
again it's a physical principle. It could be otherwise, it's not
a mathematical necessity. It could be otherwise, certainly
was it would otherwise, for Newton could be otherwise. But
it is the case in our universe.
Then letters in the last moment, and I will. I will have to
return to this afterwards.
So. So uniform gravitational fields are
are equivalent to frames accelerate uniformly routed
inertial frames, That's the frame that's accelerating
uniformly. Is this rocket frame
another version of that?
And this is the one that
Einstein wrote down. All local free falling, non rotating
observatories are fully equivalent to the performance of
all physical experiments. And all those words are important.
The free falling
and the laboratory is
the laboratory in in in the in the first picture where the the
the the books that are in space.
I I I say clean this with the happiest I've I've I've got
order wrong here is actually it was a happy thought of his idea
was what happens if you are in freefall so just falling purely
under gravity
if you if you jump out of a window
in a in a box or or or you know lift shaft and the lift cable
breaks bad situation you're gonna have a bad day. But on the
way down you can think you can meditate on the on the on the on
the delights of of young relativity as you go and that
situation where you are falling freely under under gravity you
and everyone inside the lift cabin and and and your dog is
there whenever and able opportunities are all going to
be
or being Newton's laws perfectly in the sense of of of of
accelerating here and there So I'm gardening this I'll come
back I will come back to that point
I will come back to the point and see why all all the words of
that are are important and what and what they mean.
I'll come back to that next page, I think.