Physical possibility

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.

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7 Comments

Filed under My half-baked ideas

7 responses to “Physical possibility

  1. That’s quite interesting. I can’t help thinking though that there is something like epistemic possibility being sneaked in here: because we have limited knowledge of physics, we determine what is ‘physical’, or physically possible, in terms of our limited knowledge of physics. The result, as you put it, is that we have’merely “local” principles, adjusted to fit the particular theory or the particular physical situation’.

    However, what is actually physically possible is thoroughly independent of our knowledge of physics. It may very well be that there is a ‘global’ principle that governs physical possibility — we just haven’t found it yet. Perhaps this could be the universal wavefunction or something of the sort.

    So, it’s true that a ‘global principle’ that would rule across all physical theories does not seem plausible, but that’s because these physical theories are competing explanation as to what the actual physics is like. If we had complete physics, then we *might* be able to point out such a ‘global principle’.

    • Tuomas–

      Thanks for your thoughts. Yes, I agree that once (and if) we have complete physics, then we would presumably be able to extract a “global” principle governing physical possibility. But the question then also arises as to what “complete physics” would amount to. Does it include the initial or, more generally, boundary conditions? If so, a complete theory might be characterized in that it would not consist of a set of models, but instead give us a complete description of the actual world (after all, it’s complete physics, right?). If so, there may be nothing possible beyond the merely actual. I guess what I am trying to say is that one might reject the view that possibilities are ever anything but epistemic.

  2. This is a really interesting question. The meaning of “physical” in local regions might be accounted for by our local experiences, which suggest various energy conditions. But global “physicality” is much harder to justify. Isn’t global hyperbolicity required to do QFT on curved spacetime?

    • Bryan–

      Yes, at least Wald (in QFT in Curved Spacetime and BH Thermodynamics) only defines a QFT on globally hyperbolic spacetimes. This of course does not imply that QFT on non-globally-hyperbolic spacetimes can’t be done, but it would presumably be a whole lot messier than it already is for globally hyperbolic spacetimes. But since no one really thinks that QFT on curved spacetimes is a candidate for a full quantum theory of gravity, the fact (if it is one) that QFT can only be done on globally hyperbolic spacetimes does not much work in justifying global hyperbolicity as a global “physicality” condition. You’re absolutely right: global conditions will be much harder to justify. I meant to say as much in my original post, but perhaps wasn’t fully clear on that.

  3. BTW, there are two different global-local dichotomies at play here: one marking a distinction of properties of spacetimes (e.g. global hyperbolicity is a global property of spacetime, compared to the satisfaction of a particular energy condition, which is usually taken as a local property), and the other partitioning the conditions of “physicality” operative in theories into local ones (operative in one physical theory) and global ones (operative in many or all physical theories).

    Both distinctions are non-trivial in that it turns out to be subtle to give a fully satisfactory definition.

    • Here is one stab at defining a local properties:

      Call two spacetimes (M,g) and (M’,g’) *locally isometric* if for each point p in M there is a point p’ in M’ such that the two points have isometric neighborhoods and similarly with the roles of M and M’ reversed.

      Now say that a property P is *local* if, for all locally isometric spacetimes (M,g) and (M’,g’), (M,g) has P if and only if (M’,g’) does as well.

      Anyone see problems with this formulation?

  4. Rush Mountmoore

    Is confirmation of a theory the same thing as confirming that it was a physical possibility, even before it was confirmed? How does one confirm–how can it be shown, proven, that a theory posits a physical possibility?
    Seems to me that in Physics, the question what is a physical possibility takes a back seat–far back there— to the question, what has explanatory power.
    If a physicist posits a thing and the math
    — because there is always a mathematical component– seems to work out well and be usefully explanatory, then it could (but not necessarily) gain adherents who then will
    start a search for evidence.
    Such was Relativity.
    Seems Physics is more a search what what is explanatorily possible.
    Does confirmation of a theory mean that what is described in the theory was physically possible before it was confirmed?
    Kind of irrelevant to a physicist.
    If it is asked, is there such a thing as a wave function?–is it a physical thing? Well, if you accept that Quantum Physics is an excellent predictor of certain physical events and you hold that if predictions are confirmed then the theory that predicts is confirmed, and that a confirmed theory means that the entities and processes posited in the theory physically exist—then the wave function does exist.
    But lots of physicists don’t think of the wave function as existing physically—they don’t know what to think of it. Many are reluctant to fully explore the ramifications of Quantum Theory—it is just too weird for them. The math of Quantum Physics, however, predicts very well, so they go with it.
    Apparently, it is not necessary to wrestle with the question of just what is physical existence and possible in such an existence and what isn’t, in order to get on in Physics. Einstein objected to Quantum’s indeterminacy in part because he thought that such a theory was incompletely explanatory–“God doesn’t play dice” and so on.
    Does that mean that if you agree with Einstein you should refuse to believe in the physicality of the indeterminacy or of “spooky action at a distance”—quantum entanglement–and further, believe that
    such things are physically an impossibility?
    Just how relevant is the question?

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