Matter on matter?

Question

I have been told that every body of matter (everything from the pencil I used to write this all the way to planet Earth) exerts a graviational-like force on every other body of matter. In other words: I'm somehow exerting a force on the computer screen that I'm using, not to mention everything else in this room.

But how does this theory fit in with Einsteins concept of gravity, where gravity is a direct result of the geometrical curvature of space.

Answer 1

The Newtonian theory of universal gravitation which you correctly described, is an approximation which can be derived from the Einstein theory.

In Einstein's theory there's a gravitational field, i.e. set of continuous variables, throughout space which are interpreted as describing the geometry of spacetime at each point. The ultimate source of the field is matter (energy-momentum) but the effect of any bit of matter propagates at a finite speed and interacts with the effects of other gravitational sources in a complicated way.

The basis for the (Newtonian) approximation is that the field is normally extremely weak, that is, the deviation from "flat" space is very tiny. That tiny deviation from flatness is what appears as a (gravitational) force in ordinary experience. Because the field is so weak and all sources and objects are travelling slowly (compared to the speed of light), two things are *approximately* true of the gravitational field seen at any one particular point:

(1) It depends on the instantaneous (i.e. present) locations of all sources.
(2) The contributions of all those sources are additive.

Because of this, the concept of the field can be dispensed with in the Newtonian approximation. Newton didn't know anything about fields and just described gravitation as a direct force acting between every pair of objects.

Answer 2

But it's mass that bends space.