How does the theory of field forces explain how objects could exert force on each other without touching?

Explanation:

          Every particle in nature have its own field forces. In the universe, a mass will have its gravitational field and will attract other mass towards it. And charges have their electrical field which will either attract or repel other charges depending upon the nature of their charges.

          This is given by Newton's law of gravitation, which states that very object in the universe will attract every other object by a force which acts along a line of intersection of the two points.

         Similarly, Coulombs law of electrical forces states that every charge attracts or repels other charges in their field of forces depending on their charges.

         Thus,  every objects exerts a force on each other when their fields interact with each other.

there is an explationation of this on a site called crash   course world history 1

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