Two of the original architects of the addition of The Fifth Element in the equations of Classical Mechanics are William O. Davis and G. Harry Stine. Both of these men saw the incredible possibilities of what an additional term would mean to advance the art of propulsion systems in the 1960s. Together or separately, they authored numerous articles which explained a great deal of why an additional mathematical term was essential in order to fully explain a whole wrath of observed phenomena.
G. Harry Stine went so far as to write a novel, Stardriver, in which much of the concept (as well as some of the key participants in the research) was discussed at length. The book is very well written -- particularly if you like science fiction. The linked webpage provides a few of the more relevant and enlightening passages.
Curiously, none of the writings departed from mechanics, at least in terms of developing the similarities of form of the differential equations and their solutions of electromagnetic circuits and classical mechanics. Davis did, in one of his notebooks, delve very briefly, tantalizing briefly, into a revision of Maxwell’s Equations (the ones rewritten and heavily edited by Heaviside). But neither apparently left any writings which indicated anything more than propulsion as an object in the overall scheme of things. The topic of energy generation is strangely missing from their work.
Davis did recognize that, ultimately, the driving force in physics must be experiment and observation. This is the stuff of which reality consists. The role of theory, on the other hand, should be limited to those descriptions of the results of experiment and observation which on the one hand suggest new experiments and on the other afford means whereby pure science can be brought into the practical everyday world. In this respect, physical theories are no more than succinct mathematical approximations of reality. Such descriptions are in turn limited by the theory’s fundamental Assumptions (which may be stated or unstated), and from the purely practical viewpoint the theory must allow the theoreticians to do the math! In terms of mainstream science, the inescapable fact is that mathematics in physics is really nothing more than a series of successive, solvable approximations to reality.
Davis  said that the whole structure of science “is a cracked and sagging edifice held together with masking tape and resting on the shifting sands of constantly changing theory. Nothing is known with any real certainty. Some things are merely more probable than others. Well-known theories and even laws turn out to be only partially confirmed hypotheses, waiting to be replaced with somewhat better partially confirmed hypotheses. If there is one thing we know about every theory in modern physics, it is that it’s wrong or at least incomplete. Sooner or later somebody will come along with a more general theory of which the old theory is seen to be a special case. This is not a criticism of science, but merely a description of the scientific method.”
What others have since termed, Davis Mechanics, constitutes those portions of the basic mathematics, which Davis, Stine, et al have published and/or advocated in their writings, and which have survived intact in the public domain for the last thirty plus years.
The profound result of their analysis and supporting experimental/experiential evidence is that an oscillating force with a frequency comparable to the inverse of what Davis referred to as the Critical Action Time (and what is referred in Connective Physics as the time delay of The Fifth Element) can be applied without the resulting action/reaction force of Newton’s Third Law coming into play. In effect, according to Davis, “You can get away with anything provided you don’t get caught while you’re doing it, and you leave the system immediately thereafter!”
One way to think of this is that it would be simple to rob a bank if you could move fast enough that you emptied all of the cash boxes in less time than anyone in the bank could react. (Ideally, one would hope that the speed would also be enough that no one would actually see the robbery taking place.) Again, “You can get away with anything provided you don’t get caught while you’re doing it, and you leave the system immediately thereafter.” (Of course, you may have to leave the country - i.e. the “system” - if the bank is protected by high speed cameras and indirectly by law enforcement agencies!)
In 1962 Davis, et al , presented a paper to the American Physical Society in which they first presented the possibilities. Their contention at that time was that investigation of bodies under high speed impact or during re-entry into the atmosphere must consider a third order term in the Newtonian equations of motion. They also observed that the lack of rigidity of all real bodies down to the smallest subnuclear particles leads to initiating transients when a force is applied.
The distinction between transient and steady-state forces is critical. In the real world, there are surges, jolts, kicks, and transient phenomena at the onset of a force. The system’s behavior will thus depend upon how rapidly the force is applied, and the built-in delay time of the system. The key is how rapidly one attempts to change the acceleration. On one occasion, Colonel John Stapp, the USAF flight surgeon who personally underwent numerous tests at extreme accelerations in the late fifties, estimated that the effect of a given acceleration of his body was over twice as great (when applied at very high rate) than would otherwise have been predicted by Newton’s Second Law (i.e. F = ma).
The principle of continuous transient operation is a goal that common approaches to engineering find contrary to convention because it invites structural failure. Almost without exception, the mechanical engineering design process sets the objective to attain steady-state operation as rapidly as possible so as to avoid potentially damaging effects resulting from the forces generated from starting transients. This traditional process has had the unfortunate consequence of causing potentially valuable understandings of transient behavior from being adequately investigated, and thus the possible discovery of new sources of energy (possibly being supplied directly from the universe at large).
Another hesitation of investigating transient behavior in engineering design has, of course, been that the mathematics of the non-steady state situation are generally more difficult -- and therefore prone to be avoided. Unfortunately, physical reality does not recognize any requirement of mathematical simplicity in its description. (Although, when you really get down to it, the valid theories tend to have very simple mathematics as an end result.)
Davis and the others, however, believed that transients within a very small time frame -- however often repeated in a cyclical or oscillatory fashion -- could be endured and in fact capitalized upon. Their basic assumption was that instead of analyzing the behavior of non-rigid bodies, one could “consider a real body as a Newtonian particle concentrated at its center of mass, but with a delay time in its response caused by its true compressible and viscous nature.”
Implicit in their assumption of a third derivative force was a necessary modification of the Law of Conservation of Momentum. By defining: D m a = “virtual momentum”, and “mv + Dma” as “momentic”, they derived a law of the Conservation of Momentic. For very small values of t, all of the momentic then became virtual momentum and no motion of the center of the gravity of the body was observable. This led to two theorems:
I. The observed momentum of a real body cannot be changed
II. Action and reaction in a system of real bodies cannot be exactly simultaneous. (revision of the Third Law of Motion)
Davis also observed that in a simple harmonic motion, not only is displacement somewhat less than Newton would predict for a given force -- leading to an increased apparent mass -- but reaction is no longer exactly opposite to the applied force; i.e. there is a phase angle which will be larger the longer the Critical Action Time of the system. The possible change in Mass is enormously significant, but for that matter, so is a phase angle between the action and reaction forces. Both are sufficient to make a physicist swallow hard.
Similarly, in the operation of an alternating current motor where the average current is zero, the current flows are not equal and opposite simultaneously, thus allowing work to be done. In nuclear physics where particles can exist within the nucleus if their time is too short to violate the Law of the Conservation of Energy (i.e. “virtual energy”), “virtual energy” might also derive from a mechanical force proportional to surge.
The coefficient of the third derivative or surge term in the equation of motion may represent the resistance of the system to a change of inertial field -- in the same way that self-inductance represents the resistance of a coil to a change in a magnetic field. This coefficient is what Davis called the “Intractance”. In Einstein’s case, it is precisely the so-called intractance of a system which requires that the propagation velocity be limited. If energy could propagate at infinite speed, then it would be possible to change the energy of a system in zero time. This then limits, for example, the speed of light.
It follows that if an electron radiates electromagnetic radiation when it is accelerated, then a mass having intractance will radiate gravitational-inertial radiation when it is subjected to surge. Davis postulated that the flux of such radiation is proportional to the rate of change of virtual energy. Furthermore Davis believed this new radiation would have different characteristics from EM radiation, i.e. it would not be “dipole” radiation, but more like a monopole. Furthermore, each period of changing acceleration would produce a “quantum” of radiation equal to the change of virtual energy, so that the emission might not be continuous. Davis’ thinking quickly yields some interesting speculation.
For example, this possibility of gravitic/inertial “virtual energy” might eliminate the need for postulated particles to explain the apparent violations of the Conservation of Energy or Momentum in elementary particle physics. Also, from a cosmological point of view, simultaneity would not be defined for the universe, thus making it perfectly possible to reverse entropy in a local area and not have to pay the piper for a very long time. This then might be the basis for the attempt to generate large amounts of useful energy, whose essentially inexhaustible fuel source is nothing less than the entire universe!
Davis did postulate a Fourth Law of Motion -- “The energy of a given system can only be changed in some finite length of time depending on the system and never in zero time.” -- he also conceived of a Fourth Law of Thermodynamics, i.e.: “Systems can only be considered to be thermodynamic in nature over time periods large in comparison to their Critical Action Time.” In other words, you can violate the first three laws of thermodynamics, provided “you don’t get caught while you’re doing it.” This can be the fundamental basis of transforming “far out” universal energy to locally useful energy.
Davis was apparently well aware of many of the possible implications of his theories -- even when electrodynamics is curiously missing from the list -- and specifically noted that:
· The importance of Critical Action Time is implicitly recognized in fluid mechanics and aerodynamics in the basic definitions of Reynolds and Mach Numbers, and may be particularly helpful to problems involving transonic, supersonic, and hypersonic flow.
· Simultaneity considerations involved in the hypothesis should permit new approaches in the field of thermodynamics, chemical kinetics, and combustion dynamics.
· A new general capability in methods of analyzing vibrating and rotating machinery should now be possible, as well as being able to shed considerable light on the areas of high speed impact and design of shock absorbing devices.
· Some work has apparently already been done on the dynamics of the human circulatory system utilizing the hypothesis, with possible clarification of several problems involved with heart disease and arteriosclerosis.
G. Harry Stine  has noted several other, specific implications:
· The human body responds to rate-of-onset of acceleration, a third derivative force. [This becomes extremely important with respect to ORME, and associated aspects!]
· Stress is not proportional to strain -- except in steady state conditions. Under conditions of high-rate loading, things are different. E.g. the noses of armor-piercing shells hammer their way through armor plate while the back end of the same shells proceeds inexorably forward, not knowing that the front end is hammering away.
· The mundane industrial operation of squeezing water out of paper and felt is totally dependent upon the rate of onset of the force.
· Newton didn’t have the instruments to measure high-rate phenomena. Newtonian mechanics is steady-state mechanics. Transients do not obey the simple laws.
· Newtonian mechanics is true only if the energy of a system can be changed in either zero-time or in a time interval long enough for the entire system to react as a whole.
Davis and Stine both concentrated on the mechanical aspects of the theory, and while it is highly probable that they considered electrodynamics, they never alluded to it in their published papers. But with the political motivations suggested in Stardriver, perhaps their are some very good reasons for this disparity.
Continuing with the same line of reasoning Davis and Stine overtly employed, we might consider a nuclear example, whereby the harder atomic nuclei are hit with particles in high energy accelerators, the greater the rate of change of energy that is attained, and that therefore the greater the number of wild, unexpected particles that are generated. In this view these particles are simply the consequence of rapid rates-of-change, i.e. the energy that the particle system cannot absorb instantaneously and which must somehow exit the system. [This might also play havoc with calculations on energy into and out of the system, and thus with the calculated masses of the more exotic elementary particles!]
Meanwhile, to satisfy the conservation of energy, Davis postulated a radiation of some type. If this is truly a new radiation form, it is possible that the “gravito-inertial radiation” has been identified. Effectively, the energy which cannot be used by the system (and which cannot be manifested in mechanical action of any sort) must then leave the system as radiation. But this implies that there must be something called an “inertial field”. This field may be defined with respect to a moving gravitational field in the same manner that a magnetic field is related to a moving electric field. (This latter which is essentially Einstein’s assumption in his General Relativity.)
According to Davis, it is in fact possible to apply Maxwell’s equations and predict the behavior of gravito-inertial radiation -- but with two notable differences in the interpretation.
1) In the solutions for Maxwell’s equations for electromagnetic radiation, the velocity of electrical charges moving in a conductor is of the same order of magnitude as the velocity of propagation of the radiation. In the gravito-inertial case, the velocity of motion of the gravitational mass may be many orders of magnitude different from the propagation velocity. It is important to note that the latter is not necessarily identical with that of light (contrary to Einstein’s assumption).
2) The concept of Critical Action Time in a mechanical system leads to the possibility of very large quanta of gravito-inertial radiation being generated by a mechanical system; whereas Maxwell’s equations [as edited and limited by Heaviside] leads only to the existence of quanta so small as to be beyond the range of practical importance.
Davis, Stine, Victory and Korff may be just a few of the “heroes of the physics revolution” -- a revolution that appears to be bubbling in the cauldrons of experimental laboratories and think tanks around the world. But their contributions are likely to prove to be of enormous consequence, as the full New Energy Ramifications, Inertial Propulsion systems, and a whole host of revolutionary physics implications begin arriving on the scene and begin to take hold of the paradigm of our world. Wow!
 William O. Davis, “The Fourth Law of Motion”, Analog Science Fiction/Science Fact Magazine, May, 1962.
 William O. Davis, G. Harry Stine, E. L. Victory, and S. A. Korff, “Some Aspects of Certain Transient Mechanical Systems”, Presentation to the American Physical Society, April 23, 1962, New York University.
 G. Harry Stine, “Detesters, Phasers and Dean Drives”, Analog Science Fiction/ Science Fact Magazine, June, 1976.
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