CALCULATION, BOOKKEEPING, REPRESENTATION, AND EXPLANATION: A PARABLE.
| Autor | Maudlin, Tim |
Prologue
The fundamental question of ontology is: What exists? Hence the fundamental question of physical ontology is: What physical entities exist? A full answer to that question would include all physical entities, including (for example) particular tables and chairs, but no one wants that sort of full answer. God may be entertained by enumerating the hairs on each person's head, but neither philosophers nor physicists would be enlightened by such an undertaking.
So the question of physical ontology gets restricted in two ways. First, there is a focus on types or species of physical entities: are there particles or fields or strings or space-time? Second, there is a focus on the more fundamental as opposed to the derivative. Water is a type of physical entity, but a derivative type: to be water is to be a composed of [H.sub.2]O molecules, and to be an [H.sub.2]O molecule is to be a certain bound state of two hydrogen atoms and an oxygen atom (which can be further analyzed into bound states of quarks and electrons). In some decent sense, that is all that water is, so having accounted for all the quarks and electrons (whatever they are) automatically accounts for the water. Properties or characteristics or quantities can similarly be distinguished into the more fundamental and the more derivative. The physical quantity temperature is understood as a statistical characteristic of a system composed of many subsystems, so temperature is a derivative quantity while the more fundamental characteristics are those of the subsystems that display the statistical profile. Pursued in this way, the central question of physical ontology is a request for an account of the fundamental physical properties, entities and kinds.
Of course, no one claims to know right now what the fundamental physical kinds are, as that would require having the fundamental physical theory--the correct Theory of Everything--which we do not possess. Still, one can ask questions like: "What are the fundamental physical kinds according to some theory?". And even if a theory is offered explicitly as non-fundamental, even if it is offered as some sort of effective theory valid only in a limited domain, one can ask: What are the most fundamental sorts of entities postulated by this theory as presently formulated? This is the sort of question that we have in mind in the sequel.
As a primary example, consider a cluster of questions raised in discussions of the ontology of quantum theory:
1) Is the wavefunction real?
2) What is the meaning of the wavefunction?
3) Is the wavefunction ontic or epistemic?
4) Is the wavefunction just a bookkeeping device?
5) What, if anything, does the wavefunction represent?
6) What, if anything, does the wavefunction represent about the physical system to which it is ascribed?
All of these questions are attempts to raise the same question, although I will argue that the last formulation is the best. Let's sort through the list.
Questions of ontology can become hopelessly confused if one does not cleanly separate representations from what they represent. In mathematical physics, mathematical objects are used as representations of physical states of affairs. Of course, there are completely separate questions about the ontology of mathematics: in what sense, if any, do mathematical objects and mathematical facts exist? Those are fascinating and difficult questions but are orthogonal to questions of physical ontology, for whatever mathematical objects are they are not per se physical. (1) As far as our inquiries are concerned, we will take the mathematical objects as given, with a certain uncontroversial mathematical structure. The question of physical ontology is not about the ontological status of the mathematical objects per se.
Unfortunately, in mathematical physics there is often a pervasive ambiguity in language that arises from using the same term to refer to a mathematical object and to a (putative) physical entity that it might represent. And in quantum mechanics that ambiguity infects almost all discussions. In particular, what is referred to by the term "the wavefunction" in the six questions above?
Clearly, the intent in question 1 cannot be to refer to any purely mathematical entity. If it were, then the question would be about the ontology of mathematics rather than physics. But still, there is a mathematical entity that is employed in the formalism used by quantum mechanics, and that mathematical entity is typically called "the wavefunction of the system". For example, we might be told that the wavefunction of a collection of N spinless particles is a complex function on the configuration space of the system, or a ray in a Hilbert space, or a density operator. All of these are clearly mathematical objects, and asking whether they are real is asking a question that has nothing to do with physics. Rather, what is under discussion is not the "reality" or otherwise of the wavefunction itself, but the reality or otherwise of something physical that in some way would correspond to the mathematical wavefunction. I have taken to calling this putative physical object the quantum state of a system. By definition, a quantum state would be a physical characteristic of a system, whose existence would be independent of any mathematical objects used to represent it. In this sense quantum states might not exist at all, just as it turns out that "states of caloric" do not exist because there is no caloric.
Talk of the "meaning" of the wavefunction is also suboptimal. Primarily it is representations, such as sentences in an interpreted language, that have meanings, so question 2 does put the wavefunction in the category of representations. But "meaning" is so polysemous that the question immediately demands further clarification.
Question 3 also presumes that the wavefunction is a representation, and foregrounds the question of what sort of thing it represents. The term "ontic" is slightly tendentious in this context, and should be read as a contrast class to "epistemic". To say that the wavefunction is epistemic is to say that it represents the credal state (or perhaps the ideal credal state) of some cognitive agent. This is a view explicitly endorsed by the QBists. Wavefunctions, for the QBist, are to be assigned not to physical systems per se but to cognitive agents. They provide advice to the agent about how to set their subjective credences. In QBism, these credences are not even about how standard physical systems will behave, but rather about what the personal experiences of that particular agent will be. In two words, the position of the QBist is both instrumentalist and solipsistic. Wavefunctions are mere mathematical tools for forming expectations, and the class of expectations is not about objective physical systems, but about egocentric subjective states.
Instrumentalism is an old story in philosophy of science. If all one wants out of science in general is an effective way to make reasonably accurate predictions then that's all one wants: there is nothing more to be said. Many people, however, have higher ambitions. They want to actually understand the world, not merely accurately predict it (much less only predict the content of their own experience of it). For such a person the instrumental effectiveness of a mathematically formulated scheme is not the end of scientific inquiry but rather the beginning. One wants to know why the scheme predicts so well. If the QBist doesn't want this sort of explanation, then there hardly seems reason to have a dispute: they can go happily on their way satisfied with the acknowledged predictive accuracy of "standard" quantum theory. I want more. Indeed, if all that physics aimed to provide were a reliable and accurate way to predict my own experiences, I just would not be interested in the topic at all. My own experiences are a tiny and rather uninteresting sliver of what there is in the world. I am after bigger game.
The real issue raised by the so-called "epistemic" accounts of the wavefunction isn't what the wavefunction is but rather what the whole point of doing physics is. I myself wonder why an instrumentalist solipsist of this sort would spend much time studying fundamental physics: if I want to predict my experiences of the weather tomorrow I will consult a meteorologist rather than a physicist. But de gustibus non disputandum est.
The physicist--or should we say natural philosopher?--wants not just an accurate prediction-making scheme but an understanding of why it works. Even more precisely, the natural philosopher wants an accurate account of the nature of the physical world and would not be terribly surprised if that account also allows one to make accurate and reliable predictions, although that is just a side benefit. It seems that something like a wavefunction will play a central role in the mathematical formalism used to make accurate empirical predictions. The question before us is what claims about the physical ontology of the world are implied or suggested by that fact. What, if anything, in the physical world does the wavefunction represent?
That brings us to questions 4, 5, and 6. Once one asks what, if anything, the wavefunction represents, there are only three possible sorts of answers: it represents everything; it represents something but not everything; and it represents nothing. (2)
The claim that it represents everything has long been discussed using the terminology introduced by Einstein, Podolsky and Rosen: is the "quantum-mechanical description of physical reality" "complete"?. EPR explicitly answered "no", and Bohr and Von Neumann explicitly answered "yes". In contemporary discussions, the Everettians defend the completeness of the wavefunction as a representation of the physical universe: all the (non-de-se) physical characteristics of the universe are captured--somehow--by the wavefunction. That still leaves room for disagreement...
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