I wrote a small paper on how to simulate general relativity using a numerical method.

https://github.com/sjhalayka/gr_paper/blob/main/bezier_escape.pdf​

it takes into account deflection and precession. I am wondering if anyone would care to replicate the results using their own code? If so, a modest sum can be sent to your PayPal account. Sorry if this is against the rules.

I added in 8 figures.

Anything else need a diagram?? 🙂

Idk, but i wonder why each of your papers has the same (probably totally unrelated) filename.

Remembering the thread about simulating a universe in java script, could you do the same so we can see results?

Likely it would require to set an observer, simulating anything relative to just that single observer?

Each observer (say, a sun or galaxy) would then show a different cut of space time?

Which then would basically mean that reality is unique to everybody?
So everybody has his own unique universe? Not really different from imaginary reality, or parallel universes?

Despite the confusion, could this give an interesting mechanic for a universe management sim?

Yes I’m too lazy to rename the files. LOL

I have C++ / OpenGL 1.x / GLUT codes for the whole thing, but I’m reluctant to release it without it being verified first. The precession diagram was drawn using OpenGL.

I try not to think too hard about things like the universe splitting in two every time that an observation is made.

P.s. Thanks for your input!

taby said:
I try not to think too hard about things like the universe splitting in two every time that an observation is made.

I did not mean the quantum stuff. I was thinking maybe relativity hints at many worlds too.
Because if i think of simulating two guys, one on earth, and the other flying towards a black hole, could i even do this by using only one simulation? Or would i need two simulations?
I guess just one would work if we simulate curvature of space time properly.
But if it can't work, then this would hint reality is local and not the same from any point.

Well, i guess that's all nonsense, but then coincidentally YT has proposed me this video:

So although that's something slightly different, i'm not totally off :D

Ahh, I see what you mean by that video that you linked to. It's the difference between coordinate time and proper time. Plus, to the person close to the black hole, events outside of the black hole appear to speed up. So yes, it is relative to the observer.

P.S. The coordinate time keeps track at infinity distance. The proper time keeps track at close distance. The closer you go to the gravitating body, the slower your clock goes. Thus proper time is less than coordinate time. I think that's how it works.

Define ‘coordinate time’ and 'proper time'.

I have just realized we probably need to have local time?
So something like this:

struct Particle
{
	vec3 pos;
	vec3 vel;
	float localTime;
	float mass;
};

Then could probably do my earth and black hole guys?
I could do either: Use large timesteps for earth guy, but small timesteps for black hole guy. (Or vice versa?)

How could i calculate the timesteps for both, given some scaling factor to define precision, and knowing their surrounding mass?

JoeJ said:

Define ‘coordinate time’ and 'proper time'.

Coordinate time is the time kept by someone in flat spacetime, like at an infinite distance away from the gravitating body and no velocity. The proper time is the time kept by someone who is speeding or is close to the gravitating body, or both. I'm not sure how else to describe it. As one gets closer and closer, the time tick rate on their clock slows. When the proper time clock and coordinate time clocks are compared, it will be found that the proper time tick rate is not as large as the coordinate time tick rate.

I have just realized we probably need to have local time?
So something like this:

struct Particle
{
	vec3 pos;
	vec3 vel;
	float localTime;
	float mass;
};

Then could probably do my earth and black hole guys?
I could do either: Use large timesteps for earth guy, but small timesteps for black hole guy. (Or vice versa?)

How could i calculate the timesteps for both, given some scaling factor to define precision, and knowing their surrounding mass?

Well, in my simulations, I use a number of different time steps. For Shapiro delay, I used a time step of 1/c, for instance.