I'm being passed by a truck, but I'm in motion relative to the Earth. I'm passing this car. It's in motion relative to the Earth as am I, but I'm going faster than it, so it appears to me as if the vehicles are going backward. Am I at rest, or is the other train at rest? Is it moving, or am I moving? Are we both moving? Absin external reference points in these kinds of questions. We find ourselves often lost and even a little bit confused about what's really going on. Is the other train moving, or am I moving? These are simple questions, but they lead to extremely deep insights into the nature of the cosmos. Let's begin to explore this concept, relative motion. Let's begin a mathematical exploration of relative motion or simply relativity. And I'm calling this part one because as I will hint at at the end, the subject of relative motion or relativity is quite a bit deeper than we would get into early on in an introductory course, but I would like to preview some of the importance of this subject at the end of this lecture. The key ideas that we're going to explore in this first lecture on relativity are as follows. We're going to recognize that when two observers use different coordinate systems, each one affixed to their own frame of reference, those two observers may draw different conclusions about the reasons for events happening in the universe. We're going to learn to relate those observations, however, in those two distinct coordinate systems using something which is known as the Galilean transformation. It has some observations that are a core part of the transformation, but it also has at least one key assumption built into it as well as we will see later. We will then understand that observations and assumptions that underlie that transformation have consequences, and that's what I'm going to close with at the end here. That's why this is only part one of this particular subject for a physics course at this level. To proceed, let's conduct something known as a thought experiment. One of the most famous physicists in the history of the field who was originally born in Germany would have called this a gedanken experiment. The translation of that, roughly speaking, is a thought experiment. An experiment we carry out based on the principles of what we know about the world, but we only do the experiment in our mind. Let's consider two actors in this experiment, one person named Sally and one person named Bob. And let's say Sally and Bob are friends, and they happen to have both gone to the train station at the same time, but they're going to different destinations, and so Sally gets on one train and Bob gets on another, and they arrange it so that the windows of their seats are facing each other from one train to the other. So they're sitting on these adjacent trains, and the trains originally begin parked in the station. Well, they can't talk to each other through the glass of the window, so they get out their mobile devices, and they begin chatting with each other using those devices. So they're using Skype or FaceTime or just a plain old phone or something like that, and they're so distracted with their conversation that neither of them notices the very slightest acceleration that suddenly causes one of the trains to start moving forward. Instead, they merely notice by looking out the windows at each other and suddenly realizing that somebody's moving that one of the trains must be in motion, although they don't know which one because they didn't notice the acceleration. And so they each look out their windows, and they look at each other's trains, and they remark simultaneously on their mobile devices, hey, you're moving. And then a disagreement begins. No, says Sally, you're moving backward. My train is standing still. No, says Bob. It's you who are moving forward, and my train is sitting still. So they both agree on what forward and backward are. Forward, perhaps, is east along the tracks. Backward is west along the tracks. And there they don't disagree. Sally might say you're moving westward, and Bob might say you're moving eastward. No problem there. But what they disagree on is who is doing the moving. Now, the reason that they have a disagreement at all is neither of them notice the acceleration that started one of the trains moving. The train that's moving is now doing so at a constant speed. So there are no sudden surges that can tell one of them, hey, my engine's powered up. And neither of them can see the ground or any other external reference points. They can't see the platform. They can't see a lamp post on the ground, something that would be fixed to the ground. And if that were moving, they would know that they were on the train that's moving. Be ludicrous to think that suddenly the ground is rotating underneath the train. It must be the train that's moving over the ground. But they don't have any reference points like that. All they can see are the other person's train moving past them, either eastward or westward, at a constant speed. So the question here from the physics perspective is, well, who's right? Who is the keeper of the correct perspective in all of this absent any reference points in the outside world that would immediately tell who's actually moving, let's say, with respect to the surface of the earth? Well, if you ponder that for a little bit and realize that there may be situations, in fact, you may have even been in one yourself, where you don't have any external reference points and you're stuck thinking about what might be going on with no information to make the decision, you can tell what a difficult situation this must be. And from a physics perspective, the answer is that in truth they're both correct. Each of them is right in their own way. They certainly agree on the sort of gross events, the most general things that are going on. A train is certainly in motion. But absent any external reference of any kind, they are going to always disagree on which train it is that's moving. That said, thanks to motion and its nature, which we have been exploring now for a little bit in this course, they are actually able to use space and time information to relate one observer's set of observations to the others. And using the mathematics of motion, they can provide explanations, Sally to Bob and Bob to Sally, as to why the other person observes what they observe. And this whole concept is known as relative motion or very simply relativity. We're going to begin to study the subject now using what we already know about motion. But one thing I would like to emphasize at the beginning is in the popular misconceptions of what relativity is, it's often said that relativity is a statement that anybody is correct independent of an absolute truth. But in fact, in physics, when we talk about relativity, it's not about what is different for both observers that is the key. Certainly Sally or Bob could disagree on whose train is moving. If we had a third observer, we might be able to sort out that problem. But fundamentally, in order for them to relate their observations to one another, it's not what's different that matters, but what is constant or the same for both of them, that is what matters. And fundamentally, as we're going to see, relative motion is pivoting not so much on what's distinct about what two observers observe, but rather what uniform things, what constancies in nature that they believe they can use to relate their observations. Now to begin this discussion, we have to establish some kind of mathematical framework, some kind of toolkit that's going to allow us to describe what's going on here, keeping this analogy of the trains and Sally and Bob in our minds. Now I picked trains for a reason. They're long, straight, and they mostly travel on straight tracks, and so they make an excellent one-dimensional motion example. Now one key idea that we're going to need here to describe that kind of situation in our thought experiment is something known as a frame of reference, and a frame of reference is merely a coordinate system imagined or otherwise. You could literally make a coordinate system in market, and that coordinate system is possessed by each observer, so that each observer can make measurements, and then those measurements can be compared from one frame to the other. For instance, by communicating them over a mobile device, they carry that coordinate system with them, and so we can imagine that wherever Bob is sitting, that that defines the origin of Bob's coordinate system, and east along the train is the positive x direction, and west along the train is the negative x direction, and Sally similarly has her own coordinate system, Sally's coordinate system. She is the origin of that coordinate system. When she moves, the origin goes with her, just as if Bob were moving, the origin of his coordinate system would go with him. Again, we have to think about what's the same here, and since these two trains are parallel to each other, and both observers agree what east is, and what west is, for Sally as well, even though the origin of her coordinate system may move with her, eastward along that coordinate system is positive, and westward is negative, so they both agree on what are positive directions in space, and what are negative directions in space. They may simply disagree on who's at the origin of each other's coordinate systems, because each is at the origin of their own, and that's illustrated here on the right. I've tried to generate two one-dimensional coordinate systems, you can almost think of these as trains that are parked next to each other at the station, but this is a moment in time when, for instance, if we imagine that Sally is on the train on the top, and Bob is on the train on the bottom, and each is sitting at the origin that is zero of their coordinate systems, they're slightly displaced from one another. Their origins are not in the same place. This may represent a moment in time after one of the trains has started moving, and one person is displaced along the origin of the other person's coordinate system. So one person says, oh, well, I'm still at the origin of my coordinate system, I haven't moved, and then they look over at the other person, and they see that person is not sitting at the origin of their coordinate system, and they say, you've moved. And of course, the other person can look at the first and say, no, no, no, I'm at the origin of my coordinate system, and in my coordinate system it is you who have moved, and you can begin to see the origin of the disagreement here. And since either Bob or Sally can make the claim that each of them is at rest and the other person is moving, that's all perfectly valid, we as thinkers about this problem, we have to make a choice. We have to define one of them as being at rest. We have to make that decision. We may not even really know who's moving, but it turns out it won't matter. The mathematics works out the same. All that changes in the end is, if you made the wrong decision, you wind up just realizing that there, for instance, real speed of the train that's moving your points in the direction opposite the one you thought it did. So we will always define one coordinate system in a case where we have two as being at rest, and the other as being in motion relative to the first. And really that's what relativity is. You make a choice. I choose this coordinate system to be at rest. And then, based on that, if any other coordinate system is moving relative to that one, the other one is in motion. That's how you make these definitions sane at the beginning. Otherwise, there's no way to make any decisions whatsoever. Now, the one that's defined to be at rest is typically denoted as the frame capital S. And the one that's assumed to be in motion is typically denoted as the frame capital S with a little tick mark next to it, known as a prime. So I'm gonna call this S prime for the remainder of certainly this lecture, and likely every other time I talk about this when you interact with me about the subject. Now, we could imagine, in order to kind of concoct a situation that you might be more comfortable with, that there's a third person, and we are that third person. And we're standing on the platform near the two trains. And because we're standing on a platform that is affixed to the surface of a planet, and we define the planet to be at rest, and the platform therefore affixed to it is at rest, and we standing on the platform, not moving with respect to the earth, are also at rest, we could make the decision that we, in our privileged position, are the absolute frame of reference where all things are defined to be at rest. And one of the trains, which is not moving, is also in our frame of reference, and therefore is at rest. But the other one, which is moving, is moving relative to our frame. And then that would allow us to make the decision about which one is S, and which one is S prime, okay? And the train that's moving, of course, is said to be the frame S prime. It carries a coordinate system with it that with respect to the other trains or to ours is moving. Now, let's continue to use this concept of a frame of reference, and let's think about some relative measurements. Let's do a simple relative measurement at first to build up a little bit of comfort with this idea. Let's begin by considering a situation where, yes, Sally and Bob, S prime and S, they do, in fact, have their own coordinate systems and that they begin displaced from one another. Sally maybe picked a window seat at one end of a car, and Bob picked a window seat at the other end of the car next door. So they're not sitting window to window facing each other. One is at one end of a car, one ends at one's at the other. They can talk to each other over their mobile devices. They can look out their windows and down the line of the train and see each other, but they're not at exactly the same horizontal location along the track. In that case, their origins are displaced from one another, but neither train is moving yet. So Sally's not moving, Bob's not moving. Each of them agrees that the other's train is at rest with respect to theirs. Let's consider that situation. And to illustrate this, for instance, imagining that maybe there's a suitcase, one unit of distance ahead of Sally on the train, she might look at that suitcase and say, ah, that suitcase, that suitcase in my coordinate system for I am at zero, is located at one unit of distance in my frame ahead of me. And she might, if she were to write down her observations and maybe using some program, share them with Bob via her mobile device, might draw a picture like this. So here is Sally, here is the suitcase, and she notes this as position X prime one in her coordinate system, and it's one unit of distance, whatever the units are ahead of her on her train. Now, where would Bob, where would an observer at the origin of frame S claim that to be located? Well, I drew a little dotted line to help you out here, to help you connect points on Sally's coordinate system, frame S prime, with Bob's coordinate system, frame S. And if you follow the line down to Bob's coordinate system, you see that while Bob is sitting way over here, he's displaced back from Sally in relative space, but that's the origin of his coordinate system, where he's sitting. And he sees that same suitcase located not at X equals one in his coordinate system, but rather at X equals two units of measurement. So the answer here is that in frame S, X is equal to two. In frame S prime, X prime, the measurement along that coordinate system is equal to one. Now, it's not that one of them is wrong, they're each right in their own coordinate systems. The question is, can we relate their observations? Can we find a mathematical equation that given Bob's observation, we could get Sally's, or given Sally's observation, we could get Bob's? Well, sure, neither train is moving. There's a fixed displacement, a constant displacement between where Sally is and where Bob is. Let's denote that displacement as just a lowercase letter C for the time being. And since Sally, S prime, is shifted ahead of S, Bob, by one unit along the respective axis that Bob has, we can relate their observations. So for instance, if Sally reports a measurement of the suitcase being at one unit ahead of her in her coordinate system, we would note that to get Bob's observation, all we have to do is add one unit to Sally's, and that will give us what Bob saw, which is two. So X prime plus one equals X, and that gives us two. In fact, the answer that we can see by reading it off of this picture over here. So we have a mathematical rule that we could generically apply to relate observations in one frame to those in another. If we know the offset at any moment in time, then we can relate observations in the S prime frame to those in the S frame. If we know where the S prime frames say origin is with respect to the origin of the S frame. So we take like coordinate points in the two systems and we determine their offset, one frame relative to the other, we call that C, and we simply add that. So I'm taking the offset to be measured from frame S to frame S prime. So any number we get in S prime, we have to add C to it to get the number in S. And so the equation is quite simple in one dimension. It's that any position measurement in X is given by the position measurement in X prime plus the offset. And you can rewrite this equation to solve if you know the position in S, if you know X, you can get X prime by subtracting C from X. So you can go from measurements in the S system, Bob's system, to measurements in the S prime system, Sally's system quite easily. Just rearrange this equation. From Sally's perspective, Bob is offset by negative one unit in her frame. So you can see a minus sign just crops up here in order to relate these observations. It's easy to relate these observations when something is the same for both of them. Now we've looked at relating positions. What happens now if something is moving in frame S prime? What would frame S see? So what about speeds of objects that we now place in this frame? I mean, we can imagine that Sally, for instance, throws a ball forward in her frame or something like that or somebody is running down the aisle of the train in Sally's train. These are all things that we can imagine. So let's imagine that. Let's imagine that now there's an object that can move in frame S prime. What does the motion look like in frame S? And again, let's consider a situation here where the two frames are both at rest with respect to each other. Frame S prime is not yet moving, but they're displaced from one another. So let's consider an object that in frame S prime is moving to the right with a speed of one meter per second. So I've kind of illustrated that here. It starts off originally at negative one in the S prime coordinate system. And then one second later, it's at zero. So it's where Sally is located, for instance. And then another second later, the object is again moving at one meter per second, gone one meter forward. So now the units on this scale could be meters, for instance. So it's gone one meter forward in frame S prime. And the question we wanna answer is, okay, it's moving at one meter per second in frame S prime and Sally's frame. What's its speed as observed in frame S, in Bob's frame of reference? Well, from the sequence of time snapshots that are available here, the object at zero seconds at negative one meter, the object at one second at zero meters, the object at two seconds at one meter, all in frame S prime, we can see that for every second, and in both frames, the object actually advances by a displacement of one unit in the positive direction. Let's look at Bob's perspective on this object. Bob says, oh, well, the object began not at negative one, as you say, Sally, but rather at zero where I am. And then one second later, it was one unit ahead of me, one meter ahead of me. And two seconds later, it was two meters ahead of me. It went another meter in that second. So you'll note that the deltas from one unit of time to the next in both frames are indeed the same when these frames are at rest with respect to each other. In both frames, both observers agree that delta X and delta X prime are the same. They're one unit because the speed is one meter per second. So this is great because when the frames are at rest with respect to each other, the velocities of objects are the same as measured by observers in each frame. Both agree that the object is moving forward. Both agree that the object is moving at one meter per second. They don't agree on where it is in space, but we know how to relate those observations to one another using what we did on the previous slide. Let's look at this mathematically, and the derivative calculus offers us a glimpse as to why it worked out this way. If the offset between the frames is, again, a constant and unchanging value, frames are not moving yet with respect to each other, and we call that value C, then we know that in the prime frame, the velocity of the object will simply be given by its rate of change with time of its X prime coordinate or DX prime DT. If you wanna think about gross average velocities rather than instantaneous velocities, you could instead say delta X prime over delta T, but you'll get the same answer, and I prefer to use the calculus here to nudge you a little bit to begin to think more in this infinitesimal, tiny, instantaneous, thin slice way. Now, what about in the S frame? This is the speed in the S prime frame. What about in the S frame? Well, in the S frame, it's the same equation, but with the primes gone, the speed of the object or the velocity of the object in the S frame is DX DT or delta X over delta T if you wanna talk about gross average velocities. But we have an equation that relates measurements in X to measurements X prime in the other frame so we can substitute for X in this equation and take the time derivative of that equation, X prime plus C, whatever it is that Sally measured plus the offset of Sally's frame with respect to Bob. Remembering from our previous look at this that when you have the derivative of a sum of two things, that the derivative operation distributes to the two things, you can distribute the derivative with respect to time to X prime and you can additionally distribute it in the sum to C. So you have a time derivative of X prime plus a time derivative of C. We arrive at our final answer and that is that this reduces to just DX prime DT. That is the velocity in Bob's frame of reference which was certainly DX DT in his frame also is DX prime DT which is exactly equal to V prime which we started with over here in Sally's frame. In other words, V is equal to V prime by this long chain of equivalents. Why is that? The offset is constant. The time derivative of any constant is zero because constants do not change in time and the time derivative fundamentally answers the question, how does this thing that I'm acting on change in time? And if it's a constant and only a constant, the answer is not at all, zero. So the first term in this may not vanish but the second term certainly does, DC DT is zero. And we get our equivalence. What we observed in a picture over here, we see also confirmed by mathematics which really is the reliable way to do this because mathematics after all is the descriptive language of the natural world. Let's now consider what happens when we're in a situation that's much more like the train thought experiment that began the part of the lecture. Now in that case, we had one of the frames of reference moving with respect to the other. So by our convention, let's denote the moving frame as S prime and so that's going to be the top frame in my cartoon down here. And let's imagine that it is moving relative to S which is down here at a speed of one meter per second. So let's imagine that and let's draw that motion as time moves forward. So starting here at zero seconds, the origins of the two frames, the origins of these two one-dimensional coordinate systems coincide. But at one second, frame S prime has moved one meter and so now at time equals one second, the origin of its coordinate system is no longer aligned with zero in frame S, it's now aligned with one meter in frame S. And if we let time lapse one more time, one more second, now the origin which is still zero in frame S prime is located at X equals two in frame S. And so we see that the origin of S prime is moving to the right in what both frames agree is the positive direction along their respective X axes. And the displacement now between the origin of the S prime coordinate system and the origin of the S coordinate system is increasing. So unlike before where the displacement which we denoted as the letter C was a constant, now the displacement depends on time. And in fact, if you sort of play this back a little bit here, you can see that if frame S prime is moving relative to frame S at a speed of one meter per second in the positive X direction, that it's also true that the displacement between these two coordinate systems is likewise increasing at one meter per second. So now because the displacement is no longer a constant, it varies with time. And any time now that we do some math and we take the time derivative of C, the displacement between the two frames, we have a new relationship. That relationship is that the rate of change of C with time, that is the first derivative of C with respect to time, is actually exactly equal to the speed with which the frame S prime is moving. And of course since displacement is a signed quantity, really this is the velocity of the frame S prime with respect to S. So we are no longer in a situation where frame S prime is at rest with respect to frame S and they just have displaced origins in their coordinate systems. Now it's that the origin of frame S prime is actively moving along the X axis of frame S and increasing the displacement with time. Of course, if we imagine a situation where the speed with which frame S prime is moving is exactly zero, what happens to the time derivative? Well the time derivative also becomes zero. That is to say the displacement between the two frames of reference is a constant and we return to the situation we looked at in part one of this question of speeds in frames of reference. Let's now revisit the thought experiment regarding Sally and Bob in the trains. A person on the platform outside of the trains in a kind of privileged position where they know for sure that they're standing on a platform that's affixed to the earth and they're able to call that a sort of frame of absolute reference of rest. They're gonna see that Sally's train is actually the one that's moving and it's Bob's train that's actually at rest. But because Sally and Bob both lack any reference points in some other frame, they can't know this. All they see is that one of them is sitting in one train and the other one appears to be moving. However, with our privileged viewpoint, we're able to label Bob's frame S and Sally's frame S prime. S for the frame that we call at rest, S prime for the frame that we say is moving with respect to the one we're calling at rest. Now, if the train is moving at this velocity, V S prime, then we can begin to understand Sally's point of view and of course we can also at the same time understand Bob's point of view. Bob believes that it's Sally that's moving because he can claim he's at rest and that Sally is moving forward at a speed V S prime. But Sally believes it's Bob that's moving because she can claim that she's at rest. Now, we know better, but Sally cannot know that. But something for her is in fact different. In her frame, it's Bob's train that appears to be going in the other direction. So Bob might say, ah, Sally, your train is moving in the positive X direction. And Sally would say, no, no, no, I'm at rest. Your train is moving in the negative X direction. Now they both agree that the speed is V S prime, but the direction is different, which makes the velocity different. And so we can see from this perspective that it must be true that what Sally calls V S is the negative of what Bob calls V S prime. And this allows us to relate their observations one to the other. So what if Sally now throws a ball toward the front of her train while she's moving? Now she doesn't know she's moving, she just takes a ball and she throws it forward. Let's ignore gravity for the time being. Let's pretend the ball just moves along the X axis and only along the X axis. It doesn't rise, it doesn't fall. What does she see? And what does Bob see? Let us imagine that Sally has thrown the ball at a speed in her frame of reference, which will label V prime, of one meter per second in the forward direction. Now at the same time, her train is also moving forward. And she doesn't know this, but from Bob's perspective, that speed is one meter per second in the forward direction. So let's watch what happens in this picture on the left hand side over here. Let's watch what happens to the ball from Bob's perspective as time marches forward. The ball is represented by this blue dot that begins at time zero seconds at the origin of both coordinate systems. I have chosen time zero seconds to define the moment when the origin of Sally's coordinate system in S prime and the origin of Bob's coordinate system in S are the same. If we let time go forward at one second, we can then begin to observe what each of them sees. So again, at time zero seconds, Bob sees the ball at x equals zero and Sally sees the ball at x prime equals zero. But at one second, Sally's train has moved forward one meter relative to Bob's coordinate system. And so at one second, Sally sees the ball at one meter forward in her frame of reference. Remember, she's still at zero. But her zero point in Bob's frame of reference has now moved forward to one meter in his frame of reference. So where does Bob see the ball? Well, Bob sees the ball at x equals two. So it was at zero at t equals zero seconds, but now it is at x equals two at t equals one second. The origin of Sally's coordinate system is only at one meter in Bob's, but the ball is at two, because the ball is moving at a speed that appears to be in addition to the speed of Sally's train. Let's look at t equals two seconds. At t equals two seconds, Sally is now at two meters in Bob's coordinate system. In Sally's frame of reference, the ball has only gone two meters from where she threw it. One meter per second, two seconds later, it's gone two meters. But from Bob's perspective, it's now at four meters in his coordinate system. So at time zero, it was at zero. At time one, it was at two meters. And at time two, it's at four meters. So from Bob's perspective, the ball isn't moving at one meter per second as it would appear to Sally, but rather at two meters a second. Every second, it moves two meters in Bob's frame of reference. But how? How can the speed be different? What's going on here that makes this happen? And the answer is, is that the speed of the ball has, from Bob's perspective, the speed of Sally's train added to it. So she says, I threw the ball at one meter per second. And he said, well, that's true, but your train is also moving at one meter per second. So I see it moving at two meters per second, and that's how we relate our observations. And we can see this again with calculus. So again, let's remember that in Sally's frame of reference, which is S prime, the speed of any object that she throws will be denoted V prime. So really it's a velocity. It can go in the positive direction. It can go in the negative direction. So it has directional information. And that's the first derivative with respect to time of the coordinate of that object in her frame, which is X prime. Now, transferring over to Bob's frame of reference, frame S, in his frame, the speed of the object will be denoted by V, again, velocity really. And that is the first derivative with respect to time of the coordinate of the object, the ball in this case, in his coordinate system, which is X. So DX, DT. But again, we know how to relate coordinates in Sally's frame to Bob's frame, in frame S prime to frame S. All we do is we take the coordinate as measured in Sally's frame of reference, the S prime frame, and we add to it the offset between her origin and his origin, the origin of frame S prime and the origin of frame S. That's just X prime plus C. We distribute the derivative. So now we have DX prime DT plus DC DT. But remember now that Sally's frame, S prime, is in motion with respect to Bob's frame. So again, consider the picture up here. In one second, her origin had moved one unit in Bob's frame. In two seconds, her origin had moved two units in Bob's frame of reference. She is moving with a frame speed of VS prime. And that frame speed is just the time derivative of the offset C. That's it. So DC DT is not zero this time because she's moving. DC DT is what we would call VS prime, the speed of her frame with respect to Bob's frame of reference. So this is just V prime, as defined over here. DC DT is what we call VS sub S prime, the speed of her frame with respect to Bob's. And so in the end, we find out that the speed that Bob sees is the speed she sees plus the speed of her frame. Now, if these are velocities, these can be signed quantities. They could subtract from each other and we'll explore that in a moment. It's also important to note that we now have a relationship as well between the coordinate for the ball that Bob measures and the coordinate for the ball that Sally measures. All we have to do is take Sally's coordinate and because this is right now constant speeds that we're considering, we add to that the speed of her frame multiplied by the time that has passed since zero time, for instance. So the X coordinate in Bob's frame is the X prime coordinate in Sally's frame for the ball plus the speed of her frame times time. This looks familiar, right? This just looks like one of those one-dimensional equations of motion. But here it tells us the relationship between measurements in one frame and measurements in another. It's the same equation, but it's employed for a new purpose. Now, the final consideration we're going to do for all this is what if Sally throws the ball backward in her frame of reference? So instead of throwing it in the forward direction and in the direction of increasing positive numbers, what if she throws it in the direction of increasingly negative numbers? What will be the velocity as observed by Bob? Well, we can work this out. Let's do the mathematics first. From the mathematical perspective, the velocity observed by Bob will be the velocity observed by Sally plus the velocity of her frame with respect to Bob's frame. Well, in her frame, the velocity's negative one meters per second. She threw it backward. It's going more and more negative every moment in time. The speed of her frame, however, is still in the forward direction. It's one meter per second going forward. Well, we have one meter per second in the negative direction. One meter per second in the positive direction, these cancel each other out. And so we claim that Bob would observe that the ball in his frame of reference appears to be going nowhere at all. So Bob would seem to see the ball just stand still in the air. Again, we're neglecting gravity in this little cartoon example. In reality, we'll come to what would happen in a moment. Of course, it would begin to fall under the acceleration due to gravity in the vertical direction, but it is true that in the horizontal direction, which is independent of the vertical direction in this case, the ball would appear to just sit still in his coordinate system along x. Let's confirm this using our picture to the left here. So we have the ball at time zero seconds from both Sally's perspective and from Bob's perspective. And then we advance time one second from Sally's perspective, the ball is moving backward to increasingly negative numbers. Although I haven't drawn in here, this is negative one in her coordinate system. She's still here at zero. Bob is down here at zero. Look where he sees the ball. The ball is right along x where it was a moment ago. From his perspective, it's not moving at all. Yes, Sally has advanced forward one unit in his coordinate system, but that ball is not going anywhere. And if we go to two seconds, the ball appears to hover right where Sally had been at time zero. It's not going anywhere, but from her perspective, of course, it's now negative two units in her coordinate system behind her where she's sitting at zero in her coordinate system. So indeed, even graphically, even pictorially here, we see that the ball stands still from Bob's perspective. Whereas from Sally's perspective, remember she's sitting here at zero in her coordinate system, that ball is moving backward with a velocity of negative one meters per second. So the two effects cancel out in Bob's frame of reference, but they don't cancel at all in Sally's frame of reference because she thinks she's at rest and she thinks that she's thrown the ball with a velocity of negative one meters per second, which is true in her frame, but not in Bob's. Bob explains this by saying that the speed of her train is canceled by the speed at which she threw the ball in the negative direction, and then it appears to hover there for him. So I hinted that we need to take a look at motion in two dimensions, and this is just going to be sort of a brief tour. We're not gonna go into this in the mathematical depth that we went into this in one dimension. Extending this to two dimensions is just an exercise in carrying an extra dimension around. It's not that bad. But what if we now think about relative motion in two dimensions? And there's a demonstration I'm gonna show you a short movie of right now. I showed it to you before in the lecture on two-dimensional motion when we began this subject as a contrived case where a cart is rolling along a table at a constant velocity and it launches a ball into the air, and then some distance later, it catches the same ball that it launched earlier. We've considered many cases of two-dimensional motion so far, projectile motion, for instance. But we've also looked at circular motion. Circular motion is the one case where because of the tethering of an object with some influence or force, the motion in the X and Y coordinates is not independent. But in all the other cases we've looked at so far, the motion in the X coordinate system and the Y coordinate system are totally independent of one another. And we're gonna revisit that kind of motion here again. And let's remind ourselves the independence of those kinds of motion, one along X, one along Y, by again looking at the short slow motion video of moving at a relatively constant velocity along a horizontal surface, launching a ball into the air and then it catches it a few moments later. So let's look at that one more time and see this effect. Now let's think about the perspectives that we can have on this motion. From our perspective, at rest with respect to the surface of the earth, where sitting behind a camera, the camera's sitting on the floor, the floor is attached to the earth, the table is attached to the earth, that stuff we can all say is not moving. So we can say that we're in the stationary frame, the frame S. And from our perspective, it's the cart that's moving to the right where at rest the cart is moving. And when it ejects the ball out of its top, the ball already has a horizontal component of velocity from our perspective. It was part of the cart, it was moving with the cart. And so even though the cart launches the ball vertically into the air, that ball nonetheless already has an existing component of motion along the horizontal direction. So of course, when the ball is now freed from the cart, it's simply going to continue along the X axis in the forward direction, even while it has this new component of motion that was granted to it by being ejected out the top of the cart. So that additional component of motion is nice, but it comes with some complications. Of course, the minute that the ball escapes the cart, the only force that's acting on it is gravity. Gravity will slow its velocity in the upward direction and then reverse it. And these two vectors, one horizontal and one vertical, they add together to create projectile motion, just like we've seen before. So this is an excellent example of projectile motion. So this is just like throwing a ball into the air at an angle. If you launch it with an initial velocity in the X direction and an initial velocity in the Y direction, the velocity in the X direction, which ignoring air resistance is completely unaffected by any other influences, will simply continue as it started. But in the Y direction, gravity will slow the vertical component of the velocity eventually to zero. It'll reach its apex, its highest point, and then it reverses that velocity and it begins to accelerate down where it's toward the floor. And that's exactly what happens here in this video. The cart is ejecting the ball. The ball has an initial velocity in the Y direction, but gravity slows it down. It comes to a stop and then it reverses that motion and eventually it comes right back down to where it started because nothing happened to influence its horizontal component of velocity. So that's our explanation from our perspective. But what about the perspective of somebody sitting on the cart? From our privileged position affixed to the surface of the earth, we make the bold claim that we're at rest and the cart is moving. And so, of course, the cart and the ball have the same horizontal velocity and the cart simply catches the ball later because they're both moving at the same speed along the positive X direction. In the Y direction, it's complicated, but in the X direction, it's simple. But somebody's sitting on the cart, how would they explain all of this? Well, they would make the following argument. Well, no, it's nice that you think you're in a privileged position and you're at rest, but actually, I'm also in a privileged position because I'm sitting on this cart and I'm not moving and the cart doesn't seem to be moving with respect to me. So I argue I'm at rest. And then, yeah, at some point, this ball gets shot out of the top of the cart, but I'm not moving and the ball wasn't moving either with respect to the cart in the horizontal direction. And so, of course, the ball goes straight up, gravity reverses its direction and it comes straight back down and the cart, of course, catches the ball. It was under it the whole time. The only reason you think that there's projectile motion going on with some horizontal component is that you're moving backward relative to me. You claim I'm moving forward relative to you, but I say no, no, no. The reason you think that there's a projectile motion is because the ball is staying in the same place along X in my coordinate system, but you're moving backward. So you can see how this relativity stuff can get a little confusing sometimes, but the key thing is to keep in mind what's the same for all observers. We can contrive actually a really complicated situation and in fact, I've done that for your pleasure here. We can actually use cameras in two frames of reference to recreate these two perspectives to show you that each perspective is absolutely valid and we can certainly agree that an object gets launched, an object lands someplace. The exact details will vary depending on which frame we're viewing the action from, but we can relate to each other and we'll come back to how it is we're able to relate to each other, really what's going on and why it is we're able to relate to each other our observations in a moment. But let's take a break and let's take a look at this rather Rube Goldberg-esque contrived experiment that I did along with one of the young physicists in our department, Eric, who assisted me throughout this particular exercise. So let's take a look at this. So what we've done is we have set up a camera in the audience, a camera at the top of a stand and the stand is sitting on a cart that can be pulled. Now Eric is gonna pull me standing on the cart at a constant velocity. In my hand, as you're gonna see in a moment, I'm holding an iron weight with a bright yellow rubber glove on it. Don't ask. I'm gonna drop this weight, watch what happens. The weight appears to move along with me even as it's dropped. When it's dropped in the X-coordinate system of the room, from this perspective, it's starting somewhere over on the left and when it hits the floor, it's moved to the right. Now let's take a look at the exact same experiment, but from the perspective of someone on the cart, we have a camera mounted above the weight wrapped in this yellow glove. Again, don't ask. Eric has started pulling me along. I now will let go of the weight and watch what it does in my reference frame. It falls straight down the meter stick that's mounted to this stand. That's my Y-coordinate axis and indeed it fell straight down. It never moved forward or backward relative to me on the cart. It's as if it was at rest with me the whole time. And so we can see these two perspectives, one from the frame S and one from the frame S prime. We may disagree on what happened. Either the thing was falling and moving to the right or falling just straight down, but we can relate our observations. So let's just quickly think about the mathematics that would be required to relate observations really in any number of dimensions. And fundamentally, this relationship between coordinates in one coordinate system and coordinates in another coordinate system, so one frame and another frame. This thing is known as the Galilean transformation and it's named after Galileo Galilei who did really detailed studies of motion and came to understand things like if I'm carrying an object with me and I'm in motion relative to the ground and I drop that object, the object continues to move along with me. If we have any two frames of reference, we can relate velocities in the two frames of reference using a simple vector equation. It's an extension of the one-dimensional equation that we developed earlier. The velocity in the frame S, which we call the rest frame, is simply the velocity of an object in the frame S prime plus the velocity of that frame S prime with respect to the frame S. This is just the vector version of this addition of velocities equation I showed you a moment ago. Now, if we consider a special case where the motion is entirely along one-dimensional axis, so let's say that the motion of frame S prime is entirely along the x-axis in frame S, then we can say that that velocity vector looks like this and based on this, we can begin immediately relating using the equation we developed earlier for relating positions of moving objects in the two frames just like we did before. In the horizontal direction, in the x direction, the coordinate position x of a moving object in the second frame, S prime, is given by its coordinate in that frame plus the speed of frame S prime with respect to S times the time that passes. But all the y measurements will be the same because the frame S prime is not moving along y, it's not moving along z, it's only moving along x, and so all the observations that we make along y or z, if you do three dimensions, they're gonna be the same between our two frames, but the x's won't, and they'll be related to each other by the speed of the frame times time. And this is where we have to think very carefully about what it is that's been the same this whole time that allowed us to make observations in one frame of reference map onto observations in a different frame of reference that's moving with respect to the first one. What have been so far the actual observations that we've used to draw these conclusions, but what has been the implicit assumption as well that we've used to draw these conclusions? Well, the observations are that observers in different reference frames are absolutely going to disagree on absolute positions in space. There really is no such thing as absolute position in space. I have my coordinate system, I'm at the origin of it. You have your coordinate system, you're at the origin of it. That's okay. You might say that something is at one meter along the x-axis, I might say that something is five meters along my x-axis. That's okay. We can relate using the displacement between our axes, those observations. And that displacement may change with time. We can nonetheless adapt to that situation. We know how to do that by using the relative speeds of the frames to relate coordinates. So we already know that spatial measurements are relative observations. They are relative to each other. They can be different, but we can relate them. But the assumption we have been making in order to relate them has been that something is constant. And we've implicitly assumed that it is time that marches at the same rate for both frames of reference. Go back and look at the exercises that we did before where there's zero seconds, then one second of passing time, then two seconds of passing time. What was implicit in those cartoons that I drew? That time is marching at the same rate for observers in frame S and observers in frame S prime. Now this assumption seemed perfectly reasonable for a long time. And in fact, it was good enough for a long time from the days of Galileo and those first really serious studies of motion using both experiments and mathematics through the time of Isaac Newton, which is basically the next century. And then into the 1700s and 1800s, the development of electricity and magnetism, the laws of thermodynamics, all of that really happened in the 17 and 1800s and culminated in the 1800s. And it was only at the end of the 1800s that it was possible to actually see the effects of time not marching at the same rate for two frames of reference. Now we'll come to this perhaps later in the course. Certainly if you wanna do special topics on this I'm happy to do this, but I wanna emphasize that for our purposes for this course it's pretty safe to assume that if I'm in motion relative to you that my clock advances at the same rate as your clock. And so even if we disagree on spatial measurements we absolutely would agree on time measurements. And it does turn out that that assumption is fatally flawed. In fact, in reality, time does not move at the same rate for an observer in motion relative to another observer. This may sound a little crazy, but you can do experiments that reveal this. Some of them are quite simple. One experiment you're doing all the time without realizing it is likely that you're using the global positioning system in order to figure out where you are on the surface of the earth. To go to some friend's house you've never been to before they tell you their address, you punch it into a GPS map program like Google Maps or Bing Maps or something like that and you get a dot on a map and it says, here's the best route to get there. How does all that happen? Well, fundamentally it happens because there's a system of satellites in orbit around the earth and they relay information to your phone or some GPS receiver unit in your car and that information tells you where you are now and how to get to where you want to be in this other location on the surface of the earth. But those satellites are moving extremely fast in orbit around the earth and they have extremely sensitive atomic clocks on them. And it turns out that they're moving fast enough relative to the surface of the earth that the different rate of the passage of time is observable. Their clocks will actually come out of sync with any twin clocks that they were originally synchronized to on the surface of the earth. Now, motion plays a big part of this but there are other effects that have to do with relativity that are also in here as well. It's a little complicated to get into now but suffice to say that every time you use the global positioning system, you're using a system that is constantly corrected for the drifting of time in two different frames of reference. You might ask yourself, well, if time is different in one frame moving relative to another and spatial measurements aren't the same, what is it that's constant? What is it that allows us to relate measurements in one frame to another and even correct for such effects in the first place? And it's something I hinted at earlier in the course and it is, in fact, the speed of light. The speed of light is, as far as we know, a fundamental constant of nature that is unaffected by the motion of the frame in which the light is admitted or observed. So for instance, even though satellites whipping around the Earth experience different rates of time and of course different spatial positions as a result of their motion relative to the Earth, light signals, radio, that's transmitted to and from those satellites is always observed to move at exactly the speed of light. Even though those satellites are in motion when they emit the radio signals, when they arrive on Earth, the speed of those signals is still the speed of light. As Neil deGrasse Tyson has said in the most recent reboot of the series Cosmos, which I would encourage you to watch. There is a law of nature. We don't completely understand where it comes from but we know that it's a law. And that is when it comes to light and the speed of light, thou shalt not add the speed of your reference frame to the speed of light. The speed of light is completely constant and invariant against all motion. It's an interesting fact of nature and we're able to use it to solve this relativity problem, this relative motion problem. But nonetheless, it is one of those interesting features of nature that we really have yet to fully grasp. So let's review the key ideas. We've seen that when two observers use different coordinate systems, they may draw different conclusions about the reasons for events happening. Nonetheless, we have learned to relate observations into coordinate systems and really what this boils down to is a series of relationships which are known as the Galilean transformation. They are relationships between spatial coordinates but also velocities between the two frames measured for different objects in those frames. We've come to understand that observations and assumptions go into these transformations and in the Galilean transformation, the assumption is that time marches at the same rate for all observers regardless of their state of motion. And that's gonna work just fine for us in this course. But it is true that as you advance forward in physics and certainly by the time you get to third semester physics, you will have to accept the fact that it is time and space that are both relative to observers and different frames of reference. And it is instead the speed of light that is the constant that allows us to unite the observations of those two frames of reference. So that is the reality of the nature that we live in. The fact that time is not quite the same for two observers as long as we keep our frames of reference moving at slow speeds relative to one another far below the speed of light itself, for instance, will be okay. We'll be able to use the Galilean transformations to understand the universe. But when you have extremely fast clocks and extremely fast objects holding those clocks, they are sensitive to those time drift effects and you can't use the Galilean transformation anymore. You have to use something a bit deeper, something known as the special theory of relativity or if you really wanna go full bore, the general theory of relativity. Those are topics for a different lecture but I hope you've enjoyed this little peek into the nuances of space and time revealed simply by a thought experiment about two people who disagree about who's in motion on two trains.


Hi, I'm Peter Burris and welcome to another Cube conversation from our outstanding studios in Palo Alto, California. Got a great conversation today. We're going to be talking about some of the challenges and changes taking place in the MSP, the managed service provider part of the marketplace, made possible by software-defined WAN, SD WAN Technologies. And to do that, we've got Alistair Johnson, who's a principal architect at Nuage Networks here with us on theCUBE today. Alistair, welcome to theCUBE. Thank you Peter, it's great to be here. So let's start corporate update, Nuage Networks. What's going on? Well, we've had a pretty good year so far. A number of customers that we'll be announcing over the next few months that we've established this year, in addition to the major wins that I'm sure most of the market's familiar with over the last few years. We're really seeing that in the managed services space, that SD WAN is gaining a lot of traction. We're finding that particularly outside of North America, but with increasing North American interest, that enterprises are looking towards a managed SD WAN service as opposed to doing it themselves. Going down the path of having a carrier come in and provide them with both connectivity and the service layer, or looking at taking the service layer from a managed services provider and sourcing the connectivity themselves. So this is an area that's especially fruitful and open for some significant innovation, and innovation that's going to have enormous impact on how the market behaves. So let me run something by you. So here's the observation I've made over the years. That servers, Moore's Law meant that there was this kind of smooth growth and performance. And even in software, it kind of followed Moore's Law. But network, because of the degree of interplay and natural integration amongst the components, there was always this kind of weird step function where every four or five years, the big telecommunications companies or managed service providers, would make major investments in their networks. And you got this very rough, coarse, odd step function. And that sometimes scared some of these companies away from participating in all the innovation of the cloud. Have I got that right? Absolutely. I mean, the tradition of having both your service layer and your transport layer being coupled, you know, an IP network is offering both the IP transport, but also the services like MPLS VPNs or layer two VPNs. It was meant that, you know, the tech lifecycle became relatively long. The process to qualify, deploy, manage, and then eventually automate services and the delivery of those services took a long time. SDN has presented a really interesting opportunity for the carriers along with the broader audience in the industry to really leverage software and the frequency of updates that software can give you without needing to make those hardware changes at the same time. So you can still do the hardware changes but you get a smoother upward innovation curve. Absolutely. So the underlying transport platforms, the routers, the DWDM systems, et cetera, those can be changed as needed to by capacity demands or vendor changes or new technology that comes out in those spaces. But we can use SDN or in this case SD-WAN to smooth out the service offering on the top. And as it becomes a software delivered function, we can upgrade that much faster. We can roll it out much more like we update our cell phones, our tablets, et cetera, and introduce new functionality into the service layer much faster than we were able to do in the past where we had a very much a hardware-coupled service offering. Now I made a comment that in many respects, some of the big telecommunications companies, some of the big MSPs have not participated in this explosive innovation that's associated with cloud. And part of the reason is because when you think about cloud, someone can say, I can think of a new service and then they can create it and deploy it because it's largely in software. Whereas a lot of the telecommunications MSP type companies go, I can think of a new service, but then they look around and they say, oh, the hardware's not ready and I've got to wait for the hardware to be ready. How does this notion of SD-WAN and this software-defined service layers start to alter the way that some of these big companies think about their underlying infrastructure and all structures, how they think about automation, how they think about competing for new services? Well, it becomes a very big competitive differentiator because I can be a carrier and I can offer new services much faster, as we touched on. I'm getting a benefit of automation very quickly because SD-N was heavily around automating the configuration in the service elements and I can become a lot more cost-effective with that. Customers are looking for more self-control, more self-management, information, diagnostics, tooling, et cetera, but without the overheads of running very large IT and network-specialized personnel. So the carriers get that advantage, the enterprises get that advantage, everyone is getting effectively a much more modern service experience. We saw that with the cloud, I guess, revolution, if you want to put it that way, that I no longer needed to order a server, put it in a rack, deploy an operating system, put my application on it, take six months. That changed with the cloud, everyone understands that. The network layer did not change as fast and that's where we saw SD-N and the data centers come along to address that problem, that's what we're solving with SD-WAN as well. So when we think about the relationship between big cloud players and some of these MSPs, it is that we've got the big cloud payers that are virtualizing everything, the MSPs who are still kind of physically stuck, but still have the vast majority of those last miles that are so crucial to having that end-to-end productivity and compatibility. Does that start to change as we start to think about new wireless technologies? How does SD-WAN improve the MSP's ability to both bring new automation and bring new, but also introduce some of these new technologies that will make it easier to think cloud last mile in the same breath? Well, it's an interesting point.  They were maybe reselling a carrier's infrastructure or procuring it for their enterprise customers. Now they have the ability to actually manage the service layer and they could be using Carrier A today to reach the customer's location, but they strike a new deal tomorrow with Carrier B and they can swap that customer over, effectively changing the engines on the airplane in flight. The customer experience doesn't change for the enterprise. They're still getting the same SD-WAN service, but maybe they've swapped from DSL to cable as a transport or they've added an MPLS service to a new site as well for greater reliability. So this allows the MSP's and the carriers to get services out to the customers faster, decoupling it from whatever the last mile technology may be. And this is where there's opportunities for wireless. We're seeing a lot of interest from enterprises to augment with LTE in the future, 5G, as a backup connectivity to their sites, particularly in retail. I mean, I'm sure in Silicon Valley, you've seen everyone here is swiping your card on a tablet. Well, you don't want that tablet to be offline. It needs connectivity or they're not making money. So making sure you have reliable connectivity with the same experience is a big deal for these enterprises and their MSPs. But it's now becomes part of a coherent solution as opposed to I'm going to do my cloud thing and I'm going to do my MSP thing. Absolutely. And so that's another area where we're seeing a lot of interest. I mean, even if I look at what our internal IT is doing, which is, you know, we need to make sure that the cloud is part of our WAN. And we need to make sure that we can, you know, drop an application in our private data center but have resources in our public infrastructure also using that. And the experience for me, sitting at my desk down the street from here is the same regardless of where that application is being accessed from. All right, the last thing I want to talk to you about Alastair is this notion I have. I'm going to test something by and see if I got it right and if I can, if I'm anticipating some of the changes that we're going to see. So a lot of people presume that the cloud was a one-way ticket to something centralized and big. And that had an enormous impact on how people think about the cloud. We actually think about the cloud as a strategy and a technology for more easily and coherently distributing data and distributing function to where it needs to be on a location basis. Absolutely. And in certain respects, I can look at the cloud kind of as a network programming model where some of those hybrid cloud services that are being introduced by some of the big cloud players now are really almost a layer seven. They're providing some structure to the developer about how to think about building hybrid distributed applications. Now, I want to test that. Does that resonate with you from a networking standpoint? Absolutely. And again, that's something we see a lot of interest in. A reasonable amount of demand as enterprises and their internal developers are getting their heads around that concept that the application can live anywhere, whether it be on-premises, at the branch, data center, or in the cloud. And that cloud, as you point out, can be rightly geographically distributed. And being able to be the network glue that binds all of those locations together allows the developer and the IT organization supporting that developer to have the effect of a single fabric, regardless of where the application or the user is, seamlessly connecting them. And so it also suggests, and this is nothing I want to test with you, it makes it possible to imagine greater specialization in what those distributed services look like, especially from a networking perspective, which means that if MSPs and big telecos do successfully incorporate some of these technologies, improve their automated ability, their ability to think about the service and then deliver the service very rapidly, then we could see them actually being able to pick up a sizable piece of this cloud business because they can introduce services that are specialized with a network, strong network affinity that build on that heritage of distribution of function. Absolutely, and you see that today. The carriers are already providing a valuable service connecting the enterprises to the cloud, but that goes beyond in an SD-WAN 2.0 model. I need to move certain applications to the branch. There's some things that always need to live there. And as an IT manager, I need to manage that networking effectively. But I have applications that I want to have that are running in a very public cloud, SaaS applications, et cetera. And I want to give my users the most efficient path to them. But I also have my private applications that it may be running in a public environment, but I want to carry that as if it was part of my internal corporate WAN. And being able to get that from an enterprise, services perspective, from an MSP, from a carrier that can bundle all of this together, that's a huge advantage and a time saving for me. Yeah, the one other thing I'd say is that we're actually talking to some very large enterprises right now that are discovering that their customers, their customers are demanding very concrete, strict and well-documented notions of the capabilities that they provide. And this idea of SD-WAN is making it easier for them to sell services into companies that want that digital interface, that highly competent working digital interface. Absolutely. So last thing is we think about where this is going. Is there any technology on the horizon that you think SD-WAN is going to make easier to deploy or that's going to make SD-WAN that much more important? Oh, that's an interesting question. And I think as the ongoing digital transformation of business happens, where connectivity is more important than ever, making sure it's reliable and available and that the user experience, regardless of what type of site I'm visiting as an enterprise employee, making sure that my telephony works, that my can access my documents, that my R&D teams can span the globe, that is a key requirement of today's enterprise. At Nokia, that's how we need to work internally and that's how we do work. I travel around the world, visit our offices, my experience is seamless and the same. And that I think is where SD-WAN's bringing a huge amount of automation value security in many cases and tell you some great anecdotes that we found in the SD-WAN world there. And just the management and control layer. Well, let's save another cube conversation and talk about the security anecdotes. Well, but this is Peter Burris. We've been talking to Alistair Johnson who's a principal architect at New Irish Networks about the potential for SD-WAN to increase the relevance of MSPs, telecom providers in a marketplace that is being dominated by the cloud experience and how greater automation leads to improved service opportunities for a lot of customers and a lot of cloud related service providers. Alistair, thanks very much for being on the cube. Thanks Peter. And once again, I'm Peter Burris and you've been watching another cube conversation. Until next time.


Two major crises have descended upon humanity, climate change and the coronavirus. They may seem independent of each other. In fact, they are very closely linked. The emergence of COVID-19 on top of climate change is a spiraling crisis and it's just the beginning. Volo Foundation supports research on climate change and is concerned about the dramatic degradation in our environment and its effect on our quality of life. We also support research on the COVID-19 pandemic and similarly are concerned about its effects on our future. What are the interactions? How does climate change affect COVID-19? And has COVID-19 affected climate change? We want to know and this film will help us find out. We know we have a problem with climate change. We know what's causing it and we know the solutions. We just have to deploy them. Likewise, we know we have a problem with COVID. We know what causes it and we think we know what needs to be done. These are both existential threats to the planet and to humanity.


physics channel for physics please subscribe my channel hello and welcome back to another fascinating episode of physics part now and this channel we explored the mysteries of science and technology today we are diving into one of the most confounding phenomena in fluid mechanics the hydrostatic paradox have you ever heard of it before if not get ready to be amazed by the strikingly peculiar behavior of fluids in a confined space so let's get started what is the hydrostatic paradox simply the hydrostatic paradox is the observation that the pressure at the bottom of the container filled with a fluid depends not on the overall volume or shape of the container but solely on the height or depth of the fluid itself you heard that right it does not matter if the container is a narrow tube or a wide basin the fluid pressure at any point depends only on how far down it is from the space let's understand how does it work the hydrostatic paradox is governed by the principles of hydrostatics an area in fluid mechanics that deals with the properties of static fluids remember it's not about the motion one such principle is the Pascal law which states that a pressure exerted at any point of an enclosed fluid is transmitted equally throughout the fluid and acts perpendicularly to any surface with which it comes in contact in other words if you apply a force on one point of a fluid the pressure will be the same throughout the fluid why this concept is important the hydrostatic paradox has significant implications in various areas of science and engineering let me give you some examples for instance it helps to explain how the herd pumps blood throughout the vessel in our body or how hydraulic lift works in elevators and cars it also has practical applications in determining the weight and density of objects majoring atmospheric pressure and gorging fluids level in tanks and pipelines let's go for the conclusion the hydrostatic paradox is one of the most intriguing phenomena in fluid mechanics you can see here on the screen the formula pressure is equal to raw times g times h where this is a symbol for the density times gravity times height hydrostatic paradox was discovered by blaze Pascal and still after a long time it is very useful concept in the world of physics so I think it's enough for today so thank you very much for listening and watching I hope you enjoyed the video I hope this video is useful for you so take care of yourself and don't hesitate to write an email if you have any question curie suggestion and even classes are required take care of yourself meanwhile see in the next video goodbye


And now, stay tuned for the program that has rated tops in popularity for a longer period of time than any other West Coast program in radio history. The Signal Oil Program, the Whistler. Signal! Signal, the famous Go-Farther gasoline.  I'm the Whistler. And I know many things for I walk by night. I know many strange tales hidden in the hearts of men and women who have stepped into the shadows. Yes, I know the nameless terrors of which they dare not speak. And now for the Signal Oil Company, the Whistler's strange story. You can't trust a stranger. As you walk down the crowded corridor from the district attorney's office, you can feel the stairs and hear the whispers. There's Frank Malloy. He's getting out, but not for long. It's costing you $10,000 to walk out that front door, but it's worth it, isn't it, Frank? Because you have a plan, at least part of one. Yes, you reach the front entrance, push open the heavy door, and go out into the street. There at the curb, you recognize the long yellow convertible and the attractive blonde sitting inside. She slides over as you slip in behind the wheel. In again, out again. Yeah. How was jail this time? Lay off, Vivian. When I read in the papers, they're going to put you away for a long, long time after the small formality of a trial. Well, don't believe everything you read. I'm not going on trial. You are? No. I'm going to be around long enough to give them a chance. You're going to jump bail. That's exactly what I'm going to do.  I've got plenty, and it's put away where I can get at it. Now hurry. Where will you go? We. We're going together, baby. I'm ready, Frank. I don't know how, or where we're going, but we're getting out of the States. We can bid it to Havana, and then maybe South America. I'll get a divorce, and we're all set. We've got enough money to last us the rest of our lives. That sounds wonderful, but how do you expect to get away? The moment they miss you, they'll be watching for you everywhere. Yeah, I know. VA wants to see me in a couple of days. So whatever we're going to do, we're going to have to move fast. We can't just take a plane or a train. Before we start running, Frank, we have to think of something, some kind of plan. Yeah, I know. What about a private plane and pilot? Let's find out about it right away. No. It's something else I've got to find out first. What do you mean? Going out to the ranch. I'm going to see my wife. You're going out to see Martha? That's right. Why? Vivian, didn't you ever wonder how the district attorney got hold of all my records and books that I kept? You think I sent them to him? You think I wanted the smoothest gambling syndicate in the state to come crashing down around my neck? No, but somebody else did. It had to be somebody I trusted, somebody close to me. I want to be sure it wasn't Martha. But, Frank, don't you... And they have enough on me to put me away for 20 years. I want to know where they got it. Oh, Frank, what difference does it make now? All that matters now is getting away. We'll get away, baby. Don't worry. But first, I want to see Martha. I just want to know. As you drive through the city and across the bay bridge, your thoughts dwell upon your wife, Martha, don't they, Frank?  Wondering if she knew about Vivian or any of the others. Wondering if it could have been Martha who brought everything crashing down, sending you to jail. And there are other things to be thought of.  Chartered plane and a private pilot might work. And you do have friends in Florida who would help you and Vivian get out of the country. After an hour of driving and thinking you're suddenly startled as Vivian pulls violently at your arm. Frank, look out! Did I hit him? I don't know. He's lying by the side of the highway. I didn't see him in time. What was he doing out the middle of the highway? Look, he's getting up. Come on, we better have a look at him. Come on. He is getting up.  Hey, hey, you all right? I don't know. I think so. What were you doing out the middle of the highway? I was trying to catch a ride. Does anything feel broken? No, no, I don't think so. I saw you coming right at me and I dove for the side of the road. You didn't hit me. Oh, it's a relief. Looks like my trousers are finished. You sure you're all right? Yeah, yeah, yeah. Forget it. It's my own fault for standing in the middle of the highway. Uh, what's your name? My name? Yeah. Chuck, why? Well, Chuck, I feel kind of bad about this. I think the least I can do is offer you a ride. Do something about those trousers, too. Forget it. Forget it. It's my fault. Well, we can't leave you standing here. We're going another 10 miles. Okay. Let me get my hat out of the ditch. Frank, do you have to give him a lift? He admits it was his fault. Let's get out of here. Didn't you notice something, Vivian? Something real interesting about that fella? What are you talking about? Look, he's just turned around. Look at him. Now look at me. Notice anything? Frank. See it? Looks a lot like me, huh? Same size, billed even as features. Yeah, if I worked it out right, I could get away with it. Get away with what? Just think, Vivian. How much easier it would be for us to get away if everybody thought that I was dead. If you really want to protect the money invested in your car, then the motor oil for you is Signal's amazing new heavy-duty oil that reduces engine wear 50%. Signal Premium, heavy-duty Signal Premium. Now, there's the oil that really protects your car. This proved and improved heavy-duty Signal Oil does more, much more than just lubricate. In addition, Signal Premium motor oil cools, cleans, cushions, seals and protects. Result? Tests under all types of driving conditions prove new Signal Premium motor oil reduces engine wear 50%. Your engine keeps its like-new pep and power twice as long. So if you're still using lazy old-fashioned oil that merely lubricates, it's high time to make a change for the better. Change oil next time at a Signal service station. Change to new, harder-working Signal Premium motor oil that reduces engine wear 50%. Almost every piece of the plan seems to fit together, doesn't it, Frank? If the police thought you were dead, you and Vivian could take your time about getting out of the country. You could go knowing they weren't watching for you.  I'll be real nice to him, Vivian, and get him to talk about himself. We have to find out as much about him as we can. You just leave it to me, Frank. All set, Chuck? Yeah. Let's go then, huh? Some buggy. Yeah. Always promised myself I'd have one of these someday. Look at me, I don't even have bus fare. My clothes are dirty and wrinkled, and I need a shave. I look like a tramp. I don't blame people for passing me by. Where were you headed, Chuck? Los Angeles, I guess. They tell me the nights are balmy down there. It makes a difference when you sleep in parked cars. But don't you have any friends in Los Angeles? I don't have any friends anywhere. That's a pretty broad statement, Chuck. Must have friends somewhere. Maybe back home, huh? I wouldn't know. I haven't been home in a long time. Been everywhere else, Australia, Africa, Brazil. Been working on freighters. Just got back to the States last week. Just last week, huh? Right. Been gone nearly five years. Oh, where is your home? I come from a place called Hyannis. Have you heard? It's in Massachusetts, Cape Cod. No, never heard of it. It's a fishing village. Oh. Still, it doesn't seem possible that a man doesn't have any friends. Oh, you must have a girlfriend. Yeah, yeah. Had a girl once in Hyannis. The name was Mamie. Mamie? It was a long time ago when I was young and foolish. Whatever happened to Mamie? I wouldn't know. I wrote her for a while, but when I didn't get any answer to my letters, I just forgot about Mamie. Say, Chuck, tell me, what kind of work do you do? I'm one of those guys who can do anything until you pin me down, and then it turns out I can't do much of anything. Well, I'm sure you'll fit in somewhere, someday. Just haven't run into it yet. Maybe. In the meantime, I like drifting around the world. I don't talk too much. I don't get the chance to talk to people very often, especially about myself. Everybody likes to talk about themselves. What are you going to do when you get back to LA? Look for work, I guess. I'm broke. Well, if you really want a job, Chuck, maybe I can do something for you. What, uh, what do you mean? Well, do you have a 10-bar? No. Well, I own a string of bars throughout the valley. If you're willing to learn, maybe I can put you to work as a bartender. Me, a bartender? Uh, a guy's on his feet a lot in that kind of work. You can make good money. Yeah, yeah. I can believe that. But, um, tell me something. Why all the interest in me?  I think the least Frank can do is try and help you out a little. Do you, uh, you think I could learn to 10-bar? Oh, I'm sure you could, Chuck. It's an interesting proposition, Mr, uh... Malloy, just call me Frank. I'm Vivian, Chuck. Hi. How do you like that? Yesterday I was bumming around. Today I'm going to be a bartender. Who knows what'll happen tomorrow? You know, don't you, Frank? You know exactly what's in store for Chuck tomorrow. As a matter of fact, you wonder if he'll even be alive tomorrow. Because now you're certain that he will do fine as a part of your plan. No one knows about him. No one even knows where he is. No one would miss him if he disappeared. He assured you of that. As you turn off the main highway toward your small ranch, you already have the first stages of the plan ready. You stop the car at the gate. I have to take care of some business here, Chuck. You go with Vivian. She'll put you up for the afternoon. Whatever you say, boss. Take her to my apartment, huh? Here's this key. I'll call you. When? As soon as I've made the arrangements we were talking about. Will they take long? No. Everything will be taken care of by tonight. Tonight? Yeah. And take good care of Chuck, huh? Make him feel at home. Now, well, we'll be at your place. You call me. I'll call you. Well, I'll see you later tonight, Chuck. Sure thing, Mr. Malloy. Bye, baby. Bye. You watch them disappear down the road, Frank, and then you turn toward the house. Everything seems peaceful and undisturbed, and you realize how long it has been since you've come out to the ranch. As you reach the steps and put your hand to the door knocker, you wonder if Martha will be surprised to see you. Hello, Martha. I, uh, have come to see you. Come in. You don't seem surprised to see me. I'm not. You were expecting me? Yes. Then you knew I was out of jail. Sit down, Frank. Would you like a cup of coffee? No, nothing, except... Martha, I think you know who turned me into the district attorney. Who was it? Why, I did. I did what I thought was right. You must have known, Frank. I always trusted you. You were the one person I thought I didn't have to worry about. That's it, exactly, Frank. You never worried about me. I don't think you even thought about me. There was a time when I was the most important thing in the world to you. So you fix it, they'll send me to prison. You belong in prison.  You're not the man I married 15 years ago. Little by little I watched you change. You began to make money, lots of money. And along with your money, you gained power. The more you got, the more you wanted. And anything you couldn't have, you destroyed. What did you expect to do? Own everything and every one someday? Martha, turn me in. I had to stop you for your own sake. And I did it the only way I knew how. I cried for months because I knew the only way to stop you was to... was to call the district attorney. I did what I thought was right. Now you know, Frank. You know who betrayed you and why it was done. You begin to pace around the room, walking faster and faster, bumping into things and knocking them over. And suddenly you stop in front of the manhole. You see the clock in the feeling of rage subsides. You realize that by nine o'clock tonight, things will be all right. And Martha, conscientious Martha, will have a strange punishment, won't she, Frank? She'll always believe she sent you to your death. After a long silence, Martha throws a shawl over her shoulders and walks outside. Everything all right? Yes, I've been listening to the story of Chuck's life. Seems his girlfriend, Mamie, was quite a gal. Now our bartender's in the other room practicing with your liquor. Good, now listen, Vivian. Get one of my suits out of the closet and give it to Chuck. Have him shower and shave and put the suit on. We're going to a party. I understand. Tell him you're meeting me at one of my places up at the lake. Leave my apartment by 8.30 and drive up on Skyline Drive to Mountain View Club. Now don't stop anywhere. When you get there, wait in the parking lot and back. Be there by nine o'clock, clear? Clear and simple. What exactly are you planning, Frank? Like I said, a party. Good. Make sure you've got it all. We'll see you at the party at nine. At nine. What are you doing out here, Martha? Listening to the crickets. It's a nice night. Yeah. I used to go riding on nights like this. You remember that? Of course. I'm surprised, Frank. Are you? Well, here's another surprise for you, Martha.  Oh? Matter of fact, when I leave here, I'm going for a little ride. One we often used to take together along Skyline Drive. Frank, what have you got on your mind? Just you, Martha. I'll be thinking of you. I'll get my coat, Frank. No, no, no, Martha. Wouldn't be right for you to go anywhere with a hoodlum, a criminal. Frank. Goodbye, Martha. Remember, I'll be thinking of you. The expression on her face is to recognize the light you doesn't it, Frank? Martha is still in love with you after all this time. And later, when your plan goes through, she'll have something to think about, won't she? Something that will be her punishment. Yes, Martha. Conscientious as she is will feel deeply when Chuck's body is finally found in your car wearing your clothes at the bottom of the lake.  And above all, she'll testify that you were heading for the Skyline Drive. That part will help eliminate the identification problem. High up on Skyline Drive, you pull into the parking lot of the darkened club, where you agreed to meet Vivian. A few minutes later, the headlights of her car come into view. Right on time. What? Oh, hi, Mr. Malloy. Didn't know you were here yet. Say, thanks for the suit. How do I look? Just fine, Chuck. Are we on time for the party, Frank? Oh, right on time. Oh, say, Chuck, would you give me a hand with some stuff in my car? It's right over here. Sure. Vivian said we were going to a party. Is it in that place up there? No, not there. I didn't think so. Giant looks closed down. It's your dark dog here. What are we gonna do? This Chuck, this! Yeah. Party's almost over for you, Chuck. What happened? I hit him. He'll be easy to handle this way. Pull that door open so I can put him in the car. Right. What are we going to do now?  The road makes that sharp bend around the lake. Yeah, I know where it is. I'll be waiting. I'll be waiting there, off the highway. Blank your lights as you approach, and I'll come out and wave you down. There. I thought you were going to bring Martha with you. No. I've taken care of Martha. Another way. You drive out of the parking lot, and in a few minutes you reach the sharp curve in the highway. Pull over and stop where the edge drops off into the deep end of the lake. And it only takes seconds to drag Chuck's body to the front seat behind the wheel. Carefully, you go through his pockets and remove everything. Then plant your belongings in his pockets. You put your ring and watch on him, and everything is ready. Push the clutch in, put the car in gear, and as you jump back away from the car, it jerks forward and over the ledge. To disappear in the deep black water of the lake. See for yourself. By the time they pull the car out of the water, it'll look like Frank Malloy was drowned when his car skidded off the road and crashed into the lake. Let's hope so. Be weeks before they find the body, and the water will make positive identification pretty difficult. But they'll find enough there to think it's me. And Martha will help too. Yeah, all we have to do is hide out until he's found, and we'll be free, Viv. Where do we go now? Well, first we have to stop at a couple of places down the valley and pick up the money I put away. Well, that's a must. We'll drive on to Los Angeles where we can hide out. Then we'll see. Whatever you say, Frank. Now let's get out of here. You know, it's funny how Martha tried to send me to jail. When she recognizes my clothes, her story, more than anything, will help to set me free. Throughout the western states, from Canada to Mexico, one gasoline is famous as the go farther gasoline. It's signal gasoline. Now, naturally, we're mighty proud of Signal's good mileage, which has built that reputation.  You see, today's Signal helps your engine run so efficiently. You save gasoline three ways. One, you save gasoline with Signal's quick starting. Two, you save gasoline with Signal's smooth, obedient pickup, free from balking and hesitation. Three, you save gasoline with Signal's lively power that gets you into high gear fast, helps you stay there with a minimum of shifting on hills or in traffic. So you see, considering the number of times a day you start your car, accelerate and shift gears, even a little gasoline saved each time soon adds up to a big saving. So there in a nutshell, friends, is why motorists call Signal the go farther gasoline. Why not treat your car to a tankful tomorrow and go farther with Signal? Signal, Signal, Signal gasoline.  One morning, two months later, you open your eyes in a hotel just outside the city of Los Angeles, don't you, Frank? Yes, you've been here two months, waiting for someone to find the body of Chuck and identify him as you, the missing Frank Malloy.  Now it'll be safe to change your name and leave the country with Vivian. Everything has gone perfectly, hasn't it, Frank?   You get up and search the room frantically, but the money isn't there. Operator. Yes, sir? Would you connect me with room 303, Miss Vivian Nevis Smith, and hurry? Yes, sorry, sir, but Miss Smith checked out of the hotel about an hour ago. What? Did she leave a message? Nothing, sir. No, nothing. Who's there? Vivian. Vivian. Vivian, the bag with the... That's what you're looking for? Who are you? He's from the police department, doc. The police? Yes, he picked me up at the airport. After reading the story in the paper last night, I thought it was safe enough now to leave, only it wasn't. She was taking your money and running out on you, Molloy. And why not? It would only be a matter of time before I meant no more to him than Martha.  It doesn't matter now, Frank. Sure doesn't. You see, the newspaper story was just to get you out in the open. Some fishermen did find a body in the lake, but after all this time, it was a little hard to identify. He was wearing your clothes, Molloy, and was in your car. Your wife thought it was you. But I don't see how that could... I'll tell you something, though. At the morgue, we found out different. You see, Molloy, it wasn't hard to figure out what you'd done when we found a tattoo on the drown man's chest. Yeah? A tattoo of a heart. With the words Chuck and Mamie. Let that whistle be your signal for the signal oil program The Whistler each Sunday night at the same time. Meantime, signal oil company and the friendly independent dealers who help you go farther with signal gasoline hope you'll remember, regardless of what gasoline you use, you'll enjoy more miles of happy driving if you drive at sensible speeds, obey traffic regulations, and avoid taking chances. When you take a chance to save a moment, you take a chance on that moment's being your last. Featured in tonight's story were Bill Foreman as The Whistler, Gerald Moore, Betty Lou Gerson, Shepard Menken, and Charlotte Lawrence. The Whistler was produced and directed by George W. Allen, with story by Gus Bayes, music by Wilbur Hatch, and was transmitted overseas by the Armed Forces Radio Service. The Whistler was entirely fictional, and all characters portrayed on The Whistler are also fictional. Any similarity of names or resemblance to persons living or dead is purely coincidental. Remember to tune in at this same time next Sunday, when the signal oil company will bring you another strange story by The Whistler, Marvin Miller speaking for The Signal Oil Company. Stay tuned now for Horatio Hornblower, which follows immediately over most of these stations. This is the CBS Radio Network.