General Relativity is an upwardly accelerating earth simulator.
Relativity and Accelerating Upwards:Consider a skydiver jumping out of an airplane. The skydiver falls freely, up to the effects of air resistance. According to Einstein, the skydiver's path is the straightest line possible through the curved space-time around the Earth. From the skydiver's perspective this seems quite natural. Except for the air rushing past her, the skydiver feels no perturbing forces at all. In fact, if it weren't for the air resistance, she would experience weightlessness in the same way that an astronaut does in orbit. The only reason we think the skydiver is accelerating is because we are used to using the surface of the Earth as our frame of reference. If we free ourselves from this convention, then we have no reason to think the skydiver is accelerating at all.
Now consider yourself on the ground, looking up at the falling daredevil. Normally, your intuitive description of your own motion would be that you are stationary. But again this is only because of our slavish regard to the Earth as the arbiter of what is at rest and what is moving. Free yourself from this prison, and you realize that you are, in fact, accelerating. You feel a force on the soles of your feet that pushes you upwards, in the same way that you would if you were in a lift that accelerated upwards very quickly. In Einstein's picture there is no difference between your experience sanding on Earth and your experience in the lift. In both situations you are accelerating upwards. In the latter situation it is the lift that is responsible for your acceleration. In the former, it is the fact that the Earth is solid that pushes you upwards through space-time, knocking you off your free-fall trajectory. That the surface of the Earth can accelerate upwards at every point on its surface, and remain as a solid object, is because it exists in a curved space-time and not in a flat space.
With this change in perspective the true nature of gravity becomes apparent. The free falling skydiver is brought to Earth because the space-time through which she falls is curved. It is not an external force that tugs her downwards, but her own natural motion through a curved space. On the other hand, as a person standing on the ground, the pressure you feel on the soles of your feet is due to the rigidity of the Earth pushing you upwards. Again, there is no external force pulling you to Earth. It is only the electrostatic forces in the rocks below your feet that keep the ground rigid, and that prevents you from taking what would be your natural motion (which would also be free fall).
So, if we free ourselves from defining our motion with respect to the surface of the Earth we realize that the skydiver is not accelerating, while the person who stands on the surface of the Earth is accelerating. Just the opposite of what we usually think. Going back to Galileo's experiment on the leaning tower of Pisa, we can now see why he observed all of his cannonballs to fall at the same rate. It wasn't really the cannonballs that were accelerating away from Galileo at all, it was Galileo that was accelerating away from the cannonballs!
See the bolded. "In both situations you are accelerating upwards" and the Earth is "pushing you upwards through space-time."
Different bodies have different weights because the Earth is accelerating upwards, pushing itself into bodies which have different inertial resistances to being moved through space.
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