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The Discovery is outfitted with an experimental “spore drive,” enabling it to travel much faster than other Federation (or Klingon, Romulan etc.) ships. We see its speed in Season 1, Episode 4, in which Discovery is able to rescue a primary dilithium source from an attack by the Klingon Great Houses faster than even nearby ships.

In Lorca’s sales pitch in the previous episode, he makes it sound like the spore drive can transport someone in the blink of an eye, but that might just be hyperbole. Is the spore drive instantaneous, or simply much faster than current Federation warp drives?

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    Lorca did not only boast, he was also very specific about the speed: going back and forth between "here" and the Beta Quadrant in 1,3 seconds. Which means that it is not instantaneous, but very fast. – Philipp Flenker Oct 9 '17 at 6:29
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    Honestly, I'm not sure this question is answerable until we get a few more episodes under our belt for the story to explore the mechanisms and consequences of using the drive. As of right now, evidence seems to suggest that for all intents and purposes, it is. – Michael Scott Shappe Oct 9 '17 at 22:45
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    It's also possible that the drive has a constant time of 1.3 seconds, regardless of distance, perhaps including a charging time. In that case I won't argue with a boast that it's instantaneous compared to warp. – Sman789 Oct 10 '17 at 8:22
  • Aehem they talked about maximum JUMP distance and onnly 1 time. So I would dare say that the spore drive is a jump drive in that sense that up to the maximum distance you can jump with only that time difference. But more episodes will ikely show it. – Thomas Oct 14 '17 at 8:47
  • It seems like the distance traveled is instantaneous but there is a .7 visual effect coming into and out of it. Which makes it technically not 'instantaneous', if that means anything. – Mark Rogers Jan 22 '18 at 1:24
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Yes, the Spore Drive is supposed to be instantaneous

The scientific inspiration of the Spore Drive comes from Quantum Entanglement, where two entangled particles share characteristics of their entangled twin, no matter the distance. If one particle was affected or changed, it's twin should show those changes at the exact same time, and distance is not a factor in this theory of Quantum Physics.

Episode 4 is a great example of showing that distance is not an issue for the Spore Drive in terms of time. The Discovery was able to appear over that colony in a blink, after travelling from elsewhere in the galaxy, and then blink away instantaneously after leaving ordinance in its wake for those Klingon ships.

Episode 9 is another example, where the Discovery constantly 'Jumps' in different locations around the Klingon vessel.

In both of these situations, there is no passage of time for the crew while jumping from one location to another.

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