The sense of touch and balance in humans provides an instinctive understanding of the concept of force. Sir Isaac Newton contributed a mathematical model that quantifies the definition in terms of classical physics. Key to understanding the concept is the notion that the natural state of a mass is to stay in motion at a constant speed (or at rest if that speed is 0). Speed can only be changed in response to a force, and every force has an equal and opposite reaction that conserves the energy of the system.

In the classical sense, physical force is defined as the rate of change of speed multiplied by the mass of the object. Einstein's theory of relativity altered the notion of mass however. In the new theory, mass is a measure of the energy reserve required to sustain the existence of a compound or particle as a directive entity separate than an electro-magnetic wave.

The formula for defining mass in this new equation is derived from Einstein's relativistic energy-momentum equation where p represents the total momentum of the frame of reference:

Rearranging the above formula to solve for the resting mass yields:

The final form uses the relationship that defines the square of the spped of light as the inverse of the product of electric permitivity and magnetic permeability.

Newton's definition of force holds in relativistic theory only if it is more strictly defined to be the rate of change of relativistic momentum as seen by an observer travelling at a relative speed of v. This is as expressed by:

The above equation is helpful from a conceptual viewpoint because it relates force to the electrical, magnetic and time-varying distance of an object, and includes not only the energy that defines and maintains the physical integrity of the particle(s) but also the speed of waves moving through free space. Instead of having to imagine equal and opposite reactions in terms of masses moving in opposite directions, we can think of oscillations of charged particles in phases of compression and expansion.

When talking about electric charge and current, this representation of force is insightful since the work done by electric fields is the same per unit charge whether the mass is as large as a planet or as small as an electron. No work can be performed by an electric force on a mass of 0 charge. This alters the notion of current as the motion of massive electrons.

Because a moving charge generates magnetic force, the physics of electricty is complicated. The interactions make it much more likely that electrical energy is transmitted in waves. In wave transmission, the individual disturbances of particles allow energy to travel without permanently displacing the particle. The energy moves from one particle to the next irrespective of the mass of the particle. If the energy is not propogated onward, it is either reflected or absorbed.