Tables and organisms

A common-sense response to Eddington’s two table problem is that a table just is composed of molecules. This leads to difficult questions of exactly which molecules it is composed of. I assume that at table boundaries, molecules fly off all the time (that’s why one can smell a wooden table!).

But I think we could have an ontology of tables where we deny that tables are composed of molecules. Instead, we simply say that tables are grounded in the global wavefunction of the universe. We then deny precise localization for tables, recognizing that nothing is localized in our quantum universe. There is some approximate shape of the table, but this shape should not be understood as precise—there is no such thing as “the set of spacetime points occupied by the table”, unless perhaps we mean something truly vast (since the tails of wavefunctions spread out very far very fast).

That said, I don’t believe in tables, so I don’t have skin in the game.

But I do believe in organisms. Similar issues come up for organisms as for tables, except that organisms (I think) also have forms or souls. So I wouldn’t want to even initially say that organisms are composed of molecules, but that organisms are partly composed of molecules (and partly of form). That still generates the same problem of which exact molecules they are composed of. And in a quantum universe where there are no sharp facts about particle number, there probably is no hope for a good answer to that question.

So maybe it would be better to say that organisms are not even partly composed of molecules, but are instead partly grounded in the global wavefunction of the universe, and partly in the form. The form delineates which aspects of the global wavefunction are relevant to the organism in question.

Metaphysical semiholism

For a while I’ve speculated that making ontological sense of quantum mechanics requires introducing a global entity into our ontology to ground the value of the wavefunction throughout the universe.

One alternative is to divide up the grounding task among the local entities (particles and/or Aristotelian substances). For instance, on a Bohmian story, one could divide up 3N-dimensional configuration space into N cells, one cell for each of the N particles, with each particle grounding the values of the wavefunction in its own cell. But it seems impossible to find a non-arbitrary way to divide up configuration space into such cells without massive overdetermination. (Perhaps the easiest way to think about the problem is to ask which particle gets to determine the value of the wavefunction in a small neighborhood of the current position in configuration space. They all intuitively have “equal rights” to it.)

It just seems neater to suppose a global entity to do the job.

A similar issue comes up in theories that require a global field, like an electromagnetic field or a gravitational field (even if these is to be identified with spacetime).

Here is another, rather different task for a global entity in an Aristotelian context. At many times in evolutionary history, new types of organisms have arisen, with new forms. For instance, from a dinosaur whose form did not require feathers, we got a dinosaur whose form did require feathers. Where did the new form come from? Or suppose that one day in the lab we synthesize something molecularily indistinguishable from a duck embryo. It is plausible to suppose that once it grows up, it will not only walk and quack like a duck, but it will be a duck. But where did it get its duck form from?

We could suppose that particles have a much more complex nature than the one that physics assigns to them, including the power to generate the forms of all possible organisms (or at least all possible non-personal organisms—there is at least theological reason to make that distinction). But it does not seem plausible to suppose that encoded in all the particles we have the forms of ducks, elephants, oak trees, and presumably a vast array of non-actual organisms. Also, it is somewhat difficult to see how the vast number of particles involved in the production of a duck embryo would “divide up” the task of producing a duck form. This is reminiscent of the problem of dividing up the wavefunction grounding among Bohmian particles.

I am now finding somewhat attractive the idea that a global entity carries the powers of producing a vast array of forms, so that if we synthesize something just like a duck embryo in the lab, the global entity makes it into a duck.

Of course, we could suppose the global entity to be God. But that may be too occasionalistic, and too much of a God-of-the-gaps solution. Moreover, we may want to be able to say that there is some kind of natural necessity in these productions of organisms.

We could suppose several global entities: a wavefunction, a spacetime, and a form-generator.

But we could also suppose them to be one entity that plays several roles. There are two main ways of doing this:

1. The global entity is the Universe, and all the local entities, like ducks and people and particles (if there are any), are parts of it or otherwise grounded in it. (This is Jonathan Schaffer’s holism.)

2. Local entities are ontologically independent of the global entity.

I rather like option (2). We might call this semi-holism.

But I don’t know if there is anything to be gained by supposing there to be one global entity rather than several.

Two difficulties for wavefunction realism

According to wavefunction realism, we should think of the wavefunction of the universe—considered as a square-integrable function on R³ⁿ where n is the number of particles—as a kind of fundamental physical field.

Here are two interesting consequences of wavefunction realism. First, it seems like it should be logically possible for the fundamental physical field to take any logically coherent combination of values on R³ⁿ. But now imagine that the initial conditions of the wavefunction “field” are have it take a combination of values that is not a square-integrable function, either because it is nonmeasurable or because it is measurable but non-square-integrable. Then the Schroedinger equation “wouldn’t know” what to do with the wavefunction. In other words, for quantum physics to work, given wavefunction realism, we need a very special initial combination of values of the “wavefunction field”. This is not a knockdown argument, but it does suggest an underexplored need for fine-tuning of initial conditions.

Second, the solutions to the Schroedinger equation, understood distributionally, are only defined up to sets of measure zero. In other words, even though the Schroedinger equation is generally considered to be deterministic (any indeterminism in quantum mechanics comes in elsewhere, say in collapse), nonetheless the solutions to the equation are underdetermined when they are considered as square-integrable fields on R³ⁿ—if ψ(⋅,t) is a solution for a given set of initial conditions, so is any function that differs from ψ(⋅,t) only on a set of measure zero. Granted, any two candidates for the wavefunction that differ only on a set of measure zero provide the exact same empirical predictions. However, it is still troubling to think that so much of physical reality would be ungoverned by the laws. (There might be a solution using the lifting theorem mentioned in footnote 6 here, though.)

The essential properties of our spacetime

Suppose that spacetime really exists. Name our world's spacetime "Spacey". Now, we have some very interesting question of which properties of Spacey are essential to it. Consider a possible but non-actual world whose spacetime is curved differently, say because some star (or just some cat) is in a different place. If that world were actual instead of ours, would Spacey still exist, but just be curved differently, or would a numerically different spacetime, say Smiley, exist in Spacey's place?

There are three different views one could have about some kind K of potential properties of a spacetime:

1. All the properties in K that Spacey has are essential to Spacey.
2. None of the properties in K are essential to Spacey.
3. Some but not all the properties in K that Spacey has are essential to Spacey.

Suppose K is the geometric properties. It's plausible that at least the dimensionality is essential to Spacey: if Spacey is four-dimensional, it is essentially four-dimensional. Any world with a different number of dimensions doesn't have our friend Spacey as its spacetime. If so, we need only to decide between (1) and (3).

Here is an argument for (3). Spacey's properties can be divided into earlier and later ones, since one of the four (or more) dimensions of Spacey is time. Further, according to General Relativity, some of Spacey's later geometric properties are causally explained at least in part by Spacey's own earlier causal influences. But if (1) were true, then Spacey would not have existed had the later geometric properties been different from how they are, and a part of the explanation of why it is Spacey that exists lies in the exercise of Spacey's own causal influences. But nothing can even partly causally explain its own existence. (Interesting consequence: If Newtonian physics were right, we might think that view (1) was true with respect to geometric properties. But this is implausible given General Relativity.)

Similar arguments go for the wavefunction of the universe, if it's a fundamental entity.