It was said in Voyager that Warp 10 is equal to infinite velocity and is thus perceived an impassable barrier. Yet in TOS the Enterprise once reached at least Warp 14, implying Warp Factor ∞ + 4. I suspect Spock would regard this interpretation as "highly illogical."
"Infinite" is a theoretical concept used to describe the breadth of a thing in which we've not yet calculated in totality. Thus, as far as we know, it's "infinite." This is comparable to a "bottomless pit" which hasn't had its depth measured and is thus theoretically infinite or Pi in that we've not calculated it to the final digit and so it theoretically repeats infinitely, but we aren't certain. Newtonian Mechanics would argue that infinite velocity is achievable, but we've already determined that the law fails when approaching the speed of light. One must at that juncture apply Relativistic Mechanics, which doesn't allow for infinite velocities. Consequently, current science doesn't allow for infinite velocities and we've also observed starships travel beyond Warp 10 in TOS, thus Warp 10 does not appear to equal infinite velocity.
This is to say nothing of the concept of infinite velocity in any case, which LT Paris described as occupying "every point in the universe simultaneously." As two objects can't occupy the same point in space-time simultaneously, this would appear an excellent means of perhaps not destroying the universe itself, but annihilating its contents. This capability may allow for an excellent doomsday weapon, in which the entire universe would be motivated to attack any empire aggressing against your own, as said aggressor presents an existential threat not only to yourself but to all occupants of the universe given the implication of doomsday retaliation should you be defeated. However, it doesn't appear to be a very practical means of travel.
If it wasn't for that point, it might be arguable that the conflict presented by TOS Warp 14 travel and VOY Warp 10 travel could be the result of an adjustment to the velocities associated with each warp factor. An analogy might be an adjustment from an "imperial" warp velocity measurement system to a "metric" system. For example, perhaps Warp 20 in the TOS era measurement system equals Warp 10 when utilizing the measurement system common to VOY. However, given the apparent illogic of occupying "all points in the universe simultaneously" as a means of travel, this appears unlikely.
I propose that instead, the Voyager crew are not physicists by trade nor warp theorists and in their desperation to reach Federation space intact and in their lifetimes, and as a result of ignorance of the science, produced this experiment out of pseudoscience, desperation and Federation optimism. Unsurprisingly, the experiment failed. Furthermore, they've probably heard of this "Warp 10 threshold" at some point in their lifetimes, and erroneously interpreted it to be physically impassable despite that this barrier had been breached in TOS, and erroneously arrived at "infinite velocity" either on their own or as a result to exposure to pseudoscientific misinterpretations or misrepresentations prior to the current voyage, or archived in Voyager's database.
Furthermore, they're unaware of the complete history of warp travel, to include the velocities rarely achieved in the TOS era. Meanwhile, TOS era ships were capable of greater maximum velocities than VOY era vessels for whatever reason. While this may seem strange, there are modern examples of similar events. For example, the Concorde passenger airliner was capable of reaching a velocity of 1354mph and the Tupolev Tu-144 was capable of achieving 1510mph. However, both aircraft designs have been retired from service due to issues with safety and expenditure, and today you're left to travel instead on the Airbus A380 which is capable of only 676mph, less than half the velocity of the Tupolev.
It could be that the Federation opted for slower ships in the VOY era due to safety, resource or fiscal limitations. After all, high-warp velocities like Warp 14 were extremely rare, and cost multipliers are expensive. Why spend double on a starship to rarely achieve Warp 14 when you tend to not require greater than Warp 9.975 in any case. Thus, the Warp 10 threshold may be a limitation of VOY era engine design, not a maximum velocity scientifically achievable. The Voyager crew then mistook the maximum capabilities of Voyager for maximum velocity possible according to present scientific models. Ignorance, desperation and optimism.
"Infinite" is a theoretical concept used to describe the breadth of a thing in which we've not yet calculated in totality. Thus, as far as we know, it's "infinite." This is comparable to a "bottomless pit" which hasn't had its depth measured and is thus theoretically infinite or Pi in that we've not calculated it to the final digit and so it theoretically repeats infinitely, but we aren't certain. Newtonian Mechanics would argue that infinite velocity is achievable, but we've already determined that the law fails when approaching the speed of light. One must at that juncture apply Relativistic Mechanics, which doesn't allow for infinite velocities. Consequently, current science doesn't allow for infinite velocities and we've also observed starships travel beyond Warp 10 in TOS, thus Warp 10 does not appear to equal infinite velocity.
This is to say nothing of the concept of infinite velocity in any case, which LT Paris described as occupying "every point in the universe simultaneously." As two objects can't occupy the same point in space-time simultaneously, this would appear an excellent means of perhaps not destroying the universe itself, but annihilating its contents. This capability may allow for an excellent doomsday weapon, in which the entire universe would be motivated to attack any empire aggressing against your own, as said aggressor presents an existential threat not only to yourself but to all occupants of the universe given the implication of doomsday retaliation should you be defeated. However, it doesn't appear to be a very practical means of travel.
If it wasn't for that point, it might be arguable that the conflict presented by TOS Warp 14 travel and VOY Warp 10 travel could be the result of an adjustment to the velocities associated with each warp factor. An analogy might be an adjustment from an "imperial" warp velocity measurement system to a "metric" system. For example, perhaps Warp 20 in the TOS era measurement system equals Warp 10 when utilizing the measurement system common to VOY. However, given the apparent illogic of occupying "all points in the universe simultaneously" as a means of travel, this appears unlikely.
I propose that instead, the Voyager crew are not physicists by trade nor warp theorists and in their desperation to reach Federation space intact and in their lifetimes, and as a result of ignorance of the science, produced this experiment out of pseudoscience, desperation and Federation optimism. Unsurprisingly, the experiment failed. Furthermore, they've probably heard of this "Warp 10 threshold" at some point in their lifetimes, and erroneously interpreted it to be physically impassable despite that this barrier had been breached in TOS, and erroneously arrived at "infinite velocity" either on their own or as a result to exposure to pseudoscientific misinterpretations or misrepresentations prior to the current voyage, or archived in Voyager's database.
Furthermore, they're unaware of the complete history of warp travel, to include the velocities rarely achieved in the TOS era. Meanwhile, TOS era ships were capable of greater maximum velocities than VOY era vessels for whatever reason. While this may seem strange, there are modern examples of similar events. For example, the Concorde passenger airliner was capable of reaching a velocity of 1354mph and the Tupolev Tu-144 was capable of achieving 1510mph. However, both aircraft designs have been retired from service due to issues with safety and expenditure, and today you're left to travel instead on the Airbus A380 which is capable of only 676mph, less than half the velocity of the Tupolev.
It could be that the Federation opted for slower ships in the VOY era due to safety, resource or fiscal limitations. After all, high-warp velocities like Warp 14 were extremely rare, and cost multipliers are expensive. Why spend double on a starship to rarely achieve Warp 14 when you tend to not require greater than Warp 9.975 in any case. Thus, the Warp 10 threshold may be a limitation of VOY era engine design, not a maximum velocity scientifically achievable. The Voyager crew then mistook the maximum capabilities of Voyager for maximum velocity possible according to present scientific models. Ignorance, desperation and optimism.
