In this video lecture, I just want to say a few words about writing the speed of light in convenient units, especially when we're dealing with things like gamma. So remember, of course, gamma, 1/square root of 1-v squared/c squared, the Lorentz factor that's involved in time dilation, length contraction, and the like. And we've typically been using speed of light as 300 million m/s, or 300,000 km/s. You can do it in miles per second, 186,282, actually, miles per second. And if you want to be a little more precise, where it's actually 299 and some other digits there, but for our purposes, perfectly legitimate to just take 300,000 for km/s, or 300 million for m/s. It's because those numbers are so big and just outside our realm of experience, sometimes it's just nice just to think about the fact that it's about 1 foot/nanosecond. In other words, in a billionth of a second, light travels 1 foot, about a third of a meter, so, 1 foot per billionth of a second, that's assuming it's essentially in a vacuum. If it's going through a medium, error slightly, but water or something like that, that's transparent, it will slow down the speed of light by the so-called index of refraction, but that's a whole other topic for a different course. So 300 million m/s, 300,000 km/s, no one happens off if we just deal with v in terms of c. And by the way, we've been using this because I wanted you to get a feel for the magnitude of some of these numbers or sometimes how small they are, too, when we did some of the things you've been doing, the problem sets working with some of those numbers. But let's think about this for a minute, if we rewrite v in terms of c, which certainly is useful if it's a high velocity near the speed of light or substantial fraction speed of light, for example, v = 0.9c. Look what happens when we calculate gamma then. So we've got gamma = 1/square root of 1 -, well, v is 0.9c squared, so (0.9c) squared/c squared. Well, what's 0.9c squared? That becomes 1/square root of 1-, on the top, I've got 0.9 squared. So remember, 9 times 9 is 81. 0.9 times 0.9 is actually 0.81, so we get 0.81c squared on the top there, the numerator. And a c squared on the bottom, and this is where it becomes nice because, as you probably saw before I even wrote that down, we have c squared there and they cancel. So this c squared cancels with that c squared. I'm simply left with 1-0.81. So typically, when we do this, we'll just have 1- some decimal number, some fraction less than 1 there, and which, in this case, is 0.19. So you just take the square root of 0.19, 1 divided by that square root, and you've got your answer for gamma, which, I think for 0.9c is what, it's about 2.3, if I remember correctly, something around there. Anyway, so it makes it very easy for calculations. So often, we'll have problems, or you may see problems with v as a certain percentage, fraction of the speed of light. But there's another measure that's useful to know about as well that makes our life easier, especially in terms of astronomical distances, and that is the light year, which you may have heard about. So the light year is the distance light travels in one year. So it is a distance, it is not a time. That's why, in fact, we've got year in there, it's a light year, it's the distance light travels in a year, distance light would travel in a vacuum, distance light travels in one year, And it's pretty far, right? Off the top of my head, I don't have it memorized. You can actually figure it out if you know 300 million m/s times the number of seconds in a day is, I think, 86,400. So multiply that out, then by the number of days in the year, if you take 365. And you get the distance light travels in terms of meters per year divided by 1,000, you get kilometers if you want. So, light year, distance light travels in one year. And note in terms of c then, what the units become. So, c then, it literally is just light years, Per year. By definition, it's the number of light years it travels in one year. That is c, and in these units then, it's just 1. c travels 1 light year/year, by definition of light years, the distance light travels in one year, so it's 1 light year/year. So technically, let me just, so it's clear, those are the units for c then, which equals 1, so we'll put it over here, too, just to be clear. c = 1 light year/year, and the units in general are light years per year, we'll get rid of this part there, okay. So c is 1 light year/year, or we could have light month, is the distance light travels in one month. So we could have c as 1 light month/month. Light day, so c is 1 light day/day, light second is often used, in fact, 1 light second is the distance light travels in 1 second, which is still pretty far, right? It's going 300 million m/s, so in 1 second, it's 300 million meters, okay. So 1 light second is 300 million meters, so but c is 1 light second/second. If you did 1 light nanosecond/nanosecond, then it's 1 foot. That's the distance light travels in 1 nanosecond, approximately. Okay, the nice thing about this, and physicists love to use units like this, because sometimes, you just say we're going to set c equal to 1. Because look, it just disappears in here in the form of a gamma. It's just 1/square root of 1-v squared. Now what we're going to do for our purpose is leave c in there, just remind ourselves it's there. Because especially when you are just sort of think about the concepts and try to get your minds around things like this, if you get too sort of simple, it's not really simple in the simplistic sense, but you're simplifying things and saying, just let c equal 1 light year/year. Sometimes you lose track of it, and so it's good to see it in the formula. But then when we actually do problems, if we use light years for our distance, then c is just 1 light year/year. And it works out very nicely that way. So that's just a few notes about convenient units for light, whether we write v in terms of 0.9c, or some fraction c, and therefore, it cancels out. Or we use units of light years, and if we say okay, our distances are going to be in light years, then our time is light years/year. The velocity is light years/year, and c is just 1light year/year. So if you use light years, then time is going to be in years. If you use light seconds, then your time's in seconds and so on and so forth. So as long as you are consistent with that, and it's pretty easy to keep track of it, then it makes some of the quantitative analysis and calculations a little bit easier for us.