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- [Voiceover] Let's say
this is me right over here,

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and I'm drifting through space

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at a constant velocity

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relative to any other

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inertial frame of reference,

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and so I am,

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I am in an inertial frame
of reference myself,

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and in fact I'm going to define

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my frame of reference by me,

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I'm gonna say I'm at the origin

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of my frame of reference.

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So at all times,

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I consider myself to be stationary,

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and I am at the point,

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'x' equals zero,

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and we're gonna focus on

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just the 'x' dimension,

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to simplify our discussion,

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and I have, you know,

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my oxygen and everything,

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and food,

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so no need to worry about me.

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Now, what I've drawn here

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are some axes,

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so that I can plot the path of things

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as time progresses

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in my frame of reference.

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And one thing that

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many of ya'll might have noticed

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is that I have plotted time in seconds

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on the vertical axis,

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and our position, our 'x' position,

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in meters on the horizontal axis.

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And that might be a little
bit counter-intuitive

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for a lot of ya'll,

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especially with math backgrounds,

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in fact, it's a little
bit uncomfortable for me,

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we often prefer to put time
on the horizontal axis,

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and position on the vertical axis,

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so this is a little bit counter-intuitive.

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But this is,

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you know, our choice is
a little bit arbitrary,

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in math class, we liked to think

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of our independent variable

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on our horizontal axis,

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and we think of time as
somehow driving position,

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so that's why we tend to put time there

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than we'd position there,

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but you can flip them around.

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And as we'll get more into physics,

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we'll see, well maybe we shouldn't

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necessarily think of time
always driving position,

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or maybe position in some
ways are driving time.

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But we'll get into that.

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But let's just first get a
little bit comfortable with this.

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So what would be my position over time

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on this diagram right over here?

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And you might notice these numbers,

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one second, two second,

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three second,

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and then in meters

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I have three times to the eighth,

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six times to the eighth,

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nine times to the eighth,

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so these are massive, massive numbers,

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and you could guess where
they are coming from.

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They are coming from the notion

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that the speed of light

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is approximately 3x10 to the eighth

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meters per second.

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But we'll get to that in a second.

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But let's just think about

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my position over time,

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in my frame of reference here.

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So, time equals zero,

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my 'x' position in this frame of reference

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is zero,

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I consider myself to be stationary.

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After one second,

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well my position is still zero,

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after two seconds my position

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is still 'x' equals zero,

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after three seconds my position

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is still 'x' equals zero,

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so my, I guess you could almost

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consider my path

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on this diagram,

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where I'm plotting time and space,

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at least in the 'x' direction,

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is going to look like,

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is going to look like,

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whoops, I can do a better job than that.

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It's going to look,

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it's going to look like,

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it's going to look like that.

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That would be my path

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on my little time and space axes,

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or on this little diagram that I have.

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But let's think about

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something a little bit more interesting.

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Let's think about me having a flashlight,

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so this is, I have a flashlight here,

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and I, at time equals zero,

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I turn on that flashlight,

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exactly at time equals zero

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I turn on that flashlight.

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And let's think about
the very first photon

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of light that emits from my flashlight.

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And let's plot it's path

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on my little diagram here.

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So time equals zero,

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it's exactly where I am.

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So time equals zero,

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it's position is zero meters.

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But after one second,

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where is my photon of light?

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And I'm gonna put it,

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and the photon is moving

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in the positive 'x' direction.

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So it's moving in the
positive 'x' direction

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with a velocity of 'C' meters per second

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in the positive 'x' direction.

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And so, after one second,

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it will have moved 3x10
to the eighth meters.

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After two seconds,

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it will have moved 6x10
to the eighth meters.

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And I've intentionally scaled my axes,

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so that now if I were to
draw the position of light

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relative to time,

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it's going to be at a 45 degree angle.

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And that's just an artifact

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of how I've picked my axes.

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But let's see if I can plot this.

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So it's gonna look something like this.

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And this is hand drawn,

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so it's not going to be perfect.

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So the position of that photon over time

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is going to look like that.

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After one second,

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3x10 to the eighth meters,

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after two seconds, 6x10
to the eighth meters,

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after three seconds,

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we have 9x10

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to the eighth meters.

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Alright, well that's
reasonably interesting so far,

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we're getting a little bit comfortable

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with my little diagram here,

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maybe some of us are getting

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a little bit more comfortable

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with time on the vertical axis,

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and my position on the horizontal axis.

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But now let's introduce another character.

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Another character who could almost define,

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or who could define their
own frame of reference.

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So let's say that right
at time equals zero,

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a spaceship passes me by.

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So that's,

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I have to draw a bigger
spaceship than that.

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So, there you go,

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that's the spaceship,

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and in the spaceship I have my friend,

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so that's the spaceship.

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And the spaceship is travelling

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with a pretty incredible velocity,

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in the positive 'x' direction.

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So I guess if this is,

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this vector is the speed of light,

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which this seems like
an awfully short arrow,

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but if I'm gonna say
that's the speed of light,

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then let's say that this thing

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is moving with half the speed of light.

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Which is still incredibly fast.

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So the velocity,

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the magnitude of

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the velocity here is 0.5C.

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So let's plot,

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and my friend is stationary
in that spaceship,

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the spaceship is moving

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at this constant velocity, 0.5C

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in the positive 'x' direction.

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So, they also are in an
inertial frame of reference,

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because it's at a constant velocity

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relative to me,

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which is an inertial frame of reference.

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And so let's plot my,

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let's plot her position

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on my little diagram.

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So time equals zero,

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she's exactly where I am.

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She's at the origin of
my frame of reference.

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Her 'x' position is zero.

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Now after one second,

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she's moving half the speed of light,

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so after one second she

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would have gone 1.5x10 to
the eighth meters per second.

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So she would have gone about that far.

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After two seconds,

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she would have gone as far as light can go

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in one second,

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because she's going
half the speed of light,

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so she would go about that far.

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After three seconds,

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she will have gone 4.5x10

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to the eighth meters.

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So let me put that

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right over there,

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and you see where this is going.

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So if I were to plot her path,

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if I were to plot her path,

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it would look like this.

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It would look like this,

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path of my friend.

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That's the path of my
friend right over there.

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And, I want you to just
kind of think about this,

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think about this a little bit,

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think about how these different lines are,

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what they represent,

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once again get familiar with

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the 't' on the vertical axis.

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But now in the next video,

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we're gonna use this,

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what I just drew,

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to draw her frame of reference,

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to draw a coordinate system,

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or I guess you could say

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a space time diagram for
her frame of reference,

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on top of this one.

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And at least in the context of this video

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and the next few videos,

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we're going to assume a Newtonian world,

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we're not gonna get to Einstein

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in special relativity,

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we're just going to assume,

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well,

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we'll get to that in the next video.