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I've just bought myself a shiny new spaceship equipped with the latest in FTL warp technology, the only catch is the fuel bill, this thing drinks the stuff like it's going out of fashion (still, it's better than the F150 but that's another story).

Now I'm just a humble space-cabbie but, my understanding of warp drives is that they just, well... warp the space around the ship. But then, if space-school physics taught me anything, it's that so does the Earth and the Earth doesn't need refueling every 38¼ parsecs so... where's all that energy going? I'm pretty sure you can't just burn a couple kilos of antimatter without also turning the inside of the ship into one heck of an oven... so what's going on?

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    $\begingroup$ When a helicopter hovers, where does the energy go? The helicopter is stationary, it shouldn't need constant energy input to stay in place; after all, when I hang my hat on a hook it stays there without a need for engines or fuel. $\endgroup$ – AlexP Jan 12 at 22:40
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    $\begingroup$ Go easy on FTL on ur way to space school, ur physics teacher might turn into baby ya know! $\endgroup$ – user6760 Jan 13 at 2:13
  • $\begingroup$ If it’s something like an Alcubierre Drive then you also need to have some exotic matter with negative energy in order to make the whole thing work, so the net result is zero energy being expended. $\endgroup$ – Joe Bloggs Jan 13 at 10:05
  • $\begingroup$ Also of note, IIRC, energy conservation in general relativity is a bit tricky, so if your FTL Drive works by warping space in any way then your intuitions about energy might not be right.. $\endgroup$ – Joe Bloggs Jan 13 at 10:09
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It's like the difference between natural and artificial magnetism. A natural magnet doesn't need any input but can't be controlled. A controlled and focused artificial magnetic field takes energy to create and maintain and that energy is lost as heat and other inefficiencies in the system.

While the drive is running the energy is lost as heat radiated out as a side effect of artificially warping space. Ships would leave a detectable trail of heated areas, with increased radiation and exotic particles where they have passed through.

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The good news is that your Shiny New Spaceship came with great tech that lets you control and manipulate the terrajoules per cubic meter that it takes to warp space! And, if you keep taking it in to the dealer for the (pricey) monthly tuneups, it’ll retain its excellent 99.9999% efficiency!

Unfortunately, that still leaves megajoules per cubic meter that have to be provided by fuel.

But next year, we’ll be offering SNS Model II that’s 0.00003% more efficient because of its new hybrid drive, which will save you a fortune. We’ll even take your 150 as a trade in!

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Considering a warp drive is a speculative superscience tech, here's a speculative superscience answer:

The energy of the drive is spent in warping space, so other than waste heat from inefficiency, the drive itself does not need to appear to release as much energy as is input. However, that "excess" energy is then radiated from the empty space volume of the warp field as blackbody radiation (despite being essentially a realization of virtual particles out of vacuum) at a temperature determined by the deformation the drive produces at that point.

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