There was a young lady named Bright
Who's speed was faster than light.
She started one day
In a relative way
and returned the previous night.
A.H. Reginald Buller
Just because it's a fun question, I'll give this a go. You wrote:
wouldn't its vector through spacetime be negative, meaning it is bound
to travel ever-backwards in time? Due to the expansion of the universe
over time, would the universe would be shrinking for the particle, and
all scattered masses of the universe actively unraveling and falling
towards a single point in 4 dimensional space? As space compresses,
its relative velocity would become slower and slower, until it arrives
at the CMB, or if we add its negative time into the equation, the
actual beginning of the universe, where negative time starts slowing
back towards absolute 0?
You're covering a lot of ground here so this won't be short.
First, it's entirely hypothetical so lets just make that extra clear. Second, that it would actually travel back in time relative to the rest of the universe is a popular idea, but not the only possibility. A 2nd axis of imaginary time also works mathematically.
Take the basic relativistic principal that light is always observed at c, but an object traveling faster than c, light from behind it would never catch up to it. If it was created, lets say the geniuses at CERN create an FTL particle by turning their dial up to 11 and the FTL flew on it's merry way it couldn't see the scientists staring at it's path in astonishment cause the light from their astonished faces would never reach the particle. It could see the scientists past, but never their astonishment. IN fact, as it flew by planet after planet, alien after alien would see this unique FTL and think, wow, that's cool, but they could never catch it to study it, and it would never see the alien's reaction to it as that light would never reach it. In a sense, it would carry an event horizon in it's wake, unable to see any future of anything it flew past.
An FTL particle, would see what's behind it as it caught up to that light and what's ahead of it, as that light passed it. It would see both what's ahead of it and what's behind it on the same plane in the direction it travels, what's behind it, red shifted and moving backwards in time, what's ahead of it, blue shifted and moving forward in time. Now if you flip it's time dilation, that probably flips too, but the whole thing gives me a headache trying to work it out. At relativistic speeds, observations of time get complicated. Kind of like, if you fall into a black hole you wouldn't see the universe "speed up" as your time slowed down because the light and objects you're falling in with have the same time dilation as you. Traveling FTL, the particle catches up to the past even without negative time dilation. Observed time and real time get tricky at really high speed.
Also, since you specifically mentioned a particle, particles can't "see". Particles pass by stuff without seeing it or they interact, essentially bumping into something. It's the "you can't observe a quantum particle without changing it problem".
To "see", you need a method of photon resolution and capture. In other words, a lens and a photon receptor with a surface area that's designed to catch many many photons and produce a picture, like a camera or our eye. A particle, if it bumps into a single photon it's momentum changes. Particles only "see" what they hit, like a blind person driving a car.
So, lets say your particle is carrying a camera, now we can talk about what it "sees" and, what it sees is weird both running into the light ahead of it and catching up to light from the past from what's behind it, both appearing infront of it on the same screen.
That said, with many photos and careful measurements, it could calculate that the observable universe is a sphere heading towards a big crunch, but that would take some number-crunching. It probably wouldn't be obvious or readily apparant.
Imagine if you're traveling 2c and you're holding a flashlight. If you hold the flashlight ahead of you, no matter which way you point it, you see the light shining in your eyes, because you're catching up and passing it's light no matter which way it points, but it would change color as you twirled it.
If you hold the flashlight behind you, and turn it on, you'd never see the light because it would never catch up to you. You couldn't tell when it was turned on, unless it was turned on when it was ahead of you. But even in that weirdness, calculate the big crunch if you understood dopler and had accurate enough telescopes would be possible. It takes very accurate measurement of type 1a supernovas to even detect and measure dark energy. It's quite subtle.
Now if your FTL could see other FTL objects and not just rely on light traveling at c, then the universe might appear somewhat more like we're used to.
Now, as to your question "would it go slower", no. Dark energy doesn't slow down objects. It spreads out space between objects. As a result, your FTL might see distant objects slow down over time some over long periods of time. Near by objects, the dark energy effect shrinks to zero, so it would always have it's FTL relative velocity. All it would notice is very distant objects slowing down gradually. As to what it would see at the big bang/crunch - take this with a grain of salt, but I see no reason why it would slow down, unless it collides with something, but since FTL particles don't exist, all this is very hypothetical.
If we observed this quark for a planck instant in our world, would we
know without a doubt this quark has come from the future, and could we
use this knowledge to acquire information from the quark, much like in
the movie Interstellar, except these quarks come explicitly from the
future rather than morse code from a timeless existence? Or would we
not be able to detect its existence at all as it passes through our
There's a few issues here.
We observe particles when they crash into each other or by their effects. An electron has never been directly observed for example, but it's effects have been. We have to assume our FTL particle could be observed and measured. But measuremnet doesn't prove time. We'd need to know a lot more. Decaying particles, for example, are good at demonstrating time dilation because a partcle that decays in a nanosecond that travels at close to the speed of light, travels quite a bit further than 1 light-nonosecond (roughly 1 foot). It's theorized that observation of a tackyon, you'd see it move in two directinos away from itself. like the picture below. That would be a good example of FTL, not necessarily an example of traveling backwards in time (unless I'm missing something).
Evidence of an object traveling backwards in time is tricky. You'd need to observe either information from the future, or, perhaps, a revere decay. (again, I'm not an expert). #JDługosz gives a nice explanation of that here. Needless to say it gets pretty technical.
Now, people sometimes say antiparticles are particles traveling backward through time. And that kind of works on on paper, but antiparticles don't travel faster than c and they can't bring messages from the future - so we need to approach the "travel back in time" with some hesitation. It's not straight forward and what I've read, traveling backwards in time is only possible in quantum physics if there's a loop. No going back and changing history, only, it already happened, so it can, or it must, go back in time to do what it already did. No grandfather paradoxes in quantum physics. In other words, it doesn't matter if antiparticles travel backwards in time. They don't travel backwards in time in a way that we can ever use. We can't send messages into the past using antiparticles.
The tachyonic antitelephone is a clever idea, but 1) tachyons probably don't exist and 2) even if they did, there's no guarantee they'd be able to carry messages into the past, so . . . there's issues with real time travel, even, sending mesages into the past time travel. I don't want to say it's impossible, but there are big uncertainties.
So, to summarize, if there was an FTL particle, it might be posible to detect it but detecting it and using it to send morese code to the past are two different things. It's also worth noting that detecting a particle isn't a guarantee. Many particles were very difficult to detect. The Neutrino and Higgs Boson come to mind. Dark matter too was only detected by gravity. If FTL particles exist, there's no guarantee we could detect them.
In the spirit of clarifying concrete questions, are
tachyons/antiparticles proposed to travel only backwards in time, by
some informed schools of thought? Also, how might we go about
identifying them and possibly extracting info from them? If you
answered these already, of course disregard. Bonus question, do you
feel that my interpretation is accurate, where the particle eventually
arrives at the beginning of the universe, where its relative velocity,
and the progression of time itself approaches absolute 0? If so, then
I'm imagining the beginning of the universe, where there is rapid
outward expansion of spacetime, energy, and particles, while at the
same time, negative spacetime, negative energy, and antiparticles are
all rushing towards point 0 to be consumed by a state of timelessness
Basically no. How particles experience time in and of itself is a bit unclear, but while defining an anti-Proton or an anti-electrion (positron) as a particle traveling backwards in time - from a certain perspectdive on paper, it works, but that doesn't mean it's actually traveling backwards through time and the big bang becomes a big crunch and the "end" of the universe. Covered in my detail here, but the first answer says that most physicists don't believe that. I don't htink there's much harm in it if you want to look at it that way, or use that as a though experiment, but I think it's fairly unconventional. Things can be looked at from a certain perspective, but that doesn't make it so.
To my thinking, for example, a Proton and an anti-Proton are almost the same thing they have 3 similar quarks with similar mass, just oposite spin. To my thinking, a Proton and an anti-Proton both move through time in the same direction, just one is right handed th eother is left handed. I think the move backwards through time is a clever metaphor, but not an accurate picture. - in my opinion.
Does a clock run backwards when you watch it in a mirror? Not really. But take the numbers away and it appears to.
The anti-particle question ad the FTL question are quite different. FTL may well be impossible and if it's possible, it might operate by imaginary time, not reverse time. imaginary time is fun, it opens up a whole nother series of questions. Distance dilation, as you approach the speed of light, the distance to objects grows smaller. Imaginary time, there's a 2nd axis of time, where, if you travel at 2c or 4c, at least by the equations, the distance to the person in the FTL ship grows larger, so, to the person on Earth, the trip to Alpha Centauri takes less time, to the person in the ship, the fastest trip is very close to c, as the ship travels faster than c, due to imaginary time dilation, the trip takes longer and longer cause the star moves further and further away. This imaginary time approach works better in many ways than the backwards time approach in general relativity. That said, until FTL is actually discovered, it's all just silliness.
Hope that wasn't too long and that it makes at least a little bit of sense.