Here's an interesting speculation. Assume for the moment that our universe is in fact a simulation runnning on a vast computing system created a race of beings that is far more advanced than we can presently imagine. The next logical question would be, "Why would an advanced civilization want or need to undertake such a project?"
Without debating whether or not such a project is possible, let's simply address this second question. I think that one reason why it might be of value to simulate an entire universe is to in fact understand the universe that one is already in. It may turn out that cosmology-research in "super advanced civilizations" takes place via such universe simulation rather than via observations of their own universes.
Why might this be the case? Well one reason is that Godel proved that in any formal system either there are truths that cannot be proved to be true using that formal system, or the formal system will result in contradictions. It is not possible to design a formal system (that is equivalent to mathematics as commonly defined) that is both logically complete and consistent. Perhaps because of this fundamental limitation on knowledge, at a certain level of physics sophistication, there will be a similar limitation to knowledge: either some truths about the universe cannot be proved using existing physics, or existing physics will result in contradictions.
But there may be a "workaround" to this problem -- a way to discover unprovable truths about the universe, without having to derive them from a particular formal physical system -- namely, simulating lots of potential universes, each with different physics, to see what the results are. Perhaps by doing a meta-level study of the behavior of different sets of physical laws on different sets of initial conditions, meta-laws can be discovered that apply not only to particular universes, but to all possible universes.
Perhaps these meta-laws can only be discovered and understood outside the context of one particular physics, or at least outside the context of one particular universe. Perhaps, the only way to see beyond the "Godel Horizon," is via simulation. By simulating myriad potential universes (on a hypothetical quantum computer, which could run infinite simulations on infinite data sets in finite time, for example), meta-theorems could be derived that transcended the Godel Horizon of any one particular physics or universe. This could be one explanation for why our universe is a simulation, assuming that it is a simulation at all (which I actually don't believe, by the way -- but I used to, which is why I am still interested in this question).
There may also be other reasons for simulating universes, besides just physics and cosmology research. In particular, one major motivation might be social research, genetic research, or perhaps research into time-travel and the complexity of changes in the continuum of causes and effects. These are wild speculations, I know, but worth pondering as long as we are on the subject. Another interesting possibility is that it may be easier to generate lots of universes in which various races evolve and work to solve the riddle of the universe in parallel, then to try to solve it oneself in one's own universe using only one's own resources. But this would only be practical if in fact it were possible to run such simulations at the same clockspeed, or better yet an even faster one, than the clockspeed (the speed of light) of one's own present universe.
Now an interesting follow-on idea that stems from this concept is that perhaps there is a way to detect whether or not our universe is a simulation. We simply need to look for some phenomena that no formal system can fully describe -- something that cannot be simulated perfectly, even on a suitably complex computer. If we can find such a phenomena then our universe cannot be a simulation or formal system, at least not one based on our concept of what a formal system is. I propose that consciousness is an example of such a unsimulatable-thing. If we find that consciousness cannot be simulated by a computer, then I would conclude that our universe (which contains consciousness, seemingly) cannot be a computer simulation. It might still be a simulation however -- but not a simulation running on anything equivalent to a Turing Machine. For example, perhaps in really advanced civilizations there is another way of simulating things that does not rely on Turing Machines -- for example, a simulation technology that relies instead on the application of dreaming as a means to generate and test various possible worlds. But that is an extreme fringe-speculation that I would be the first to admit is even farther out in the realm of science-fiction than the rest of this article.
If it turns out that we cannot find anything in our own universe that cannot be simulated perfectly such that it is effectively synthesized, in principle at least, then that does not prove that our universe is a simulation, only that it is not impossible for it to be a simulation. To prove that our unvierse IS a simulation, we would have to locate certain facts about our universe that are inconsistent with what we would expect if it were not a simulation. For example, perhaps there are certain non-random patterns in space-time, or our number system, or the physical constants that are extremely unlikely to have happened by accident. In fact, such patterns have been found. But even this is not sufficient evidence to convince me, or most scientists, that our universe is intelligently designed and just a simulation. So that won't suffice as proof.
What might suffice? Well for one thing, assuming that there exists a civilization advanced enough to simulate universes, perhaps they are also clever enough to find a way to add clues about their existence and the simulated nature of their universes, into their simulated universes so that they can be found by intelligent beings within those universes. But why would they bother leaving such clues, even if they could? Perhaps they might do so in order to generate recursive computations. For example, they might be able to find their Big Answer faster if the intelligent beings in their simulations could eventually evolve to run their own universe simulations. And in order to help them along in that process, really smart universe-simulators might insert clues and knowledge into their simulated universes necessary to help their simulated civilizations to evolve the technology and knowledge necessary to start running their own simulations of universes!
Now let's assume for the moment, that our universe is such a simulation, and that the simulators are clever enough to leave us clues to discover this fact -- where might they leave them? Well it wouldn't be in our DNA -- that is far too high level and emergent. It would probably have to be in the underlying structure of space-time and the physical laws and constants themselves -- for that is the level at which our simulation would most likely be encoded. Perhaps there is a message hidden for us to discover in the fabric of mathematics, space, time and physics. It's worth a look, if nothing else to rule out the possibility that it is there.
After thinking about this further for a while, a few additional interesting follow-on ideas emerged:
- If in fact our universe is a simulation being run on an advanced simulation system by some ultra-advanced race of beings, then it would increase the probability that THEIR UNIVERSE (our meta-universe) is also just a simulation being run on a computer system by an even more advanced race of beings! So perhaps one reason why an advanced race of beings might want to attempt to simulate a universe is in order to determine whether it is possible that their own universe is a simulation. Furthermore, if their own universe is a simulation and if that simulation is a formal system then their knowledge of their universe is certainly limited by Godel's theorem, and therefore simulating further universes is the only way for them to see beyond those limitations.
- Another interesting thought is that if a given universe U is a simulation running within another universe U' then the question arises, how might communication take place between the beings in those two universe? Consider our own case. Life on Earth has only been around for a tiny blip on the cosmic timescale of this universe; and our solar system is a miniscule backwater of our galaxy, let alone our entire universe. Furthermore, we may not be that unique or that intelligent -- there could be billions of other species that are equally or more interesting than us. In order to establish communication with our creators, we would have to somehow get their attention first, and this is a cosmic signal-to-noise problem. What could we do to get their attention? I think there are a few options:
- Do something that affects a large region of space. For example, create a clearly non-random, non-natural arrangement of stars, assuming we could do that. Create a bunch of black holes or pulsars, or make a pulsar emit energy in a noticeable way. (Interesting side-thought -- maybe pulsars are beacons created by advanced races within our simulation to signal their presence to one another and to the creators of our simulation -- that would be one way to get noticed).
- Do something that affects a large region of time. We would probably need time-travel technology to do this -- but if we had it we could potentially go back to a time just after the Big Bang and make a few simple changes that would result in a vastly different universe today. That would certainly send a big signal, if we could do it.
- Hack their simulation and try to create a bug or error. This is risky though -- it might result in our own accidental destruction (lost or corrupted data; or a bad computer virus running rampant through the cosmos, etc.) or the entire simulation (our universe) being shut down by an annoyed cosmic bug-fixer.
- Do something that affects the fundamental properties of our universe. For example, could we do something that would change the physical constants somehow? If looking at these properties is a logical place to search for a hidden message from our creators, then these properties might also be a logical place to send messages back to them. I have no idea how we could modify the fundamental physical constants of our universe.