I wouldn’t be the first to describe the difference between hard and soft science fiction. In fact, Tor provides a quite reasonable guide.
From the advent of sci-fi there have been at least two camps. In general, Jules Verne suggested the grand adventures technology might make possible while H. G. Wells and Mary Shelley offered cautions about the potential consequences.
Roughly a century later, the voyages of the USS Enterprise might have begun nearer to Verne. The final frontier gradually became less about exploration of a boundless sea and more an unending series of tensions played out upon it. If not Wells’ territory, certainly near the neutral zone.
How much attention is paid prevailing scientific theories depends on balancing the needs of the story. The world-building for Astral has been to provide an understanding of the hardship the characters have faced before the story begins. The action takes place on a world quite distant from Earth so part of this process has been devising reasonable rules and repercussions for faster-than-light (FTL) travel.
In soft sci-fi FTL simply works at the often literal press of a button. How long the trip may take, what fuel is used, and some understanding of what laws of physics are being broken and how never enter the picture. As the genre approaches the other extreme, nothing superluminal (neither travel nor communications) happens; light not only has a speed limit but it’s one that’s part of the definition of the universe. In between there are warps, jumps, and hyperspace – and that’s where Astral sits presently – on a scale from 1 to 10, somewhere near 5.
NASA is exploring the possibilities of EM Drive and, while decidedly thrilling, the realities of that are now firmly in the realm of scientific speculation rather than speculative fiction. On the other side of the coin, hyperspace will be forever associated with the Star Wars franchise – at least in the mind of this author.
Making something sound like science can give rise to La Forge syndrome:
“The phase inducers are connected to the emitter array. The override is completely gone and the pattern buffer’s been locked into a continuous diagnostic cycle.”
I’m not a mathematician and I don’t want to run the risk of actually getting some critical math completely wrong. Similarly, I’m not ready to plant a flag and reclaim luminiferous aether in the name of voyages extraordinaire. Some time was spent in study of certain theories of Henri Poincaré and Hendrik Lorentz. While this did not result in a formula it pointed (perhaps tangentially) to answers I can use.
The characters would not be making hops of several light-years in less than the blink of an eye. The farther the actual distance traveled it would still take longer. In Astral a trip from Earth to δ Pavonis would take between two weeks and nine months depending on the equivalent of a warp factor or calculations from a navicomputer. These durations compare to a single Atlantic crossing by steamship at the dawn of the Victorian era or three such journeys under sail combined during the mid-1700s, respectively. A hop of even one light-year would depend on finding a shorter distance than Euclidean geometry would permit.
Ultimately there’s no actual need within the story to know the precise settings of any phase inducers. In the original Star Trek series, the set designers put the label “GNDN” in several places. When asked what this stood for they replied, “Goes nowhere, does nothing.” This in-joke can also serve as a warning to a writer. When it can’t serve the story it can’t be included.
People don’t usually talk about travel unless something goes wrong. Otherwise, a long car trip is reduced in the telling to roads taken and noteworthy sights along the way. With all of this in mind the only reality of FTL travel that matters is what impact they may have on the characters who undertake a crossing.
Non-Euclidean geometry, in strictly mathematical terms, does not equate to things Lovecraft. But while traveling along any weird topology suggested by an extradimensional, self-intersecting manifold what might be seen if looking out a portal? What do the characters think it means? Does it shape their point of view without twisting it to madness?
The navigation of Astral may be in Verne’s spirit but the story winds up at the intersection of Wells and Shelley.