This is something I've been working on for a while. It should not be considered gospel - indeed, it is mostly me forming a hypotheses, or "Lorecrafting" to use the local vernacular. New developments (including your ideas and contributions) will likely serve to amend or improve the theory. And the theory itself is about the various FINAL FANTASY worlds and how they interconnect. While we will get to XIV later, for now I want to springboard my theory off FFXIII:Lightning Returns, because it explicitly shows us a world undergoing destruction and recreation.
===SPOILER WARNING===
This topic assumes you're familiar with the ending of Lightning Returns and the later parts of Bravely Default, as well as events in the main scenario of XIV:ARR. If you care about such things, turn away now.
===SPOILER WARNING===
This video is from the very end of Lightning Returns and is what got me thinking on this topic. Start at around 25:30, but the part that is most important starts at about 32:00.
Yes, that's Saturn, Mars and the Moon we pass by on our way to Earth, the new world, with us looking down on Africa and Europe. The 14th day epilogue even juxtaposes Lightning's character model into what looks like rural France.
The time of crystals and gods is over, vanished into a past that no longer is.
Humankind will be born afresh. Ours is a new future, bright with promise.
Sometimes shadows will darken our path, we shall tremble in fear before the night. But we won't be alone. We will reach out our hands...
and in the warmth of another hand holding our own, we will know hope.
We will survive, and prosper.
The crystal age is just a legend, from before the world was born.
And it ended before you were born.
So what the <kupo> is going on here!?!
Well, this is the core of my hypothesis. The world of Lightning Returns is in fact that same as our own. Bhunivelze created Earth from the dying wastes of Nova Chrysalia, complete with basic technology, history to enjoy, and the first set of human bodies for souls to inhabit. (I presume people picked up on the use of the term God with a capital "G" there? This is the monotheistic creation theory in a delicious twist.)
As with all fantasy stories placed in our world (I'm looking at you, Harry Potter), the laws of existence are based upon our current understanding and then some liberties are taken to explain the unexplainable. I now want to look at the Final Fantasy multiverse through this lens (and we can start talking about XIV more as we go further along).
E=mc^2 and crystals
Energy and matter are interchangeable. The atomic bomb proved that. What we mundanely lack is a way of easily containing and controlling the energy that is released, not to mention an easier way of breaking down matter into energy in the first place. The Final Fantasy multiverse seems to have found such a solution - crystals. And XIV may be the best example of this.
Those crystals you're using in crafting? They are crystallized forms of energy in differing formats. Science (magic?) has developed a way to break that back down to an energy state to heat your forge or blow-dry your wood. Nature has developed a way (elementals?) to also allow the formation of these by converting energy into a safe, crystalline state. With that talent also comes the ability to break yourself down and reform it in teleportation as you ride the energy (aether) flowing through the planet. Those aetherytes? Crystalised energy hot-spots.
It kinda also implies that Primals are themselves crystallized from energy/aether and further explains why tearing them apart returns energy to the planetary system. And also why it's a bad idea to summon/crystallize a really powerful being. Like Bahamut. Or Zodiark. Or maybe Hydaelyn...
The datalog at the end of Lightning Returns explicitly says that Bhunivelze's true form was a giant, inexhaustible crystal. That kinda sounds like Hydaelyn. And in that ending sequence, we saw it shatter, with the energy dispersing to the world around it, much like how a primal returns to the flow. ...I think I'm wearing that darksteel tinfoil hat again, don't you think?
Dark Matter and Dark Energy
Mundanely, scientists have identified that the universe shouldn't be able to hold itself together. We can only see about 5% of the total matter and energy that the universe has to have in order to account for how it behaves. The rest is about 25% dark matter and 70% dark energy - things that must exist and consistently permeate space in order for the gravitational effects we can witness in visible matter to be possible. We call them dark not because they are evil or anything, but because we are blind to it and can only measure it by virtue of its influence on visible matter.
In the Final Fantasy games, this matter and energy appears to be both identified and utilised. Particularly in the XIII games, it appears to be referred to as the "Chaos". From dark matter, the Fal'cie convert it into visible matter, such as food and fuels for energy. Human souls are also made of chaos, in this case Dark Energy, which Bhunivelze and his creations (other than Etro) cannot manipulate like they can Dark Matter.
In XIV you, that's right you, can utilise dark matter by applying it to repair damaged equipment. That's pretty awesome. But read the description closer...

Originally Posted by
Dark Matter
It has recently been discovered that this substance of unknown origin has the faculty to assimilate with other forms of matter, effectively restoring them to their original condition.
Why now, amidst the coming calamity of the Seventh Umbral Era? Given their affinity to all things dark and powerful, I can't help thinking that the Ascians are masters of dark matter and energy and this "discovery" was deliberate.
/darksteel tinfoil hat on
Does the Echo actually represent a capability of engaging with and manipulating dark energy?
/darksteel tinfoil hat off
Quantum Probability and alternate dimensions.
This is the meat of the hypothesis and Bravely Default explains it rather well (I gave you that spoiler warning, remember?), even if it doesn't need to fit with the hypothesis itself. In it, Airy has found a way to pierce through alternate dimensions so she can power up in each. Each dimension is just a little different, where something has played out a bit differently in each instance. For example, in one world Til survived the chasm instead of Tiz. In another, Holly has the foresight to case reraise. And so on and so forth. This is quantum theory at play.
Quantum theory asserts that there is an equal chance of different outcomes occurring, but impossible to discern which until it is measured. And until it is measured, both scenarios can exist simultaneously. The theory goes on to say that if one scenario was measured to occur in the apparent dimension, the alternate possibility occurred in a different dimension. And so there are an infinite number of dimensions each containing an alternate course of the universe's history. Some are not to dissimilar to our own, others may be seen as highly exotic, and in others the universe may have not even condensed into habitable space. The stranger and less hospitable worlds might be collectively referred to by Eorzeans as the Void and its denizens Voidsent, beings that seem "to be not of this world".
Of course, Quantum theory relies upon causality being linear. So if you were able to find a way to unravel causality by breaching spacetime, you could theoretically unlock those alternate dimensions. We see this most explicitly in XIII-2, where the paradoxes caused by Etro's messing with history have caused all manner of weird and wonderful creatures to slip into Gran Pulse.
If we play with this idea further, we can theoretically tie those times and places where the veil to the void has been substantially broken to events where the world's order has been royally messed up. In Eorzea, these are the Umbral Eras, the seventh of which saw Bahamut/Dalamud messing with aether/energy on a scale to royally mess things up.
Meanwhile, certain entities have devised ways to travel between dimensions. Chief among these are Gilgamesh, Omega, Shinryu and of course Shantotto who takes pleasure in pointing out that the theory is sufficiently complicated to break your brain.
A final thought for the darksteel tinfoil hat.
In XIII, Barthandelus tells us that the maker (Bhunivelze) departed his world, and that in order to summon him back would require the simultaneous sacrifice of millions of people such that their souls would tear open the gate and allow him back in that he might recreate the world anew (which he eventually does in Lightning Returns). In short, a massive amount of dark energy tearing open causality.
Similarly, in XIV, Lahabrea tells us quite openly that in order to call forth Zodiark, a chaotic confluence of untold proportions must needs be brought about.
It's a very striking comparison between Zodiark and Bhunivelze. And then there is the resemblance between Bhunivelze and Hydaelyn in their form of a great crystal. If A=B and B=C...