General relativity says that the force of gravity is felt the same way an acceleration is felt. If you are travelling in a car and you press harder on the accelerator, the forward force of the car from the wheels pushing against the road is somewhat greater than all the forces in the opposite direction (wind resistance, friction, etc.) There is a net forward force and the rate at which you travel forward increases until a new equilibrium is reached with the opposing forces and your velocity becomes constant. During acceleration the seat was pressing against your back because there was a net forward force. This is not the result of the seat emitting more gravitons that it would otherwise (the gravitational force of the seat is negligible).
Gravity behaves a little differently. I feel the force of the Earth and I am accelerating towards it, but my feet have met the ground, which pushes up with equal and opposite force. The net force is zero and therefore my position does not change. The SOURCE of the gravitational force can be said to be matter, which is emitting gravitons, but accelerations can come from other sources (e.g. electric or magnetic fields, being in a car and depressing the accelerator, etc.)
Answered by: Mikhail Klassen, Applied Physics Undergrad Student, Columbia U, NY
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