programming (and other) musings
30 Nov 2009

# time

Some months ago, the FQXi ran a contest on essays on the nature of time. Many interesting articles were submitted, and most if not all of the awarded ones are worth reading. Perhaps my favourite among them is Carlo Rovelli's Forget time (PDF). You can read an abstract and some reader comments here.

Rovelli's a thought-provoking and quite fun to read article (i happen to like Rovelli's writing quite a bit). The main idea is to get rid of a singled out time variable in the Hamiltonian formulation of general relativistic mechanics and, by extension, quantum mechanics. It is argued that our usual time parameter, as it is used in Newtonian and quantum mechanics, as well as in special relativity, is not well-defined in a general relativistic context. Therefore, it must be replaced by a notion of coordinated events that conform a configuration space. Physical systems follow special orbits in the configuration space. often parametrizable by a finite set of state variables (think for instance of the amplitude and phase of a pendulum), so that we can pair events and describe the evolution of one in terms of another. These special orbits are obtained from a variational principle, derived from a Hamiltonian function. When the latter has a separable time we're in a classical, non-relativistic regime. But this is not usually the case. It is then shown how our everyday notion of time can be given a statistical interpretation, and derived in terms of the Gibbs theorem and the postulate of a Gibbs distribution for equilibrium states.

While i don't feel really qualified to properly criticise Rovelli's approach, i must say that it sounds reasonable and quite beautiful. Julian Barbour's The nature of time also seeks to get rid of time as a fundamental concept by defining it as a (quite different) derived quantity, although i don't find his arguments as compelling; the same happened to me with his book The end of time. And of course there are other physicists with some serious arguments on the opposite camp: Sean Carroll's essay What if time does really exist? in the same contest, and Lee Smolin's survey article The present moment in quantum cosmology: Challenges to the arguments for the elimination of time are some of the readings that could help making up your mind (or, if you're like me, increase your incertitude!).

Or you can also watch all the talks in the seminar held at the Perimeter Institute last year, The Clock and the Quantum. Although i haven't had time to do much more than skimming over a couple or three videos (for instance, Barbour's and Roger Penrose's), it looks like a pretty interesting set for those of you wondering what's this queer thing we call time.