So here is our x-axis, some origin,

some tick marks representing how close we want our measurements to be.

Tens of meters, meters, billions of meters or whatever.

Everything happens along the x-axis.

And again, we imagine our lad as a grid of clocks along that x-axis.

And so, we could record a series of events.

If something happens here and then here, and then here, and then here.

Maybe four flashes.

To represent that in a spacetime diagram, we add, of course, a time axis.

And then we say, okay if something happens at time equals 0, we plot it along here.

If it's at position 4, time equals 0, it'd be right here.

Just put a little dot there.

So position 4, x equals 4.

Time equals zero, it happens sort of right there.

Don't want to mess up my marker too much there.

Let's get some more tick marks up here.

And of course, if it happens, anything that happens at time t equals 1,

assuming it's one seconds, two seconds, three seconds, four seconds,

that'd be anywhere along here.

So if I have another flash, maybe at position two that happens at one there.

It'd be there and so on, and so forth.

So any given event that occurs at a certain x value and

a certain time value, I just plot the x value and

then the time value and then we expanded more with our

the idea of a spacetime diagram and talk about world lines.

So that if we have an object moving along the x-axis here, constant velocity.

We start off with that case, then what we get is a straight line.

Something like this at a certain slope or angle there and

this represents the world line of a object.

Remember, it is moving along the x-axis through time.

So we can see at time equals 1, it was about position 1.

At time equals 2, roughly it was in position 2.

At times equals 3, it was position maybe 3.25 and so on and so forth.

Actually, that wouldn't be constant velocity motion.

But hopefully, you get the idea that constant velocity,

straight line motion like that.

We also did some other examples of world lines, just remind you of a few of them.

So, that the world line of an object moving to the positive x direction.

If you have something moving in the negative direction,

it's going to be look something like that for constant velocity motion.

If you have something that's just like this, so we're aligned like that.

That is something that is sitting at x equals 2, as time goes on.

Time is going up here and so this object is just sitting at x equals 2 there.

That's a stationary object on this spacetime diagram.

Another example is something like a curved line.

You have a curved line, that's something that is accelerating or

decelerating as the case may be.

In this case, we can tell it's actually accelerating.

Because you can see for a given amount of time here,

it's traveling a farther distance than it is down here.

So when it bends over, it's accelerating.

If it was going something like that, let's not quite do that.

Let's get the infinite acceleration there or deceleration there, I mean.

Let's just do something like that.

So this is something that's decelerating, it's actually slowing down and

another reason we can tell that is we talked about velocity.

And let's not do the accelerating or decelerating so much here.

Because as we've mentioned, we're just dealing in this

course with constant velocity motion, but it's important to know that a curve line

is something where the velocity is essentially changing.

It's not a constant velocity, because if we talked about,

if you have a straight line like this,

velocity is just distance covered by elapsed time.

So distance covered say,

if it goes to this point right here maybe, something like that.

One, two, three, four.

It's covered four units in three units of time.

Distance covered 4 divided by 3.

So, it would be four-thirds meters per second or

whatever units we would be using there.

So we talked about velocity related to the slope of our world line and

we talked about velocity being run, the run divided by the rise.

So that if we have a world line like that,

that's a big run divided by a relatively small rise.

That's a high velocity object.

It's a object that's moving at a higher velocity, it covers a lot of distance in

a relatively short amount of time versus a world line for an object like this,

lower velocity.

It covers less distance in a bigger amount of time.

So we noted that the slope of a line, this is a line with bigger slope than this,

because slope, remember is rise over run.

Velocity on our diagram is run over rise, the inverse of the slope.

So low slopes,

smaller slope on our spacetime diagrams means something that's going faster versus

bigger slope means something that's actually going slower there.

So, that's how velocity works on our diagrams.

And so then if we, let's do a green one here.

Go back just to the acceleration case very briefly.

If you have something like this,

you can see the slope of this line is gradually bending over more horizontal.

That means it's getting faster over here.

It's accelerating versus if you have something going the other direction,

the slope of the line is getting steeper again on our spacetime diagram.

That means it is slowing down, it's decelerating.

And it's still moving to the right, but it's decelerating as it does that.

Remember once again, I repeated this a number of times that this is

not the actual motion of the object.

It's not shooting off at some angle or curving this way, or that way.

It's just going along the x-axis.

So this green line would be something that start off fast along the x-axis and

now is gradually slowing down, still moving in that direction.

This one here is an object moving fairly, quickly in that direction.

This object here is something that's moving relatively slower in that

direction.

This world line here represents something moving in the negative x direction

at a constant loss velocity.

So in our assessment quizzes, we did a lot of examples with world lines.

So hopefully, if you haven't already, you'll be working through those and

you'll see more of them on the week two review quiz as

well based on the things that you did in the assessment quizzes.

So, that was spacetime diagrams and world lines.

Then from there, so I think we covered everything, again, the main points there.

A lot of examples, again, in assessment quizzes to The work on,

okay, let's look at next topic which was I think we're up to number five now.

Frames of reference [SOUND] spent several video

lectures looking at frames of reference,

did examples with Alice and

Bob and maybe Earth is involved as well.

In assessment quizzes we introduced drifts into some of our examples.

What's the basic idea here?

Well the basic idea goes back to our lattice of clocks idea.

And so, in fact we've had some props here.

Here's Alice, say in her space ship.

This is her lattice of clocks in the X direction.

And we can imagine that as far as she's concerned, she's just sitting there.

And she's watching Bob fly by in his spaceship.

She can measure his progress by taking photographs as he goes by each of her

clocks, there are more clocks here too, just not shown.

So every single point has a clock where if she wanted to take a photograph at that

point as Bob flies or whatever happens at that point,

it records the time and the location of Bob.

And therefore, she can track his progress, but

her frame of reference then is her lattice of synchronized clocks.

And as far as she's concerned, with respect to your frame of reference,

she's just sitting there.

She's not going anyplace at all.

But of course, Bob you can say, is also in the same situation.

Now, he's moving by here like this.

But as far as he's concerned, he could be sitting there and it's Alice who's moving.

In this case, she'd be moving backwards.

I would say hey Alice, I'm not moving, you're moving backwards.

And Alice would say I'm not moving, you're moving in that direction,

in the positive X direction.

So, Bob also has his frame of reference which consists of his lattice of clocks.

And his frame of reference is, as far as he's concerned, he's at rest.

He's got his lattice of clocks.

he can measure anything, any spacetime event.

According to his frame of reference.

Alice can measure any space time event with vector her frame of reference.

And a little bit we get to the Galilean translation that allows us to

convert between the two different measurements.

What Alice might measure versus what Bob might measure

in terms any given space time event.

But, before we got to that,

we had to make sure the concept was clear of a frame of reference again.

Imagine, if these props help, or if these images help, imagine it as, let's see,

for Alice here, just her lattice of clocks, or any observer.

It doesn't have to be Alice and Bob and their spaceships.