I think this depends on the nature of space itself. Are we just objects sitting on top of space, or are we composed of space in the same way that the the surface of a balloon is? If we look at your model, it looks as if you're postulating a kind of "friction" between objects and space. That's why the discs with springs will only move further apart a little bit. If the rubber sheet was completely smooth, there would never be any increase in distance whatsoever since they'll just "slip" over it.

If there is no friction, then it doesn't matter even if there is acceleration. Like if it was a sheet of ice instead of rubber, everything would just sort of slide around. What is this friction, how do we measure it, what causes it...? I'm not really aware of such a mathematical quantity. For these reasons I'm just assuming that we're more than just objects in space. We are space.

And of course I could be wrong. I have no idea really...

Well, in a spring case the attraction increases with distance (upto a point of course). But I think if the rubber sheet was stretching and pulling the two balls along with it (balls are 3-D objects, so to make it a better analogy we should perhaps be talking about infinitely thin disks sitting on the rubber sheet) then the spring will eventually stretch, stretch and snap...

In this case, yes the line is paint and is sitting on the surface of the balloon. It's an imperfect analogy. But we're not just objects "on" space. We are space in addition to bending/warping it or whatever. So while all objects will increase in size, I don't think there's any data to indicate that the fundamental constants will change. So in a simplistic model if we look at the force of attraction between a nucleus and an electron via the inverse square law of electromagnetism, the increased distance will eventually reduce the force between the two causing the electrons to slip away. And the nucleus itself will burst apart.

Of course it could also be that I understand none of this and that I'm talking off the top of my head :) . In fact, that is most likely the case!

In this case, you're not pulling the ruler. You're stretching the very fabric of reality itself. The ruler becoming longer is just a side effect. Think of it as a line on a balloon. When you blow air into the balloon, you're not pulling the line itself. But because the balloon is becoming larger, the line just happens to increase in length.

The force should keep decreasing as the distance increases regardless of acceleration. I mean, space expansion is accelerating, but I don't think that should make a difference to the rip...

I thought hyperspace was supposed to be a fictional alternate dimension ala Asimov. What has that got to do with the bending of spacetime by objects?

The attraction is a function of distance - the inverse square or whatever is the equivalent in the quantum world. The strong force in particular works only when the nucleus is tightly bound. Any relaxation in the distances should destabilize the whole thing. So yeah, we will eventually get ripped open. Even atom in our substance will disintegrate.

Space itself is expanding and there is no limit to how fast that can happen. It can be at 1000 times the value of c if necessary.

The speed of light in a vacuum is always c. It doesn't matter if you're moving at 0.9c. If you shine a torch of light ahead of you, it will still move at speed "c".

What is meant here however is that there is no limit to how fast space itself can expand. So say we have two ends of a ruler 1 meter apart. After a while, space itself would expand meaning that the ruler will now be longer than what it was. There is no theoretical limit to how fast this can happen. It can be greater than c.

After a while, the space between the nucleus and electrons or within the nucleus itself will become too large, ultimately ripping apart for the fabric of reality itself.

Wormholes ok, they at least have a theoretical framework in modern science. Warp drives...well if you're talking about moving a space bubble relative to space itself. But since when did "hyperspace" become even a remotely scientific theory?

Tell that to the photons reaching us from the event for whom it literally just happened. There's no such thing as an absolute time scale. Thank you special theory of relativity!

I'm a very happy product...

Well, I don't know if other people are conscious. I only know that I am. And there's no reason for me to think I''m not a machine. I'm a biological robot after all...

Or did no one think of that? Reminds me of some other science paper which said that no machine can ever be conscious. As if somehow we are not machines.

So dumb...

How is the brain not a computer? Pfft...ridiculous conclusions.