All right, we've been talking about frames of reference and I have a couple more things to do with them. First, I want to introduce the term inertial frames of reference. Where does that come from? You've probably heard the term inertia, it actually comes from the Latin word inert, which can mean things like lazy. And how does that apply here? Well, it actually goes back to Newton's, Isaac Newton's First Law of Motion, where essentially, he stated that any object that is at rest or in motion, in constant velocity motion, it's inertia is resistance to it's change of state. In other words, if it's at rest and you need to put it into motion. The more inertia it has, the harder it is to change it from rest to some velocity. Or if it's traveling with constant velocity, the difficulty you have in terms of actually changing it to a different velocity. So that's where the term inertia comes from, at least in physics terms. So we talk about an inertial term of reference. For our purposes, what this will mean, as we've been talking about Alice's frame of reference, Bob's frame of reference. An inertial frame of reference is a reference frame that's either at rest or in constant velocity motion, that there's no acceleration or anything else going on like that. And the special theory of relativity deals with inertial frames of reference. Later on Einstein, about ten years after the Special Theory of Relativity was able to put the final touches on his so called General Theory of Relativity that dealt with non-inertial frames of reference. And that could be something where you're accelerating. But if you imagine, think about just being in a car. Even as you go around a curve you're sort of thrown to the outside. That's a non inertial frame of reference, there are some acceleration involved in that circular motion or that turning. If you're going straight along in a car at constant velocity, you don't feel yourself push back in the seat or thrown to the side. So that's one piece of evidence that you're in a non-intertial frame of reference if you feel that acceleration, if you feel yourself being pushed back in the seat. Or if you feel yourself going around a curve, thrown to the side, and so on and so forth. Or actually, a gravitational field is a non-intertial frame of reference. But that's beyond our course, that's the general theory of relativity, as I mentioned. So In this course, anytime we talk about a frame of reference we will assume it is an inertial frame of reference, unless otherwise specified. So again, inertial frame of reference just means it's either at rest or in constant velocity motion. So we talk about, one frame of reference, maybe Alice's versus Bob's frame of reference and we know they're inertial if the motion between them is just constant velocity. There's no acceleration going on. So inertial frames of reference. Other thing we want to mention here is combining velocities. Now, everything we're doing here is actually before, pre Einstein, so we haven't gotten into that yet. So this is combining velocities in what we would say the low velocity limit when velocity are low enough not near the speed of light then everything we've said so far applies. Again we'll see how it changes when we get to Einstein's principles and his two key principles we'll be getting to, and then the implications of those as he worked them out. But, so combining velocities, let's just do a little example here. Let's say we've been talking about Bob and Alice. Let's go back to Bob's spaceship here. So here's his Spaceship, here with his cockpit. And he's going, Alice is observing him. So maybe he is going by with some velocity v. Now remember, for Bob, as far as he's concerned, he's not moving. He has his whole grid or lattice of clocks all synchronized with each other. And so he can measure events in his frame of reference. He's an inertial frame of reference. Because as far as he's concerned, he is at rest there. And he can tell that because he doesn't feel any acceleration going on. So he has his lattice of clocks there. And we're going to imagine here that he has a spaceship such that if something goes wrong, he has an escape pod. And so we'll just put the, not a very fancy spaceship here, but we'll assume the escape pod is just that spherical object there. And so if necessary he can get in that escape pod or put something else in that escape pod and have it shoot off from his spaceship. And so we're going to assume that if he does that it will shoot off from his spaceship at a velocity v. So know what's going on here. From Alice's perspective, from her frame of reference, Bob is traveling by at velocity v, but he's also shooting off his escape pod at velocity v. So let's backup to Bob's perspective. From Bob's perspective he's just sitting there in his cockpit. He actually maybe sees Alice going, receding in the background from him. But he assumes that she is in motion, not himself. He assumes he's at rest. He can see all his lattice of imaginary clocks, as it were. And so he shoots off his escape pod at velocity v. So he sees that escape pod going away from him at velocity v. And he can measure that on his clocks and his measuring apparatus there. So what does Alice see? So here is Alice here. So there's Alice. She's observing Bob go by. Question is, what velocity does she see the escape pod going at? Well, very simply we just add the velocities and so if the escape pod is receding from Bob's ship at velocity v going away at velocity v. And then from Alice's perspective Bob's ship is actually going at velocity v, then the velocity of the escape pod to Alice. The escape pod to Alice equals v + v, which of course is 2 v. And we've chosen the same velocities in this case but it works for any velocities. We could say maybe the escape pod is shooting off at 3 v. And Alice sees Bob going by at velocity v then it's v plus 3 v and you get 4 v. So that's the velocity of the escape pod as Alice sees it going along there. If you want a maybe a more prosaic example, think about if you're throwing a ball. Throwing a baseball or something like that, and maybe you can throw it at 50 miles an hour, or if you want, 50 kilometers per hour. Obviously they're different, but just pick whichever set of units, system of units you want there. so you can throw it at some velocity to your friend over there, whose catching it and then you get on a truck or something like that, or even a bicycle, or just even running towards them, and then you throw it at the same velocity. So the velocity then of the ball coming toward your friend is going to be the velocity of the throw itself. Assuming 50, plus whatever velocity. You're either running or riding on a bike, a pickup truck or something, obviously, don't try this at home, perhaps, or be very careful if you do things like this with moving vehicles. But the person who's catching the ball is going to see that added velocity. It's going to be the velocity of the moving vehicle, whether you're just running, or whether it's a bicycle you're on, or some sort of car or truck, and as you throw it to them, you throw it with the same velocity. In other words, it's leaving your hand with the same velocity, say 50 kilometers per hour, but then the velocity of your movement as well adds to that and so your friend feels, you know has to catch it at a higher velocity there. Or if you go the other direction as well. If you're going away from your friend at say 50 kilometers per hour and you're throwing it toward him or her at 50 kilometers per hour, it cancels out. So, you've got 50 going that, you're throwing 50 that way, and the ball, in principle, just drops right down. If you ever watched the show, Mythbusters, they tested that one time and it took some doing to get everything set up right but they were able to get at least get one case where they had perfect velocity of the truck going by this way. It had a little apparatus that shot out a basketball or something like that, and so be able to shoot it with this velocity and cancel it out with the velocity of the truck going the other way, and using the high speed camera, they saw the basketball just drop straight down. So that's the idea here that when you're combining velocities in frames of reference, the velocities just add. So again, in Bob's frame of reference, he shoots out his escape pod with some velocity. In Alice's frame of reference, she's at velocity v in this case. The escape pod is moving away from Bob at velocity v and so to Alice, the escape pod is moving at velocity 2v or again, if she's going in the other direction it would cancel out. So if Bob was moving with V this way and he shot the escape pod the other way at velocity V, the escape pod to Alice would just sit there. Again to Bob, it would still be going away from him, but to Alice the movement of the spaceship that way plus the escape pod that way would mean the escape pod would just sit here in her frame of reference. So that's how we added velocities before Einstein came along. And as we will see with his two key postulates or principals of his special theory of relativity which will be coming up here in a video clip or two I think two video clips away. We'll talk about those in more detail. Some of the implications of that are this doesn't work. It works for low velocities, velocities that we encounter in, for the most part, everyday life. But once you get up to velocities near the speed of light, you can't just add things like this. So if Bob's velocity here is near the speed of light, his spaceship is near the speed of light, and he shoots off his escape pod at some velocity v, it's not just as easy as this. It's not a simple combination, a simple addition of velocities. So that's one of the things we are heading towards. In the next video clip, we'll want to say a few more words about things with frames of reference and spacetime diagrams and then we'll get on to Einstein and his two principles on which he based his special theory of relativity.