Ludicrous Speed? 
Speed of Light can absolutely not be attained or surpassed by any object of nonzero mass. Some speculate that Tachyons – particles traveling faster then light exist.
Agree 100%. Tachions may or may not exist.
To work out what a hypothetical traveler on a spaceship travelling at FTL speeds might see when they look out the window you have to construct a reference frame for the ship, but this is problematic. Lorentz transformations, which are used to transform between reference frames are only applicable to subluminal frames of reference and trying to extend them to superluminal frames of reference runs in to difficulties. For the more technically-minded, one example of the problematic nature of trying to create superluminal reference frames is that changes between frames of reference correspond to symmetries in spacetime, but there are no corresponding symmetries for transforming to a superluminal frame of reference.
Thing is that math also is a language that allows questions that can seem like nonsense but which are are grammatically correct … and which can lead to interesting and useful things. Like the square root of negative one or maths in which parallel lines intersect … A ball with a negative diameter as a mathematical construct? Hmm. Would every tangent to its surface be a hyperbolic cone? Pretty sure in any case that it could be described using formulae that allow for complex numbers.
In any case the math works at every speed other than the exact very point c itself, both above and below. As a theoretical construct aren’t particles are popping in and out of existence every Plank second? The fantastical system would be one that allows for all the particles contained in and of the ship to pop out and back in together right before and after hitting c.
Another alternative would be to convert the matter of the ship completely into a code of photons for the duration of being at and only at the point of c which somehow reforms into matter at a speed of just over c.
The question is best answered by describing, if possible, what would happen as one asymptotically approaches c and from the point just beyond it getting faster.
Traveling faster than c we’d be, in the direction of our travel, hitting light from distant stars sooner after they left so they’d look older than before and seem to age more rapidly the faster we went. Alternatively we’d be catching upon the light that had left from the stars behind us some time ago. So that would be light from an earlier time but we’d be hitting it with our fronts. So a lot of light hitting us in front and blackness in backness.
I’m no physicist, but, yeah, this.
But again, so? Describe, if you can, what it would be like from the POV of coming infinitely close to (or one Plank whatever) c, skipping the exact speed c itself, and accelerating beyond it from a point that same (infinitely or Plank whatever) close above it.
Or be a threadcrapper.
Too long for me to watch maybe one of our math wonks is interested and would care to comment upon what on skim seems an interesting lecture on the maths involving circles with an imaginary radius (which of course could then be extended to spheres)?
But the describing of the situation would be based off of physics equations, and if what you are doing violates the physics equations, then the physics equations can’t be used to describe it. In your description, you didn’t address what the effects would be given that the object travailing faster than light would have negative/imaginary mass and energy and be traveling backwards in time, which is what tachyons would be like if they existed according to physics. So this goes back to “pretend some parts of physics are completely and absolutely wrong, then describe it using the physics that is completely and absolutely wrong.”
Sorry but you are wrong and your post explains why you are wrong. It is completely within the equations of physics to describe tachyons. Yes, using physics equations their mass would traditionally be described using i. And is completely possible using physics equations to describe what they would be like at just above c and at speeds much higher than c.
What the physics states is that no particles except photons can travel at c. A particle traveling below c will always be below c and if one existed traveling above c it must always stay above that speed. From the theoretical POV a particles can travel just below c and there could be particles traveling from just above c (with absurd energy) to infinity (with no energy).
So put that number line open circle around point c and describe what the physics would be as close as it is theoretically possible be above and below that exact point and outwards both ways. That would address the op.
As far as traveling at the speed of the exact point itself … again, information can travel at that speed encoded in light, and there is no theoretical reason that information can not be used in a Star Trek transporter manner … converting matter traveling below c into information traveling at c and then converting that information into matter with mass described using i traveling just above c (if we only knew how). At no time is matter with mass in that scenario traveling at the speed of light. The fact that even if tachyons exist there is no currently imaginable way to execute that plan is immaterial to the thought experiment.
How would particles with mass described using i interact with “normal” mass? It seems that the the lowest energy state for a tachyon would be traveling infinitely fast. If so then each the same one traveling infinitely fast is around us many times at the same time have circled the universe in zero Plank seconds? What that would look like depends on the answer to question one.
The issue isn’t describing superluminal (tachyonic) particles/ spaceships - special relativity can describe FTL trajectories, even if they are physically suspect. The main issue is trying to construct a faster-than-light reference frame and this at a basic level is not possible. An easy way to see this for those familiar with reference frames in spacetime is that there are no timelike vectors from which to derive the time coordinate from which are tangent to a FTL spacetime trajectory and if you try to use a spacelike vector instead to act as the time coordinate all you are really accomplishing is switching the sign of the spacetime metric.
But is that really an “all”? I ask this out of honest simple ignorance and trying to develop an imaging of spacelike and timelike spacetime. It seems to be saying that the manner in which we experience space and time is flipped if spacelike?? Space behaving more like how we consider time and visa versa? Or am I too far off to even explain to?
And can you explain if or in what way a particle with mass along the imaginary axis would interact with regular matter that it was zipping by from the future into the past?
Naively it appears for a superluminal observer what they perceive as their time ‘direction’ is what some other subluminal observer perceives as a purely spatial direction. At this point you may say: “well it’s a bit weird, but not necessarily impossible”, but if you look deeper all you’re really doing is a relabelling exercise and you’re actually constructing the reference frame of the subluminal observer.
Imaginary numbers don’t enter into it as space and time are described by real-valued quantities and entering superluminal values in to the subluminal Lorentz transformations and trying to make sense of the imaginary values is the incorrect approach.
So the real answer to the OP is “whatever you want to happen”. You’re engaging in science fiction, so as author, you can make up any details you want.
I’ll add one thing, though: Make it consistent. Make the problems and the solutions related to this make logical sense, such that the reader has a constant sense they know how the fictional world works and, most of all, that the solutions to various problems aren’t cheats. Technobabble isn’t bad because it’s nonsense, it’s bad because it’s a lazy way to get your characters out of a tight spot.
Establish the rules. Keep track of the rules. Use the rules to create tension. Really, it’s no different from making your characters have consistent character traits.
When you go faster than light, blue shift stops and instead, light begins shifting toward other colours; specifically, that set of colours everybody has heard of, but nobody is quite sure what they look like; Taupe Shift and Puce Shift are the most common, but Carnadine Shift is also possible.
“Within one Planck speed of c” is just a fancy way of saying “at rest”, since c is the Planck speed.
But OK, let’s suppose that you start off really close to c (in some reference frame), and then accelerate. You’ll now be even closer to c.
It’s like asking “When I’m slicing up a pie to share between a group of people, the more people, the smaller the amount of pie each person gets. How many people do I need before they all get a negative amount of pie?”
Infinity plus one!
All that is disallowed is being exactly at c. So as infinitely close as you can be to it without being it. From the approach below it and separately either slowing down to as much of an infinitely close spot above it or accelerating from it. Describe what the universe appears as from some hypothetical particle perspective doing that. Or don’t. Or answer that current math and theory does not give us an answer. But it does not disallow for it.
I was asleep the day we talked about FTL travel in physics class, but doesn’t mass increase as we approach light speed, like up to infinity? My WAG is that the ship would immediately implode into a black hole prior to exceeding light speed.