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All right, as we move along here our next topic is Frames of Reference.

Before we get into that, I just want to do a quick reminder of what we were talking

about in the last video clip, which was spacetime diagrams.

So remember the idea here is that we're just looking at motion along the x axis.

Just in one dimension here.

And we're recording certain events,

perhaps flashes of light or just some moving object as it goes along.

We're recording it at certain times, certain locations in the x direction,

whether it's positive, to the right, negative, to the left.

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And then we have the idea of actually plotting this

with time as a vertical axis.

So, again, if you think about horizontal slices here, the x axis as drawn,

is what the x axis looks like at t = 0 seconds.

And then, we have another slice at t = 1 second, t = 2 seconds,

3 seconds, and 4 seconds, and so on, and so forth with that.

So if we were to imagine a situation where we have an object moving and

we're taking flash photographs of it and recording position at given times.

And we'll just pretend say at t = 1 second it was at position 1 along the x axis.

So we put a dot there, a mark there.

And maybe at 2 seconds, we saw that it was actually at position 2 along the x axis,

and at 3 seconds it was at position 3, and so on, and so forth with that.

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And the velocity of an object when we do this plot

is essentially distance traveled over elapsed time.

So the distance traveled, sometimes we call this the run

along the horizontal direction, distance traveled, divided by the elapsed time.

So in this case, if I traveled three units, maybe three meters,

in three seconds, clearly the velocity would be one meter per second.

Three divided by three.

And so the slope of this line gives us an indication of the velocity.

Now technically the slope is not exactly equal to the velocity.

Because let's look at another situation here.

Let's say that in one second it only went half a meter.

And so in one second it'd be right here.

And then in two seconds it was at one meter.

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And at three seconds it was at one and a half meters.

So it's going at a steady velocity there, a half meter per second.

We can pretty much see that.

Draw the line here, and

that represents a different path, or perhaps a different object, or

the same object second time around going at a different speed.

And we see here that in the first case It was going one meter per second.

And in this second case, it's going half a meter per second.

So, we can see that, when the slope is higher, a higher slope, larger number for

the slope, more vertical line, is, slower velocity, a lower velocity.

Versus, if the slope of the line is lower, then we get a higher velocity.

So, when we do this type of plot, this type of spacetime diagram, with

time being vertical, x being horizontal, the velocity, if we have a constant

velocity object, we get a plot of it, and it's going to be a straight line.

And, the slope of that line is inversely related to the velocity.

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So large slope,

which means it's marked closer to the vertical, means a slower velocity.

Smaller slope, means it's closer to the horizontal, gives us a larger velocity.

Intuitively you can think about this by thinking about the proper

plotting here again.

If, in one second, so if I go up one second vertically, I move five metres,

that is a slope like that, and that's going to be a higher velocity.

I've moved a larger distance in a given amount of time,

versus one of these other examples- here, I've only moved one metre in one second,

or even half a metre in one second.

Slope of those lines is more vertical and therefore it's lower velocity.

Just something to keep in mind because when we do this later on and

actually apply relativistic effects to these types of diagrams,

it'll be important to remember that higher slopes, larger slopes,

more vertical slopes means lower velocity.

And as you bend down this way it represents a higher velocity object,

again everything being constant velocity here.

We're not going to deal with cases of acceleration.

If you do acceleration, so the loss is changing on an object, you get curve lines

going inverse directions, so not straight lines like that.

So, just a reminder about spacetime diagrams.

Again, everything is in the physical reality here is in the x direction,

the horizontal direction.

We're just plotting things along the x direction.

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The actual physical reality is not objects moving at some angle here, but

just moving along on the x axis.

And we're plotting their position in time and therefore we get these straight

lines representing different velocities as they travel along the x direction.

Okay, so that's little reminder about space time diagrams.

We're going to do some more of these in this video clip on frames of reference.

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And want to remind you too that, I hope you did the little

priming the brain exercise with the moving sidewalks and all that.

We're actually going to really do that same sort of concept,

instead of moving sidewalks, we'll use spaceships here.

So let's imagine that we have the classic use of names here is Alice and Bob.

We also use these things in cryptography.

Alice and Bob sending messages back and forth to each other encrypted,

comes probably from A and B right, so instead of just saying person A,

person B, we give them names Alice and Bob.

And if you don't like the names Alice and Bob,

you can use your own names here if you like.

So we've got Alice and Bob, and they're in spaceships.

So each of them has their own spaceship, and let's consider Alice first.

All right.

So I actually have Alice here and her spaceship,

and what do these circles represent?

Those circles are clocks.

We talked about how to record events in space and time.

We need essentially a measuring system, and

clocks at each of those points on our measuring system to measure time.

Essentially we have the lattice or grid of clock.

So that's what this is supposed to represent here,

this nice little stick with Alice's spaceship, A is for Alice of course.

And the clock's along here.

So as far as Alice is concerned, we'll just start off with her at rest.

And she has all her clocks set up there.

And so she can record any event that occurs along her horizontal axis here.

So there is Alice.

And now let's bring Bob into the picture.

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So Bob will have an orange space ship here.

And we can imagine that Bob is flying by Alice like that.

She's just at rest.

Bob flies by and perhaps as he flies by, each of her clocks, her stationary clocks.

And remember, I should have mentioned.

Their synchronized clocks, so all of Alice's clocks here record the same time.

They're not out of whack or

anything like that as far as she's concerned, everything's good.

So as Bob flies by, then we can see that pressed,

he trigger some sort of photographic clock.

And so

the record of his fly by passed Alice here can be recorded on each of her clocks.

And then she go back later and say, okay at t equals 3.2 seconds you

pass this clock right here, and then later on he was passing this clock here,

it equals 8.9 seconds or something like that.

And from you can measure figure out what his velocity is passing by her.

So let's pause there for a second and

actually do a spacetime diagram of just Bob flying by Alice and her clocks here.

So if we do that, we'll say, okay, so

here's our spacetime diagram.

And by the way, we'll nearly always assume unless specified otherwise

that when they're together right here, that's t = 0.

Okay, so we can imagine he's coming in here and they set their clocks.

There's a clock on Alice's spaceship as well, not shown.

So she has a clock at each point along her axis here.

And so right here is t = 0 and then as he goes along here,

Alice's clocks measure his position at those times.

So we always assume that when we're talking about Alice and

Bob, their clocks are synchronized.

Bob has a clock on his spaceship.

She has a clock on her spaceship.

They're all synchronized at t = 0.

So often we'll be starting at our point t = 0 here.

So this will be time for Alice and

position for Alice, as Bob flies along.

We're going to plot Bob's path through Alice's space, as it were.

So, at t equals zero they're right together.

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And then right here, we'll start our clock right here at t = 0.

And then as Bob goes on the various clocks, we'll record Bob's position.

And remember, all these are synchronized so maybe right here he's at time t = 1,

so all Alice's clocks would read t=1 at that point according to her, and

then t = 2 perhaps here, t = 3, t = 4, t = 5.

So what we get is, we'll use red a little bit here,

so let's put some tick marks in, like that,

so position 1, 2, 3, 4, 5, 6.

And some times, 1, 2, 3, 4, perhaps.

So this is what Alice would record.

Alice would record, again we'll just say at time t = 1,

Bob was at position one, clock number one there.

So right there, I guess we'll put it in red, using red here.

At t = 2 is in position 2, t = 3 position 3, and so on and so forth.

And again, assuming constant velocity, we get a line.

If we did more recordings of all these positions,

we'd get that line representing a certain velocity.

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This goes 1 meter per second, perhaps,

or something like that, whatever our units happen to be.

Maybe 1 mile an hour, or 1 lightyear per hour, per second, something like that.

So there is his,

by the way we'll talk about lightyears a little later on in the course.

You've probably heard that term, you may be a little fuzzy on exactly what it

means, so don't worry about it for the moment.

So just constant velocity for Bob here, but this is what Alice

would observe and just to sort of jump ahead in terms of what we're talking about

here in terms of frames of reference, this is Alice's frame of reference.

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They have photo recording devices so any time something goes by and she needs to

record and event at that location, she'll have a record of that at that clock.

And she's watching Bob fly by here.

So this is Alice's frame of reference and

Bob is traveling through Alice's frame of reference.

And so Alice is plotting Bob's path through that.

And so it was at one second he was at position one, at two seconds he was at

position two, at three seconds he was at position three, and so on and so forth.

And we indicate, this is Alice's frame of reference,

Alice's perspective, because we're saying here, t sub A and x sub A.

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This is, these are Alice's measurements of Bob's flight

through her frame of reference.

But we could also ask, well what about Bob?

What's he observing?

If we're out there in space, there are no other reference points, we'll say, nearby.

So as far as Bob is concerned,

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And so we can also ask what would this be like in Bob's frame of reference?

And in fact, just to make it a little clearer, Bob has his own lattice of clocks

which he can record anything in his frame of reference along the x direction, and

each clock represents the time frame.

All his clocks are synchronized.

All of Alice's clocks are synchronized.

Later on, next week, we'll see that was one of Einstein's key insights

that Alice's synchronized clocks in this case Bob has his synchronized clocks,

but as far as Bob is concerned, Alice's are not synchronized and

also Bob's are not synchronized to Alice.

But that's jumping ahead a little bit.

We need to make sure we understand how

these frames of reference work because even though the idea is fairly simple,

in my experience I find that later on it can cause some confusion.

Like I've said before, if you don't get the these foundational issues down solid.

So again, Alice sees Bob flying by.

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Bob, from his perspective, sees Alice receding,

really flying by backwards if you want to put it like that.

And he can record Alice's path with all his clocks.

And again they're synchronized for him and Alice's clocks are synchronized for her.

So if he did that, what type of diagram would he see here?

Let's draw another one over here.

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1, 2, 3, 4, negative 1, negative 2 and

now we're running into Alice's plot there.

And then the time again, 1, 2, 3.

Well, more or less, you see I've got different scales here,

but we'll assume it's the same.

It doesn't really matter for our point here because plotting Bob,

then he sees Alice plotting Bob's perspective.

Okay remember from Alice's perspective time t = 1,

he's at position one, time t = 2, he's at position two.

For this simple example we'll assume it works the same way for Bob.

So he sees Alice at t = 1, he sees Alice at his negative 1 position, and then,

negative 2 position, negative 3 position and so on and so forth.

And so, we get something like this, at t = 1,

he sees Alice right there, and at t = 2, he sees Alice here.

And so, again, if we continued on, we get a line going like that.

In other words, it's just pointing in different directions.

It points to the left, this one points to the right,

because as far as Alice is concerned, Bob is moving to the right.

As far as Bob is concerned, Alice is moving to the left.

Then just to indicate this, this is Alice from Bob's perspective,

from his frame of reference.

And this is Bob, from Alice's perspective.

One moves to the left, one moves to the right.

And the whole concept here of a frame of reference is that

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neither could tell which is really moving and which is stationary.

Really, the whole concept of the principle of relativity that we're working our way

towards here and we'll get to it very soon, not quite in this video clip,

but coming up in a couple of video clips here we'll talk more about that.

But we can already see hints or indications

of the principle of relativity here that if you're out there in outer space,

they are in their two space ships, there are no other reference points around,

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one can't tell whether the other is moving.

And perhaps you've had that experience if, say, you've been on a train, or

even a car perhaps, where there's another train or

car next to you and the road is very smooth, the tracks are very smooth,

and so you see movement and you're not sure are you moving?

Or is the other train moving?

It can be disconcerting there for a minute.

But that's really the key concept of the principle of relativity.

Alice and Bob, Alice sees Bob moving, Bob sees Alice moving.

As far as Bob's concerned, he's stationary.

As far as Alice is concerned, she's stationary as well.

So this is the frame of reference concept.

The frame of reference is a perspective of a stationary observer,

like Alice or Bob, with their frame of clocks.

And so this is Alice's frame of reference.

This is Bob's frame of reference with his lattice clocks, synchronized clocks.

And whole idea here that we'll explore more as we go along in the course

Is some of the surprising results of the fact that even

though it seems like if Bob's clocks are synchronized, and

Alice's clocks are synchronized, they should see things the same.

In actual fact, they don't see things the same, because of some surprising results

due to the speed of light, as Einstein was really the first to understand that.