The next few chapters deal with special relativity. So, the main problem with the relativity of motion that I was talking about in my last post, and that he was talking about in the first part of the book, is that light seems to contradict it. We are taught that light moves at a constant speed, "c", which is about 300,000 km/sec. When we were first taught about this in school, we were taught that it was sort of the "universal speed limit", that it was as fast as anything could go. This is sort of true, but is kind of missing the point. Light in a vacuum
always moves at speed c, never slower, or never faster. If we think of our "common sense" geometry and physics, what would this look like? Well, we could Imagine we're on a train that's moving at almost the speed of light. Then we turn on a flashlight. What happens? The "common sense" intuition might be that the light slowly oozes forwards out of the flashlight, so if the train was moving 2 mph slower than the speed of light, then from our perspective it would look like the light is moving slowly at 2 mph out of the flashlight. That's the "speed limit" intuition. It would also make sense if we imagine the guy outside the train standing still: if he looked at us turning the flashlight on, from his perspective the light would move exactly at "c", since he's standing still.
But that goes against what we just said, that there is no such thing as "standing still" on its own, every motion is relative. So when we say the speed limit is "c", we have to ask, speed limit relative to
what? It turns out the answer is that it's the speed limit relative to
anything, no matter how fast it's moving. What actually happens when we turn on the flashlight in that super fast train is that it looks, from our point of view on the train, just like any other time we turned on a flashlight. The light zooms away at "c". It doesn't slowly ooze out. But how is that possible? Doesn't that mean that for the boy standing still outside, it would appear as if the light were moving at "c"
plus the speed of the train, breaking the speed limit? It turns out the answer is no, from his perspective, the light is
also moving at "c" relative to
him, and from his perspective, it does sort of look like it's oozing slowly out of the flashlight relative to you on the train. But how can these two contradictory sounding things be true? It's true because it turns out that lots of
other things are relative too: space, time, and simultaneity are all just "relative" to something else as well. Contrary to our intuition and common sense, the distance between two things and the time between two events are relative. An hour for me might be 20 minutes for you. A mile for me might be three miles to you. If I say two things happened at the same exact time for me, they might have happened ten minutes apart for you. (Now you can see why so many people don't want to believe that special relativity is real! It makes you sound crazy!
)
Most of the math and physics of special relativity is sort of like an attempt to solve the riddle of the flashlight on the train... how can we make sense of the fact that the flashlight beam is moving at exactly "c" both from the point of view of the guy on the train and the guy standing still? Everything flows from that answer. Space and time and "simultaneity" all have to be adjusted in order to make it work out. Here's what actually happens:
First, in order to make it easier to visualize, let's imagine that "c" is a much lower number, since it's hard to think about things moving as fast as a flashlight beam. Let's say that instead of a super-fast train and a light beam, it's a slow-moving bus, and you're throwing a ball. There's a guy standing on the side of the road watching you. Let's say the bus is moving at 5 feet per second, and you throw the ball at 10 feet per second. The only thing that separates this from our earlier "common sense" scenario is that this time, the speed limit is 10 feet per second, and the ball has to appear to be moving at exactly 10 ft/sec both relative to you and to the guy on the street. How?
From the perspective of you on the bus: The world outside of your window appears to be moving backwards at 5 ft/sec while you are standing still, just like an ordinary bus ride. You throw the ball forward at 10 ft/sec relative to yourself, right as you line up with the guy standing outside. If the bus is 20 ft long, that means the ball needs to hit the front of the bus in 2 seconds. It works! Intuitively, you might be thinking that the total speed of the ball was "actually" 15 ft/sec since you know that you're "actually moving" and the guy outside is "standing still", but that's not the case. There is no such thing as standing still, and there is no universal "actual" space to measure against, it's all relative.
From the perspective of the guy on the street: The bus has to be moving 5 ft/sec relative to him, and the ball has to move 10 ft/sec relative to him, which means it has to look to him like the ball is only moving 5 ft/sec relative to you. If the bus is 20 ft long, the ball would then have to hit the front of the bus in 4 seconds. But the ball only took 2 seconds to hit the front of the bus for you, how can it take 4 seconds to hit the front of the bus for him? The answer is that from his perspective, the bus is actually shorter than 20 feet, and you are moving in slow motion. He sees you slowly throw the ball and everything inside your train is moving in slow motion, and it takes about 3 seconds to hit the front. In addition, you are horizontally squished, and the train isn't actually 20 ft long, it's shorter, say, 15 feet, so it works out that the ball hits the front in 3 seconds; that's the 5 mph relative to you that the guy on the street sees.
This is weird enough on its own, but it gets weirder. You'd think, if this were true, then the intuitive thought would be, "Well, if I'm moving in slow motion and I'm squished relative to him, then he must be moving in fast-forward and stretched out relative to me". But that's not the case. Since from your perspective, he's moving backwards and you're standing still, he
also appears to be moving in slow motion and squished from your point of view. How can you both appear to be moving in slow motion relative to each other? The answer here is that "simultaneity" (the observation that two things happen at the same time) is also relative.
Let's say the guy outside decides to throw a red flag as soon as the ball hits the front of the train from his perspective. From his perspective, the red flag and the ball hitting the front of the train happen at the same time. From your perspective inside the train, he's moving in slow motion, so the ball hits the front of the train first, and then a few seconds later, he throws the red flag. There are a lot of other examples that show the weirdness of all this going on, but usually one of the first questions we think about is, well, what happens when I finally get off the train and go talk to the guy, how does everything sync up? Am I further in the future than he is, or vice versa? Special Relativity is actually pretty complicated when trying to figure out how things happen while you're changing speed, but luckily, General Relativity makes it a little simpler to figure out, plus it includes gravity as well, which is yet another wild card. That's the next section!
or is that 
? 
Club and welcome too springs to mind 