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Current time:0:00Total duration:7:55

Starting to set up a Newtonian path–time diagram

Video transcript

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 going to say I'm at the origin of my frame of reference so at all at all times I consider myself to be stationary and I'm at the point x equals 0 and we're going to focus on just the X dimension to simplify our discussion I have you know my oxygen and everything so and food so so no need no need to worry about me now what I've drawn here are some axes so that I can plot I can plot the path of things as time progresses in my frame of reference and one thing that many of you all 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 counterintuitive for a lot of you all 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 counterintuitive but this is you know our choice is a little bit arbitrary in in math class we like to think of our independent variable on our horizontal axis and we think of time is somehow driving position so that's why we tend to put time there that we position there but you can you can flip them around and as will get more more into physics we'll see well maybe we shouldn't necessarily think of time always the driving position or maybe position in some ways our driving time but we will we'll get into that but let's just first feel get a little bit comfortable with this so what would be 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 have three times 10 to the 8th 6 times 10 to the 8th 9 times 2 VA so these are massive massive numbers and you could guess where they are coming from they're coming from the notion that the speed of light is approximately 3 times 10 to the 8th meters per second but we'll get that and we'll get to that in a second but let's to think about my position over time in my frame of reference here so time equals zero my exposition 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 and 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 the axes are on on this little diagram that I have but let's let's let's think about something a little bit more interesting let's think about me having a flashlight so this is 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 that very first photon of light that emits from my flashlight and let's plot its path on my little diagram here so time equals zero it's exactly where I am so time equals zero its position is zero meters but after one second where is my photon of light and I'm going to put it and I'm and the photon is moving in the positive x direction so it's moving in the positive x direction with a with a velocity of c.c meters per second in the positive x direction and so after one second it will have moved three times ten to the eighth meters after two seconds it will have moved six times 10 to the eighth meters and I've intentionally scaled my axes so that now if I were to draw the the position of light relative to time it's going to be it's going to be at a 45 degree angle and I that's just a artifact of how I picked my pick my axes but let's see if I can plot this so it's going to 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 after one second 3 times 10 to the 8th meters after 2 seconds 6 times 10 to the 8th meters after 3 seconds we have 9 times 10 to the 8th meters all right well that's that's that's reasonably interesting so far we're getting a little bit comfortable with my little diagram here where maybe some of us are getting a little bit more comfortable with time on the vertical axis and and my position on the horizontal axis but now let's introduce another character another character who could almost define there 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 can draw a bigger spaceship than that so there you go that's that's the spaceship and in the spaceship I have my friend so that's that's that's the spaceship and the spaceship is traveling with a pretty incredible velocity in the positive x-direction so I guess if this is if this is the specter is is the speed of light which seems like an awfully short arrow but if I'm going to 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 0.5 C so let's plot and and my friend is stationary in that spaceship the spaceship is moving at this constant velocity 0.5 C in the positive x direction so they also are in an inertial frame of reference because it's a it's at a constant velocity relative to me which is in an inertial frame of reference and so let's plot my let's plot her let's plot her position on my little diagram so time equals zero she's exactly where I am she's she's she's at the origin of my frame of reference her X 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 1.5 times 10 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 would go in one second she's going half the speed of light so she would go about that far after three seconds she will have gone 4.5 times 10 to the 8th 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 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 going to use this what I just drew to draw her frame of reference to draw a coordinate system or 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 in the next few videos we're going to assume a Newtonian world we're not going to get to Einstein in special relativity we're just going to assume well we'll get to that in the next video