Hovedindhold

## Minkowski spacetime

Aktuel tid:0:00Samlet varighed:7:55

# Starting to set up a Newtonian path–time diagram

## Video udskrift

- [Voiceover] Let's say
this is me right over here, and I'm drifting through space at a constant velocity relative to any other inertial frame of reference, and so I am, I am in an inertial frame
of reference myself, and in fact I'm going to define my frame of reference by me, I'm gonna say I'm at the origin of my frame of reference. So at all times, I consider myself to be stationary, and I am at the point, 'x' equals zero, and we're gonna focus on just the 'x' dimension, to simplify our discussion, and I have, you know, my oxygen and everything, and food, so no need to worry about me. Now, what I've drawn here are some axes, so that I can plot the path of things as time progresses in my frame of reference. And one thing that many of ya'll might have noticed is that I have plotted time in seconds on the vertical axis, and our position, our 'x' position, in meters on the horizontal axis. And that might be a little
bit counter-intuitive for a lot of ya'll, especially with math backgrounds, in fact, it's a little
bit uncomfortable for me, we often prefer to put time
on the horizontal axis, and position on the vertical axis, so this is a little bit counter-intuitive. But this is, you know, our choice is
a little bit arbitrary, in math class, we liked to think of our independent variable on our horizontal axis, and we think of time as
somehow driving position, so that's why we tend to put time there than we'd position there, but you can flip them around. And as we'll get more into physics, we'll see, well maybe we shouldn't necessarily think of time
always driving position, or maybe position in some
ways are driving time. But we'll get into that. But let's just first get a
little bit comfortable with this. So what would be my position over time on this diagram right over here? And you might notice these numbers, one second, two second, three second, and then in meters I have three times to the eighth, six times to the eighth, nine times to the eighth, so these are massive, massive numbers, and you could guess where
they are coming from. They are coming from the notion that the speed of light is approximately 3x10 to the eighth meters per second. But we'll get to that in a second. But let's just think about my position over time, in my frame of reference here. So, time equals zero, my 'x' position in this frame of reference is zero, I consider myself to be stationary. After one second, well my position is still zero, after two seconds my position is still 'x' equals zero, after three seconds my position is still 'x' equals zero, so my, I guess you could almost consider my path on this diagram, where I'm plotting time and space, at least in the 'x' direction, is going to look like, is going to look like, whoops, I can do a better job than that. It's going to look, it's going to look like, it's going to look like that. That would be my path on my little time and space axes, or on this little diagram that I have. But let's think about something a little bit more interesting. Let's think about me having a flashlight, so this is, I have a flashlight here, and I, at time equals zero, I turn on that flashlight, exactly at time equals zero I turn on that flashlight. And let's think about
the very first photon of light that emits from my flashlight. And let's plot it's path on my little diagram here. So time equals zero, it's exactly where I am. So time equals zero, it's position is zero meters. But after one second, where is my photon of light? And I'm gonna put it, and the photon is moving in the positive 'x' direction. So it's moving in the
positive 'x' direction with a velocity of 'C' meters per second in the positive 'x' direction. And so, after one second, it will have moved 3x10
to the eighth meters. After two seconds, it will have moved 6x10
to the eighth meters. And I've intentionally scaled my axes, so that now if I were to
draw the position of light relative to time, it's going to be at a 45 degree angle. And that's just an artifact of how I've picked my axes. But let's see if I can plot this. So it's gonna look something like this. And this is hand drawn, so it's not going to be perfect. So the position of that photon over time is going to look like that. After one second, 3x10 to the eighth meters, after two seconds, 6x10
to the eighth meters, after three seconds, we have 9x10 to the eighth meters. Alright, well that's
reasonably interesting so far, we're getting a little bit comfortable with my little diagram here, maybe some of us are getting a little bit more comfortable with time on the vertical axis, and my position on the horizontal axis. But now let's introduce another character. Another character who could almost define, or who could define their
own frame of reference. So let's say that right
at time equals zero, a spaceship passes me by. So that's, I have to draw a bigger
spaceship than that. So, there you go, that's the spaceship, and in the spaceship I have my friend, so that's the spaceship. And the spaceship is travelling with a pretty incredible velocity, in the positive 'x' direction. So I guess if this is, this vector is the speed of light, which this seems like
an awfully short arrow, but if I'm gonna say
that's the speed of light, then let's say that this thing is moving with half the speed of light. Which is still incredibly fast. So the velocity, the magnitude of the velocity here is 0.5C. So let's plot, and my friend is stationary
in that spaceship, the spaceship is moving at this constant velocity, 0.5C in the positive 'x' direction. So, they also are in an
inertial frame of reference, because it's at a constant velocity relative to me, which is an inertial frame of reference. And so let's plot my, let's plot her position on my little diagram. So time equals zero, she's exactly where I am. She's at the origin of
my frame of reference. Her 'x' position is zero. Now after one second, she's moving half the speed of light, so after one second she would have gone 1.5x10 to
the eighth meters per second. So she would have gone about that far. After two seconds, she would have gone as far as light can go in one second, because she's going
half the speed of light, so she would go about that far. After three seconds, she will have gone 4.5x10 to the eighth meters. So let me put that right over there, and you see where this is going. So if I were to plot her path, if I were to plot her path, it would look like this. It would look like this, path of my friend. That's the path of my
friend right over there. And, I want you to just
kind of think about this, think about this a little bit, think about how these different lines are, what they represent, once again get familiar with the 't' on the vertical axis. But now in the next video, we're gonna use this, what I just drew, to draw her frame of reference, to draw a coordinate system, or I guess you could say a space time diagram for
her frame of reference, on top of this one. And at least in the context of this video and the next few videos, we're going to assume a Newtonian world, we're not gonna get to Einstein in special relativity, we're just going to assume, well, we'll get to that in the next video.