Is Flat-Earth's Gravity Theory Flawed Due to Relativistic Acceleration?

[Mentallic]

I just recently heard about how this small but still existent flat-Earth society believe that gravity on our supposedly flat Earth is caused by the Earth always moving upward at a constant velocity.
Now obviously assuming the Earth is flat and that gravity isn't caused by mass attraction, then this still couldn't be the case because you would need a constant acceleration upwards rather than a constant velocity to have the same effect as gravity.

So I was wondering, in this scenario - whatever the force is that is accelerating the Earth - would it be possible to keep accelerating it indefinitely? From an observer not on the Earth, it would seem that the mass of Earth would increase without bound as it reaches the speed of light and thus the acceleration couldn't be maintained with the same force being applied. However, for an observer on the Earth it would still be experiencing the same acceleration since from its perspective they are still stationary in a sense.

Are both these observations correct? And would observing that the humans on Earth are experiencing the same gravity effects even when their acceleration is now negligible in the other frame of reference be pretty much the same as observing them slowing in time?

 

[quZz]

yes =)
p.s. "flat-Earth society" - fantastic...

 

[DrGreg]

In relativity, acceleration is relative too. Although all inertial observers agree whether an object is accelerating or not, they disagree over the value of a non-zero acceleration. An inertial observer who is momentarily at rest relative to an accelerating object ("comoving inertial observer") will measure a larger acceleration than observers who have non-zero relative velocity, and the acceleration tends to zero as the relative velocity approaches the speed of light.

The acceleration measured by a comoving inertial observer is called "proper acceleration". It the "g-force" that the object experiences and what is measured by an accelerometer attached to the object.

If the "flat earth" was accelerating upwards with a constant proper acceleration of 1 g, the acceleration measured by an inertial observer would gradually decrease to zero.

 

[Mentallic]

Thanks for your contributions