In physics in general, and in general relativity (GR) in particular, the mathematical apparatus of a theory is generally too liberal in the sense that it admits models of the theory which are not considered physically reasonable (or “physically possible” in a narrower sense). In GR, for instance, many spacetimes which satisfy the Einstein equations are not considered relevant in that they violate some allegedly obvious additional “conditions of physical reasonableness”. In electrodymanics, retarded solutions are admitted as physically sensible solutions, but not their advanced counterparts. Although space invaders are strictly speaking possible in Newtonian physics, they are routinely declared “unphysical”. And so on and so forth. But what is it exactly that underwrites these judgments?
In GR, this role is often played by local stipulations such as energy conditions or global conditions such as singularity freeness or global hyperbolicity. These two categories are quite distinct, not just in terms of whether they are considered local or global, but also in that the justification of the former, but not so much of the latter, relies on other physical theories. That is, an energy conditions receives its justification from some other theory, typically a quantum theory concerned with the behaviour of particles. There are not usually different theories available that would serve the justification of the mentioned global conditions. And their justifications are typically less solid. Consider singularity freeness; today, nobody would still insist that any physically relevant spacetime has to be free of singularities, although the presence of a singularity may still be considered a problem that needs to be addressed in a full quantum theory of gravity, or perhaps as a sign that such a theory is needed. John Earman, Chris Smeenk and I have argued that an a priori demand of global hyperbolicity is similarly misguided (see my papers). To simply insist that, e.g., a spacetime cannot contain closed timelike curves seems too weak in the face of the obvious possibility that a physically relevant spacetime may contain closed timelike curves (such as Kerr-Newman spacetime), or that it may be possible to operate a time machine, i.e. that it may be possible to shuffle matter-energy around so as to create a region, somewhere to the future, that contains closed timelike curves where none such region would have existed otherwise.
In other theories, causal principles of one form or another are invoked to mark the difference between “physical” and “unphysical” solutions (arguably, this is so in the electrodynamical case mentioned above). Or the conservation of energy. Or symmetries more generally. When I visited Hannover last October I discussed physical possibility with my host Paul Hoyningen-Huene. As we walked through the empty street of Hannover late at night, he remarked, quite rightly in my view, that one should not expect there to be of any one principle that would rule “globally” across all physical theories and determine, at this level of generality, what is “physical” or “unphysical”. Instead, one would expect that there would be many merely “local” principles, adjusted to fit the particular theory or the particular physical situation. Disappointing perhaps, but intuitively correct.
What do you, esteemed reader, think? Any thoughts? Does anybody know of places where this issue has been addressed in the literature? Any reactions welcome.