Why Does E=mc2_ - Brian Cox [38]
How are we to picture spacetime? Real spacetime is four-dimensional but the four-dimensional nature poses a stumbling block to our imagination, because human brains cannot directly picture objects in higher than three dimensions. In addition, the fact that time makes up one of the dimensions just sounds plain weird. A picture that might help make it all a little less mystical is to imagine a motorcycle roaming over an undulating countryside. Roads criss-cross the landscape, allowing our motorcyclist to wander this way and that. Spacetime is rather like the rolling countryside. The analogue of our motorcyclist traveling due north might be an object moving only in the time direction through spacetime. In other words, the object would be stationary in space. Of course, statements like “stationary in space” are subjective and so it is to be understood that the identification of “due north” with “the time direction” implies a particular point of view, but that is okay; we just need to bear it in mind. Now, the roads criss-crossing the spacetime landscape are all restricted to lie within a bearing of 45 degrees of north; roads due east and west are disallowed because to travel along them our spacetime “motorcyclist” would have to exceed the cosmic speed limit through space. Think of it this way: If the motorcyclist could travel due east, then he could go as far as he wanted in the easterly direction without any time passing at all, because he would not travel any distance up the northerly time direction. This would correspond to an infinite speed through space; he would get from a to b instantaneously. The roads have therefore been built so that the motorcyclist cannot travel too fast in an easterly or westerly direction.
The analogy can be pushed even further. We will very soon show that everything moves over spacetime at the same speed. It is just as if our motorcyclist has a device that fixes the throttle on his bike so that he always travels at the same speed over the spacetime landscape. We do need to be a little bit careful here, for when we talk about a speed in spacetime, it is not the same as a speed through space. A speed through space can be anything provided it does not exceed the cosmic speed limit—e.g., our motorcyclist might take a road close to a bearing of northeast, and in doing so he would be pushing as close to the cosmic speed limit as he could. In contrast, a road bearing close to due north would not lead to much movement east or west and consequently a journey that is well within the speed limit. The statement that everything moves at the same speed through spacetime sounds rather profound and perhaps a little baffling. It means that as you sit reading this book you are whizzing over the spacetime landscape at exactly the same speed as everything else in the universe. Viewed like that, motion through space is a shadow of a more universal motion through spacetime. In a very real sense, as we will now show, you are exactly like the motorcyclist with the fixed throttle. You are moving over the spacetime landscape with your throttle fixed open as you read this book. Because you are sitting still, your journey is entirely up the northerly time road. If you glance at your watch, you’ll see the distance in time ticking by. This is a very strange-sounding claim, so let’s go through it carefully.
Why does everything move at the same speed through spacetime? Consider our motorcyclist again and imagine 1 second passes according to the watch on his wrist. In that time, he will have traveled through spacetime by a certain distance. But everyone must agree on