Mathematical Models and What Reality Is Like

This problem of mathematical formalism and what it represents becomes particularly acute with the general theory of relativity and with quantum physics and quantum cosmology. General relativity tells us that space/ time is curved. Interpretations of quantum theory tell us that there may be ten or eleven dimensions, of which space/time is only a selection of four, most of them so small that we cannot see them. And quantum cosmology suggests that, below the Planck length (approximately I0-35 cm) space itself breaks up into a sort of topological foam, rather than being a continuum.

What we have is, as Bernard Carr puts it, "A sequence of mental models, each of which is progressively removed from common-sense reality" (2004, 54). Are these models telling us the truth about a reality that our senses disguise from us? Or are they mathematical abstractions that do not stand for anything objective but are pragmatically useful in helping us to understand common-sense reality better? Or is there some other way of understanding them?

In the formalism of quantum field theory, electrons are represented as probability waves in Hilbert space, and the square of their amplitude gives the probability of locating a particle at a specific point on a prepared surface. Now ask the question whether that is what electrons "really" are, and you will get a variety of diverse answers.

Many quantum physicists will simply say, "Don't ask." The mathematics works. It produces accurate predictions. It is a beautiful formalism. Yet it doesn't necessarily tell you what is really out there. Thus, leading quantum physicists like Niels Bohr thought that the mathematics is definitely a model, not a picture. It does not represent what is really out there. It is a useful abstraction that gives us predictions we can use (though only probabilistic ones). The real world is the world of observations. Mathematical physics tries to explain it and is very successful, but, as to what is really there, underlying the appearances, the mathematics does not tell us. This may be very frustrating for physicists, and debate continues to rage among those interested in such abstruse questions, which it is not necessary for physicists to resolve in order to get on with their work.

My point is simply this: modern physics need not be taken, and is very widely not taken, as a form of "direct realism," telling us what the world is objectively like. It can very well be taken, without any harm to physics—and possibly with some benefit to common sense—as a set of mathematical models that point to some hidden underlying structure of what appears to us but that do not undermine the reality of what we see. What we see is real. What underlies it and explains its ultimate origin and nature, we do not know. Mathematical models provide useful abstractions that help us to understand reality, but they do not help us to picture reality or delve into its ultimate nature.

We could take the mathematical models of space/time, or of a ten-dimensioned space/time and of the many space/times that are used in some physical models, precisely as abstract models. They point, no doubt, to what Bernard d'Espagnat calls a "veiled reality" underlying this. But they do not undermine the reality of what we experience; they only provide an abstract schema of Ultimate Reality without introducing us to its final mystery.

We may not wish to allow physicists, or the classical theologians either, to tell us that time is an illusion, whereas the underlying reality is a timeless whole. We can say that the flow of time from fixed past to open future is an irreducibly real feature of both our experience and of the world as it is. We do not have to say that there is one absolutely simultaneous "now" with which all flowing times have to be correlated. There may be many flowing processes, not temporally correlatable with one another.

Where now will God stand? God will stand at every leading edge of every process, moving with it toward its own open future. God will not be confined to a particular time but will move forward with many non-temporally related times. It follows that the divine experience will not be linear in the way that human experience is. It will enter into all processive times and will, thus, not be reducible to one linear temporal series into which they are all put.

This is well beyond the possibility of human imagining, and some may think that the idea of an experience, even a divine one, that contains temporally unrelated segments of time is incoherent. There is no problem with the idea of such unrelated segments as such. The problem is with their being elements of one experience. However, if God can experience many unrelated space/times anyway, as the classical view seems to imply, it should be possible for God to experience them as processive, if that is what they really are. We might say they will be related in God's unitary experience, but they will not be spatially or temporally related to each other. In this way, God will be both supratemporal and temporal. The idea does not seem to be incoherent, though I can understand someone thinking it is inconceivable. No more so than some quantum physics, perhaps!

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