| > Time does appear in fundamental concepts in physics? Sure, in that it is a component of a spacetime, and events happen at different points in spacetime. How you slice up spacetime into space and time is essentially up to you. That is what Rovelli is talking about: it's not that there is no time, but rather that slicing up a spacetime in any fashion will still not produce a global "now". Setting down a system of constant pseudo-Cartesian coordinates: > ds^2 = c dt^2 - dx_1^2 - dx_2^2 - dx_3^2 (nit: c^2) versus some other set of coordinates on the shame spacetime doesn't change a pair of infinitesimally close field-values on field filling that spacetime, nor their relative positions -- it just changes how one describes the latter. We can still chose a now and describe the difference between now-1, now, now+1 as operations within the "now" spacelike hypersurface. However, does this justify a view that now+1 is undetermined at now-1? What operations happen where in the same volume of spacetime for an observer using a different slicing? The exact metric is less interesting here than that the spacetime is Lorentzian; that feature is what constrains slicing choices within a causal cone, or alternatively provides the diffeomorphism invariance under arbitrary time parametrisation. "Timelessness" doesn't get rid of that sort of ordering: a relativistic field's field-values at different points in spacetime depend on it, however one wants to formalize that dependency, e.g. they must transform under representations of the Poincaré group, Poincaré invariance must be implemented unitarily on the state space, or the action must be Poincaré-invariant. What timelessness does challenge is some notions about operations within any spacelike hypersurface. |
I thought that was just already accepted as part of relativity that there is no global now (I feel like you are saying there is no global interial reference frame?).
I really mean that there is this more general concept of time which looks like what humans perceive as "time" locally. The ordinary human perception of time is obviously not quite the whole picture. Our lives are just slow enough that we don't notice relativistic effects. We are just fooled into thinking its ordered linearly, but there is a more general picture.
But saying that there is no "time" because it doesn't quite match our intuitions is wrong. Its just that we have to expand our thinking.
Further, I think relativity still has an "arrow of time". Thermodynamic quantities can transform under reps of Poincare group - "Relativistic Thermodynamics" is certainly a thing. Landau and Lifshitz has a few chapters on it I believe. So the idea of time "passing" (entropy increasing at least carries over.