I’ve been reading The Present Moment in Quantum Cosmology: Challenges to the Arguments for the Elimination of Time by Lee Smolin of loop quantum gravity fame (phil-sci archive). Mostly I’m reading because I’m an addict for anything involving the notion of “the present.” In the article he discusses two questions raised by Stuart Kauffman in the context of biology and economics which Smolin has ported over to physics:
- Is it possible that there is no finite procedure by means of which the configuration space of general relativity or some other cosmological theory may be constructed?
- Even if the answer is no is it possible that the computation that would be required to carry out the construction of the configuration space is so large that it could not be complete by any physical computer that existed inside the universe?
I’m not much of a fan of the first, (Penrose-ish) question…I find it hard to imagine noncomputability being of any practical consideration because it seems to me that one always needs an “infinity” of sorts to make the noncomputable arguments. (Apologies to Michael Nielsen quant-ph 9706006.) How do I verify that the universe is doing something noncomputable with my finite means?
The second question also strikes me as a bit odd. What I like about the question is that it talks only about the construction of the “configuration space.” This is, in a way, a specific computational problem. But it also seems that it glosses over a lot because in order to use a physical theory one needs a lot more than just the configuration space. The way in which I present a configuration space has a lot to do with what I can do with this space. And even if the full physical configuration space is not tractable, this doesn’t render it useless…there are probably tractable configuration spaces. Indeed, in a beautiful universe, the tractable configuration spaces will correspond to the tractable experiments. But this is wrong in some way: we know that we can use a quantum computer to simulate a quantum experiment, but this doesn’t mean we can use a quantum computer to output the amplitude of a particular basis state: there are nontractable questions about the theory even though we can use the theory to simulate the system.