The history of science has taught us many things, among them that asking new questions often leads to new insight. Often, these new questions had not been asked before because they seemed to be too philosophical, unanswerable or even mostly unscientific. Here, I would like to confront you with a question that, at a first glance, might seem to fit into these categories. Nevertheless, I will show that discussing this question, specifically applied to quantum theory, leads to deep insight.
In the computer age we have grown very familiar with the concept of simulation. We can simulate practically anything we have understood physically, and we do that for very complicated and large systems like climate models of our planet. Of course, we are using approximations to reality so that our computers can handle the complexity. This, however, is a limitation that we can easily imagine not to exist. The concept of simulation remains the same, even if performed on a hypothetical machine without any practical restrictions.
We could think of any consistent set of mathematical rules and simulate it on a computer. In some sense, we would be creating our own universes with the rules that we make up. Some of these simulations might be just complex enough to allow for an internal observer to evolve, an individual that would have an inside view of our simulation. And if we had the means of communicating with him, we could ask him what he is observing.
We will possibly never get to the scientific sophistication that would allow this sort of real experiment, so what is the point of proposing it? The universe of our hypothetical observer is purely mathematical, a list of rules and an initial state, not more. The reality perceived by him must emerge in some way from the mathematical rules. Surely some aspects of his observation will be highly subjective, like the perception of color, taste or anything that just developed by chance without any profound direct connection to material reality as perceived by him. But other aspects of his observation will not be so subjective, but shared by all other hypothetical observers in the same simulated universe.
So, the question I would like to ask is “How does reality as shared by all possible observers emerge from the mathematical rules that describe the universe these observers inhabit?”. Maybe I have already convinced you that the question is not so esoteric after all. But quite certainly not, that it is even remotely possible to answer it. How would one distinguish objective features from subjective ones? And would we not have to know about all the emergent structures of the simulated universe first, like atoms and molecules or even brains?
I do share the above concerns, but I can also offer a way to circumvent them entirely. Let us assume that our virtual observer is not just any observer, but in fact a physicist who tries to formulate his own mathematical theory of his perceived reality. If he is a good scientist, his theories will only include those aspects of his observation shared by all other observers, and if he is successful his final theory of all things he can observe will be a perfect mathematical description of the objective emergent reality in the virtual universe. This is an extremely helpful assumption, because it allows us to actually talk about mathematical structure instead of a fuzzy and partly psychological concept. With this we can reformulate the fundamental question to “What mathematical model does a virtual observer use to describe his perceived reality?”. This formulation sounds much more reasonable and there is some hope that we may find a way to mathematically deduce the emergence of this internal view from the mathematical structure of the universe we simulate.