I use the word separation in place of distance or length because for me the word separation infers the existence of two distinct objects. I use the word time to represent a measurement of how long something continues to exist, or to put it another way, I use the word time to mean the measurement of time. Time seems to be a concept which is based on our observation of a steady and uniform repetition of object separations. If you want to consider life, birth and aging processes, I would relate time to atomic- and molecular-scale contact and separation processes which include force fields. At the atomic scale, the existence of time may become quite variable like an on and off chance condition. Thus, I do not consider time to exist except as a measurement of an interactive process between objects.

The derivative of separation (s) with respect to time (t) is ds/dt, where dt may be measured in terms of a cyclic dS, wherein the dS is representative of the cyclic space repetition and infers some kind of movement between objects. This movement between objects introduces the concept of velocity. Even the cyclic frequency emitted by an atomic clock, or a blinking light means nothing unless we can relate it to the change in position or state of objects we observe.

In the first derivative (ds/dt) we see a changing separation at a constant rate. We call this a constant velocity (v). A velocity ds/dt cannot develop without an acceleration event. With velocity, objects may come into contact, join, bounce apart, or damage the condition of each other. We feel no force moving at a constant velocity.

In the second derivative, d2s/dt2 = dv/dt, we see separation changing at an increasing rate. This is acceleration of separation. It is the velocity that is now changing at a constant rate, which is also called acceleration. We sense this as a force, a fixed constant force. This is an acceleration of a steady constant value, and velocity might approach infinite values if a resistance is not encountered. We do not see infinite object velocities with our limited senses. Thus some form of resistance appears to be present to limit object velocities. We perceive a force on a mass as being required to produce acceleration. Thus the paradigm limitation of E = mc2, and the speed of light limitation. This introduces a circular argument of physics because classical physics is based upon and limited to its expression in the form of F = ma. I do not see that Einstein did much to change that.

The third derivative is d3s/dt3 = d2v/dt2 = da/dt. Acceleration a is no longer constant, it is changing at a constant rate, velocity is changing at an increasing rate, and separation has become absolutely livid, having no idea of whatever happened to the concept of a spatial separation. A simple take on the third derivative is that the force is increasing at a constant rate, just as the acceleration is increasing at a constant rate. The problem is that you cannot continue to increase acceleration or force very long before things start coming apart. We don’t have much sense of the third derivative beyond that of an impact. Thus, the third derivative enters the experience of sound shock waves, impacts and onset rates, wherein materials fail structurally or deform locally rather than move. The impact of a hammer at the end of a long steel bar does not move the bar if the onset rate is fast enough. This property is dependent on the response of molecular bonds in the steel material that is being affected by the third derivative. We see it as simply a matter of brute force, and of how fast it is applied. However, the amount of force and how fast force is applied are quite different matters, since response time (da/dt) now becomes an important factor. The fact is, we are fairly limited as to how fast we can apply a force, explosions being the primary technique.

The fourth derivative is d4s/dt4 = d3v/dt3 = d2a/dt2 = W. Separation by now is a mere abstraction and any sense of separation is little more than a theoretical mathematical pipe dream. Even the concept of velocity is starting to get jerked around pretty badly. Our human senses can no longer cope with what is happening, let alone our body processes. People who got seasick with the simple da/dt have long since dropped dead.

A lot can be imagined at d2a/dt2. Force is no longer changing at a constant rate, but at an increasing rate (be it + or -), and may need to be cyclic to exist. How quickly it increases can become hard to imagine. A second derivative of acceleration is an acceleration of the already increasing acceleration rate. Even concepts of the atom become endangered by such a derivative. Could an atom respond to such an onset other than to be utterly smashed to bits? Of course, when we think of atomic dynamics we are still in the realm of second derivatives, velocities and accelerations. Energy, which sort of deals with force and distance (or velocities) has also sort of lost its meaning. After all, distance is now a mere abstraction, irrelevant in this world.

We can imagine the fourth derivative as one of accelerating forces, a hard thing to measure. A lightning or spark discharge might represent this condition. It is a world just on the edge of our ability to study. It is the world of atomic forces and interactions which we can hardly know. Is a spark discharge our only sense of what happens at the fourth derivative? What about quantum effects? Are these an exhibition of the fourth derivative? Certainly time has no meaning, even though we use it to express a fourth derivative. Remember, time as we define it is really based on separation changes in a constant repetitious manner. We might just as well say that separation distances are changing with such a nonlinear accelerating rapidity that our simple expressions of electric and magnetic forces might be very misleading in our models of the atom. I am at a loss in trying to imagine a fifth derivative of distance. Distance has lost its meaning, as also have time and energy.

The speed of light is a constant of interaction between the electric and magnetic forces of an atom. It has the units of velocity by definition. This constant of interaction does not establish the existence of time (or velocity), but rather a method of measuring with an electrodynamic interaction which occurs at a constant value, and which we can then relate to the larger world around us, or vice-versa. We can give third and fourth derivatives real meaning, but this has been difficult to express in the form of physical laws which exist beyond our senses.'