The Theory of Relativity

Jacob H. asks, "I understand that causality is no longer valid with the theory of Relativity. Can you please explain this?"

Ah, Jacob, this certainly is one of the more peculiar aspects to Relativity! First, however, let us start by establishing a few basics of Einstein's Theory. In Relativity we deal with what are called inertial reference frames, which are simply the frame of reference for any observer moving at a constant speed (a non-inertial reference frame, on the other hand, is a reference frame that is accelerating, and things there become much more complicated). One of the key concepts of Relativity is that while the physical laws are the same in all reference frames, there is no frame of reference that can be said to be at absolute rest. All we can say is that one reference frame is moving relative to another, and whether we choose frame A to be moving relative to frame B or the other way around, it makes no difference, both are equally valid. We can easily visualize this principle when we are riding in a car. To someone standing on the road it appears that they are at rest and we in the car are moving. To us in the car, however, it feels as if we are at rest and the person on the road moves past us. According to Relativity this is more than a mere perception and it is perfectly valid to say that we in the car are in fact the ones at rest with the whole of the world moving relative to us.

Now at normal, everyday speeds this still doesn't make much of a difference for us, but if we are moving at speeds that approach the speed of light, things become much more interesting. For example, the closer we go to the speed of light, the slower time moves (what is termed time dilation) and a clock held by a moving observer will tick more slowly compared to one help by a stationary observer. This can even be seen at relatively slow speeds - an atomic clock on an airplane will eventually run slow as compared to a similar atomic clock that remains on the ground. The different will be incredibly small, but real, and is a result of the clock's motion while sitting on the airplane and not any fault of the timepiece.

"But wait, Dr. Volt, didn't we just say that there isn't any absolute reference frame? We did, as long as it's not accelerating. While the plane is in the air, moving at a constant speed, it will appear to someone on the plane that it is the clock on the ground that is moving and thus running slow. But because the plane must eventually stop on the ground (thus entering the reference frame of the ground clock) it will at some point experience an acceleration which ultimately allows us to say more absolutely that the plane's clock is the one running slow.

So now let's let look at the issue of causality. When one inertial frame is moving near the speed of light relative to the other, then each frame can legitimately say that they are the frame at rest. Now let's imagine that in frame A we have a garage with a door on both ends, and in frame B we have a vehicle. Furthermore, the garage doors are automatic such that as soon as the car reaches one it will instantly open, and as soon as the car has passed through it will instantly close. Now, when both frames are at rest relative to each other the car is longer than the garage. However, another strange feature of Relativity is that when an object moves close to the speed of light its length contracts. So let's assume that the car in frame B is moving fast enough that it's length contracts to a point where it is now shorter than the garage. When it drives through the garage in frame A, an observer in frame A will see the car at some point fully contained within the garage. But wait! The driver of the car in frame B can say that he is the one stationary with the garage moving past him. In that case it is the garage that is moving close to the speed of light and thus becomes shorter, and the driver in frame B will never see a moment in which the car sits entirely within the garage.

We have here a seeming paradox - two observers making fully accurate observations cannot agree on what actually occurs. Either one of them is wrong or our assumptions are incorrect. Relativity says that both observers are correct and that it is indeed our assumptions that are wrong. Specifically, our assumption that events that happen at the same time for one reference frame (i.e. the events of both garage doors being closed) happen at the same time for all observers. The solution to our paradox lies in the fact that they do not. In this example the two observers see the same events happen at different times because the large relative speed between them causes events that are simultaneous in one reference frame to not be so in another. A consequence of this is that there can be certain events in one reference frame which cannot affect certain events in another reference frame because while the "cause" may happen before the "effect" in one reference frame, in another it may be the "effect" that happens first!

So as you can see, Jacob, the world of Relativity is a both fascinating and perplexing place, but I hope this has given you (and our other readers) a taste of this intriguing theory. Its elegance, and dare I say beauty (which you must delve into the mathematics to fully appreciate), speaks volumes of Einstein's great genius.