When I was writing "Mr NoisyClock's Consciousness-World Physics," I once imagined a final localization hypothesis. The motivation for the problem is this:

In the consciousness-world, there exist both definite and suspected nonlocal phenomena. They are, respectively, quantum entanglement and the supernatural powers described in Buddhism (seeing the past and the future). Either kind of nonlocal phenomenon poses a very serious challenge to our basic belief in causality.

According to "Mr NoisyClock's Consciousness-World Physics," I believe that our basic belief in causality should be preserved, because it is a basic condition for the generation of the consciousness-world. This can be treated as a hypothetical axiom. So when we say that the basic belief in causality should be preserved, what do we mean? We mean that locality can be restored in a more fundamental state space.

Thus we can propose the final localization hypothesis. Its basic idea is this: if the physics of this world (represented as a dynamical equation f on a state space A) is legitimate (that is, it conforms to the basic forms of cognition and to known physical facts), and if it contains nonlocality, then we can find a larger space B on which there exists a dynamical equation f'. Through some mapping, f' gives the same predictions as f for the physics in A, but f' contains no nonlocality. In other words, by lifting the state space, nonlocality can ultimately be eliminated.

A stricter formulation is as follows:

Let (A, f) be a legitimate physical theory, where:

If the dynamics f exhibits nonlocal correlations in the state space A, then there exist:

such that:


P o f' = f o P

and f' is completely local.

Why do I have this conjecture? Imagine a thought experiment. Two-dimensional creatures live on the surface of a sphere in three-dimensional space (that is, in the space as we understand it). The physics of their world is basically the same as ours. Light propagates along the surface of the sphere, so they probably have physics and physical theories much like ours. Let us call their world Java Kingdom, and let us call their physicist Little NoisyClock.

Then we somehow create a microscopic correlation mechanism. This mechanism synchronizes states through light-path communication along strings. In principle, this is possible.

Eventually, Little NoisyClock will be astonished to discover that superluminal correlations exist in their world. He names this phenomenon quantum entanglement. Java Kingdom debates it for several hundred years, and everyone finds it completely incomprehensible.

But from our world, this is the most ordinary thing imaginable: their spacetime sphere A is embedded in our spacetime B, and our physics (NoisyClock physics) projects down to their physics (Little NoisyClock physics). Their action at a distance is, in our world, a perfectly ordinary local action, and it fully conforms to causality.

So what does this suggest? The nonlocal phenomena we observe may very likely be only the result of an incomplete geometry in our cognitive model. We have failed to include certain dimensions that exist but are unknown to us. It may not be that there really exists an irreducible action at a distance.

This is an existence argument. That is, the physics of Java Kingdom can very easily be lifted into the physics of our world, thereby eliminating nonlocality, and this lift is natural. When Little NoisyClock of Java Kingdom develops relativity and discovers that spacetime has curvature, the most natural thought is that the spacetime of Java Kingdom was originally the surface of a sphere embedded in another, more fundamental spacetime.

Now let us return to our own world. What reason do we have to firmly believe that four-dimensional spacetime just happens to be fundamental? None at all. If we generally live on a sphere, then quantum entanglement is not mysterious at all.

Now let us go one step further. If we somehow give Little NoisyClock of Java Kingdom full access to the third dimension, then he can fully see the light propagating through the strings inside the sphere. For the people of Java Kingdom, Little NoisyClock would then have supernatural powers. He could see the past, present, and future beyond the light cone, and in some sense could even "manipulate" certain things. But Little NoisyClock would always say humbly: causality is not false. The people of Java Kingdom would not understand.

But people in our world would understand it perfectly clearly: Little NoisyClock is merely living in four-dimensional spacetime. His so-called supernatural powers are all completely ordinary when seen from this space, and causality is indeed not false.

In our world, Little NoisyClock has a name: the Buddha. I think the clue to new physics lies in humanity's scattered reports of supernatural powers and paranormal phenomena.