Simplified general relativity simulation

Question

I've been thinking how massive space battles might play out when vessels travel at significant portions of the speed of light (e.g. 0.01c-0.2c). I wondered if it was possible to simulate such actions from the perspective of a single reference frame (i.e. from a fleet commander's perspective on one of the ships). It intrigues me how the perception of the battlefield would be out of date (proportional to distance); also, the trade-off between closing speed and reaction time.

I understand the basic principles of special relativity, e.g. time dilation and the constancy of the speed of light in any frame of reference. However, I've read that special relativity breaks down when the objects (ships) are accelerating/changing direction. Is the idea of creating a simulation (and ultimately game mechanic) of relativistic fleet manoeuvers just too complicated; or are there some relatively simple approximations that can be used to realistically give the impression of such battles?

In the simplest form, I could use a 'universal reference frame' and store the history of ship movements, showing where ships were in the past, based on the distance from the observer (and the speed of light); but this seems too minimalistic. I could extend this to making the 'computation time'/actions allowed for each ship be inversely proportional to its speed in that universal reference frame - effectively providing a trade-off between 'universal speed' and the ability to react to changes. These together would present a fun mechanic, but it's not that representative of reality is it particularly with the concept of a universal reference frame?

I would appreciate any suggestions or insights, I'm an experienced computer scientist, and have a basic background in physics (I took some modules at university 20 years ago!), but would be really interested in anything anyone has to contribute.

Answer 1

I wanted to do this several years ago too. Good luck!

If you set-up your game such that it has some fixed points - for example stars around which your bases orbit - that's a natural (although, of course, not unique) frame to use internally as your "master" frame for storing the location of everything. That's part one of your question.

Special relativity can handle acceleration, so you're misinformed on that part. What it cannot handle is gravity in cases where that has important relativistic effects. You can probably set your game up such that you don't enter any such regions, and then you can work in special relativity only. Once you're in a regime where special relativity is appropriate, then you probably don't need serious approximations to the physics beyond that. As your ships move through the space, you'll apply appropriate Lorentz transformations to convert between moving frames and the "master" frame that you're using internally to track the overall positions. There will be some integrals to compute when the ships accelerate, and you'll need to figure out how to estimate those. Standard numerical integration techniques may be sufficient though, depending on your level of fidelity.

Visualization may be an issue (although probably very cool) if you want to be able to "see" the effects of the movement. If you have scenarios where you need to show ships moving at large relative speeds in real time, the you may need to do something like Lorentz transformations on all of the polygons in the visual representation of your ship. That could be intensive.

I just did a search for "acceleration special relativity" in my usual search engine and got a lot of hits. I suggest that you do the same to get more detailed information on that part the question.