Okay, let's do a review of what we've just been doing, just to make sure we're understanding this as best we can, and more or less on the same page here. Then, we're going to make further observation as well with this whole idea, the relativity of simultaneity and especially, what Bob is observing here. So let's remind ourselves, this is really a combination of this last three video clips, or video clip one and then this previous one, where we were dealing with light pulses. So, here's Alice's perspective on her spaceship. As far as she's concerned she's not moving, she has the light pulse apparatus here. She shoots one light pulse that way. One light pulse that way. Her clocks are synchronized. So the light pulses both go off at the same time at t a equals zero here. Her time, in each light pulse is traveling with velocity c and because they're equidistant from each other, the two clocks from the middle here, she sees the two light pulses hit her two clocks at exactly the same time. Capital T sub a in each case. That's what her observation is. So, as far as she's concerned, nothing's wrong, nothing weird going on or anything like that. So now, let's look at Bob's perspective and what we've done here is we have his frame of reference again, his lattice of clocks all synchronized as far as he's concerned. And really three situations here. So, we've taken the previous diagrams and tried to sort of like little animation effect here, stop motion animations, say okay At t sub b equals zero. When all his clocks down here read zero, he observes the light pulses go off at that instant right there. A little puff of smoke or something and he would note what his clock says at that point. If it said zero, then it says all his clocks would be zero at that point. And then, as the light pulses are in flight, remember the key thing is even though Alice's spaceship is traveling with velocity v in that direction, that has no effect on the velocity of the light pulses. The velocity pulses to Bob will be c, just as Alice saw the velocity of the light pulses to be c. They will not be c plus v or c minus v. And what that means is that because this rear clock on Alice's spaceship is moving toward this light post coming toward it, this light post will hit this rear clock, before this light post can reach that clock. And of course in real life, light is so fast and typically velocity is so small here we don't notice this difference, but if you can get large enough velocities, this will, this effect will come into play. But what do we know at this point? We know this light pulse just hit this clock, we know from Alice's observations, if we take a flash photo right at that point, we'll see that the clock reads t sub a, just like over here. That has to match, at that instant in time and space, the light pulse hit that clock, Alicesaw something on her clock. What does Bob see on his clock? He sees t b one. So at that instant in time, this clock right here, he would take the flash photo as well and they both could examine that photo. Her clock would see, would read t sub a. His clock would read t b one, whatever that happened to be. And then moving on, note, of course, this one is still in transit just like pulse is still in transit as far as Bob is concerned. And so at later time, capital t b two, Is when he sees the second light pulse, the rightward going light pulse hit over there. And so he could, a photograph would be taken. And it'd show that Alice's clock, red t a, just like she observed, but his clock, his clocks then would read, take a photo at that point, t b two. And so, all his clock through be t b two in fact this one as well. Because they're all synchronize of course from his perspective. And what does this mean. Well he read, t b one for this flash over here t b two at a later time for this flash or the light pulse hitting the clock and triggering at there. That means this clock right here if he took a photo right there, and said okay I'm at t b two here. What's this one? We know it's got to be a time greater than t sub a, so got that, I mean this is one of those things. We're constructing mental models here that are very different from our regular experience. We'd expect that Alice saw the two light poles hits to be simultaneous on her clocks. Clearly Bob should observe the same thing, but because again the speed of light does not participate in the velocity of the spaceship. But is always c no matter which observer talking about. Bob, Alice, or anybody else. We get this weirdness coming in that Bob is. Right, let's start with Alice. Alice is saying, what's the big deal? My clocks are synchronized. They hit exactly the same time. My clocks read t sub a. Everything is fine. Bob is saying, wait a minute here. It's my clocks that are synchronized and clearly these photons did not hit at the same time. I read the first one at t b one, the second one at t b two and in fact, when I recorded the second one at t b two, according to my lattice of clocks all synchronized, your mirror clock Alice over here, was at a time greater than t sub a. Cause clearly, it's later in time. So Bob sees Alice's clocks as unsynchronized. And you could reverse the analysis and look at it from Alice's perspective looking at box plots. She also would see Bob's clocks unsynchronized. Because otherwise you can't make sense of the situation. The photographic evidence here does not lie that when you take the photographs, it's gotta be t sub a here because that's what Alice sees. It's gotta be t sub b one for Bob at that point. And it's gotta be t sub a over here for Alice because that's what Alice sees. And yet, it's t b two for Bob. Okay, so that's just another review of what we were saying before. The relativity of simultaneity. Simultaneous events, clock synchronization it's relative. There's, you cannot absolutely synchronize clocks such that everyone agrees they are synchronized. If you're stationary, if Bob and Alice were both stationary they could agree they're synchronized. As soon as you put one of them in motion, especially at a velocity v that starts getting close to the speed of light, these effects start coming into play. So another way to say that, really, is absolute time cannot be defined. There is no way to define an absolute time scale, or a way of measuring time, such that both Alice and Bob would agree, because Alice is saying Bob you messed up, your clocks are not synchronized. Meanwhile, Bob is saying no, it's not my problem. It's you Alice. Your clocks aren't synchronized and yet each individually, have their clocks perfectly synchronized. Okay, so what's this one more observation here that we're going to come back to later in the course? Let's look at Bob' perspective here and he sees Alice flying by at velocity v in her spaceship. What does he see on her clocks here? Okay. Let's look at this final situation here, where he sees the second photon going to the right. He sees it triggering her clock. Photo is taken. Her clock reach t sub a. As Alice observes too. No disagreement there. They can't disagree over photographic evidence at the same location here, the same event. His clock reads t b two at that point. He also though says, hey, my clock back here also reads t b two and I just took this picture, but your clock Is going to be a time T greater than T sub a, so the rear clock is going to be a higher value than the front word phasing clock the front clock here ,as Alice moves on. This is a principle, and we can state this as such, we'll use this a number of times it's this. Leading clocks lag. Leading clocks lag. When you are talking about a situation where you have an observer like Bob, and he's observing Alice's clocks going by her lattice of clocks is flying by there, he will, if you pick any two clocks, say one here, and a trailing clock over here, the leading clock will lag the trailing clock. This clock, t a is behind this clock from Bob's perspective, remember all Bob's clocks are synchronized to him, so you could take a flash photo right here, his clock would read t b two, you take a flash photo at the same time as far as he's concerned, he reads t b two here, he'd see Alice's clock read t sub a but he'd see this clock of Alice's reading a time greater than t sub a because this clock passed t sub a earlier. When that photon hit, that light poles hit. And so again, leading clocks lag that if you have Alice flying by or is flying by it at a speed v that gets up close to the speed of light. Well, in later video clips coming up here, we will actually look at how fast we have to be going for these effects to start becoming noticeable but, for now we're just doing qualitatively and clearly the weird result here, takes awhile to get our minds around this, is that, and this is why sometimes it's just useful to state it in a very succinct principle and just memorize that principle, leading clocks lag. So, that Alice's clock's here as far as Bob is concerned, the leading clock on the leading edge as she's moving that direction is going to be behind a clock, a trailing clock, wherever it might be. And later on, in the course we're actually going to do like calculation so, we can figure out exactly how much does this clock lag this clock, and it's going to depend actually, on the distance between them there, okay? So, a review of this first real aspect of weirdness we get, the relativity of simultaneity, the relativity of clock synchronization Bob synchronizes his clocks, Alice's synchronizes her clocks. But Bob thinks Alice has messed up, Alice thinks that Bob has messed up in terms of his clock synchronization. And this idea that leading clocks lag. Not only do you have the, well it's really a result of this whole idea that simultaneity is relative, synchronization's relative, absolute time cannot be defined, and that if you have a set of clocks moving by you at a high velocity, the clock that's leading will trail in terms of its time keeping trail the clock back here, assuming that their clocks were synchronized in their own frame of reference, in Alice's frame of reference here. So just remember that principle, leading clocks lag.