So now we come to this question, why do these distant galaxies look red? And that is actually evidence that universe is getting bigger. Universe as a whole is expanding, so the distant stars and galaxies actually look red. And that's the same phenomenon as something we're also familiar with. So when you have an ambulance approaching you, the pitch of a siren, sounds actually high. You are familiar with that. Once the ambulance passes in front of you, all of a sudden, the pitch of the sound of a siren actually goes down. So that is something called a Doppler effect. So approaching, object would give away a high pitched sound, receding object would give away a low pitched sound. So that's about the sound, but what about the light? So, if you have a star, that say, that is supposed to be yellow. But if this star is moving away from you, it would actually look red. So the reddening, it's the same thing here, as, the pitch going down, because the object that is letting the sound or light away is actually moving away from you. And if you're familiar with the calculus, you might have seen these formula, for the Doppler effect. The frequency of the sound. It's different when you listen to it from the original frequency of a sound that was let out by the object that's moving. And here, this big V is the velocity of the sound. Little v is the velocity of the object. But you see there are two different formulae here. One of them is when the object that's letting the sound out is moving. The other formula, when you are moving, relative to the air. But there is no air that lets the light propagate in outer space. So the correct formula for light turns out to be the geometric mean of these two formulae. So this is the correct formula in the case of light. Again, this big V is supposed to be the speed of light, little v is the relative speed between object that let the light out. And object that receives the light. If you do something called Taylor expansion, if you're familiar with this calculus. You can expand this formula out in the approximation that the speed of the object is much much smaller than speed of light. And using this expansion, you find the first term, which is pretty much the only important, for most cases. And that is actually going to look like this. So, if the object is moving away from you, frequency is subtracted by an amount proportional to its velocity, so the frequency looks less to you. And for the sound, when frequency is less, the pitch is low. In the case of light, if the frequency is less, the light is stretched and looks redder. So that's what happens with this Doppler effect. So, the way we understand now that this galaxy look red to you, it means that it's actually moving away from you. But then, do you think that we are sitting at the center of the universe? And all the other galaxies know you are at the center, and you're trying to escape from you? That clearly is not the right picture, right? We have seen in the video, that, no place in the universe appears very special. So that can't possibly be the explanation. So what could it be? So that's the idea that space itself is getting bigger. So as Einstein told us, that gravity is, in some sense, an illusion, that space bends, and warps. That is the true nature of gravity. So if you think of the universe as a box, a container, kind of static. That's not the right picture we should use anymore. So according to Einstein, universe is in some sense a live box. It can bend, twist, warp, expand, or even collapse. So that's the way we should view how the space of the universe should behave. So, it's possible that universe as a whole, can get bigger because it's a live box. It's not a static box. So that would allow us to understand, why all the distant galaxies look red. So, if the universe is getting bigger, then, let’s look at actually this picture here. So let's imagine that universe is sort of a grid system. Each galaxy is actually on a grid point. None of the galaxies thinks it's moving, because it's at the grid point. But, let's imagine that this grid is sort of a rubber sheet. You can just stretch it, and if you're watching, for example let's say this is your galaxy; you're watching this other galaxy over here. At this moment you see the distance is only this much. But, at a later time, you see the distance from our galaxy, the other one looks like it's farther away, right? So if the grid itself is getting bigger, the other galaxy seems to be moving away from you. But it's not special to our galaxy. If you happen to live in this galaxy over here and watching that galaxy, again, later time you see that that galaxy is farther away from you. No matter on which galaxy you live in, all the other galaxies seem to be moving away from you, because space itself is getting bigger. So that's the idea of expanding space. And if a galaxy lets out a, say, blue light, and light is actually a wave, so it actually repeats itself over certain distance called wavelength. And this light, with this wavelength is traveling through space. It's not doing anything rather than just going with speed of light, but before it reaches the other galaxy, again, the underlying space is stretched. So how quickly it repairs itself? The wavelength of the light is also stretched together with the expansion of space. And once the wavelength is longer, then we actually observe a red light instead. So that's how the original color and color you see are different. And everything looks redder, because the light is stretched by the expansion of the universe itself. So, that's how we think the universe must be expanding. The fact that all the other galaxies look red to you, must mean that universe itself is expanding. Because you don't think you have a very special point in the whole universe. And if the universe is getting bigger, let's say you imagine a, a helium balloon. You might have your birthday party. Let it just fly up, and it's going to expand. And, as you can imagine, it actually gets cooler and cooler if you keep going up that way. So something expanding, would actually cool down. So, as the universe expands, it must be getting cooler. And, if you managed to tape the universe, and if you run the video backwards, you'll find the universe would start getting smaller and smaller. And also getting, hotter and hotter. So just base, based, on this fact that you would think, universe must’ve been much smaller than it is today, in the past. And it also must have been much hotter than it is today. So universe started small, and hot, and there you go. That's the idea of the Big Bang. And if you're a little familiar with the way the wavelength of light and the energy of the light is related, this is the formula. This little h is called a Planck constant. If you don't, are not familiar with this question, it's completely fine, you can forget about it. But this is really telling you, as the wavelength of light lambda gets bigger, energy of the light gets smaller. So, as the universe becomes bigger, the wavelength is stretched and becomes longer. And energy goes down, and therefore, universe gets cooler. On the other hand if you go back in time, the wavelength was shorter, energy was higher, and universe was hotter. So we start with hot, small, universe, the Big Bang. But now is a question to you. So how do we know this is the right picture? We did see that distant galaxies indeed look red. Is that enough? Is Big Bang just an idea or is there an evidence for it? So, we'll come to the evidence in a moment.
