In the most recent episode we learned, via Discovery making the trip from Jupiter to Earth in roughly ten seconds with the warp core powered down and all it's Dilithium hidden on another ship, that Discovery's fusion engines can get the ship traveling somewhere around 262 times light speed. Which according to the official scale puts it somewhere around Warp 6 on the TOS scale, and somewhere around Warp 5 on the TNG scale. This means that with just Discovery's level of Warp technology, Discovery's level of Fusion technology, and Discovery's reactor size to internal volume, warp travel should have still been viable, if limited to slightly above/around Enterprise era speeds. But before people say that still might not be enough, look at the three qualifiers. Because 1) We know from DS9 that the Federation has improved it's fusion technology, 2) we know from VOY that the Federation has improved the warp geometry and field formation of its ships, 3) we know from Enterprise that they can make ships which are bigger on the inside, and 4) we know from discovery itself that's there's a lot of extra space they could install additional fusion reactors if they needed to. So why do they need Dilithium?
My guess is consistency of output. My only real analog is cooking with gas vs. cooking with propane. Propane burns well enough but is super inconsistent depending on temperature that I'm working with.
We don't know that it is consistent for warp jumps though. It might be consistent enough but dilithium is more so, and would be much more preferred.
They can't replicate dilithium by this time? Or bend time-travel bans to boldly plunder stockpiles? Hey! Maybe they tried that on Praxis and that's when it went kerblooey!
Preferred =/= Required. And we do know that it's consistent enough for low warp speeds, because they just showed it in the most recent episode. And their whole fake out relied on the idea that that was how they had traveled to earth from out of the system. So while Dilithium based antimatter might allow for higher per cubic foot of generator output, the simple fact is this episode proved it's not needed.
Until I have more information I am simply going to assume that dilithium offers something in terms of output for sustainability of warp fields. The warp fields always seems to be fragile and throw it off and things won't go right. So, dilithium is needed because it offers consistency and no risk of catastrophic failure. Hopefully explored more. But, that's sufficient for me.
Again, this episode directly shows and tells us that's wrong and fusion is consistent enough for long term warp trips.
Not being able to see this one until tomorrow, I still hazard the guess that the ship did not warp to Earth at all. That is, unless we were shown the warp streaks. Mere apparent travel time tells nothing, because it's subject to cuts. (Although we may further decide that the ship traveled from Jupiter to Earth in ten seconds at sublight. It just took a few hours for the ship to get from A to B - but Einstein made sure that those hours felt like ten seconds to the heroes.) Timo Saloniemi
There were no cuts in the scene, it was appear at Jupiter from a spore jump, head to Earth, arrive in the same scene 10seconds later.
Nope, that was Jupiter, hence the lack of rings. Anyways, Saturn would have been almost twice as far away, so...
I've kind of looked at dilithium--at least since TNG--as a combination energy converter/regulator. It takes the raw energy from a matter/antimatter reaction (micro-singularity, or whatever energy source) and changes it into a controllable electrical energy. It may not matter if you have warp drive, slipstream drive, spore drive, or ludicrous drive, but dilithium may still be the most efficient means of converting raw energy into something strong and stable enough to run a starship, even in the 32nd-Century.
Perhaps using fusion for warp drives are too slow for interstellar travel, especially if the warp corridors do not exist and the Cochrane factor is close to 1 everywhere?
Can we assume that somehow the space scenes showing Discovery traveling from Saturn to Earth were sped up a bit? Like a fast motion thing for audience convenience? I remember Saturn in the episode too. It's 71 light minutes from Saturn to Earth according to https://image.gsfc.nasa.gov/poetry/venus/q89.html#:~:text=Mercury 0.387 193.0 seconds or,or 159.6 minutes Neptune 30.058 . If Discovery were going at near light speed, relativity would be in effect and inside the ship it wouldn't feel like 71 minutes but much less, thus explaining why it feels so short to the Discovery crew. Outer space shots can be explained as the show fast forwarding the space travel for audience convenience.
What the exact purpose of dilithium is has never been established other than "regulating the rate of reaction" as put by the TNG Technical Manual, and we can only infer from the episodes themselves that is in fact a crucial component. Plotlines in specific stories, such as Kirk & Co's urgency to recrystallize their dilithium in The Voyage Home indicate that it probably does something more than merely making it easier to use the warp drive. Whatever dilithium is, it certainly isn't something superficial like a tempomat in your car that you could easily do without. Also, was it ever established that fusion power can generate enough power for FTL speeds? They only ever used fusion reactors for the impulse drives and for space stations. You are mentioning the TARDIS tech from Future Tense, but why should it be taken into account? Why should the writers of Discovery be aware of random pieces of technology that have only ever appeared in one single episode, never to be mentioned again? TNG never reused the soliton wave drive or the Cytherian tech Barclay used to transport the Enterprise to the center of the galaxy, Voyager never reused TNG's metaphasic shielding, the Sikarian spatial projector, the Vaadwaur tunnel network, Tash's graviton catapult, or even whatever the Caretaker used to abduct them, and so on. I am once again asking the question that never seems to be answered: why should Discovery be held to a different standard than the previous Star Trek series? Why should Discovery be expected to revisit and take into account things that TNG, Voyager and Enterprise never did, nor were expected to? Not to mention, I'm being petty, but it was Saturn, and it did have rings, albeit quite dark because they faced away from the Sun, like they often do. Even without the rings, the overall yellow coloration going into bluish at the poles together with the cloud bands being straight as opposed to wavy-swirly should be a dead giveaway for it being, well, Saturn. As for the travel times themselves, when have they ever been consistent on Star Trek? Bajor was anywhere from a few minutes to five hours of impulse travel from DS9, depending on the plot. The only time I ever remember a travel time being consistent with the calculations was in Discovery, when Burnham's shuttle traveled 27 million kilometers to the Emperor's flagship at Warp 1, which should've taken about 90 seconds, and the travel actually shown on screen was indeed just a little over one-and-a-half minute. Other than that, starships always seemed to travel at the speed of the plot, especially at substellar distances. We're talking about a franchise where vessels being described as hundreds of thousands of kilometers away are shown within spitting distance from each other on screen. Sci-fi writers don't have a sense of scale, and they never had, not just in Discovery, not just in Star Trek in general, but in all of science fiction. So, again, why should Discovery be held to a different standard?
Except it's not too slow. If it was Jupiter, they were traveling about 300+ times the speed of light, if it was Saturn somewhere around 600 times the speed of light. That puts them at somewhere between Warp 5 and Warp 7. Which is greater then Enterprise era speeds.
It's a mistake. With it's warp core powered down Discovery should have had only impulse. Someone in production forgot or overlooked or simply didn't care what a "realistic" amount of time would be to get from Jupiter to Earth on impulse only and therefore the ship traveled at speed of plot and pacing. And travel at the speed of plot or https://tvtropes.org/pmwiki/pmwiki.php/Main/ScifiWritersHaveNoSenseOfScale are time honored Star Trek traditions. It's a goof. Ignore. Other than that: 1) Since this is likely a mistake how much the Federation improved it's fusion technology should be dismissible, because Discovery's speed is too high for the situation described and we would be comparing DS9 with literal nonsense numbers. 2) See number one. 3) That's one of those things that I would be very happy to see ignored and left to the likes of Dr Who, but if we have to handwave it, that technology was somehow one of the associated technologies to time travel and was lost with time travel technology. 4) The fusion reactor don't power the ship's warp directly. It just the first step. Federation ships, and the ships of most other species, need a warp core to reach faster than light travel. We know that the energy needed for sustained warp comes from controlled matter-antimatter reactions within the core by smashing deuterium and anti-deuterium together. And we know that dilithium is the stuff that can interact with and regulate the anti-matter used in warp cores and turn the resulting energy of the matter-antimatter annihilation into electro-plasma. It's essentially harnessed energy and can be transferred by plasma conduits (and eps conduits to other ship systems) and is what ultimately makes the ships go wroom wroom. The fusion reactors for impulse are also creating plasma and can propel the ship, but even in the TNG era max impulse was "only" a quarter of the speed of light, so I'm not sure if simply propping up some more normal fusion generators will do the trick here, since I'm assuming that the plasma it generates is not nearly as highly charged as a warp core output. That's what they need dilithium for. You can get to at least warp 1 with normal nuclear fusion. Whatever Zephram Cochrane used to create warp plasma (from what BTS stuff I remember some repurposed warhead) got him there. But that was a one minute flight, and we have no information if the ship would have been capable to sustain that for any lengthy amount of time. What we do know is that Federation ships need warp cores, or a lot of plotlines from the older shows would have stopped after three minutes with, "Oh, warp core's damaged? Just hook up the impulse reactors and then onwards at warp 3".
I did a little math from https://www.phy.olemiss.edu/HEP/QuarkNet/time.html , and assuming Discovery was going at 99% the speed of light without warp, it would feel like 10 minutes for the Discovery crew on the ship due to time dilation even though it's really taking about 71 minutes to get from Saturn to Earth (Saturn is 71 light minutes away from Earth: https://image.gsfc.nasa.gov/poetry/venus/q89.html#:~:text=Mercury 0.387 193.0 seconds or,or 159.6 minutes Neptune 30.058 ). So actually it works out just right for the characters on the screen that from their perspective it only takes about 10 minutes. If you read my calculations above, it's actually not a mistake and follows time dilation from the theory of relativity rather correctly. I'm a Physics major that worked with 2 Nobel laureates of Physics in my undergrad years. Yeah that was long ago and I'm a bit rusty, but I think my calculations are still sound. Anyone's free to correct me.