Hello.
I recently encountered this web site on my wanderings about the internet, and needless to say am a bit curious about the entire premise of this site. Being a physics major about to enter another year of study, I was naturally drawn to this particular discussion.
This is a VERY long thread, and I read the first few pages (quite a bit), but then skipped to the end and read the last few to see where things stand. Even if I were to grant the Lorentz-based equations that were provided at the beginning of this thread were correct (I will have advanced far enough in math to check them myself by this winter), and accept that even though from an inertial frame of reference the Earth appears to have an exponentially decreasing acceleration that the Earth itself would still feel a constant acceleration, there is still a glaring question that comes to mind:
Where is the energy coming from?
As pointed out much earlier, getting to light speed from ANY frame of reference would require infinite time (good for the acceleration argument for Earth's gravity), but it also requires an infinite amount of energy.
In the real world, objects do not simply accelerate for no reason. Objects accelerate when they have a force exerted on them. The application of a force, any force, no matter the origin, on any given object for any period of time constitutes a transfer of energy. If an object is accelerating, then some kind of energy is being transformed into kinetic energy in the object.
So, granting any mechanism you want for the acceleration of not just the Earth-disk but also every observable celestial object, be it futuristic warp fields, giant rockets on the underside of the Earth-disk, or maybe just those turtles underneath there just running really fast (on what I can't imagine), there still remains the problem of the source of this enormous amount of energy.
Even though I didn't read it directly, I did see posts referencing Dark/Zero-point energy as a potential source. If someone could provide an explanation on how this energy is converted oh-so-conveniently into our forward motion, or point me to the post where this is stated, I would appreciate it.
Aside from the mechanism of transfer of energy, and why it is conveniently transferring it at just the right rate for a reasonable simulated-gravitational field for humans and the rest on life on this planet to live and evolve in, I would like to point out that most evidence points towards zero-point energy being vanishingly small, much too small to extract any useful work on the macro, or even the micro scale. You can read more in this Scientific American article here:
http://www.padrak.com/ine/ZPESCIAM.html