Hello everybody.
OK, technology sorted out. Possibly and possibly sorted out
because
although these electrodes are being recorded on X360, I am not
100% sure which microphone they are taking things from. It may
be that one, it may be this one. When I've listened to the
recordings they're a bit faint, but I can't find a button to
switch the input, so we'll just have to hope for the best. But
anyway, I am making separate recordings of these so we can
fall back on those if necessary. No, the plan today is to go
through the the, the, the last section of the axioms bit we got
last time we got as far as,
uh,
as this question, this rather mysterious question about people
moving, moving past each other. Plans to finish off this chapter
go straight into chapter 3, and the plan is to spend lectures
3-4 and five on chapter 3:00 and 4:00, so that should be about
the right length of time. That's the goal. Anyway, we'll see what
happens in actuality,
so the ruining bit, so, so on to the the last part of Chapter 2.
The remaining bit here is there's not a lot to say about
it in a way, but the important bit is the consequence of the
second axiom.
Before I go, I go, I go into that. I want to just
recapitulate this. This quick question that we asked we
address at the very end of last time because it is so very
important.
So if you recall, I have a friend moving past me a rocket
and rush for 6 speed, and relativistic speed means
something moving at some appreciable fraction of the
speed of light.
Observe her watch be taking slower than mine for reasons
that we haven't come to yet but which we will get to very
shortly.
She examines my watches I at the same time and the question was
it's taken faster or slower than hers and asked you to think
about that a little bit and then I came back and said that the
answer is my watch. We're taking slower than hers,
so her watch is ticking slower than mine, and my watch is
ticking slower than hers.
How can that be
the we'll come to the reasons why that is not insane in a
moment, but the point is that you don't even have to go on and
talk about next chapter
or the second of the of the of the second section of relativity
to know the answer to that. Because the first axiom says you
can't tell you're moving.
And if one of us could discover that the others watch was moving
slow in an absolute sense, then we could tell that we were the
one that would move,
or vice versa, or whatever, like that. So just by itself, the
first axiom tells you that something weird happening here.
I mean, extra weird, but it's really more than the usual, more
than the obvious weirdness happening here.
I'm sorry, we'll come back to that. What will we return to
That? Definitely. But I wanted to impress upon you the last
thing I said last time,
and this is also a very important remark.
This is Einstein's version of the of Galileo's principle of
relativity and the
following on from.
But he says, and also there's a second postulate
who's only apparently only apparently irreconcilable with
the. With the former, they appear to be inconsistent with
each other. When you look at them first, the he's saying that
they're only apparently inconsistent with each other.
The light is always propagated in empty space with the definite
velocity C which is independent of the state of motion of the
emitting body.
We have to understand what that means.
There's a number of things
I could be going.
All the other more, there are a number of things that the speed
of light could mean.
It could mean if I have a torch and a shame it against the wall,
how fast does the light leave? It could mean how fast did the
light go through empty space like like like water waves on
water they have a speed and that speed is relative to the to the
to the water.
OK. Or the speed of light could mean
how fast is light moving? Quite nice. Very nice when I see it,
or when I detect it, or when I do an experiment which involves
light.
These are all three different things. In principle, that light
could mean
and the first two. They both seem fairly obvious.
It's the third one that is the case
the speed of light. The the the major speed of light is the
speed of light that
when you detect it, when it enters your your eye or your
camera or your physical apparatus, and it's that that's
independent of the state of motion. So if I am going on a
train going through a station at hospital light and I shine a
light forward,
then it'll leave
and it'll leave my my my torch at the speed of light.
He didn't think the 2nd, 2nd and anyone on the on the on the on
the train who measures the speed of that light. However, we'll
get three to 10/8 metres a second and someone on the
station platform
who sees this light being shown from the train
to them to their eyes on the station platform, If they
measure the speed of light, they will see it not as at the speed
of light plus 1/2 plus the speed of the train. They'll see it as
just the speed of light.
So bizarrely what what the second action was saying is that
speeds don't add the way you expect when you get when you're
talking about light. But more generally when you talk things
needs people like,
so I'm this shining the torch forward to shining it into the
eyes of someone on the on the station platform. It's not it's
not like plus the train. It's just the speed of light, and
there's something is happening there
that makes those speeds not add in the way you expect.
So I'm. I'm, I'm. I'm adding up weirdness here.
I think it is. Is that having a say though? Because
a mic
I see,
right? That's not helpful.
I'll try.
I'll try there.
That's not really working, is it?
Well, touching it. The wire,
you think. The wire.
I'll try touching myself some differently.
Perfect.
OK, so I'm adding up. Weirdness is here, and the resolution is
coming soon. I promise,
and so the the point here is that that that is basically all
I have to say about the 2nd axiom. It's strange, but go with
it for the moment.
The the last point that is important to mention in the
in the notes is just. I'll I'll point you towards section 221 on
the idea of synchronising clocks. I'm not gonna say much
about it
because it's there as a sort of pre placed footnote.
So when you think start thinking this through and go hang on. But
how do we have the same time everywhere? Because remember I
said that when we make observations on the station
platform of the train moving past, all the observers have
synchronised clocks.
You know they're all, they all know where they are on the
station platform because there's a scale marked long station
platform
and all the watch the synchronised because that's how
we do it and you may think how and how do we organise that is
that is there is there a problem there and no there isn't there's
process mentioned in the notes section 21, just for when you
start worrying about that go back and have a look at that. It
all works out,
but it's not. But it would distract us to, you know, step
through it. Just here. Just here.
OK, that is
so the. So just to be absolutely clear, what is the key, the key
points here, there are only two postulates we're going to talk
about, only two physical statements, 2 new things about
the universe you didn't know and all the rest is in a sense
logic. It's the deductions.
I mean that the physical statements, not logical
statements. You know, they could, you can imagine them
being otherwise. That's what I mean by physical sickness,
garlic, principal activity. You can tell you're moving.
Push it to the speed of light of the same value in all reference
frames,
and
I'll just mention in passing that there are a number of a
number of different things that postulate 2 could be. There's a
number of alternatives there.
One could spend a lot of time talking about this, but that is
the probably the most useful way to what wanted me to make
progress with. So before I go, I go on while I'm changing the
slides,
are there any puddles that are, that are that are outstanding
there
talk to me.
I don't. I mean,
I think it's possible for you to think, OK this is all
transparent, clear why making so much of A fuss about this,
that's perfectly reasonable.
Some of the puzzles are maybe yet to come and maybe over
egging this. It's weird bit but but don't worry. Just you
and
what we're going to talk about quite a lot, the idea of
simultaneity.
That's the question of two things happening at the same
time. And again, why do you think that was a big issue? The
reason it's a big issue is because there's a variety of
types of confusion
that you that that that that happened if you don't think
about these things in exactly the right way. So what what I'm
doing here is sort of training you to think about things of
this type.
We would be in the right way to avoid confusion
and a lot of the the you you will see on the Internet. I
think Oh my God relatively wrong because X or someone to come up
with a new theory which which doesn't involve Rushton dilation
or something because X. In almost all cases, these
confusions, these wrong
accounts of why relatives is wrong, come from not
understanding
the importance of thinking in the right way about simultaneous
events. So that's where the confusion comes from and it's
again, it seems like we're making more of a fuss about this
that we want, but it is terribly important
objectives.
So this is a tree garage
just
either sitting in this inflation or we're just thinking about it
from the point of view of people in the train carriage. There's
two observers,
one each. End
and there are light flash in the centre, like a strobe or
something whatever. A flash of light, an event,
and the light goes off. No directions. In particular. It
goes off toward the front of the tree of shrinkage and towards
the back of the garage,
and it takes 3 units of time
to get there. What are these units? We'll come to that, but
they're very small units. Clearly it all takes 3. It takes
three of them to get flight travel, say 3 metres, then
then that's the time on the clock of the person this end,
the 10:00 on the person at the end. And there's absolutely
nothing surprising about what I've just said there or what you
can see there, because this light flash is in the middle of
the carriage,
so it takes the same amount of time to get to the to each end.
So both the people, each end will record the same time, the
same time of arrival time of the light at the end. Nothing
complicated there,
no.
Let's imagine the same thing happening, but this time not
from the point of view of the people in the
carriage train carriage, but from the point of view of people
standing on the station platform watching this train go past.
How does that? How is that different?
Get the top one. There,
that's the late flashing,
Then a, you know, visual world leader.
The light has
travelled a bit, a little bit forward and backwards and the
train characters moved forward because it's moving
a little while later,
the late has travelled further out from the the, the, the, the,
the flash and the
indeed, and at the same time the train characters move forward.
So at this point the light flashes. Hit had arrived at the
end of the back of the train carriage
and the you remember Einstein's remark. All our measurements of
time are remarkable simultaneous events.
So here the light arriving at the end at the back of the train
carriage and that reservoir of what showing three our
simultaneous events they have. They are true events which
happen in the same place at the same time. It's like 2 cars
crashing.
There's no ambiguity about that
so the late so so we have to know this argument is saying we
have. It has to be the case that this observer what shows three
when the light arrives at the
and the. The way we've drawn this has used the second, the
the the 2nd postulate. Because you see here,
the light isn't moving forwards faster than it's moving
backwards. It's not getting, it's not picking up some extra
speed from the speed of the train
is moving forward at the speed of light,
which is why
the back runs into it before the light going forward has reached
the front.
If you if you think of that a Galilean world,
then the late moving forward would have picked up some extra
speed of the train, and so it would catch up at the front. 2nd
axiom says that's not what happens.
The light arrives at the back, but the light hasn't arrived at
the front yet.
So if we were to sort of take a photograph of this moving train,
at the instant when this arrives at the back,
the watch that we can see, so we can see the window of the train
carriage and we can see that the servers watch that can't be
written 3 yet
because it hasn't got there yet. It has yet to arrive, so has yet
you got as far as three. In other words,
although in the train carriage,
the back watch, but the back was ever reading back observers
watched reading three and the front observers watched reading
three are simultaneous events. They happen at the same time
coordinate
in the station platform.
The back was ever watch reading three and this front was
watching something like one. They are simultaneous events.
They happen at the same time coordinate because you imagine
this photograph taken of the train that goes past. In other
words, simultaneity
is relative.
These events are simultaneous in this frame.
These events three, one or similar things in this frame.
Depending on
what frame you're in,
things are simultaneous at different places.
Are relative. There's no, there's no there's no There's no
question about the the the the light arriving at the back and
that clock reading 3 because they happened at the same place.
That's the two cars, you know. There's no, there's no
ambiguity. Two cars crashing
but two vents which are separate?
It depends.
You're at this point allowed to go gasp. OK,
but we have this is a straightforward reduction from
the two
most of the the the the 2nd axiom.
OK, that's a bit strange.
So now imagine you know everyone goes back to where they started
off and we we we now have two trains going through the station
at the same time
at the same rustic speed going in opposite directions and we
can see both of them. So the top one that's the the the trains
heading off in in that direction and and by the same argument
there was ever Barbara for the back there was ever afraid at
the front there three and one are simultaneous in our frame.
But we'll set things up so that at the same time with actually
passed through the train station there's another train Yvette and
70 who going to do the same thing but in the other direction
and of course it's quite symmetrical. So in that case,
the reader observer,
the watcher showing three, the front observer Yvette, what we
showing one.
OK. So that's that makes sense.
Right now I've got to make sure I see the next bit in the right
order.
Umm,
because it's possible to confuse things
and
keep,
and we're going to pause a moment and take another
a set of observations just a short fraction later. With both
trains have moved slightly onwards and there's some
observer in the top carriage who can see,
who can see. Deputies watch at that point and we're going to
leave that? There for the moment. But what we're going to
assume by the way is that these two trains are going past like
that
we thought the the very close to each other so that Elaine or
whatever is you know knows glued up against the the train window
and can seize everybody's watch as if as if she were Co located
with it. So these are in principle at the same position.
OK, so there's no time flight stuff
to hold on to that. Thought for more.
And they're a little bit later
and the trains have moved further, further, further
forward and Barbara and Zebedee see each other's clocks and
they're both showing 11.
OK, there's that. No.
And I said, what's in the order?
So everyone calms down,
come back together, have a cup of tea and discuss their
results.
And
Barbara
says I I saw the front of the other train
at time 3.
And Fred says, oh that's interesting, I saw the back of
that train at time 1.
So but the about time three,
you know when Barbara saw the front of the train at time 3,
the back of the other carriage was well past Fred.
And if you remember last time I talked to how we would measure
the length of of a of a moving train if that bench we're moving
it or something we're moving through here at high speed. The
way we measure the length of the moving thing.
If everyone had you know we're looking at the watch and I'd
appreciate a pre arranged time they looked up and if they see
the the the the the the the the the the train in front of them
they they write that down and we should we we measure the length
of the moving object by asking did you see the end of the
train. You saw the end of the train. Subtract 1 distance from
one coordinate from the other, and that's the length of the
moving of the moving train.
That's our procedure for measuring the length of a moving
object.
But look what happened here at time 3.
Barbara Singh
for another cage was was level with me and Fred, said Ohh at
time 3 the front those guys was was passed to me.
We don't exactly weird but it was certainly passed trade. In
other words, at time 3, the front of the carriage
was levelled in the server down over here.
In other words, the people in the top carriage
have measured the other carriage, the bottom carriage,
to be shorter than theirs.
OK.
And
umm,
the next thing they can do is, you know, they'll park that for
the moment,
Fred remarks.
I I noticed the deputies watch was 2 units faster than mine.
Ohh, they they're what they watched a faster than ours. They
watched a set ahead of ours,
but Barbara goes
no, because when I looked as if he's watch, you know, colocation
with me watch wasn't faster at all.
So Fred has seen deputies watched by two units fast.
Barbara sees deputies watched not be fast at all.
In other words, these watches going slow,
they have and that's a measurement. It's not, it's not
some weird optical illusion the the point of all this, you know,
making an observation local to you and blah blah blah that that
is saying we are making observations here measurements.
It's not just this is not optical illusions.
So
the people of the top top carriage have measured the
bottom carriage to be shorter than theirs and this clock to be
moving slowly.
But again I see this. Hope everything here is symmetrical
through the exactly the same.
Like, no argument
could be made by Yvette and Liberty. So they would measure
the top carriage to be moving slower, to be shorter than
theirs,
its length to be contracted, and they would measure Barbara's
clock to be initially ahead of theirs and later in time. So
they would measure Barbara's watch to be moving slower than
theirs,
and it has to be and and and it has to be the case. This isn't
just a symmetry symmetry argument that has to be the case
by the 1st, 1st axiom, because if one of them could make could
see that the other was absolutely shorter than, they
could tell they're moving.
This has to be symmetric,
and this is so. So what's happening here is that both of
these sets of observers measure the other to be less contracted
and both of them measure the other to be time dilated. Let's
contraction things get shorter. Time dilation clocks go slow.
Umm,
and you're you. And that's another thing you are quite
permitted to be to to to gasp and stretch your eyes at.
So a Porter moment. There are the other outstanding puddles
that that probably can't be right because
you will reread this and you'll it'll percolate into your
percolation.
So
which of the following statements are true, referring
to the preservers at the front of the train carriage?
So Fred and Bubbles watch the mission synchronised with each
other and measured their frame.
Friend bubble watches. Do you synchronise with the clocks in
the other frame?
Fred and Barbara measure the garage to get shorter when
they're moving.
True or false. The the first statement all those states true.
Obviously it's false.
Second statement
very much always synchronised with the clocks and the other
carriage. True.
False.
Friend Bob Major. The case to get shorter when they're moving
true.
False.
Good
excellent mother I think the the the majority of the the come
from majority of everyone's got that right. So we won't deny
other than say yes the whole thing about because friend
Barbara aren't mutually aren't mutually moving
the the the synchronizer watched by a procedure which we can talk
about and this dating advice there's no complication there.
You can hold on to that thought when you thinking through these
things.
And yes, the whole point of this is, is that there's a difference
in the measurement of the passage of time.
And yes, it cannot be the case that Fred and Barbara measure
the character you shorter when they're moving A because that
would violate productivity
be because as far as they're concerned, they're not.
They're standing and shrinkage, OK, happens, the world is moving
past them at high speed. But nothing, everything that happens
when you're stationary has to happen in the train characters
as well. So that can't happen.
Excellent.
I should be going faster.
Key points, right? We'll move on
and talk about the light clock. Now this isn't a useful clock,
but it's a way of materialising the passage of time in a way
which depends on the moving speed of light or the speed of
light. So this is our light clock.
It consists of
when we were flashes
a mirror at the top and observer back at the bottom again and and
one tick of the lake clock is flash buying detected OK
and the person who's standing by the lake clock so that they are
Co located with the with the flash rather the code with the
flash. They have a stopwatch, they see the late flash start
the stopwatch, the late travels a distance. L bounces off the
miracles back troubles since 2L and they stop the stopwatch so
they they time how long it takes for that in their framework. In
the watch of the person on the on the on the watch, the person
standing by the by the sector.
Nothing complicated there. So so delta T prime is 2 / C distance
between time, distance, speed times time is another thing that
you can hold on to.
Now imagine that late clock is moving or had to rise for 6
speed or treating carried through station blah blah.
And now what is being observed by someone who by a set of
observers
and including this one on the station platform.
The light flashes,
but the time makes it across the to the side, the leap of of the
light clock. The whole thing has moved, moved along because it's
moving at a significant fraction of the speed of light and so but
it bounces off the middle at the top. It's bouncing off the
middle. When it's over here,
he's moved on the track a bit and bouncy comes back and
eventually rise back at you know
where it started more or less in that frame. And the same being
observed by someone on the station platform.
But again, second axiom,
the light moves
at to be late.
It doesn't. It doesn't get a speed boost from the fact that
the light the flashlight here is moving seems speed, but it
travels a longer distance,
so the time it takes to go
a
it's good. That longer distance is.
It is
speed times time.
It seems that that that time so that so that triangle from the
play here is C dot t / 2
is the total time it takes divided by two.
And if the whole thing is moving at
at speed V,
then that distance from there to here it of course
we just does this be template. So that thing is, it's half V
dot of. TI
thought it was the theorem.
Umm,
would you to?
And
yeah, I thought one of the only one of these recorded on E360
and I don't know which one it is. So just have to
hope it's the right one.
Ohh, how are you? Hello
So what we have is
and
see delta t / 2 V delta t / 2
that distance is L
Now why is it L primed?
Does that I've just written only that L the same as in in the
light clock when we
was stationary. So there isn't an LNL primed. You may or may
not have noticed.
And that's because that doesn't change. And we can think we can
work out that it can't change by using the principle relativity.
Because imagine
I've said that the length contraction along the direction
of motion.
Perhaps there's length contraction perpendicular to the
direction of motion.
OK,
let's go with that for a moment. Say you're you're you're driving
along, you're in this on the on the stream and see
the the length contraction, see length traction exists and it
had the effect of making that train actually shorter.
The trick then the training wheels will fall into the train
tracks and the whole thing will crash. That's a very bad thing
because there's been a length contraction that way.
But from the point of view of the people on the train, it's
the world that's moving past them.
So the the the the train tracks are the ones that are moving, so
they're going in the other direction. But if there's a
perpendicular length contraction then what will happen is the
train track, the sleepers on the train will get shorter
and the and the distance between the tracks will get shorter. So
the train wheels will end up outside. The train track will
crash, it will be it will be a crash. But in one case because
from one point of view it's because the the train actual
have we have got shorter and they end up inside the train the
train tracks and the other view is the sleepers be shorter. The
train wheels have ended up outside. You can't have both.
It's not possible for them to be both
and that argument depended on the assumption that perhaps
there was a a perpendicular length contract
to the camper.
So that's L and not L prime.
OK, so Pythagoras theorem we have. Well first of all from the
simple case
and the detector that we know that
2L is equal to
see
delta T prime. That's where delta T prime is the time that
the round trip time on the on the watch of the person standing
by this.
So now we have C
delta t ^2 / 2 ^2 plus is equal to L ^2 plus
the Delta t
/ 2 ^2. Just Pythagoras theorem.
So or in other words, C ^2 delta T ^2 is equal to two L ^2 +
D delta
square.
But we know what L is, so that's C
debt primed squared
plus C ^2 delta T ^2.
I'm going to, you know, just ignore the cancel out the seas
and we end up. So I've written the wrong thing. I've said
that's V ^2. Why did no one stop me?
Eastwood.
All right, I need V ^2, Delta t ^2,
v ^2, Delta t ^2
or Delta t ^2 is equal to
Delta T prime squared plus v ^2 / C ^2
go to t ^2. I'm rather middle of this of this algebra, but
therefore delta T is equal to
and you know 30 primary equal to Delta T 1 -, V ^2 / C ^2.
It's about 1/2 square root of.
So this simple construction has allowed us to work out
the relationship between the time between these two clicks as
measured in the on the watch of the person.
Umm,
conversation platform
and the time between You seem to Click to events on the watch of
the person in the in the train and that they are different.
And we're going to write that as Delta T is equal to
gamma,
Delta T primed where gamma is equal to 1 -, E ^2 / C ^2,
tomato half. And you'll see that factor appearing again and again
and again.
So we've already got a
mathematical expression for the time dilation effect,
just for the two axioms and a bit of ancient Greek geometry.
It was aghast at that
Question
Time in the stationary no dirty prime. That's the time on the
watch of the person who's standing by the light clock. So,
so, so, so, so the light clock is, is on the on the train, the
standing by there with, with, with, with, with with with
their. Their.
So so so this in standard configuration
is X prime X.
That's the the frame moving at speed V The light clock is
is there and
delta T prime in that frame. And these two events are
because the key in this in in in this room standard figuration,
meaning that the **** prime axis are lined up together and the
clocks are synchronised to to zero at the point where the that
the the the the the frames.
We'll call it heated,
as you can check at this point. This is a good prompt for you to
go back and look at the section in chapter one which said
exactly what the standard configuration was.
OK.
Yeah.
Um,
so I mean and and and. This is essentially that that question.
When discussing the lake clock we saw the phrase one tickets
time at delta T seconds.
So
that which is that what your person on the train the watch of
person in the platform edge station, the station clock or
the OR the temperature of the photon of light? Who would say
it was watching a person on the train?
Who was the Was the watch person on the platform edge?
Who was it? Was the station clock
who received the time attacks the fortune of late
Who hadn't put the hands up yet?
OK, I'll do that again. Put your hand up at something. Guess it
doesn't matter. I'm not keeping track of who says what. No one
keeps track track. I'll just make some sort of commitment to
yourself but we'll which it is who say with the watch of a
person on the train.
OK, who was the? It was the watch of some of the platform
age
who was there with the station clock.
Who is he? With the time of the Fortune of Light
chat, you never tell them why. You're right.
OK,
so asking that again,
doesn't she? Doesn't in that construction I remember we're
talking about is
the setup here.
There's tea. There is the water person on the train,
the watcher personal at the platform edge,
the station clock.
What time is your fortune of late?
OK, it's the watch of a person on the platform edge
because, and this is, it's always very important.
It doesn't matter what what his tea, what's tea framed the all
the frames are equally good.
But then, This is why when you're working through problems
like exercise like this, you always have to say
T is the time in this frame, T prime in the time in this frame.
You have to be explicit about it because you know all options are
are OK. In principle there's a sensible way of doing it, but
the sensible ways of legitimate too.
So the way I set this up,
I could have set up a different way. The way I did set it up was
that delta T was the same with observers, plural on the, on the
on the station.
Does TT Prime were the the watch at the time when the watch this
person standing by the light clock and that's moving and the
different times we could define them differently. We didn't in
that we set them up
and it's not
on the station clock. Can anyone see why it isn't the time on the
station clock?
It's not like the same reference frame. Well, it's not in the
same session. Yes, that's it. It is in the same reference frame.
So the station and the station clock are not moving with
respect to each other,
so the decision from clock is fixed to the station. So it's
going to be synchronised with the with delta T with all the
observers who are at rest in the station but the one we are
looking at the the, the the the the the person who's who's, who
notes
we are we we are recording in Delta T is is the the watch of a
person who is standing by the bit where the the light came
back to the bottom bottom like light lock
that is simultaneous in their frame with everyone else in that
frame. But it's their watch we're looking at. They are the
observer that matters.
So that's why a question there, Why does it matter so much that
the
ohh right.
That's a very good question. Why does it matter? And I think it
matters. It matters because
if we all would make sure that's the only person we're talking
about, then we know exactly what we mean by the time of the
event.
It would be possible to see that and look at the look at the
station clock at the same time and you could walk it out. But
it would involve do also extra sums about the light travel time
and worrying about what what simultaneous and what's not. So
the person who's at the whose Co located with the event in
question, the event being the like getting back to the
detector. There's no ambiguity there. There's no question about
there's no light travel time. There's no question about there
are complications about simultaneity because we've said
things which are
contains the same position automated. Absolutely. So it
just it it ties up with the boys. There's no there's no
there's no quibbles at this point. So and that's why we have
this, this profligate collection of observers everywhere. So that
anything that happens in our frame, we've gotten Observer Co
located and it's their watch we pay attention to.
So we could do otherwise, but we don't. So be it. But I think
it's important to to to to to to to to mention. And that last
one. A bit of a red herring,
because it's hard even to talk about the time of photon. A
photon doesn't have a clock.
I mean, you know, in a trivial sense, but also because it's
moving, actually atmosphere, light, everything goes a bit,
you know, 1 / 0 at that point. So we end up just not really
being able to say anything sensible about this time
attached to a photon because there's a sort of 1 / 0 problem.
Basically when it comes down to it, it's not mathematically
sensible thing to talk about
blah blah.
So that's what I wrote. I scribbled down, written down
that the time the moving frame is or the same in the quarter
stationary frame is gamma times the time in the in the moving
frame or or whatever. And when you do exercises and you will be
doing exercises
right, there's something like that,
but you will lose marks if you are not clear what you mean by
T&T frame
because it can be other either way up. And the thing you
remember is that it's called timed deletion. Moving clocks
run slow and you will work out. Do I multiply divide based on
that?
I mean, really, I suppose I should write delta T prime
equals delta T over gamma and let's say that that factor of
gamma you'll see again and again and again enough that you won't
even have to memorise it. You write down so many times it will
just stick in your head
and that's what it looks like as a function. And you can see it's
pretty close to to one for most speeds, from zero up to the
speed of light.
It's only it only gets to two at about just under .9 of the speed
of light. So, and This is why we never we never noticed it before
the 19 century, because it doesn't make any difference
until you're 90% spotlight, at which point it could have been.
So it shoots up to Infinity at at this beautiful
so that you have that picture in your head.
He points
right.
Um,
now that is. I've gone through through that rather quickly
actually,
and
more quickly than I worried about, so
it's not worth starting on Chapter 4. But I I will post
chapter 4 promptly
and in the last couple of minutes rather than hurry on
other other questions I think are really good questions like
that, that, that, that that are
boiling over in your head.
OK then
think of some.
I'll post the notes, have a look at them for next time. I I think
it's quite important to to to go through these, the the, the the
notes afterwards and make sure they make sense because it's
sort of thing where ohh, yes, it made perfect sense and then in
half an hour you'll explain to someone else and we'll go. I
have no idea what's going on, so it's just it needs to settle
down. I'll see you next week.