FTL 101…and I’m the student.
Let’s say someone develops the deus ex machina drive that pushes a ship past the speed of light-what happens next? Does the ship just travel that much faster to it’s destination, or does it “jump” some incredible distance? What do the people inside the ship experience?
I stuck this in IMHO because I expect there to differences of opinion on these matters(and others that will probably pop up).
I believe that the ship would need to slowly increase speed so the passengers on the ship don’t die. you’d most likely see all black out the ship windows. maybe flashes of light from passing a light sources path. this is a very interesting topic and i’ve never seen the film you’re referencing
That’s because I’m not referencing a film.
Not to be a threadcrapper, but you are asking “what does physics say would happen if something that physics say is impossible happens.” Physics as we know it says that matter with a positive rest mass can’t be pushed up to light speed and beyond. So if our physics proved to be unreliable on that, it would be unreliable in describing anything beyond that.
For an object with a positive rest mass (even a single proton) to reach the speed of light would require a literally infinite amount of energy. So an object with a positive rest mass (even a single proton) traveling faster than the speed of light would have a more than infinite amount of energy. If faster-than-light objects existed, they would have a negative rest mass (weigh literally less than nothing), would take an infinite amount of energy to travel as slow as light, and would move backwards in time.
Since this is in IMHO, I’ll just open my big fat uneducated mouth: It would probably depend on how this deux ex machina accomplishes it. Is it breaking the laws of physics or has it found a loophole. Because as I understand it, FTL is basically considered impossible but some kind of catching a fold in space-time is theoretically possible. So just faster for the former, some kind of jump for the latter.
For the purposes of this discussion let’s say it found a loophole, but the inventor of the drive sealed it with a adamantium/gorilla glue amalgam so all you know is that it seems to work.
For the purposes of this discussion the deus ex machina works.
You say that it would travel backwards in time. Would it also travel in space?
During a class (Pitt later half of the 70s) on physics in science fiction we actually got into a rather extensive discussion of this. IIRC things behind you would gradually appear to move to the front of you until you broke LS and then return to normal until your next jump to say 2x LS, then rinse and repeat each time you broke a new level of LS. I forget the math but at the time it made snese. The time was also college when a lot of various substances also made sense. 
As an aside, what happens to the universe if some idiot pulls this off?
edited to add: Needless to say, the Drive in my scenario doesn’t work that way. Maybe it sucks the energy out of an alternate universe instead?
Any kind of “what-if-you-could?” answer is going to be wrong, I think, because it’s asking for an answer that we think does not actually exist - it’s like asking “But what if you could divide by zero?”
It’s sorta-reasonable to extrapolate and say that because time slows to an apparent stop at c, that it should go back the other way beyond c, but that might just be an overly simplistic view. but as we don’t know, we might just as easily say that time doesn’t go backwards, but goes ***sideways ***instead. What does that mean? Who knows - we’re off the map.
See, the issue is that I don’t mean that it would take “a lot” of energy to push anything with a positive rest mass (even just a proton) up to the speed of light, I mean it would take a literally infinite amount of energy. Meaning that all the energy in a trillion, trillion, trillion, trillion, trillion universes wouldn’t even begin to approach being near the beginning of enough. It is back to the whole “0.9999999999999 does not equal one” thing. It is like saying “what would happen if someone wrote down every possible number”, it is a divide by zero / does not compute scenario.
O.K., I understand now. So let’s say The Drive works in a way that doesn’t need an infinite amount of energy, and leave it at that.
Anything that is completely and utterly outside known physics is completely indescribable by known physics. The relativistic mass increase, time dilation, and length contraction involved in describing what a relativistic traveler would see would have to be tossed out if you toss out relativity. You’ll turn into a tiktaalik and mate with Kate Mulgrew is as accurate a description as any.
Again, not trying to be difficult, but asking what things would be like if you could do something that can’t be done isn’t really an answerable question. It is like saying “what would it be like if you could fly a normal-sized 747 inside of a normal-sized toothpick at 500 MPH for 3 months non-stop without turning around but without shrinking the 747 or enlarging the toothpick–what would the passengers inside of a 747 flying at 500 MPH in a toothpick see?”
Sounds like you’ve invented the Imagination Drive. With it, you’re free to roam the universe at any speed you like without breaking the laws of physics, or anyone being the wiser. Best feature is that it runs on cereal, or bacon & eggs if you’re planning on travelling past lunch. You never even need to change out of your pajamas or get off the sofa.
Remember what the name of the drive is?
As soon as the spacecraft exceeds the speed of light time runs backwards taking the ship back to the past just before the point where it exceeded the speed of light. At some point it runs out of fuel and finds itself right where it was before it began trying to do this.
Boomerang Drive? 
Well, I’ll take on your hypothetical.
I would envision that a ship using your drive would see nothing out the windows. Either there would be nothing to see, or the blue shift would be so severe that even long wavelength light would be shifted into or beyond gamma rays. So no looking out the windows! And the outside of the ship would have to be shielded somehow. Probably an ablative coating to protect against extremely short wavelengths. (I’m assuming there already is some sort of “deflector” for normal space dust.)
Inside the ship things would seem perfectly normal. Might even be zero-g, depending on how the drive works. No sightseeing on the way, so make sure the ship carries a lot of booze. Probably have to make the ships like cruise ships, lots of entertainment.
Unless you postulate some sort of FTL sensors, all navigation would be blind. You’d set your course ahead of time and hope your charts didn’t omit something in the way (that’d end your trip real quick, wouldn’t it?). But since space is mostly empty, it might not even be an issue. A rare rogue asteroid or a fellow traveler would have to be exactly in your path. A miss by even a foot is still a miss. Good thing you can’t see out!:eek::eek:
There would of course still be collisions. Cost of doing business. Unless you got lucky in your investigation, you’d never find even a bit of the wreckage, which would be mostly dust, and maybe a random chunk that missed the direct collision.
Someone in normal space when your ship went by wouldn’t notice, most likely, at least until after the ship had already gone by. They’d probably see a blinding flash of light, and if they could see anything afterwards ( :eek: 
) the ship would be invisible after it passed. Again, it is good that deep space is mostly empty space.
If you were in orbit, say, around a planet that got in the way of one of these FTL ships, well, it would be something you never forgot! The Holdo Maneuver would be a mere firecracker in comparison.
Since there is no physics for this situation, I can’t say if there would be time dilation, or even worse, reverse time dilation. But if you traveled back in time during the flight, that’s not exactly a problem, believe it or not. Once you reach your destination, you do a “correction” maneuver where you fly at .99+c for the proper amount oftime until you “catch up” to the current time. No one will be allowed to use the drive for time travel. And I’m sure no one will cheat and “forget” to make the correction. Who would do such a thing?
When you hit lightspeed, you’d be on the null cone, so you wouldn’t experience time.
See, in Special Relativity, you measure time by computing the length of a particle’s path through spacetime (its interval) as per the Minkowski metric, and, once a particle is on the light cone, and is traveling light speed, its interval is zero, regardless of how much three-dimensional distance it covers. This is why the light cone is also called the null cone.
And before you ask, the Minkowski metric is Special Relativity. All of the effects of Special Relativity come from the various four-vectors moving around in a four-dimensional space where length is defined by the Minkowski metric. Remove it, and you’re back to Newtonian physics with Galilean relativity, and the speed of light is no longer special.
Of course, those four-vectors include the mass-energy four-vector, and that vector’s rotation in a space-time plane is why it’s commonly said that a particle with positive mass would become infinitely massive if it were to go lightspeed: It’s precisely a divide-by-zero error in the relevant equations. So once again you hit a logical wall.
Human language doesn’t prevent us from saying logically inconsistent things, like “the square triangle” or “the four-sided pentagon” or similar, so it allows us to talk about massive particles accelerating to FTL speeds as if it made sense. Trying to investigate those statements quickly reveals them as nonsensical.
Plaid. Lots and lots of plaid.