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Exceeding FTL (and breaking causality) is basically a sci fi trope at this point with about as much credibility as psychics. To have at least some credibility you need one of: a testable hypothesis, or an unexplained phenomenon. Right now we have neither. At best, we have some equations, that work below light speed, where we can extrapolate past light speed and see how the math works. The problem is: none of these equations are testable as they all contain infinities or other asymptotic features that prevent passing light speed itself. So, if there's no viable math to get from sublight to FTL, and there's no unexplained phenomena, then what we're left with is nothing.
Even quantum entanglement, which is a darling of sci fi whenever they need a plot device (hello Le Guin and the ansible), has categorically been shown to obey causality and the light speed limit in every lab test.
At some point it's like asking for negative mass, antigravity, or other things that the math would allow. Except our universe doesn't.
I've got a wormhole to sell you ;)
Obviously if we were to exceed light speed we would turn into lizards and mate with each other and have lizard babies. I thought this was common knowledge.
in scifi there seems to be several types of ftl: one is typical warp like drive of trek, and star wars, and hyperdrives which is similar to transwarp/slipstream/xindi vortex travel, which is interdimensional travel so not technically violating light speed. and the least common one is interdimensional teleportation, BSG reimanging uses this tech, although they dint bother trying to explain it with technobabble at all, because of the showrunners allergy to trek-speak. STD, and a single episode arc of tng a group of terrorists were using interdimensional transporters.
trek also had other forms of ftl, but those are very rare, and its pretty much similar to the last 2.
And every one of those are as grounded in reality as sci fi's agelong obsession telepaths, telekinesis, or mutants with powers.
There is a class of modern sci fi authors are all coming to terms with this.
I'd recommend checking out stories like Neptune's Brood -- sci fi which takes on interstellar economics in slower than light scenarios.