The Strange Behavior of Time

22.06.10

Time is a difficult concept. For what is time? Is it constant? Has it always existed and will it continue to exist forever? Where did time come from? All these questions challenge our minds and philosophers and scientists have devoted a great amount of work studying the idea of time. And all that work gave fruits during the nineteenth century when Albert Einstein released his work on the theory of relativity. The theory of relativity takes many aspects of our universe into account (time, space, matter etc.), but I will only discuss it's ramification on the concept of time.

For starters, it helps to imagine time as another dimension. You have length, width and depth which make up our three space dimensions, but each event happening takes place at a specific point in the time-dimension. Imagine if we were to meet for lunch. We must first agree on where to meet (i.e. where in space) but also where in time to meet. Also, if I am standing still for an hour, I haven’t traveled in space at all, but I have traveled in time. I’ve become one hour older.

Time is however not constant. It is relative. This might sound strange at first, but I will try to explain it using a famous thought experiment involving a moving train. But before I do that, I have to explain what a "frame of reference" is. A frame of reference is, quite simply, a set of coordinates which is attached to a system.

For instance, if I am standing still looking at a car running at constant speed, the car is moving in my frame of reference. I myself on the other hand, am standing quite still. If we now move the frame of reference to the car, the car is, in its moving frame of reference, standing still and I am now moving away from it. You can have other frames of reference, such as attaching coordinates to a rotating system and other interesting stuff, but we will manage with the car-person-frame for this purpose.

The next part is a bit stranger. The theory of relativity tells us that the speed of light must be constant in all reference frames. This is very counterintuitive if you are used to Newtonian physics. You are perhaps used to think in the following way:
Say that you are standing on a train moving at 10 km/h. You now throw a ball in the same direction as the train is going at 2 km/t. In your moving frame of reference, the train is standing still and the ball is moving at the 2 km/h you gave it when you threw it. Now, if I am standing next to the train observing all this, I will see that the ball is moving at the 2 km/h you threw it at, plus the 10 km/h the train is moving, ergo 12 km/h. We have now established that the ball has a different velocity in the two different frames of reference. Adding velocities like this is ok for speeds that are way below the speed of light.

Light however does not behave this way. It always moves at the constant speed of light (which is about 300.000 kilometers per second) in all frames of reference. So if you and I are in two different frames of reference and we both send out light for each other to measure the speed of, we will both reach the same speed. This is unlike the ball-train-example mentioned earlier.

If you find this strange you can at least take comfort in knowing that you are not alone. The very nature of light is something which continues to puzzle scientists even today. We don't really know what light is, as it inhabits the behavior of both waves and particles.

But what does all this have to do with time and the question whether time is constant or not?

Consider now that you have built a clock to measure time with. It works in the following way. You are standing in a hallway with mirrors placed on the floor and in the ceiling. There is also a beam of light traveling up and down between these mirrors. We imagine that the mirrors are "perfect" so that the entire beam is reflected each time it hits the mirror. We can now calculate how much time the beam used to get from the floor to the roof by dividing the distance between the mirrors by the speed of light (which is constant). Let us say that the distance is so that the light used one second. (In other words it is a waaaay tall hallway.)

Imagine now that the hallway is moving, say, placed on a train moving at constant speed. When you are standing inside the train looking at the beam, it makes no difference to the previous example. In your frame of reference the mirrors are still standing perfectly still and the light is moving up and down giving you the same time of 1 second when you do the measuring.

But what if you are watching this from outside the train? You will then see the light leaving the mirror on the floor and as the beam makes its way towards the ceiling, the train moves as well making the path the light has to take slightly longer. I've tried to illustrate the two cases in figure 1 and 2.



This means that if I am standing outside looking at the train, I will measure a time which is slightly longer than the time you’re measuring from inside the train. In other words, time moves faster for you than for me. This effect will only become more and more dramatic as the train starts approaching the speed of light. Oh dear.

Now if we actually conducted this experiment with a real train and thus are limited to speeds way below the speed of light, the effect would not be noticeable. So for almost all purposes on earth, we can say that time is constant, and this is exactly why the idea of time not being constant is so counterintuitive at first. There are however cases when this effect needs to be taken into account, for instance when working with satellites and GPS. The small difference in time must be corrected for or else the satellite sends you off path when you try to navigate.

But such small effects are boring when you think of the bigger picture. This effect opens the very exiting door which has “time travel” written all over it. Oh yes, if you are able to travel at near the speed of light you can indeed travel in time which is incredibly awesome and I want to try it now fast. Unfortunately it has to remain in the idea bin for now – you would need incredible amounts of energy to reach such velocities; in fact you would need infinite energy to reach the same speed as light itself.

Phew, this became a rather long post but I hope I was able to explain this rather strange concept in a sort of understandable way. If you have any questions, please post them below in the comment box and I will try to answer them as best I can.

Now I need to go fantasize and draw another time-machine-sketch.

TO INFINITY-