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I have painstakingly assembled a highly realistic relativistic raytracing 3d renderer and plausible geometry and position for nearby stars.

Here's a render of the view to starboard:

I'm sure you can appreciate the thousands of hours of compute time that went into this.

Less facetious answer:

Leaving aside the issues of whether there's any time for your observers to experience stuff in, lets look at the boring relativistic things.

Here's a thing that Einstein cobbled together using some of Lorenz's work, describing relativistic aberration.

$$cos theta_o=frac{cos theta_s-frac{v}{c}}{1-frac{v}{c} cos theta_s} ,$$

This is the effect by which things in space (that are effectively stationary background objects, relatively-speaking) around you appear to be warped to bring light sources together into a region in front of you, centred on your direction of travel. $theta_s$ is the angle between your direction of travel and the direction of travel of the photon shooting at you. $theta_o$ is the observed angle of the incoming photon's trajectory The exact reason for this is kinda hard to articulate in simple terms (but related to the fact that light always seens to be travelling at lightspeed for an observer, regardless of what sublight-speed they may be travelling at), but you can reasonably take it on trust that those two gentlemen knew what they were talking about.

This means that as your velocity approaches the speed of light, your entire view gets concentrated into one tiny spot in front of you. You can see that the equation simply resolves to 0 when you reach lightspeed. There's nothing to see to the side. That image above? Totally plausible for an ultrarelativistic traveller.

Here's another thing: relativistic length contraction.

$$L =L_{0}sqrt{1-v^{2}/c^{2}}$$

Here, $L$ is the length of the ship as observed by some "stationary" observer, and $L_0$ is the actual length of the ship. You'll note that from the point of view of this observer, an object passing at lightspeed has no length. If I shoot a laser at a passing C-ship, how can I hit a side window, when it has no side? I can still hit the front, but that's about it.

I'm fairly certain that this is another way of stating the same sort of thing described as relativistic aberration above. Someone who actually knows relativity, rather than just trying to bluff confidently, feel free to correct me...

On a ship traveling at exactly c, Victoria wouldn't have any time to see any stars -- for her, the ship would arrive at its destination instantaneously due to time dilation.

Sorry for the slightly lame answer...

Edited. - as per edit to the question.

Assuming the Current model of the universe.

Fore: nothing, because - Photons blue-shifted beyond the furthest reaches of the EM spectrum (way beyond human perception) as the Doppler shift would seem to predict - you would think.

Aft: Nothing much, surely all would be shifted to the lowest conceivable frequency, the wavelength of the universe - you would think.

To the side: perhaps a thin line of white light, tinged at the fore edge with blue, at the aft with red? - You would think.

There would be heat death before she'd had time to move to the window, before she'd taken a single step, before a single neuron in her brain to enact the intention to move to the window had fired, before a single electron had completed a trillionth of its orbit about its nucleus... Entropy has consumed the universe.

She gets to the window, looks out, catching the sight of her own reflection in the plexiglass, apparently next to the ship in an identical, but reversed room and an eerie strip of light. She raises a hand and brushes a curl aside - "Hey, it's all dark out there, can someone turn the lights on?"

"Let it be so."

In terms of Physics

The ship is two dimensional to an outside observer - a flying pancake of zero thickness, it is unclear whether a photon would be able to enter or leave the ship from the side as the side would be dimensionless. And that's not taking into account its mass - it is now essentially a singularity of mass tending to infinity and shouldn't even be two dimensional.

• An interpretation would be that all the light from the ship is reflected back in the form of a thin dimensionless vertical line, that tracks the head's movements to always remain perfectly perpendicular to the direction of travel (a bright ring around the belly of the ship, the same direction from every porthole: ie. effectively at infinity), as a result of light being unable to escape (*except photons whose polarization exactly matches the angle of the slit ie. probably none).

No light would get "in" (probably none).

(If you ignore her disappearing behind an event horizon into a dimensionless point that is, but then again, maybe even there there's hope....).

Aside:
The more I thought about this question, the more I realized the limitations of what I know, especially from the point of view of a Flatlander.

There is a game (made by/with physicists from MIT some years ago) that models the player approaching the speed of light. This leads to multiple effects on vision:

• Doppler effect:
  
  red- and blue-shifting of visible light, and the shifting of infrared and ultraviolet light into the visible spectrum


• Searchlight effect:
  
  increased brightness in the direction of travel


• Time dilation:
  
  differences in the perceived passage of time from the player and the outside world


• Lorentz transformation:
  
  warping of space at near-light speeds


• Runtime effect:
  
  the ability to see objects as they were in the past, due to the travel time of light

I don't understand the physics behind this well enough to do more than copy pasting what the game description lists, but as far as I remember the game includes further explanations (and you can of course use the names of these effects to look for more details).

Let's throw the whole relativistic discussion out the window and just work on the assumption that the ship is doing "something" in such a way that after one second, it is one light second along it's path.

The view outside is incredibly boring. Let's assume I am standing there looking out the window, the view takes up 60 degrees of my vision so that means a star which crosses my view starts 60 degrees from my left and ends 60 degrees from my right. Here's a diagram:

Let's assume my path is the bottom line, does this look familiar?

It's an Equilateral triangle. So if the star starts and ends one light year away, then my path is one light year, which means, at light speed, it took one year for the star to cross my window.

Space is really empty so most stars are even farther away than that.

You can walk up to your window, draw little dots on it where the stars are, go about your day, come back and nothing would have moved.

Looking out the window is boring in terms of natural objects, but maybe there's traffic outside, other ships to watch, but that's up for you to write.

Yalls' universe is so boring!!

Naturally, what little Victoria Luise actually sees from the view port (one could have hoped she'd discover this wonder from the starboard side smoking lounge, but one supposes that's for adults only, and not small girls!) is far more interesting than mere science can describe! A wonder indeed for the eyes and a feast for the imagination. And how lucky she is to experience it first hand!

First, it's important to understand that bits of Light travel along their appointed paths, wavewise, very quickly. Like the velocipedes Miss Victoria Luise is used to seeing speeding along in her home city. Because she is a well to do little girl, her accustomed mode of transport is a sedan chair carried along by two amiable fellows of the household staff. So, she's used to seeing the electro-telegram boys with their curious flashing devices strapped to their backs whizzing by at such a rate that she can scarcely make out their House liveries, to say nothing of the contents of the e-tels they're carrying. And like the velocipede riding boys of home, she knows from her physioastrological studies that Light moves even faster than the fastest velocipede, faster than the great tram-ships that ply the oceans and faster than the fastest of electro-trains that can bring one from the kaiser's busy parliamentary capital of The Hague all the way to the Oriental Empire's capital at Peking overnight!

Second, it's important to understand that these bits of Light are travelling in all directions all the time. It's just like the traffic whizzing through, around, over and under St. Wyziwygus's Circus downtown. At first glance, all seems a bizarre chaos of velocipedes, electro-trams and pedestrians. They're all moving in every conceivable direction and all just as fast as they can. Apart from the poor walkers, who appear to be slothily trudging along among a whizzing cloud of faster traffic.

But now little Miss Victoria Luise has gotten herself upon the proverbial velocipede and she can now see Light for what it truly is!

The View Aft

Looking aft, as the Prinzessin accelerated towards her magic velocity, she'll see what appears to be a fuzzy wave approach the grand Ship. Due to the amazing properties of the view port itself, she can just make out the lines of Light, breaking like dolphins on the ocean, at the Edge of the luminal breakwater. What she can not see from her vantage, and this is a shame, is that the Edge surrounds Prinzessin entirely and demarcates that place where the mighty engines have brought the ship up abreast of the Light cast off from the Sun some hours ago while the crew were easing her up to cruising velocity. The Edge looks fuzzy because it is not possible to maintain perfect velocity. For some fractions of a moment, Prinzessin might be travelling just shy of or just more than 1 luminal; thus there will be moments when she eases ahead of the light from Sun and some moments where that light catches her up and passes by, which causes a bit of haze to surround the vessel back towards the engineering department. Adding to the haze of the Edge, of course, is orthogonally travelling Light, that is moving perpendicular to their course. As Prinzessin whizzes by those pathways, the Light appears to sort of bunch up, mixing and separating in wonderful bands of colours and hues that compress at the interface of the Edge. A spacebow that travels with the Ship and would appear much like a glory or rainbow surrounding an airship.

Perhaps just at the edge of her perspective, she might get a glimpse of the Void! This is a spectacular phenomenon that can really only be appreciated when the Ship travels just slightly faster than 1 luminal for a short time. If the engineers can provide such a mighty burst of speed, Victoria Luise will notice that she is suddenly failing to see the Edge. As Prinzessin overtakes the Sun's ever older Light, that Light which they were just flying abreast of has now disappeared behind the vessel's wake and, being slower than the Ship, is now invisible. As the Prinzessin slows again, the Light will rapidly overtake and that part of the universe will again become visible. But the change will not be so fast that it is not noticeable! Victoria Luise will actually be able to see the Front as it careens forward like a cavalry charge overtaking its lead horse. The sizzle of photons as they overtake the Ship will form a brilliant and electrically exciting spectacle!

The View to Starboard

Luckily for little Miss Victoria Luise, her viewing port allows her to see quite a bit of interesting external infrastructure of the great Ship. From this vantage, she can tell when Prinzessin is charging forth towards 1 luminal. For there is a bright beacon light some distance below her port which illuminates some of the vanes of the great Scoops that draw in interstitial matter for the powerful engines. As the Ship moves faster, she can see the leading edge of the beacon's light. As with the Front of Light coming in from the Sun, so it is with the lesser lights of the beacons: as the Ship catches up to them, she can see the effects of the photons dancing at the edge, beyond which there is no light. As Prinzessin gains speed, the Front wavers and churns, its bright hues alive with squillions of photons bunching up in the wave; until at last, the Ship passes into superluminality and Front dissipates, and all the Light is sucked from beacons and disappears into the Void!

The View Fore

Peering towards the front of Prinzessin as she plies the interstitial main, little Miss Victoria Luise will be in the view of her life! For there she may see all the stars familiar from her astrology lessons, but their colours shift and waver, now bluing and now redding in an exciting arc of lights emanating from the bow of the great Ship! Here is a the light fantastic, the mad tarantella of ancient photons dashing in from the depths of space beyond her comfortable world, and like two madly careening velocipede boys passing in the streets of the city, Victoria Luise can catch no more than a searing blur as those bits of Light careen screaming through the Bow Arc and pass like a burst of sudden lightning out of sight into the Void beyond Prinzessin.

She will see a flash of white, and then she will be permanently blinded.

Because:

It is certainly true that Victoria experienced no time while traveling at the speed of light.

For practical purposes, the trip is instantaneous. That means all photons that impact on the kid's retinas do so at the same time.

The longer the distance travelled, the greater the amount of photons caught. For even just a light second, she is going to collect an awful lot of radiation. Even if you filter X-rays, UV... There is still much more in a light second trip than what you would get from a strong laser pointer.

To find out the damage: find out how much light she would be getting in her eyes if she were travelling at regular interstellar speeds (i.e.: the sun's orbital speed around the galaxy, 200km/s). Multiply that luminosity by the distance travelled, since her retinas will cover that much area in zero time.

Next time keep the spawn away from the windows.

Horizontal Stripes.

Your question explicitly states that in your universe no spacetime distortion or whatever happens, so the answers based on theoretical physics are altogether wrong. They are, with some exceptions such as frequency shift (which is very much provable, and observable), mostly unprovable speculations in our universe, too -- but they're by definition wrong in the universe you depict.

So what you would see is the same kind of horizontal stripes that you see in a high-speed train, only much darker. Very distant things being somewhat less blurry than closer things (though due to your ship moving very fast, things would have to be very far away).

Why?

Because, well, your eyes still have the same basic properties as they have in our universe (unless you say they don't).

While the eye tries hard to re-fixate ("saccade") when stuff is moving, there is a limit to what those poor little muscles can do (plus, your neurons are not infinitely fast). Which is approximately an angular speed of 720° per second, maximum. If the exterior moves too fast (or rather, is stationary and you move), the eye becomes unable to re-fixate. That's the blurry view outside a high-speed train.

By itself, our eyes are extremely susceptible to motion blur. Every photoreceptor is, more or less, even the fastest camera chip. Biological eyes, however, which involve a complicated G-protein coupled signal pathway going off, are prone to motion blur or "afterlighting" in particular.

Why would your view be much darker? Well, you move so fast that the larger amount of light moves backwards, the "sideways" component of any light ray, or photon, being smaller than usual. Thus, everything will be "darker". Since light coming from the front will travel at twice the speed of light, and light coming from the back will be "standing still", your blurred stripes would be lighter (flashing white) towards the front, and darker towards the rear.

Moving at exactly the speed of light means that no time at all passes inside the ship for the entire duration of traveling at the speed of light. All the light that impacts the ship during that duration hence hits the ship in literally no time at all, meaning that the surface is subjected to light impact of literally infinite energy density. Each photon and atom impacting on the front would also have infinite energy. I can't imagine any material able to stand up to that, much less any human eye trying to view it (even if there was any time to view it, which there isn't).

Another issue is that your ship would have literally infinite mass. At the moment it hits the speed of light, all objects in the universe would start moving towards it with infinite acceleration, reaching near-light speed in an instant. The universe would start collapsing on itself. This acceleration would be delayed until the gravity wave reaches the stars and galaxies, but the effect would be instantaneous from that moment, no matter the distance.

Even if you use hand-waving metaphysics to bypass the mass/gravity problem (which might be necessary to reach light speed), you still have the problem of impacting photons and atoms.

One way to get around all this: Convert your entire starship to light, which per definition travels at light speed, have it received by a large dish, which then converts the light back into solid matter. In this case, however, there would be no view, as the passengers would experience no time at all for the journey.

Frame challenge:

We don't know, and may never know

As per our current understanding of physics, objects with mass can not be accelerated to the speed of light. As such, there are no images to confirm or deny any of our speculations, and there may never be. It may be physically impossible to take a photograph at the speed of light as we may never find a way to accelerate objects with mass to 100% the speed of light. This means we would never have a point of reference to compare Victoria Luise's experience to.

Little Victoria Luise would experience something indescribable, it would be like trying to explain colour to someone who was blind, or love to someone who could not feel, or life to someone who could not experience death. She would see something beyond what words could explain as currently we are blind, we can not see through her eyes to experience what she has experienced – mere words would not be enough to explain it, you would need to see it, to feel it, to be in the presence of it, to have any idea of what she has seen.

And I think that is something truly magical, how this little girl would have seen something that she, and only she, would ever know.

If she is looking outside, horizontally, then she would likely see a whole bunch of horizontal lines. If the ship is moving in any sort of arc, then the lines would follow that arc, but that's another problem.

Every body in her field of view (assuming she is flying in space where planets are too far away to see) will emit light in a more-or-less spherical manner. This means there is a functionally solid sphere of photons in a radius of (age of the star * c).

By intersecting through this sphere with your character's eyes, the eyes are looking at an eye-sized slice of this sphere of light. This goes for every star within her vision. She would only be seeing whatever photons are in that particular point in space.

Mileage would vary depending on the thickness of the craft, as it needs time to pass through the ship to her eyes, however any window where her position relative to the bow-side of the window is further than the thickness of the glass would do the trick.

An interesting effect is that, if she is looking towards starboard, stars to her left will have their light shifted towards blue and eventually become invisible, while stars to the right will shift towards red, and eventually become invisible. For an indefinitely small period of time, a star in the direct middle of her field of view would appear it's original color. Additionally, due to the shifting outside of the visible spectrum, this band would be incredibly thin, so it would look like French flag confetti in the middle of the window.

There is no consistent model of reality in which massive particles are moving at light speed and other particles are not, and the two interact.

In order for the person on the ship to see the universe, there must be a way to transform their frame of reference continuously into the frame of reference of the emitting light. And there isn't one.

You have asked the question "what is the height of a square triangle", without the mathematics to understand that you are asking for a figure to have exactly 3 and exactly 4 sides. The "warp bubble" or "bending of space time" is how physics can generate a continuous transformation of reference frames between the light-speed traveling light-seers and not light-speed traveling light emitters.

Physics answers the question of what light you see by tracing what paths the light travels over. With no path, there is no light to see. With no "bending of space time", there is no path.

Now, what you could do is try to throw out our current physics.

You could talk about worm holes, or equivalently you could have the ship move perpendicular to our 3-space into a hyperplane that has a shorter route to the destination. We could be a simulated reality on some hyper computer, which when you type in the console cheat code the laws of physics change along a path permitting light-speed travel. As you travel, the computer displays some physics-unrelated UI in demonstrating where you are. When you give the halt command, the computer builds a brand new reality in which everyone remembers you being at the source location, but you are at the destination location, in such a way that all sentient beings in the simulation have roughly the same experience and continuity of consciousness.