A Changing time scales

1. Sep 21, 2016

I feel like this concept itself is a bit out there, but thought I'd try to find more information on it (and why perhaps none of it makes sense).

I've been studying the metric expansion of space in my courses and been really interested by it (as most here are). As far as I can tell, we do not quite understand the origins for this expansion; we have simply observed evidence for it. Now it's likely been discussed and dismissed in the past, but I couldn't find any pertinent answers for my ensuing question—or maybe I just didn't understand my lessons on relativity well enough. In any case, I was just wondering if an analogous phenomenon (intrinsic scale changing) occurs in the temporal domain? Assuming isotropy as in the case of spatial expansion, is having the scale of time changing in flat space possible or even testable?

I realize we make time the dependent variable for a lot of models simply because it's most helpful for us in terms of testing and personally understanding the models. And I realize symmetry isn't necessarily necessary, but assuming such a change in time is possible, I can't help but wonder (e.g. perhaps the FLRW metric has a corresponding $a(x)$ term for the $-c^2dt^2$ term).

To my knowledge, the answer to all of the above is no as we don't have any proposed mechanism for this to even take place, and are not able to experiment at the same point in space at two separate times (yet, hopefully). It also seems to violate special relativity. I realize I haven't formulated much except a very broad question, but is there much discussion on the above that you could refer me to? I've been reading up on the differences and similarities between the spatial and temporal dimensions. Although why we have expansion (or contraction) in one and nothing in the other is still puzzling to me.

2. Sep 22, 2016

Orodruin

Staff Emeritus
Having nothing in front of the dt^2 in the metric is a coordinate convention. You could perfectly well write down coordinates where this is not the case, but they would likely be less useful.

However, writing an arbitrary function of x is generally not going to match observations.