From Canon SourcesEdit
The time barrier was a theoretical barrier in the development of mid-23rd century warp drive. This obstacle was overcome sometime between 2236 and 2254 (between the time of the crash-landing of the SS Columbia on Talos IV and the arrival of the USS Enterprise, allowing Federation star ships to travel significantly faster than ever before. Episode - (TOS: "The Cage")
Star Trek: Origins Time LineEdit
For many years the Starfleet, like many other races of the Alpha & Beta quadrant, try to reach warp 8. But was limited at warp 7.3, by some kind of speed "barrier". One of the most popular hypothesis about this "barrier" and it gave name to the problem, was that thought there a desync of time in the subspace field around the bubble that surrounds the ship at high speeds above warp 7 . The problem was called the temporal barrier or "Time barrier".
This problem was discovered around 2200 when new ships try to reach warp 8 and only get a max speed of warp 7.3 which subspace field stability problems at these speed. Over the next 35 years, the UFP was unable to reach more of warp 7.3.
To get a more speed of warp 7.3 and reach warp 8, the UFP was designed a new warp core and a new warp coils from scratch. The Klingons build a Warp 8 core, before of the UFP, based over reverse engineering of captured Hydran ships, but there were flaws in the design of the coils, which kept it from truly breaking the barrier. So the Warp 7.3 barrier was still unbeaten, except for some older warp races, like the Hydrans. The new warp core of the UFP, generated a bit more output energy that the Klingon Warp 8 core. Plus, the Federation are in the final stages of testing it at 2235 in two ships of Arizona class. At the same time, the Federation are testing a new design of warp coils in the first ships of the Legend class.
The Legends class, was designed, originally, to be mainly a deep space explorer and break the "Time barrier" with it's new warp coil designs and the new warp reactor.
Why this barrierEdit
Mainly this barrier, is a false barrier. It come from mainly of bad knowing of warp fields equations. The equations of Cochrane, are only a 75% of the real equation. The unaware parts of the equations, are really showed when the ships reach high warp and can see that was a mistaken in the theoretical speed and the real speed. In the first years of the 23rd century, not was knew yet it, so when they try to get warp 8, in truth, they not was trying to generate a 8th field in the warp field yet. The truth was that they need a lot more of energy to archived it ! In the late mid-23rd century was really begin to discover this bad knowing of the warp fields equations. One of engineers that show this problem and give a first approach of how are the unaware part of the equations, was Montgomery Scott, the Chief Engineer of USS Enterprise. He based over some data obtained of max speed tests of the refitted ship at 2270 and later. He used it to show that Trans Warp tech of the Excelsior must fail. Which his notes, and more deep warp field studies, was developed the new warp scale around the last years of the 23rd century, that give a more right view of the real speed and energy used, plus show that cannot reach warp 10, because the 10th warp field layer, always collapses in to 9th warp field in the simulations. This is the main reason of the warp 10 asymptotically speed increase.
So... When is breakEdit
When STO launch some chapters, will be show it. We only can conjecture that should be in 2236 or 2237.