A fundamental assumption is an assumption which underlies assumptions. Since this blog is written by a Christian lets take the example of the branch of theology known as Christology. Christology is the study of Christ Jesus. A fundamental assumption of Christology: Christ Jesus is fully God and fully man. If you abandon this fundamental assumption in your study of Christ Jesus your explanations will fail.
A fundamental assumption in physics is all objects are interconnected. All atoms are connected to all other atoms. All objects made of atoms are connected to all other objects made of atoms. All matter is one network. There is no such thing as a discrete particle. Not in this universe. This assumption is simple and yet in its totality complex and subtle beyond imagination. It is profound.
This fundamental assumption is intuitive to human persons. The secretary at my workplace tells me everything is connected. She might not be able to explain why, but she knows. This assumption is not a wives tale or some New-Age non-sense. It is common sense. Try telling a mother that her body is not connected to her child's body after he or she exits the womb.
The connection is not conceptual. The connection is not merely spiritual or psychological. The connection is physical: objects interconnect with objects via objects. We are not angels, and we do not live in a universe made of spiritual substances. All things are connected to all other things physically by way of physical mediators inherent to the atoms.
It is rational to hold this assumption for this is the only way action-at-a-distance i.e. non-local interaction of objects, could be explained. The mediators between all atoms are not a concept, e.g. spacetime. They are real 3D threads, intrinsic to the atoms. God created them. They are objects. They have shape. They meet, weaving atomic shells. These threads are the fundamental physical substance. They have unique standalone properties consistent with light phenomenon, e.g. they can pass right through one another like two light beams; they can superimpose like light, clustered objects can pass right through them like they can through light.
There are no discrete particles in the universe. In this 2D cross-section picture of two gold atoms colliding I see threads radially dispersing from the electron shell, not discrete particles or mere waves:
Image: Brookhaven National Lab
Blessed Anne Catherine Emmerich described that all things are connected. She says:
I saw the interior, the organs of man as if in the flesh, in corporeal, corruptible images of creatures, as well as their relations with one another, from the stars down to the tiniest living thing. All exert an influence on man. He is connected with all of them; he must act and struggle against them, and from them suffer. But I cannot express it clearly since I, too, am a member of the fallen race. (Mysteries of the Old Testament)
How could stars exert an influence on man unless the atoms in his body were connected with all the atoms of the stars through physical mediators? All things are connected with all other things via threads and this is what enables relations such as light and gravity. Light and gravity are mediated by way of real threads intrinsic to the atoms themselves. It can be no other way.