This page is dedicated to introduce energy as a "function of time". New "concepts" and "terminology" are needed. Methods of closing a system to motion as a "function of position", may lead to a mistake of generalizing a special rule.

Hamilton teaches that energy is not preserved, when motion is a function of time and LaGrange equations do not stand. Relative Motion as a "function Of time" solves Hamilton statement, by equating time as a form of energy exchange, where energy preservation is re-established, but with time also becomes a source of energy.

Relative Motion as a "function of time", teaches that a net force, not only subjects an object to acceleration, but also as a "function of time", we may have more than one dimension or one field of acceleration. To simplify the concept, we may suggest that a similar net force and a similar object would act differently, if the field of motion was different, like a simple field of vacuum, air, water or electrical, with different levels of pressure, or combined with a field of relative motion, like a surface and tidal waves acting on a ship, etc. No matter how complicated such a field can be, from an energy prospective; acceleration can only be of the power square; while variables relevant to any space coordinate, become controlled by TIME, and that is what we call time dependency, not to be confused with the function of time.

A second acceleration is a continuous force-equilibrium relation between motion kinetics, and between its potential source of energy.

is based on identifying fields of acceleration under energy conservation principles, requiring that "relative positions" in a motion, are calculated as "functions of time"; which is an equation of the second power, and with these considerations, we can advance to a very important example in applied physics by saying:

- As a "function of position", Pascal can increase available force (Newton/s) for a loss in metric distance.
- As a "function of time", Pascal can increase available work energy ( Joule/s) for a loss in time lapse distance of acceleration. To have a mechanical design open to time, Relative Motion conditions need to be met.
- "Time lapse" under a chosen universal acceleration, is a new scale that is needed, to measure distance when motion is a "function of time".

Time accelerates potential energy as force accelerates a mass.

- Motion is a "function of time", when acceleration is of the power square.
- Relativity as a "function of time", measures available work energy, and means of traveling at a different "time lapse" of a universal acceleration between positions A and B, despite equivalent initial thermal potential.
- Acceleration under certain conditions may result in creating a non-particle negative mass (a space void).
- Accelerating a Negative mass, is a source of energy, which must have been the method of how nature is feeding our universe with energy needed for its accelerated motion.

An argument we had to deal with during our latest research efforts, made by a friend:

- “In simple terminology, it is ( the cylinder) proposed to carry out the compression stroke separately and in parallel with the power stroke by means of a secondary piston. This, it is argued, will have the effect of increasing the number of power strokes in a given time. So for example if we double the number of the power strokes then in principle the power will double (not fully correct since there will be other induced losses and also the secondary piston will absorb power to function”. and
- "So far the engineering argument appears reasonable though the proposal continues to make claims regarding performance and emissions that are at best unjustified and in my opinion unrealistic"

And our argument was, first, a second floating piston, can not absorb power, because it is not mechanically linked to the crankshaft drive, and because the cylinder system is closed, and second, "engineering argument appears reasonable" is great news that we do not take for a granted, however, claims can only be justified by simulation and not by opinion.

all our initial cylinder simulation and product visualization tests, started around may of 2017, confirmed that our friend's conclusion held a good logic, where no matter how the second piston shape looked like, inserting an object into a high pressure compartment in a hybrid mode, will utilize an outside source of energy or deduct its share of motion energy according to Pascal as a function of position, as for example, two pistons moving under combustion forces in opposite directions, a second piston will split an expansion distance and a power stroke energy with a first piston.

We tested in different fluid mediums, And the first failed cylinder simulation test was also failing because we did not understand Pascal as a function of time.

Early 2018,

We were looking to hybrid a magnetic and combustion forces in one cylinder, to variably insert a space occupying rod, during an expansion stroke, thinking that

the utilized magnetic source of energy, shall recover by increasing the cylinder internal pressure, and by minimizing the cylinder displacement volume.

The arrangement design and method, was based on absorbing the initial combustion shock, using a supporting spring, that will store the combustion energy and release it later on during an expansion stroke, along with added magnetic force. The system was not closed as a pascal , and results failed showing a work graph that is lower than that of a comparable conventional one, and that is in agreement with our professor conclusion, however we realized the reason of failure, when we simulated two pistons, housed in one cylinder and moved by combustion forces in opposite directions, where the resulting graph was similar to that associated with the spring design, and where Pascal does not apply unless we count the combined surfaces, and distance of travel to both pistons.

A week later, we decided to remove the spring and have the insertion rod becomes a second floating piston, taking its motion power from the combustion forces, with surfaces shaped that, it can allow the floating piston to accelerate along with the first crankshaft piston, in the same initial direction, but also to change direction later on during an expansion stroke, due to variable surface interfacing the combustion pressure, as in our video presentation . The results came victorious with the floating piston succeeded in taking its complete kinetic power, used to initially suction fluid, and then to perform a compression stroke, not only without deducting any kinetic power from the crankshaft piston, as the only output surface in a Pascal, but with adding an unprecedented performance enhancement to the crankshaft piston work, due to competing with the combustion fluid for space, where the calculated combustion mass acting on the crankshaft piston, have a space void added, that we called the negative mass, responsible for adding a second acceleration vector of the crankshaft motion, and with that, declaring the birth of the Relative-Motion Mechanics of Pascal as a function of time, and the existence of the negative mass rule, where to comply with Newton's principles, we had to conclude that a net force, in a Relative-Motion field, subjects an object, a crank-shaft piston in this case, to acceleration of the second power, as a function of time.

As a result, and with more testing we learned how to increase the cylinder internal pressure, in a process we now call an acceleration of potential energy, and how to increase the kinetic energy output of a first crankshaft piston, beyond thermal assessments, and that was how we learned the new introduced physics, and how the term Pascal as a function of time formed.

Later on we started testing on turbo charge arrangements, where most compression energy input was recovered as an additional combustion forces, opening a complete new chapter, to the business of pressure accumulation mechanics.

Another argument was:

- "it is important not to confuse energy with power; when energy becomes a function of time it becomes power. "

And we argued that this is simply wrong, and a better statement is:

- when energy becomes time dependent, then it becomes power.

Sometimes, even with advanced scholars, it pays off to go back to the basics, as we find that some engineers, tend to mix the concepts of energy as time dependent, and energy as a function of time, where the first is relevant to speed and the second, is relevant to an equation of the second power.

- So when energy is time dependent? or time independent?

case 1:

Moving a 1 kg object to a 1-meter of linear physical distance is time independent, meaning same energy is needed every time, regardless of speed or time, And

case 2:

doubling the distance would require double the time, when similar force, at similar conditions as in case 1 is used; energy difference between the two cases is time dependent, and the problem in using the term "function of time" in this case, is that it is being applied to a situation where energy is preserved. while according to Hamilton, when energy is a function of time, then energy conservation does not stand and LaGrange equations do not apply, including Lorentz transformations, which is the engine of relativity as a function of position. On the other hand, Hamilton equations like Jacobi introduced the time variable as a function of position, this why Hamilton equations can only handle energy as time dependent and not as a function of time. Special relativity, introduced the (t') variable, to deal with the dilemma of energy conservation, supposedly in an open system, but we know mathematically that a variable can be dealt with by elimination, and as a result the (t') again locks the special relativity behind the limits of energy as a function of position.

case 3:

if we had to move 1 Kg to a physical distance of 1 meter, like in case 1, but under different path conditions, and found that double the energy is needed, then the statement can be properly expressed as a D'Alembert question, where energy is a function of time in a relative motion condition.

If cases 1 and 3 were Pascal cylinders, then energy input and output would differ and Pascal as a function of position would not stand , and the energy difference can not be thermally estimated.

For that reason, we are introducing Pascal as a function of time in our Relative-Motion cylinder, and for this reason we decided to disclosed this very simple physics, where the main challenge is that, even though D' Alembert introduced the concept few centuries ago, we still do not see it in classical mechanics, simply because the Relative-Motion cylinder was not invented yet.

In our Relative-Motion cylinder, energy output as a function of time, was greater than its comparable value in a conventional cylinder, and the difference can be mathematically calculated from the negative combustion mass created by our secondary floating piston, Where work energy gained ( -W= -F * D).

Our favorite argument, was in the Colorado APS, physics conference, on April 13th,2019. And the quote was:

- we know that Pascal results can not allow output differences that is more than the assessed friction values, which is, let us suggest 5%, How is it possible for anyone to suggest a performance enhancement on a cylinder, that is 100% or more? is there an over-unity statement ?.

And the Relative-Motion argument was, breaking the 5% limits, was initially done when engineers discovered the direct injection method, which exceeded 35-50% performance enhancements, and as Tesla once said, today's engineering is based on experimenting rather than on theory. Physicists so far, attributing the difference to better burning, has failed to calculate and failed to realize the function of time role in the direct injection method, which we are taking to a next level, And for this reason, our argument drops any over-unity statement, based on our new physics of " time as a form of energy".

A physicist fellow asked, how space-time and Relativity as a Function-Of-Time may relate or compare ?

Our Relative-Motion argument understands that,

- Newtonian-Galilean relativity attributed non-conservation to the function of time.
- space-time as an observer art, where squaring the velocity in the famous equation, E=MC^2 is not relevant to the mathematical square in the equation of position as a function of time, and despite using the time prime concept, it continues to be a function of position method, in dealing with the non-conservation issue and with the equality of energy and mass.

Relativity as a Function of Time, based on an Observer independent equation, introduces the equality of energy and Time, which is in complete agreement with Newtonian laws and with classical mechanics, as long as time lapse of acceleration is adopted as a measure of distance, when motion is a function of time, and concludes that the only reason behind the non-conservation statement was not identifying time as a form of energy.

Our equation, finds energy potential to be proportionate with time cube, which is in approval with the natural energy governance of the earth path around the sun example, where Kepler's calculations also pointed to the time cube governance, and that is what allows Relativity as a Function of Time, to solve that energy preservation is a part of energy acceleration and creation from the sustainable source of time, in the process of growing our universe, while all other relativity theories, were locked behind the bars of a cold expansion of universe, where the total available energy is fixed and is created at what they observe as "a big bang".

The very first question one faces upon working with patenting and prototyping is, do you really believe that you can have anything new and novel, in today's high tech, multi-billion-dollar investment per project? The truth is, if we can find that a physics argument is broken somehow, somewhere, then neither high tech nor the multi-billion-dollar projects can have a chance, whenever a competing novel idea is identified and persuaded; and if anyone is in doubt, we recommend blending in a conference among engineers, and ask:

- When a motion is a function of time? and count how many fellows answer, when motion is a function of speed.

It does not mean, that they are not good at what they do, but it simply means, there is an opportunity, or some opportunity is waiting ahead for you, given you are willing to think deeper.

We understand, the project is still at a stage of an infant steps toward realizing a new sustainable source of energy that, in the end can only be the fruit of a combined thinking and researching system made by those willing to do what it takes, for a better human future. Negative arguments at this stage can be more fruitful than positive ones.

Time as a form of energy presentation . Copyright 2019

2019-04-13 APS -V4 (pdf)

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