I'm sure he wanted to punch that Vulcan in the face, sure...but if he had then Trek history would be a lot different, most likely. Fist contact? C'mon.
According to old Trek novels, dilithium is found on Earth - but was often mislabelled as simple quartz. Many museums became rich overnight by ransacking their exhibits once dilithium's fourth-dimensional properties were discovered. Here's a random instructional film: [YT]http://www.youtube.com/watch?v=hemM8rrx2Yw[/YT]
Or that dilithium, trilithium, paralithium or any of the other types of lithium crystal would be necessary ingredients for warp overall. But we know that Feds, Klingons and Romulans alike appreciate and mine the substance (even though large Romulan warships in the 24th century utilize a superior, supposedly dilithium-free power source), and that even minor cultures recognize its value, so apparently it does provide some sort of an advantage. But it's clear there are many ways to skin this particular cat, and Cochrane might well have used one that doesn't call for any materials more exotic than the titanium for the hull. Timo Saloniemi
I was always under the impression that dilithium was the most efficient fuel source for matter/anti-matter reactors. Some other type of reactor and fuel source may have been used for the Phoenix's short-range test flight. Star Trek: Fist Contact would have to be a Kirk movie.
Science isn't my strong point, but, I thought that in the fictional Trekverse, Dilithium crystals focused the matter/antimatter reaction. Duterium is the inert fuel mixed with the antimatter. I always assumed that since Cochrane's warp core is a tiny demonstrator, he must have found some other more conventional way to focus the reaction. Geordi was probably being kind by not mentioning the gross inefficiency (compared to what he's used to) of Cochrane's ship.
I've never seen an episode of Star Trek where they state you can only achieve Warp Drive with dilithium crystals. Of course, this appears to be the preferred option - but we've seen lots of others (the romulans use a quantum singularity) so cochrane could have been using anything. Then again, there is nothing in the dialogue that says they don't use them...
I just figured he somehow reconfigured the nuclear warhead to fuel the thing. Dilithium was just a power source in the 24th century. Like most cars today run on gas, but it's not the only thing in the universe that conceivably propel a car.
Why do people saw Dilithium is a fuel? All it seems to do is catalyzes the M-AM reactions. Canonically is there any dialogue or graphic saying Dilithium or antimatter was used?
There's also this bit from "Peak Performance": That seems to suggest that the function of the dilithium crystals is to somehow regulate the matter/antimatter reaction, rather than to provide the fuel for it.
Given Cochrane's desire to retire to a tropical island filled with naked women, I have no doubt the first warp ship was powered by testosterone.