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Has any episode, game or novel provided an in-universe answer?

This answer seems give an approximate size, but as the question states:

how much of Space is included in the Federation-explored region of the Star Trek Universe?

I'm referring the the universe as whole with and without the Federation.

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As already pointed out in the comments:

There is an unstated assumption here that the Star Trek universe is different somehow than our universe

which AFAIK does not hold: there is no indication that the Star Trek universe at large is different from our own one.

Given that Gene Roddenberry in the introduction to his TNG writer/director's guide (aka The Bible) talks about "our galaxy" in realistic numbers, and that surrounding galaxies like Andromeda and Triangulum are common to both universes (Star Trek and our own), there is no reason to believe that the rest of the series universe is different. For what it may worth, Star Trek takes place neither in Middle Earth nor in The Matrix.

Arguably, the reason is that any such difference would be actually irrelevant for the series fictional world: for all its grandiose, Star Trek actually takes place in a relatively tiny vicinity around Earth, which does not even include the whole of our own Milky Way galaxy.

In TOS episode By Any Other Name, it is made explicit that even a trip to the nearby Andromeda galaxy is actually way off consideration, since it would take thousands of years for a Constellation-class starship of the era to make the trip, even if subsequent advances in technology would lower that time to only some hundreds of years at maximum warp.

Given this setting, it is only natural that any actual consideration of the whole universe's size or shape is actually absent from the show; even if we may be able to unearth some obscure slip-of-the-tongue relevant statement from some cosmic being like Q, admittedly one should not rush to take it at face value, in-universe or otherwise...

desertnaut
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  • @Randal'Thor thanks, but it would seem that the linked thread is actually about the history, and not the universe (or Universe?) in the literal meaning of the word, as asked here – desertnaut Nov 28 '19 at 17:38
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    Right, but if the history of the universe is the same as ours up to a specified point in time, that strengthens the evidence for the assumption that the physics matches up with ours. – Rand al'Thor Nov 28 '19 at 17:43
  • @Randal'Thor oopss... fair point indeed! :) – desertnaut Nov 28 '19 at 17:44
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    I think Where No One Has Gone Before firmly establishes that the Star Trek universe is significantly different from ours, both astronomically and in terms of physics. (That's if you weren't already convinced by the nebulae.) – Harry Johnston Nov 28 '19 at 20:32
  • @HarryJohnston sorry, can't see it; you are very welcome to elaborate. – desertnaut Nov 28 '19 at 21:40
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    Star Trek has a lot of speculation about physics, and that's what the question is about. It's very possible that Star Trek canon contradicts what current scientists say about the size and shape of the universe. – Jetpack Nov 29 '19 at 03:21
  • @Jetpack today's scientists contradict what was said some decades ago (no problem with that of course, this is how science progresses); my point here is that the show's creators didn't need to enter such speculations, since it would offer nothing to the show's plot and drama. And 'very possible' maybe it is, but still waiting for relevant evidence - shouldn't be that hard for one of the most heavily analyzed & annotated shows in TV history. – desertnaut Nov 29 '19 at 10:47
  • See Where No One Has Gone Before at 20:30, they're in some sort of strange-looking "other space" even though the Enterprise is said to be only a billion light-years from Earth. In the real world that would only be about 2% of the way to the edge of the observable universe, and everything would look and be perfectly normal. Later in the episode it is established that not only does space look different, but the very laws of physics are changed. This just isn't compatible with the idea that ST is set in a universe that is similar to ours on the large scale. – Harry Johnston Nov 30 '19 at 19:32
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With relation to size we learn, in VOY: Threshold, that the universe is infinitely large since it requires infinite velocity to occupy every point in the universe.

KIM: Nothing in the universe can go warp ten. It's a theoretical impossibility. In principle, if you were ever to reach warp ten, you'd be travelling at infinite velocity.

....

JANEWAY: It would appear that the theory of infinite velocity is correct. It may be possible to occupy every point in the universe simultaneously.

As to the shape of the universe, it would appear that the physical universe (consisting of all matter) is expanding into a infinite void and is roughly spherical.

We see it from the outside (at the ripe old age of about 2 seconds) in VOY: Death Wish.

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Valorum
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    I don't see how the quote implies that the universe is infinite in extent; even a finite universe could require infinite velocity to be everywhere simultaneously. Beyond that, the quote doesn't even imply that that infinite velocity is even required; it could be a sufficient but not necessary condition. – Daniel R. Collins Nov 29 '19 at 02:50
  • No. Just no. Not even the writers of "Threshold" consider it canon. – Jasper Nov 29 '19 at 13:55
  • @Jasper - You are mistaken. They consider it terrible, but not non-canon. – Valorum Nov 29 '19 at 17:20
  • @DanielR.Collins - The universe must be infinite in extent in order for infinite velocity to be a requirement. Otherwise a lower speed could be used. QED – Valorum Nov 29 '19 at 17:22
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    @Valorum. That's not true. E.g.: Say the universe has 100 particles and your speed is 1000 particles/sec (or whatever units make sense); then you're "at" each particle at best every 0.1 sec, not simultaneously. Change those to whatever finite numbers you like and you still get a finite delta between particles. Only infinite velocity serves to bring the time delta ratio to zero. (Or alternatively a universe with zero particles.) – Daniel R. Collins Nov 29 '19 at 22:22
  • @DanielR.Collins - But Janeway says that only with infinite velocity can all points in the universe be occupied at the same time. That implies an infinite universe. – Valorum Nov 29 '19 at 22:45
  • It really doesn't. As Daniel explained, even if the universe is very small, you still can't occupy all points at the same time without infinite speed. Arguably, it's the other way around: infinite speed should only allow you to occupy all points at the same time if the universe is finite, since otherwise, you would only occupy all the points on a particular line. – Harry Johnston Nov 30 '19 at 19:16
  • (Uh, technically that would be a half-line; starting at your point of origin and stretching out to infinity.) – Harry Johnston Nov 30 '19 at 20:24
  • "As to the shape of the universe, it would appear that the physical universe ... is expanding into a infinite void and is roughly spherical." A closed (spherical) universe (probably) can't be infinite. An infinite universe is either topologically flat or open (saddle-shaped). See shape of the universe – BMF Dec 01 '19 at 18:33
  • @BMFForMonica - Since Voyager is outside the universe looking at it explode, it tells us that the physical universe exists within a larger expanse. Either that or Q(uinn) has played some serious jiiggery-pokery with existence as we know it. – Valorum Dec 01 '19 at 18:35
  • @Valorum Looks like we have ourselves a semantic dilemma, haha. I think the OP means topology of the universe, but you're describing the actual "shape" of it, expanding into what looks to be an empty universe that could be of any topology! – BMF Dec 01 '19 at 18:42
  • @Valorum Perhaps I was mistaken. Nevertheless, trying to extrapolate things from the science in this episode will lead to inconsistencies with other episodes all over the place, so using it to extrapolate something as simple as the size of the universe doesn't seem like a warranted course of action – Jasper Dec 12 '19 at 12:06