Modern inertial mass is a seminal concept in Newton's work. Inertial mass refers to a static concept. A picture. Inertial mass refers to an object's resistance to being pushed and pulled by other objects in the vicinity. In this context we could replace the word 'object' with 'atom' or 'proton'. Then we have to ask ourselves how is it that this object, this atom, resists being pushed or pulled by other objects in the vicinity? The reasonable explanation seems that an atom's resistance originates in all the atoms of the Universe gently nudging that atom from all directions . . . toward them. AS WELL that sample atom gently nudging on all atoms of the Universe toward it. All the atoms of the Universe are in a constant tension with one another. When an atom assumes a succession of locations all atoms of the Universe gently nudge on it and it gently nudges on all atoms.
When a proton (or H atom) moves in a given direction by the proton's in the vicinity, for example in what we call gravity, the same is tugged in the opposite direction by all other atoms of the Universe. Inertial mass is always in the direction(s) opposite the net effect of gravity. It seems very reasonable to assume that all the atoms of the Universe are physically connected by some sort of fundamental object that is inherent to the atoms, to the very protons themselves . . . ALL OF THEM.
Newton came very close to this conclusion when since he thought that the resistive forces were innate to the object. He uses the expression "innate force possessed by an object" or "innate resistive forces". What he failed to do is explain HOW or WHY these resistive forces are innate to all objects, and in our modern context all atoms. He did not understand the Form of an atom. An atom derives, or assumes it's Form from the same object that performs the work of light, gravity and inertia to and from all atoms. We could call this a double helix EM Thread, and there is a grand scope of implications that such an assumption entails. The object that performs the work of light to and from all atoms has wholly unique properties (such as the ability to superpose, overlap, or intersect without disturbance up to some critical anomaly or density). These properties are assumed by the atom itself for the atom seems to assume its Form from the same object. This is one of the reason's why we have seemingly inexplicable anomalies at the quantum scale.
When two objects, say stars, like the Sun and the Earth come close, the number of these double helix thread connections INCREASES, exponentially in effectiveness. A decrease in distance, between the two sample objects in Newton's equation, say Earth and Sun, spontaneously generates a geometric increase in the number of effective thread like EM helices connecting all the atoms of these two objects. The M1 and M2 in Newton's equation represent the number of potential connections. When Earth and Sun are theoretically separated at great distances, beyond the inverse square regime, the nudging between the two is unidirectional and this would perhaps almost be the same between Earth and a star in Andromeda. Ineffective in terms of the concept of gravity, but effective in terms of inertia. When the two stars come close enough, many pairs of atoms are in a sideways tension with one another at various angles. The tension is multi-directional, a sideways tension from multiple locations. Effective. The 'innate resistive forces' are happening at various angles between the two objects considered in the equation and used for explanation. The net effect of local tension (gravity) is as if objects are being pulled straight down toward one another, but in statement in fact in assumption, an astronomical object like Earth or Sun would have effective EM ropes from multiple locations opposite the target object considered. Many pair of atoms between these two objects are in tension with one another at various angles. The closer they are the steeper the angles of many atoms nudging on one another.
We can use this assumption that all the atoms of the Universe are connected by an double helix EM thread to make manifest and define inertial mass so that this concept is crisp, clear and used consistently in all physical contexts. For example we could use this definition in context to Einstein's equation. That equation seems to tell us that inertial mass is inseparable from the work of light because we have c squared on the right side of the equation with m. Atoms constantly flickering light signals to and from all atoms via the fundamental physical mediator of light (which connects all atoms) maintains this bi-directional tension necessary to explain inertia. This bi-directional tension maintained by the atom's constant work of light (or radiation) obeys Newton's action-reaction principle. For every radiation the atom performs there is an equal and opposite reaction. From here we could get into Mach's principle.
E on the left side of Einstein's equation refers to an atom's capacity to do the work of light. All E does is calculate an object's capacity to do the work of light, specifically receive and send off light signals. What is interesting is that the more resistance an object has to being pushed or pulled is proportional to that object's capacity to do the work of light. An exponential increase in an object's 'Energy' or capacity to do the work of light seems to imply that that object has more fundamental and permanent connections to all the atoms of the Universe. So a Caesium atom has more fundamental and permanent connections to all the atoms of the Universe than a Hydrogen atom.
Matter is an ill-defined concept come out of Greece.
We could define it as the set of objects, or the set of existing objects.
The fundamental unit of matter is the atom, but there also seems to be an object that is more fundamental connecting all atoms and from which all atoms are derived. This is an EM Rope or double helix thread. This object is inseparable to all the base hydrogen atoms (or protons), or in other words the proton assumes its Form or derives its From from this fundamental object.
Object refers to that which has Form
Exist refers to that which has Form and location OR simply that which stands out. Atoms and the fundamental object connecting all atoms exists in spite of the fact that the features of the atom (e.g. proton, electron, neutron) as well as the fundamental object has unique properties, such as the ability to superpose, overlap or intersect to a critical density or critical anomaly which initiates fundamental interactions (such as light, push, pull, etc.).
Mass (Inertial) refers to an an object's resistance to being pushed or pulled by objects in its close vicinity.
Energy refers to an object's capacity to do work (in Einstein's equation the work referred to is distinctly the work of light or radiation)