From the last episode, we know the advanced tech is at least 15 years more advanced than anything the Federation as we know it has.
I know it isn't canon, but quite a while ago I read on a fanboy site about how the Federation tried to adapt the technology for use on their Starships. It was actually really interesting to read, although because of events in the various films, many parts of it are unlikely to come true.
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The attempts to copy the technology were an almost total failure, as they were unable to get the replicator tech to function efficiently enough for the armour to repair itself at a viabe speed. The damaged sections of the armour drained power from the ships' systems faster than they were able to produce it, and eventually the weapons systems had to be shutdown to prevent a total systems shutdown.
Due to these deficiencies, the Federation decided that they would seal away the technology, the results of the research, and all ships that had been refitted with their many attempts at copying the technology for a period of no less than 15 years.
This would mean that there would be few repurcussions to the timeline, and would give the Federation enough time to achieve a tech level where the use of the armour could become viable.
The Transphasic Torpedo technology was to be permanently sealed away, except for use in extreme need/dnager for the Federation. It was felt such weapons would provoke the other races into developing even more powerful weaponry, leading to an arms race similar to that of the Cold War of the 20th Century.
However, the Transphasic Torpedo technology did come into common use during a second Dominion invasion during the 27th century.
The Dominion had been planning a second attempt at conquering the Alpha Quadrant ever since their devastating defeat at the hands of the Alliance of Alpha Quadrant powers.
They had recovered from the effects of the disease that had been planted by the Federation in the 24th Century. They had used their Genetic engineering skills on themselves, and were now stronger than ever...and had learned from their mistakes.
Instead of making Alliances with small powers, they had began to conquer everything in their path. They retreated from near the exit of the Bajoran Wormhole, and set up a line of bases along their new borders.
The new Outposts were fitted with an Advanced Communications technology that allowed them to infiltrate the Communications network of the Federation so they could misinform Starfleet Command of movements of ships once they had gone through the Wormhole. This allowed them to capture ships without the Federation's knowledge, and the Dominion gained a good insight into Federation Technological advancements - a trick they had learned during their non-aggresion treaty with the Romulans.
Vast new Jem'Hadar Hatcheries were developed so they could produce Troops faster than ever before. The Jem'Hadar were developed further to make them physically even stronger and more resistant to weapons fire.
Their healing ability and life expectancy was also increased - the Dominion realised that if their Troops were to be more effective, they would need to be able to live longer so they could have longer to train. Instead of considering each Jem'Hadar as expendable, they saw them as an investment, and created anti-Alpha-Quadrant training programs so their Troops were better able to strike at their enemies with minimal losses.
The Dominion had a new tactic to use against the Federation - they simply sent young changelings onto Federation ships before they passed through the Wormhole. These changelings killed and replaced the leaders of the Planets and systems they found their way to.
The planted changelings spread fear and confusion amongst the member worlds of the Federation, and several minor worlds left the Federation within a week of the first 'replacements.'
Then, in September 2643, the weakened Federation had it's first official encounter with the new Dominion threat. The Dominion had been massing a Fleet behind their new borders for almost two decades, whilst they developed a new Temporal distortion generator.
Using the generator, they were able to negate the power of the Wormhole aliens. Whenever the aliens tried to remove their Fleet from the timeline, more took their place. The Dominion were able to pass through without fear of losing their Fleet again.
Bajor was obviously the first Federation world they managed to capture. The Federation defense network was largely unprepared for the invasion, believing they would never again come under attack from the Dominion. They had been lured into a false sense of security by the 'reports' that the Dominion had fabricated.
The Dominion did not head straight for Earth. instead, they attacked all the systems which would be most likely to take over the lead of the Federation, should Earth fall.
The Dominion were planning that when they finally attacked Earth, there would be no way for the Federation to regroup itself. The Dominion would be able to then focus on Qo'Nos, Romulus, and especially Cardassia, who they blamed for the loss of the war. Their treachery had not been forgotten by the Dominion, which had sworn revenge.
An unusual turn of events stopped the Dominion from fullign reaching the fruition of their plans, however.
Their intention of conquering the Alpha Quadrant had been so great, that at first an attack on one of their colonies near the Delta Quadrant went largely un-noticed.
It was only when shipments from a Ketracel refinery ceased that a taskforce was sent to find out what the hell was going on with their colonies.
But the taskforce was never heard from again.
Finally, reports started to come in of a massive object heading through Dominion space at incredible velocities. Not only was it destroying all resistance in its path, it was on a direct course for the Dominion homeworld.
The vessel was ignoring all attempts to make contact. It was also able to repair itself at a phenomenal rate - the Dominion had had it's first encounter with the Borg.
Since the Dominion had never encountered the Borg before, they had no idea how to deal with the threat. Their weapons were seemingly useless, and their tactics soon became obsolete, thanks to the adaptability of the Collective.
The Dominion had no choice but to recall it's nearby Fleets for the defense of it's Homeworld. The massive Pyramid-shaped ship was larger than anything the Dominion had even thought of attempting to build, was capable of wiping out whole Fleets, and was practically invincible.
It was only because of the Borg that the Dominion eventually had to pull out of Federation space.
The weakened Federation increased the defense of the Bajor system, and re-established a minefield around the Wormhole. Contact through the Wormhole was severed, and federation life went largely back to normal.
The same could not be said for the Dominion...
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That's about all I can remember from what i read on the site. I wish I could remember where I read all that to, coz I could have gone into...*ahem* more detail...*ahem*
