Fields and finetuning

Here is an interesting fine-tuning issue, inspired by a talk I heard from Brian Cutter at the 2023 ACPA meeting.

It seems likely that physical reality will involve one or more fields: objects that assign values to points in space (“ordinary” space or configuration space), which values then govern the evolution of the universe.

The fine-tuning issue is this. A plausible rearrangement principle should allow any mathematical assignment of values of the field to the points in space as metaphysically possible. But intuitively “most” such assignments result in a configuration that cannot meaningfully evolve according to our laws of nature. So we want to have an explanation of the fine-tuning—why are we so lucky as to have an assignment that plays nice with the laws of nature.

For a toy example, consider an electric field, which is a vector field E that generates a force F = qE on a particle of charge q. Intuitively, “most” vector fields will be nonmeasurable. But for a nonmeasurable electric field, we have no hope for a meaningful solution to the differential equations of motion. (OK, I’m ignoring the evolution of the field itself.)

For another example, suppose we think of the quantum wavefunction as a function over configuration space rather than as a vector in Hilbert space (though I prefer the latter formulation). If that function is nonmeasurable—and intuitively “most” are nonmeasurable—then we have no way to use quantum mechanics to predict the further evolution of this wavefunction. And if that function, while measurable, is not square integrable (I don’t know if there is a sense of “most” that applies here), then we have no way to use the Born rule to generate measurement predictions.