Now, for big, clunky things like ourselves, made up of vast numbers of atoms, this is as far as it goes. But consider what it takes for atoms to have similar views. Atoms have many fewer degrees of freedom, hence fewer relational properties. So atoms which are far away from each other in space may still have similar neighborhoods, just because there are vastly fewer configurations their local neighborhoods could take. This suggests that perhaps similar atoms, with the same constituents and similar surroundings, interact with each other just because they have similar views.

These interactions would be highly, highly nonlocal. But in my recent work, I have showed that this could be the basis of quantum physics. Consider a hydrogen atom in a water molecule dancing in the air in front of me. This has a first neighborhood consisting of an oxygen atom, and a second neighborhood consisting of the whole molecule. The same is true of every hydrogen atom in a water molecule everywhere in the universe. So I am going to trust my relational instincts and take the crazy step of positing that all these atoms are interacting with each other, just because their views are similar. More specifically, I will posit that the interactions act to increase the differences between these atoms’ views. This will go on until the system has maximized the variety of views the atoms have of the universe.

In a recent paper, I showed that the hypothesis of maximal variety leads to the Schrödinger equation, and hence to quantum mechanics. This happens because there turns out to be a mathematical similarity between the variety and Bohm’s quantum force. As a result, Bohm’s quantum force acts to increase the variety of a system. It does so by making the neighborhoods of all the different particles as different from each other as possible.

In this approach the probabilities in quantum mechanics refer to an ensemble that really exists, the ensemble of all systems with similar views. This is a real ensemble, in that the elements are not located in our imagination; they are, each and every one, a part of the natural world. This is in accord with the principles of causal completeness and reciprocity.

This was the basis of a relational hidden variable theory I proposed, which I called the real ensemble formulation of quantum mechanics. From it, I could derive the Schrödinger formulation of quantum mechanics from a principle that maximizes the variety present in real ensembles of systems with similar views of the universe.