Top Down Causation Doesn’t Help

Top down causation is the idea that the laws of a system at low resolution can dictate the laws at high resolution. I have depicted this with theory five in Figs. 2 and 3. Again we don’t know any case in which this happens.

I said above that we have no examples of top-down causation, but we certainly have wrong examples. Since these seem to be widespread, allow me some comments.

A typical argument goes like follows. The chief of CERN speaks the word “Go,” and in response someone pushes a button which will set into motion two proton beams that collide and produce a Higgs-boson. Human speech, as a perturbation of density fluctuations in the air, takes place at much lower energies (i.e. lower resolution) than elementary particle collisions. Hence, a top level process has caused a lower level process. Another example is that I swallow a pill, so that a big, low-resolution object like my arm causes a chain of molecular reactions. Reductionism must be wrong!

But such examples merely show that large systems often have interactions at a variety of energies at different places and at different times. Therefore, some parts of the system might lend themselves to a description at low energies (sound waves) while others do not (proton collisions). To demonstrate top-down causation, you would have to show that it is not possible to derive the sound wave’s propagation from the high-resolution theory for the air and its atoms and these atom’s constituents and so on. And there is no reason to think this isn’t possible, never mind that you won’t be able to actually do the calculation.

Another type of argument uses (possibly global) boundary conditions. Since the boundaries are usually large-scale (say, conducting plates) and yet constrain the behavior of the system at shorter scales (possibly large integer fraction of the plate’s distance), this is taken to mean a top-down causation took place. Again, however, to demonstrate top-down causation it would be necessary to show that the boundary conditions (the plates) could not themselves have been described at high resolution.

A related but somewhat different case are topological constraints. The equations of general relativity, for example do not determine the topology of space-time. But just because the equations do not determine some property of a system doesn’t mean that property cannot be determined from the system’s (entire!) small-scale configuration. A good way to see this is to think of a chain. Each link of the chain has two neighbors. If you look at any element of the chain and its neighbors (the “local” information) you cannot tell whether the chain is closed (ie, you cannot tell its topology). But of course if you have the complete information about the neighbor-couplings you will be able to tell that the chain is closed.

Yet another argument that seems different at first sight but is wrong for the same reason as the example with the chain is that entanglement realizes top-down causation [12]. The argument here is that entanglement is a non-local property of a system. Hence, if you have information only about a small part of a system, you have no way of knowing whether the system will begin to show novel effects due to entanglement if you look at the full system. Again, though, it is clearly possible to derive the behavior of the whole system if you have information about its entire microscopic constituents which, of course, includes entanglement between them.

In summary, we have no viable example of either strong emergence or top-down causation. Free will isn’t free. Effective field theory seems a fool-proof argument. So far.

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