Sunday, February 8, 2009

Wilson on the Missing Physics

In “Determinism and the Mystery of the Missing Physics” (BJPS Advance Access) Mark Wilson uses the debate about determinism and classical physics to make the more general point about “the unstable gappiness that represents the natural price that classical mechanics must pay to achieve the extraordinary success it achieves on the macroscopic level” (3). Wilson focuses mostly on Norton’s “dome” example and Norton’s conclusion that it shows that classical mechanics is not deterministic. The main objection to this conclusion is that Norton relies on one particular fragment of classical mechanics, and only finds a counterexample to determinism by mistreating what are really “descriptive holes” (10). By contrast, Wilson argues that there are different fragments to classical mechanics: (MP) mass point particle mechanics, (PC) the physics of rigid bodies with perfect constraints (analytic mechanics) and (CM) continuum mechanics. Norton's example naturally lies in (PC). Each fragment has its own descriptive holes which become manifest when we seek to understand the motivation for this or that mathematical technique or assumption at the basis of a treatment of a given system. Typically, a hole in one fragment can be fixed by moving to another fragment, but then that fragment itself has its own holes that prevent a comprehensive treatment. As a result, Wilson concludes that there is no single way the world has to be for “classical mechanics” to be true, and, in particular, there is no answer to the question of whether or not classical mechanics is deterministic.

I think Wilson has noticed something very important about the tendencies of philosophers of science: philosophical positions are typically phrased in terms of how things are quite generally or universally, but our scientific theories, when examined, are often not up to the task of answering such general questions. It seems to me that Wilson opts to resolve this situation by rejecting the philosophical positions as poorly motivated. But another route would be to try to recast the philosophical positions in more specific terms. For example, if, as Wilson argues, descriptive holes are more or less inevitable in these sorts of cases, then a suitably qualified kind of indeterminism cashed out in terms of the existence of these holes can be vindicated. Other debates, like the debate about scientific realism, seem to me to be in need of similar reform, rather than outright rejection.


Bryan said...

I'm sorry, but Wilson's analysis of the dome doesn't make sense to me. He says:

"Any friend of determinism should be cautious about allowing forces to be glibly divided into 'reactive' and 'constraint' categories, for that's how Norton's loss of determinacy secretly enters the scene" (p.6).

What does that have to do it? Throughout the paper, Wilson describes a general a problem for the theory of motion constrained to a surface: it's not clear how describe constraint/inertial-force decomposition in a way that's consistent with other idealizations in Newtonian physics.

However, as interesting as this is, it's not sufficient for Norton-style indeterminism. Most systems that we analyze using constraint/inertial decomposition (such as a block on a hemisphere) are deterministic: a differential equation describing constrained motion on the surface has a unique solution. So why does Wilson think this is how indeterminism 'secretly enters the scene'?

Chris Pincock said...

This is a fair place to object, I think, and I am reluctant to disagree with you on a point of physics! I take it, though, that Wilson rejects the idea that a system described by a differential equation with a unique solution is sufficient to reach the deterministic conclusion. It seems that he would ask also for the motivation for the boundary conditions and perhaps also for the make-up of the differential equation itself.

In the Norton case, Wilson says "from the points of view of our alternative foundational starting points, this kind of 'active/constraint' decomposition may prove strictly unwarranted and can only be justified as a form of convenient approximation" (p. 6). This is clarified in the next paragraph, where we find out that "orthodox MP [mass point] mechanics rejects the assumption that forces can be strictly apportioned into 'active' and 'constraint' classes: all forces are wholly 'active'" (p. 6). There is more on "generalized coordinates" starting on p. 14.

This is why I said in my original post that Wilson demands that we "understand the motivation for this or that mathematical technique or assumption." Exactly how this understanding can be cashed out or why it is required is, then, the crux of the issue for me.