'Living Witness' episode occurred in Voyager's 4th season (towards the end of it).
Meaning the year was probably towards the end of 2374.
700 years later would mean, the events of Living Witness happened in 3074.
The Burn happened between 100 to 120 years before 3188... so it would have happened between 3168 and 3188.
From Living Witness we have this:
TABRIS: It was a pivotal moment in our history. As a result of the Doctor's testimony, a dialogue was opened between our peoples. Eventually, we found a new respect for our divergent cultures and traditions. The efforts of people like Quarren and the Doctor paved the way for unity. Quarren died six years later, but he lived long enough to witness the Dawn of Harmony.
KYRIAN SPECTATOR: And the Doctor?
TABRIS: Well, he served as our surgical chancellor for many years until he decided to leave. He took a small craft and set a course for the Alpha Quadrant, attempting to trace the path of Voyager. He said he had a longing for home. This way.
So, Quarren died around 3080... and after that the Doctor served as surgical chancellor for 'many years' before he decided to leave.
We don't know how long the Doctor remained a surgical chancellor... or how fast that small ship he took from the Kierans/Vaskans was (though I suppose its possible it would be at least as fast as Warp 9.9 or 9.91 - allowing him to traverse 60 000 lightyears in about 2.5 or 1.25 years).
'Many years' doesn't exactly strike me as just 8 years for example (even if the Burn happened only 100 years prior to 3188 - and if anything, its closer to between 100-120 years) - but it also depends on Kieran's/Vaskans interpretation of 'many year' and how they conceptualize tiime.
The timelines don't quite match if you want to take into account the Burn (which would have to have happened before the Doctor's backup left to trace Voyager's path).
Since nothing was mentioned of the Burn in the closing dialogue by Tabris, this could be explained with the premise that only the Dilithium in the entire Federation exploded (not the entire Milky Way as it was insinuated because Trek has a very annoying/inaccurate penchant for saying 'the Galaxy' when it meant 'the Federation').
So, if only the Dilithium in the Federation detonated/exploded, that would make more sense (plus we know the writers don't exactly have a good idea of calculating stuff).
Anyway... if the Doctor's backup left lets say in 3100 towards the Alpha Quadrant... we don't know how long it would have taken him to reach the Federation... and its also possible he already reached it long before then, but didn't know that because he had no idea of the geo-political situation or how/where the Federation expanded into the galaxy.
At any point, I don't think the Doctor would have necessarily encountered Starfleet ships because majority blew up during the Burn... and he may not have encountered other Federation worlds in the Delta quadrant because the Federation shrunk from 350 member worlds to just 38 just after the Burn.
If of those 350 member worlds were say Klingons and the Founders... its possible their entire territories would have automatically been absorbed into the Federation and there's maybe a few minor species that could have joined easily (since the late 24th century) to encompass such a large portion of the Galaxy - but those species are nowhere near the D.Q.
The Delta Quadrant could have been left largely on its own... but we don't know which species from the D.Q joined the Federation (if any of them did).
Meaning the year was probably towards the end of 2374.
700 years later would mean, the events of Living Witness happened in 3074.
The Burn happened between 100 to 120 years before 3188... so it would have happened between 3168 and 3188.
From Living Witness we have this:
TABRIS: It was a pivotal moment in our history. As a result of the Doctor's testimony, a dialogue was opened between our peoples. Eventually, we found a new respect for our divergent cultures and traditions. The efforts of people like Quarren and the Doctor paved the way for unity. Quarren died six years later, but he lived long enough to witness the Dawn of Harmony.
KYRIAN SPECTATOR: And the Doctor?
TABRIS: Well, he served as our surgical chancellor for many years until he decided to leave. He took a small craft and set a course for the Alpha Quadrant, attempting to trace the path of Voyager. He said he had a longing for home. This way.
So, Quarren died around 3080... and after that the Doctor served as surgical chancellor for 'many years' before he decided to leave.
We don't know how long the Doctor remained a surgical chancellor... or how fast that small ship he took from the Kierans/Vaskans was (though I suppose its possible it would be at least as fast as Warp 9.9 or 9.91 - allowing him to traverse 60 000 lightyears in about 2.5 or 1.25 years).
'Many years' doesn't exactly strike me as just 8 years for example (even if the Burn happened only 100 years prior to 3188 - and if anything, its closer to between 100-120 years) - but it also depends on Kieran's/Vaskans interpretation of 'many year' and how they conceptualize tiime.
The timelines don't quite match if you want to take into account the Burn (which would have to have happened before the Doctor's backup left to trace Voyager's path).
Since nothing was mentioned of the Burn in the closing dialogue by Tabris, this could be explained with the premise that only the Dilithium in the entire Federation exploded (not the entire Milky Way as it was insinuated because Trek has a very annoying/inaccurate penchant for saying 'the Galaxy' when it meant 'the Federation').
So, if only the Dilithium in the Federation detonated/exploded, that would make more sense (plus we know the writers don't exactly have a good idea of calculating stuff).
Anyway... if the Doctor's backup left lets say in 3100 towards the Alpha Quadrant... we don't know how long it would have taken him to reach the Federation... and its also possible he already reached it long before then, but didn't know that because he had no idea of the geo-political situation or how/where the Federation expanded into the galaxy.
At any point, I don't think the Doctor would have necessarily encountered Starfleet ships because majority blew up during the Burn... and he may not have encountered other Federation worlds in the Delta quadrant because the Federation shrunk from 350 member worlds to just 38 just after the Burn.
If of those 350 member worlds were say Klingons and the Founders... its possible their entire territories would have automatically been absorbed into the Federation and there's maybe a few minor species that could have joined easily (since the late 24th century) to encompass such a large portion of the Galaxy - but those species are nowhere near the D.Q.
The Delta Quadrant could have been left largely on its own... but we don't know which species from the D.Q joined the Federation (if any of them did).
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