Let's spend a minute or two exploring the Lorentz Factor, which is often given the symbol gamma, Greek letter gamma. So, just remember it's 1 over the square of 1 minus V squared over C squared. Came out of our Light Clock Analysis as the key factor in the Time Dilation equation, in terms of moving clocks running more slowly. But the question arises of course is why don't we see this in everyday life? And the reason we don't see it is this v squared over c squared factor. If this is small compared to 1 then this is pretty much 1 over 1 and gamma is about 1 and we don't see any difference. The elapsed time in a moving clock is the same as the elapsed time on an identical stationary clock, in terms of how precisely we can measure it. So, what we've done here is just list some speeds and then the results for gamma for each of those speeds and it's a useful and or fun exercise where you just plug in some numbers here, do the calculations and come out with your own values of gamma. But here they are. So speed 0, we've done this before. Then v is 0 so just 1 divided by 1 is gamma is 1 so no effect. If the two clocks were actually right next to each other. If we have a speed of 0.5 kilometers per second, which is 1800 kilometers per hour, and if you think in terms of miles per hour, it's about 1000 miles per hour. And roughly the speed of say a supersonic jet. Okay, so that's pretty fast in our ordinary experience of seeing a supersonic jet going by at that speed. You know the speed of sound is about 700 miles an hour depending on atmosphere pressure and a few things like that. And therefore you'd definitely be getting a sonic boom out of this. But look at what the gamma factor is, okay. I don't know exactly how many zeroes we got there. But it's way out here in the, think this is probably about 100 billions right here, and on. So, even at supersonic speeds, very, very small difference between, in terms of the clocks being measured. Moving clock, versus a clock on, the ground, as it were a stationary clock. Although, should say, that they've actually done experimental tests where they've had two identically prepared atomic clocks. So very accurate clocks. And they kept one on the ground, they put one up in an airplane, essentially a jet. Not, I don't think it was a supersonic jet, but just a large jet. So it was flying at, certainly several hundred miles per hour, kilometers per hour, 600 probably in that range, 600, 700 miles per hour. 1,000 or so kilometers per hour. And, they were able to see a difference actually when the brought the clock the clock was traveling back down again the clock then move and compared it to the original clock. Now they also had to take in to hold bunch of other things in that experiment including gravitational effects and the general theory of relativity, but using the results from the special theory of relativity, they were built in that experiment as well, and it was confirmed there. Some other speeds here, now we're going to switch to 0.001 c. So, tenths, hundredths, thousandths, this is one-one thousandth the speed of light, about 300 km per second, or, there's a miles per hour, it's, what is it, about 190 miles per hour or something like that. I think around 200 miles per hour, not quite 200 miles per hour. So obviously, you know, very fast, I'm sorry not miles per hour, miles per second here, okay? 300 kilometers per second. About 190 miles per second, okay? So we're not talking about a fast race car here, we're talking about something, getting into say rocket ranges and things like that with this. Or even rockets aren't going 200 miles per second typically. Maybe get up there. And look at the gamma factor okay. Again tens, hundreds, thousandths, ten thousandths, hundred thousandths, millionths. It looks like it's in the ten millionths place there in terms of the effect. So again very, very small effect. Then as we increase the speed, you can see what happens. So now we go up to one tenth the speed of light. 30,000 km per second, okay? 30,000 km per second. This is probably a little less than the circumference of the earth, at the equator. I know it in miles, it's 24,000 approximately. So, going to be a little bit more than this, but roughly, once around the world, give or take a little bit. As, that speed in 1 second and gamma factor 1.005, and then as it goes up half the speed of light. Now, we're sort of getting some place where we can see some effects, not that you couldn't see it before, but they're pretty small, 1.2 there. 0.9 tenths the speed of light, and objective moving at 9 tenths the speed of light 270,000 kilometers per second, roughly 2.3 for the gamma, then 0.99c, 99% of the speed of light, 7.1. And then 0.9999c, four nines there, 71. So it does go up fairly rapidly as you get to speeds very close to the speed of light. And of course, if, as we mentioned, if you have v equal to the speed of light, you get infinity. There, which would therefore imply it's some sort of an absolute limit. You can't quite ever get there. Okay, so that just gives us a sense of when we're talking about relativistic effects, at least for special relativity, most of the time we're going to be dealing with things if we're actually going to see any effects, with speeds at about half the speed of light, or greater. So, somewhere half the speed of light, up to 0.9c, maybe a little higher than that. Whether we can get those speeds, that's another matter. We can certainly generate speeds like that, and even higher in particle accelerators. And that's where you really see relativistic effects, in fact the design of current day particle accelerators you have to take the special theory of relativity into account in order for them to work right. So this is very practical matter for engineers and scientist who are working on those matters. So just a little bit exploring the gamma factor, the Lorenz Factor, gamma- give you an idea of when it actually becomes a larger factor in terms of the speeds involved.