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I am a CG artist working on a specific shoot, that I have no clear answer to how it would look. And I seek your help. :D

The idea for the shoot is a flyby of two Interstellar Vessels named ITV Europa and ITV Lea Sudux.

Europa is flying back to Earth while Sudux blast to where Europa is coming from. Thus I figured that the two would meet quite close to each other, as the two systems don't move with respect to each other. Thus the paths for both ships should be the same. But I am not sure about that.

Anyways, the shoot is supposed to be a GoPro-like view from the Sudux looking ahead. And this is where the problems start.

I know that the Universe at this kind of speed is probably reduced to the CMB, so the Skybox may look like this. enter image description here But as far as I can tell, this is only true for what is in front of the Sudux. I am not sure how the rest would look. Or how much it is Blueshifted.

The next major issue is, what does the Europa look like? We know that we can not just add the two speeds. From this equation:

enter image description here

We can figure out, that from the Sudux´s POV, the apparent Velocity of the Europa should be equal to 13/14c or around 0.93c. And since Europa is flying in the other direction, all the Light emitted from her and her Shield´s should be redshifted. But I have exactly zero clues how the flyby would look. Now sure, it would be fast. Really fast. And since the ships themself are not that high, some might say you wouldn't see anything. But here is a catch. Each ship has 2 shields. One that is mounted to the main body and one that is way bigger and aerodynamic a few light seconds ahead of the craft. These shields are, in both cases, 3.5 km heigh. They are that high because of the ITV´s need to flip 180 degrees in interstellar space.

Thus my assumption is that the big shields would be the one thing you could even see at a distance. Although it would still go by really fast. In the best case, the shields might appear as a star Exponentially growing and then getting smaller once they are past each other.

Now of course, how much you see depends on the distance. I would assume there is a distance where you could actually follow the other ship with your eyes. For example, if the two are 380 000 km away from each other at there closest. The closer the two get, the bigger they appear but also the smaller the time window in which you can see anything. For now, I would like to keep the distance close so maybe 100 km?

So I guess there are really two connected questions.

The first one being: "How would the space around you look like if you were to go 0.8c in deep space?"

And the other one: "How would a ship passing by you at pretty much 1c look like if it were to go the other way?"

Maybe the answer to one is also the answer to the other, but again I don't know.

EDIT #1 Here are some WIP Pictures of the Situation. Not renders because, as it turns out, in deep space there really is no sun :D

enter image description here

This shows the 2 Stages of Modelling most things. One very low detail mock up to get the idea across and then the high detail one, which as you can see is still WIP. You can see the Multi Layered Shield of the Craft, the Radiators are still missing though.

enter image description here

This one shows what everything might look like, at least without fancy light. The Europa is around 150km away and once it is at its closest point, it will only be 100km away. The Main shield is already out of view at this point. Also, Human for scale.

Qmechanic
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Erik Hall
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  • Hi! Maybe a picture of the situation will clarify the question even more (though you explained the problem very well!). Why is the abbreviation ITV and not ISV? – Deschele Schilder Oct 09 '20 at 11:27
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    Hello there :D I hope the Clay Viewport Images helped a bit. @m4r35n357 gave me a really good video and i think it is possible to just create a programm that displays all the effects at this speed in an accurat way. Famous last words. ITV stands for Interstellar Transport Vehicle. I thought it made more sense as these ships main objective is to carry stuff and people from a to b. – Erik Hall Oct 09 '20 at 11:57
  • Not renders because, as it turns out, in deep space there really is no sun Good point! That's what I always think when I see SF movies where you see spaceships floating in deep space, between the stars. "Where are the huge studio lights...?", I ask myself. Succes with your project!!! – Deschele Schilder Oct 09 '20 at 19:38

2 Answers2

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Surprisingly, 0.8c is not really fast enough to do anything visually freaky! You need to go much closer to the speed of light (according to some observer or "scene").

What you actually see is rather more complicated than the "compressed" scenery in most pop-sci "explanations" (looking at you, Mr Tompkins!). It is described by a combination of Doppler Effect (red/blue shift), and relativistic beaming (brighter in front, darker behind), aberration (things you have gone past can appear to the side in front of you!). All these effects are derived from the Lorentz Transformation, but the transformation is not the whole story.

Anyhow, enough bluster, there are a few artifacts on the internet that can give you some idea:

This really old video

A Slower Speed of Light (unfortunately now abandonware)

My videos

Of course there are plenty of others, but you should now have enough pointers to look around for yourself!

m4r35n357
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  • Not gona lie, the old video is gold. It shows the effects which should be easy to copy inside the 3D Software. Although it will be a shi*show getting everything to work as it should the first time. As always with equations... I love the game. Really trippy. Is it ok if i get back to you with a basic Shader Setup ? Aka a look at how things would look according to my now updated understanding . – Erik Hall Oct 09 '20 at 12:11
  • @ErikHall no point I'm afraid, I know nothing about shaders, I made my videos using POVray, a ray-tracer! http://povray.org/ – m4r35n357 Oct 09 '20 at 17:27
  • In that really old video, 0.8 c is apparently enough to see a whole bunch of relativistic effects, so I am confused at your statement that it is not fast enough to see anything interesting. – CR Drost Oct 09 '20 at 19:36
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    I think he meant this in terms of what you would see in deep space. In created a shader with all the effects as shown in the video and tbh, there aint a lot to see till .95c. The Red / Blueshifting is just about the only thing happening and even then, its not a lot at 0.8c. So really the lack of any light is the problem. But the Redshift looks really cool – Erik Hall Oct 09 '20 at 20:26
  • @ErikHall Be warned the colors in "A Slower Speed of Light" are 100% wrong. Their Doppler shift simulation makes no sense at all. The colors in the first video (rendered by Backlight) seem more plausible. – benrg Oct 09 '20 at 22:57
  • @CRDrost I specifically used the word "freaky". Of course the effects are noticeable, but not nearly enough to justify their inclusion in a computer game! – m4r35n357 Oct 10 '20 at 08:38
  • I had a look at some of your videos just now. I had watched some of them a long time ago having seen a link to them on SE but I didn't comment because I could not make much sense of them. I did not, until just now, notice the clock in the upper left hand corner of the screen. The vids make a little more sense now (10 % compared to 5 percent in the past). I am in awe of anyone who can code graphics like yours, and I wish I could. I am a beginner student of Python, and have coded along with one or two YouTube videos showing some simple projects making graphics in 3D using Python and OpenGL. – Matthew Christopher Bartsh Apr 21 '23 at 14:56
  • Have you read Relativity Visualized by L Epstein? It was only after reading that (my third book on relativity) that I got a grip on the basics of it. I then saw how ,many authors of books about relativity failed to maintain a clear distinction between how things are in each frame of reference, and how things appear. For example, a moving clock runs slow, always, although it can sometimes appear through a telescope going by the image to be running fast. – Matthew Christopher Bartsh Apr 21 '23 at 15:11
  • Likewise a moving rod (or clock) is shortened in the direction it is moving, but it only appears to be rotated. It looks blue-shifted through a telescope, but this is only the appearance, a mere trick of the light. Everywhere, I see physicists say things like a moving clock appears to run slow, and appears contracted and rotated. This is very confusing, because it conflates mere tricks of the light with the real situation. The twin paradox was I guess designed to originally to highlight that some of the effects in this case time dilation in SR, are absolutely real in every sense. – Matthew Christopher Bartsh Apr 21 '23 at 15:12
  • Therefore there are two stages to making a game like a slowed down speed of light or whatever it was called. First the code must calculate the actual situation in the frame of the player's character, and I'd hope that would include the time shown on each of a large number of clocks, and what the position and shape of each clock would be taking into account shortening, and then the code must work out how all those clocks would look, including the effects of blue or red shifting, and other illusory effects caused by signal delay such as rotation, and wrong reading of time displayed by clocks. – Matthew Christopher Bartsh Apr 21 '23 at 15:22
  • In my question the other day: https://physics.stackexchange.com/q/760414/295887 How difficult would it be to make an accurate and complete computer animation of the twins paradox of special relativity? what I had in mind was a simulation with two settings. – Matthew Christopher Bartsh Apr 21 '23 at 15:37
  • On one setting you see what is in each frame. On the other you see what is in each frame distorted by the tricks of the light and thus you see what an observer would see looking through a telescope. If the difference between these settings is not clear, read my https://physics.stackexchange.com/questions/662666/what-is-the-meaning-of-clocks-and-rods-in-special-relativity/718723#718723 (this explains the meaning of a frame of reference in SR and the how to measure velocity, length, and time in SR. - quite a lot actually). Writing such code could be done in two stages, I would guess. – Matthew Christopher Bartsh Apr 21 '23 at 15:37
  • And having completed stage one, you'd have something extremely useful, and as far as I know, unique, a simulation that showed you what is in each frame (of reference, of course), without the obfuscating, and, to me, less interesting optical illusions. Oh, and I'd have all major objects be asymmetrical and either right or left handed. I thought it was a mistake to make that gate in "a slower speed of light" symmetrical. – Matthew Christopher Bartsh Apr 21 '23 at 15:38
  • In short, "what you see" is a bit ambiguous in relativity. Some take it to mean what happens in your frame reference (i.e. what you would detect using a rods and clocks framework), such as time dilations and Lorentz contractions. Others take it to mean the tricks of the light like blue shifting, and moving images of fast-moving clocks, and apparent (illusory) rotation of objects. L. Epstein put it this way: "What you see is not what happens." – Matthew Christopher Bartsh Apr 23 '23 at 19:14
  • It is not ambiguous in the slightest. What you see is what intercepts your retina. Anything else is not what you see. My videos show what hits your retina. – m4r35n357 Apr 24 '23 at 08:07
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This problem is best treated from the rest frame of the Europa (the ship being photographed), not the Sudux (the ship taking the photographs).

In that frame, the Europa is at rest for a long period of time, and space around it is filled with a static pattern of light. Ordinary 3D renderers simulate a camera at rest somewhere in this space. You want a camera in motion somewhere in this space.

If you idealize the camera as a pinhole camera with an infinitesimal shutter time, then a moving camera and a stationary camera detect the same light if their pinhole is at the same location when the shutter opens. The actual photo looks different because of what happens to the light after it's passed the aperture. You can simulate this by transforming the light between the Europa and Sudux frames at the aperture, and doing a standard simulation of the camera interior.

To summarize: work out the position (in Europa's rest frame) where each frame of the video will be taken, render to a cube map with an ordinary 3D renderer, then "distort" it with aberration, Doppler shift, and brightening/dimming. This will get you an accurate simulated image without the need to import your models into some obscure relativistic renderer with limited features. You still need a simple relativistic ray tracer, but it only has to support a static skybox at infinity.

(Fisheye Quake is an old project that used this technique to simulate a different kind of lens distortion.)

To calculate the aberration and Doppler shift, for each pixel on the camera's sensor, calculate a unit vector representing a ray at the aperture using standard ray-tracing math, then add a time component equal to -1 (so you now have a lightlike four-vector), then Lorentz transform it from the Sudux frame to the Europa frame. The time component of the result is (the negative of) the Doppler shift factor, and the spatial components are the direction in which you should shoot the ray to the cube map. The brightening/dimming factor can probably be approximated accurately enough by the product of the angular difference between adjacent horizontal and vertical pixels. (This will cause vignetting even in a camera at rest, so you may want to compensate for that.)

If you want a starry background for the shot rather then just blackness, then render the ship to a transparent background, distort it, then composite it on top of a skybox that's distorted by the same algorithm, but using the speed of the Sudux relative to the galaxy instead of relative to the Europa.

Don't forget the gamma factor when calculating the position of the camera. In the Europa rest frame, the separation between the locations of adjacent frames is $γvΔτ$ where $Δτ$ is the proper time interval between frames (e.g. 1/60 second).

To correctly simulate the appearance of a Doppler shifted spectrum, you need to know the whole spectrum, or at least the part of it that's shifted into the visible range. You can't correctly simulate Doppler shift on RGB colors. You could try to correctly simulate the whole spectrum, or you could just fake it. The appearance of surfaces under arbitrarily colored lights can't be correctly simulated in RGB either, but people do it anyway.

benrg
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