Pedagoguery

What is time? It is a trickier question than it first appears. Most physical laws that we know of has the concept of time bound inextricably into them. Yet, by extrapolation, we can conceive of an end of time. How exactly would we define that? Time has four properties, each of which may end separately or in conjunction with the others. Those properties are directionality, duration, causality, and structure.

The directionality of time stems from the fact that it flows in a single direction – from the past into the future. This seems unremarkable to us, yet most physical laws have a strange property – they work the same regardless of whether you run them backwards or forwards in time. What then, provides time with its directionality? The answer is entropy. Take, for example, a teacup dropped onto the floor, where it shatters. There is nothing in the equations that would prevent billions of air molecules from acting on the pieces in such a way to cause them to coalesce back into an intact teacup, and the teacup to jump up from the floor into your hand. We never see that happen, however, since the broken teacup is a more disordered system. The precise definition of disorder in this case is that you can rearrange the particles of the system in more ways that yields essentially the same system. Using our example, you can rearrange the pieces of the teacup on the floor in a multitude of ways, and the system is essentially the same. Those pieces, however, can only be arranged in one way to yield an intact teacup, so the broken teacup is a more disordered state, and thus has a higher entropy. That leads us to the question of what happens when the entropy of the universe gets as high as it can get? Things could change, but the total disorder no longer increases, so it is no longer possible to determine time's directionality. Such a state of maximum entropy is what is referred to as the “heat death” of the universe. A time far in the future where the only thing left in the universe is radiation, whether it be the far red shifted remnants of the Big Bang, or the quiet particles that evaporated from black holes, if radiation is all that is left, there is no way that the universe can get more disordered, and thus time loses directionality.

Duration is the concept that events take place over a span of time. Seconds are shorter than minutes, which are shorter than hours, and so on. However, in order for time to have duration, it must be measurable – you have to be able to construct a clock. An atomic clock, for example, relies on the atomic transition between two energy states of a cesium atom. In a universe filled with just radiation, construction of such a clock is impossible. Radiation of the appropriate frequency may exist, but you have nothing to measure it with or compare it to. Thus, you could not measure the difference between a second and a minute. Without the ability to measure, you cannot distinguish the differences and thus duration ceases to exist.

Causality is the property of time by which effects follow causes. This is a key way in which time is different from space. Time restricts how events can appear within it, whereas space places no such restrictions. When you type a key on your computer keyboard, the appropriate letter appears on the screen. Thus, the two events, adjacent in time, are linked. However, two items adjacent in space, such as your keyboard and a note pad, may have no relation to each other at all. How can causality be broken? According to one brane theory, the universe we experience could be just a four dimensional construct within a higher dimensional space. We are confined to this 4-d brane, and cannot move off of it, while the brane itself is free to move within the higher dimensional space. If the brane we are on starts to accelerate or to become strongly warped, then things on the brane must move faster to get from place to place. Eventually, if the acceleration or warping becomes strong enough, then objects on the brane would have to move faster than the speed of light to move at all, so physical objects would be locked into place. No movement is possible, so time acts just like another spatial dimension, and causality ceases to exist. Beings within the brane would not notice this since their clocks would be slowing down. The only thing they would observe would be that distant galaxies would appear to be accelerating away.

Even if directionality, duration, and causality cease to exist, time can still have structure. Events can still be ordered on a line and said to have a relationship with each other, even if that relationship is simply proximity. Structure can too be lost, however, and the hologram theory provides a means for this to happen. A hologram is a two dimensional picture that can appear three dimensional. By the same token, hologram theory postulates that our universe is really two dimensional, but is ordered in such a way to appear three dimensional like a hologram. However, just as not all two dimensional pictures produce holograms, not all two dimensional laws of physics look three dimensional. In certain areas, such as those around black holes, the underlying two dimensional system becomes increasingly disordered as the star collapses. It is a phase change similar to a melting ice cube – as a solid, the water has structure but the liquid does not. So, in a similar phase change in a black hole, the third dimension simply melts away. So within a black hole, time becomes a spacial dimension – is depends on your distance from the singularity. But distance within the black hole becomes meaningless and thus it no longer becomes possible to say that an event takes place at certain times or locations. Time ceases to exist at all.

Next time, are there dark matter worlds?