Is the Universe Fundamental?
Beables serve as the ontology of theories but are they fundamental? In other words, is there a reality deeper than beables? This is an interesting question in the context of a universe.
If we were to naively think of a universe as an object and then ask whether or not it was fundamental, the answer would be unclear since we know that most universes contain things like matter and energy and we might consider our universe to be constituted of such things. But that’s not the sense I mean in this instance.To Bell, beables certainly are fundamental within a given theory since they form the ontology for that theory, i.e. what the theory is about. For most theories, we can think of the universe as a bit like the substrate on which the beables of those theories reside. But for theories concerning the universe itself, we want to know more about the substrate. To put it another way, if we were to build a universe from scratch in a reductio-deductivist sense, it seems logical to start by formulating a wavefunction as a functional of a set of field configurations. But there’s a problem with this. Presumably, if we have defined our universe in terms of a functional of some set of field configurations, one would assume that we would also need to define the fields. Our definition of a universe references something else. That suggests that, at least in this context, we have a beable for a theory that is not actually fundamental. Of course there is nothing inherently wrong with this in the sense of Bell’s conception of beables since he made no explicit requirement that they be fundamental. On the other hand, how could a universe not be fundamental? It’s hard to imagine anything more fundamental than a universe.
But, let’s return for a moment to the colloquial definition of a universe as the totality of all that exists. In a way, that definition suggests that the concept of a universe is meaningless without something else, specifically all that exists.
In that sense, a universe isn’t fundamental. What actually defines it is that from which it is constructed. A universe without structure, without elements is meaningless. As such, a ‘universe’, as envisaged here and consistent with Bell’s notion of beables, is not fundamental.We shouldn’t read too much into this conclusion, however. This result applies only to universes that can be modeled using Bell’s notion of beables. It is possible that there might be ways to define a universe that cannot be a beable in any theory. In addition, given the minor ambiguities associated with Bell’s notion of beables and the way in which the idea took shape in his writing over the years, it is possible to reach a different conclusion in this matter. But it is important to remember that the wavefunction in the Wheeler-DeWitt equation is not the same sort of thing as the wavefunction in non-relativistic quantum mechanics. It doesn’t suffer from the same nonlocal transformation. In fact it doesn’t transform at all! It simply is. As Bell said when he introduced the concept of beables, “it should again become possible to say of a system not that such and such may be observed to be so but that such and such be so” [6]. The universe’s existence is independent of our observation of it. We don’t simply observe that it exists, it does exist. Of that I am sure, even if I wake up tomorrow in a monastery.
Acknowledgements I would like to thank Travis Norsen, Tim Maudlin, Hans Westman, and Travis Myers for a stimulating and enlightening discussion that helped to shape this essay.