You don't really need a local time. That's governed by speed and depth in the gravitational field.

Well, i guess the coordinate time is basically like a Newtonian reference frame for time, similar to our world space for spatial coordinates.

So if we do everything in the coordinate time frame, the timestep for the earth guy would be 1/60.
But the timestep for the black hole guy would be zero at the even horizon.

If so, the problem is, when playing as the black hole guy, we need to integrate infinte timesteps to the earth guy each step. It's like the whole earth future happening in one moment. Impossible to calculate.

So i was thinking we could just use constant timesteps for both, dodging the problem by using local time.
But i see that's wrong and can't work.
To make it work, we would need an entire local reality, unique to both. So basically one has not to bother about the other, somehow. Which makes sense, since one can not affect the other anyway.
That's where my initial idea bout local reality comes from.

But actually i'm just confused.
I did read about Einsteins stuff as a kid, and i've thought i get it.
But later it turned out i do only really understand the things i could simulate with a computer program.
And thus i realize that i do not understand relativity at all. It's not any better than quantum physics. :D

I'm stumped. You bring up very good points.

P.S. The official first version of the paper is at https://www.techrxiv.org/doi/full/10.36227/techrxiv.171470734.46233134/v1

You mention diagrams and figures in the paper, but there are none?

I was thinking more about local reality.
Let's say we want to simulate gravity of a universe.
For practical reasons, we will introduce some level of detail representation.
E.g. Mip maps for a 2D universe. For distant galaxies, we will only integrate low detail texels, each representing many distant galaxies with a single point and mass. Because they are distant, the error is small and acceptable.

Maybe the same works to simulate the universe considering relativity?
If earth solar system is distant, it's local time does not matter, since it will not have much effect on it's center of mass.
So at increasing distance, we can ignore time dilation and change to an increasingly amount.

Thus, i should be able to simulate both my example observers in the same simualtion as desired.
Both have their local clock, both have a different timestep for coordinate time, but both use the same 1/60 timestep for their local clock.

The error would become noticeable only if the black hole astronaut comes back to earth, and his with is still alive.
Luckily true black hole explorers do never come back. >: )

The figures are at the end of the paper.

The Universe is a 3-sphere; the surface of a 4D ball. There is no centre of the Universe. Barnes-Hut?

P.S. https://physics.stackexchange.com/​ is a good place to get answers to physics-related questions. I'd ask for you, but I got banned LOL, cunts.

taby said:
The figures are at the end of the paper.

Oh, indeed. Probably i saw the list of reference and thought it's over.

taby said:
The Universe is a 3-sphere; the surface of a 4D ball.

Why do you think so? Because we have x,y,z and time, so 4 dimensions?
Personally i do not count time as a dimension. I can move forth and back in x, but not in time. So time is not the same as x.

taby said:
Barnes-Hut?

Yeah, i guess that's what i mean with levels of detail.
but maybe it's not just about computational optimizations, but a fundamental property of reality?
Like Heisenbergs uncertainty principle, but at large scales. Maybe you can not measure or define space and time at large distances? Might help to explain why measurements of cosmological constant etc. don't work.

taby said:
P.S. https://physics.stackexchange.com/​ is a good place to get answers to physics-related questions.

I guess they would ban me too. Lacking academic background i would sound like a noob all the time.
Often i do have physics questions, like calculating ground reaction force of a ragdoll, recently.
But i never ask anymore. I just keep trying until i figure it out well enough for my needs.

No, 4D space. I also believe that time is not the same as a spatial location.

But why 4d space? For what is the 4th dimension, and where does it hide?

Well, you could always assume that there is no inside or outside of the universe, only the 3-dimensions. I dunno. 🙂

I see.
Idk if scientists agree on the question ‘what's beyond the universe’. Maybe there is infinite space of nothing, but more likely they claim that spacetime itself does not exist until the universe expands to create it with itself.
Idk. But at least i know that i don't know. Scientists often think they would, but i don't buy it.

One day they will discover certain laws of the universe, and they will confirm and explain why we can't and will never know.
That's all i expect there is to find… ;D