The Nature of Space
In the effort to develop an ultimate model for the universe, a crucial first step is to think about the nature of space—for inevitably it is in space that the processes in our universe occur.
Present-day physics almost always assumes that space is a perfect continuum, in which objects can be placed at absolutely any position. But one can certainly imagine that space could work very differently. And for example in a cellular automaton, space is not a continuum but instead consists just of discrete cells.
In our everyday experience space nevertheless appears to be continuous. But then so, for example, do fluids like air and water. And yet in the case of these fluids we know that at an underlying level they are composed of discrete molecules. And in fact over the course of the past century a great many aspects of the physical world that at first seemed continuous have in the end been discovered to be built up from discrete elements. And I very strongly suspect that this will also be true of space.
Particle physics experiments have shown that space acts as a continuum down to distances of around 10^-20 meters—or a hundred thousandth the radius of a proton. But there is absolutely no reason to think that discrete elements will not be found at still smaller distances.
And indeed, in the past one of the main reasons that space has been assumed to be a perfect continuum is that this makes it easier to handle in the context of traditional mathematics. But when one thinks in terms of programs and the kinds of systems I have discussed in this book, it no longer seems nearly as attractive to assume that space is a perfect continuum.
So if space is not in fact a continuum, what might it be? Could it, for example, be a regular array of cells like in a cellular automaton?
At first, one might think that this would be completely inconsistent with everyday observations. For even though the individual cells in the array might be extremely small, one might still imagine that one would for example see all sorts of signs of the overall orientation of the array.