Lego developer Traveller's Tales (TT Games) was founded in 1989 by Jon Burton who has now, speaking on Coding Secrets, talked at length about Ratchet & Clank: Rift Apart's SSD magic. Well, magic might not be the word he'd use, as he claims that it could've been done on the PS4 or even the PS3.
As spotted by VGC, Burton stated, "The way the Rift gameplay was represented before launch was pretty misleading. [What was shown as] amazing sequences of Ratchet zipping between many other worlds all chained together into awesome action sequences [ended up being] mostly just cutscenes or very short sections of very limited gameplay."
Burton isn't necessarily saying that the SSD isn't being used to make this possible. Rather, he's saying that the SSD isn't necessary to pull off the same set-pieces. For instance, he highlights Pocket Dimensions which, in-game, are those smaller interdimensional zones you can travel to for extra goodies like armour, raritanium, or bolts.
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Due to them being smaller stages, he claims that they could be done without the SSD. "Now, they could be using all kinds of Solid State Drive trickery to pull these off, but because it's just one Rift and it always goes to the same area, this can easily be achieved on older hardware.
"The Pocket Dimensions are really graphically basic, and in fact, just seem to use a lot of the same generic objects like crates that would already be available in generic memory. So, it's pretty much a sky dome, a few small platforms, generic objects, and nice lighting, so on older hardware, it wouldn't take much memory, especially since it also uses the generic objects, all of which make it quick to load."
He elaborates to talk about things like the grindrails or speeder bikes, saying that "none of this is optional, it's forced." According to Burton, it means that "you can pre-load the grind rail section while you are playing the speeder section." However, he clarifies that he's "explaining how other pretty simple techniques can be used to achieve the exact same thing on older hardware."
Rift Apart throws you between different worlds. It isn't a fake location in a much smaller box with trickery being used to make it feel like the real place you visited earlier - you are bouncing between these actual, tangible levels. That's the key difference that requires the SSD since you are, in essence, loading up a level within a level seamlessly. Imagine going between Super Mario Galaxy's Castle Gardens and Honeyhive level without so much as a blink of black screen. That's what is impossible in older games.