Originally published at: Here Is There | The Eldraeverse
This is another post which has fallen through a wormhole from the future, since the device in question won’t be invented until well into the 9th millennium. But since they’re going to appear before too long in Timeo Eldraos et Dona Ferentes, it is probably best that they be mentioned here first. What is important to understand where the Claves-Catala translocator is – or to give it its more common name, translocation rings are – concerned is that they do not utilize any of the classically theorized methods of teleportation. (The Indeterminacy Barrier and its corollary, the uncloneability lemma, prevent…
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Hm. Now why does the above remind me so much of the discussion between Twilight and Moon Gleam at the beginning of Friendship is Sufficiently Advanced Chapter 9 ? 
To wit:
The discussion could be heard approaching long before those having it were in sight.
“…you really can’t do that? I thought you used a similar technique to get here?”
“Yes, but I needed two stargates each the size of a small moon to do it. And they use wormholes, and you can’t have been using wormholes because the drift equations get rapidly chaotic in bent space-time. Even a short distance jump on the planet’s surface would have turned us both to quark fog. Give me the short explanation of yours?”
“Okay! So, the matter doesn’t move at all. You define your departure and arrival volumes as fivespheres in sixspace encompassing the pieces of threespace you want to move, and then you can exchange them along the free axis at minimal energy cost, swapping the threespace volumes. The matter comes along with it. But there’s more to it -”
What happens if the spacetime curvatures at the translocated volumes don’t match up? Translocating from near an event horizon to interstellar space is an extreme example but it would still apply to a lesser degree when translocating between planets since even seemingly flat spacetime is slightly warped, wouldn’t that distort the geometry of the hyperspheres enough that they aren’t identical?
As an amateur earthling physicist, I’ve got two theories. If the underlying space is also swapped in the transfer, I’d say the difference in hypersphere geometry is probably dissipated as gravity waves or something. If the underlying space weren’t, I’m not quire sure what would happen, if anything. The objects would be hyperspatially distorted relative to the local environment, but I’m not sure that’s qualitatively different from moving around continuously in an existing gravity field, just more abrupt.
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Well, y’know, no sense in using two pieces of phlebotinium where one will do the job. 
[In that particular shardverse, it is probably safe to assume that you can trace key elements in the design of the translocation rings and probably also the frameslip (“friendship”) drive to Twilight.]
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@JHPrime’s first theory is pretty much correct. To quote myself
Energy and momentum are conserved, but for the purposes of calculating the necessary compensation and buffering that must be provided by the ring-sets, the hyper⁶spheres may be treated as ontomathematical points.
…and this is another case where you can treat them as ontomathematical points, such that the curvature of space-time within the hyper⁶sphere isn’t really relevant for the (effectively instantaneous) transfer; if it is notably different between one and the other, you get discontinuities at the border of the hypervolume which collapse immediately in a gravity wave splash. This effect isn’t usually enough to do more than make travelers queasy in those cases where it’s particularly high.
(On the other hand, if you tried using a ring-set which was near a (small) black hole’s event horizon, or the surface of a neutron star, or the edge of a wormhole throat, or other places where gravitic and tidal forces are particularly strong, and overrode all the safety systems, the results would be a lot more messy.
On the gripping hand, those are generally pretty unhealthy places to be, period, so it’s not like it would make you any deader in the slightly longer run.)
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