> As a result, there could be empty regions of space in which billions of years more have elapsed
If they are empty, those billion years didn't happen. But nothing is really empty, right?
If they are empty, those billion years didn't happen. But nothing is really empty, right?
No, that's not correct. Here's a better way to look at it:
In our cosmological models, we "slice up" the spacetime of the universe into slices of "space at a constant time"--each slice is like a "snapshot" of the space of the entire universe at a single instant of "cosmological time". The models, which assume homogeneity and isotropy, assume that the actual elapsed proper time at every point in space in each "snapshot" is the same--in other words, that "cosmologcal time" is also proper time for comoving observers everywhere in space at that instant of cosmological time--the time actually elapsed since the Big Bang on a clock moving with each observer.
What these supernova papers are examining is the possibility that "cosmological time" and proper time (clock time) for comoving observers do not always match: roughly speaking, in areas with higher mass concentration (galaxy clusters), proper time lags behind cosmological time (the time we use in the math to label each "snapshot" slice of the space of the universe), and in areas with lower mass concentration (voids), proper time runs ahead of cosmological time. The idea is that this mismatch between proper time and cosmological time can be significant enough to affect the inferences we should be drawing from the supernova observations about the expansion history of the universe.
As far as I know the jury is still out on all this; claims by proponents that what is presented in these papers is already sufficient to require "foundational change" are, I think, premature. But it is certainly a line of research that is worth pursuing.
That's not a good way of describing the actual law in a curved spacetime, i.e., a spacetime that contains gravitating masses. In such a spacetime there is no single global definition of "speed"; you can't compare speeds at spatially separated points.
A better way to state the law is that the light cone structure of the spacetime constrains the motion of all bodies: timelike bodies move within the light cones, lightlike bodies (like light itself) move exactly on the light cones. But once you state it that way, it becomes obvious that this law does not impose any constraints on "time/space fluctuations".
The "twin paradox" [1] is a prime example. The two twins depart from a common point in time and space, go about their separate travels, and meet again at a common point in space-time. Despite both twins always having the same constant speed of light, one of the twins takes a shorter path through time to get to the meeting point--one twin aged less than the other. In the paradox case, the shorter/longer paths are due to differences in acceleration. But the same thing happens due to differences in gravitation along two paths. (In fact, IIUC, acceleration and gravitational differences are the same thing.)
Just thinking about the math makes my head hurt, but it's apparent that two different photons can have taken very different journeys to reach us. For example, the universe was much denser in the dim past. Old, highly red-shifted photons have spent a lot of time slogging through higher gravitational fields. As a layman, that would suggest to me that, on average, time would have.. moved slower for them?... they would be even older than naive appearances suggest. I don't think the actual experts are naive, so that's been accounted for, or there's confounding factors. But I could also imagine that more chaotic differences, such as supernovas in denser galatic centers vs. the suburbs, or from galaxies embedded in huge filaments, could be hard to calculate.
Sure, it's just a convenient choice of coordinates. Even in a model that is not exactly homogeneous and isotropic, it can still be a convenient choice of coordinates to have cosmological time track some kind of average of the low mass and high mass regions. As I understand it, that's basically what the alternate models described in the article are doing.
> I thought one of the key parts of relativity is that which events happen simultaneously depends on your perspective.
That's true, but it doesn't actually mean very much. In a particular spacetime geometry, you can still have particular things that are picked out physically by the properties of that specific spacetime, and one of them can be "cosmological time". In an exactly homogeneous and isotropic model, that time is picked out by the symmetries of homogeneity and isotropy. But even in a model where homogeneity and isotropy are only average properties, their average is still picked out physically--for example, by the CMB, which is much, much closer to being exactly homogeneous and isotropic than galaxies and galaxy clusters (it's homogeneous and isotropic to within about 1 part in 100,000). So picking "cosmological time" based on observers who see the CMB that way is a physical method of picking them out; it's not an arbitrary choice.
Bear in mind that in special relativity, when you talk about relativity of simultaneity, you are talking about spacetime that is empty--there are no gravitating bodies anywhere. So all inertial frames are indeed equivalent in that spacetime, not just mathematically but physically. But as soon as you put gravitating bodies in, that symmetry is broken: the gravitating bodies have a definite state of motion, and that picks out certain choices of coordinates as being aligned with the gravitating bodies. So while it's true that you don't have to use those coordinates, they are convenient and they do reflect an actual physical property of the spacetime, and so does the definition of time they give.
Even if the space was truly empty, the expansion of that space would have gone on for longer, and thus things on opposite sides would eventually notice they were more distant.
But also yes the space isn't really totally empty.
(This connects in a funny way to Vernor Vinge's SF idea of slower and faster areas of space. The "high" / "fast" space is mostly empty, so the time passes there faster than in the "unthinking depths" around galactic cores, and hugely more progress is done by civilizations in the "fast" space, as observed from the "slow" space.)
His ideas were more ambitious: there are advanced technologies (e.g. FTL travel) that work in "fast" space but completely stop working in the "slow zone" (where the Solar system is located). On the other hand, even human-level intelligence would stop functioning close to the galactic center, the crew would not be able to operate the ship and would be stranded.