Anything that can be measured can be encoded in a single number. Take for instance the trajectory of a stone thrown into the air. Its position in relation to the point of launch and the time it has taken to reach that point can be encoded into a set of numbers, three for the spacial dimensions and one for the time dimension. This can be done for all the points that it passes through. These individual numbers can then be encoded into a single number that uniquely identifies the trajectory of the stone.
Or, a physicist can describe the motion of the thrown stone by using generic equations and plug in the starting position and starting velocity of the stone, which can then be encoded, probably in a simpler fashion than the above point by point encoding.
If we can imagine a set of equations that describe all the possible physical processes (the “laws of nature”?) and we can imagine that we can measure the positions of all the particles (including photons,’dark matter’ and any more esoteric things that might be out these), then we could encode all this in a huge number which we could call the ‘number of the universe’. Such a number would be literally astronomical and I do mean ‘literally’ here.
The most concise expression of the state of the universe over all time is probably the universe itself and the laws that govern it. Each individual particle has its own attribute, like charge, mass, position and so on as well as things like spin, charm and color. Some of these change over time and some are fundamental to the particle itself – if they change so does the nature of the particle. The rest of the universe consists of other particles which have a lesser or greater effect on the particle, all of which sum together to describe the forces which affect the particle.
There are a couple of things which might derail the concept of the number of the universe. Firstly there is Heisenberg’s Uncertainty Principle and secondly there is the apparent probabilistic nature of some physical processes.
What follows is my take on these two issues. It may make a physicist laugh, or maybe grimace, but, hey, I’m trying to make sense of the universe to the best on my abilities.
People may have heard of the Uncertainty Principle, which states that there are pairs of physical properties which cannot both be accurately known at the same time. You may be able to know the position of a particle accurately, but you would not then be able to tell its momentum, for example.
It is usually explained in terms of how one measures the position of something, which boils down to hitting it with something else, such as a photon or other particle. The trouble here is that if you hit the particle with something else, you change its momentum. This is, at best, only a metaphor, as the uncertainty principle is more fundamental to quantum physics than this.
Wikipedia talks about waveforms and Fourier analysis and an aspect of waves that I’ve noticed myself over the years. If you send a sound wave to a frequency analyser you will see a number of peaks at various frequencies but you cannot tell how the amplitude of the wave changes with time. However, if you display the signal on an oscilloscope you can get a picture of the shape of the wave, that is the amplitude at any point in time, but not the frequencies of the wave and its side bands. Err. I know what I mean, but I don’t know if I can communicate what I mean!
The picture above shows a spectrum analysis of a waveform. I don’t have the oscilloscope version of the above, but below is a time-based view of a waveform.
In any case, the uncertainty doesn’t imply any indeterminacy. A particle doesn’t know its position and momentum, and these values are the result of its properties and the state of the rest of the universe and the history of both. This means that the uncertainty principle doesn’t introduce any possible indeterminacy into the number of the universe.
On the second point, some physical processes are probabilistic, such as the decay of a radioactive atom. I don’t believe that this has any effect on the number of the universe. The number incorporates the probabilistic nature of the decay, including all the possibilities.
There is an interpretation of quantum physics called the “Many Worlds Interpretation“, where each possible outcome of a probabilistic process splits off into a separate world, resulting in an infinity of separate worlds. I don’t believe that this tree of probabilistic worlds is a useful view of the situation.
No, I think that there is a probabilistic dimension, just like time or space. All the things that can happen, ‘happen’ in some sense. The probability of you throwing 100 tails in a row with a fair coin is very small, but it is possible. As I see it the main objection to this view is the fact that we only see one view of the universe and we don’t appear to experience any other possible views of the universe, but this is exactly the same with the dimensions of space and time. We only experience one view of space at a time as we can’t be in two places at the same time. While we could be in the same place at two times they are two distinct views of the universe.
In any case the number of the universe encompasses all probabilities so if you still adhere to the single probability model of the universe, our universe and all possible universes are encoded by it. The question then becomes how you can extract the smaller number that encoded the single universe that we experience. I believe that that is not a question that needs to be answered.
The question that does remain open is – why is that number the number of our universe? Why not some other number?